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McGRAW-HILL PUBLICATIONS IN THE 

AGRICULTURAL SCIENCES 

LEON J. COLE, CONSULTING EDITOR 



METHODS 

of 
PLANT BREEDING 



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SELECTED TITLES FROM 

McGRAW-HILL PUBLICATIONS IN THE 
AGRICULTURAL SCIENCES 

LEON J. COLE, Consulting Editor 

Adriance and Brison - PKOPAGATJON OF HORTICULTURAL PLANTS 

Brown COTTON 

Cruess COMMERCIAL FRUIT AND VEGETABLE PRODUCTS 

EckleSj Combs, and Macy MILK AND MILK PRODUCTS 

Fawcett CITRUS DISEASES % 

Fernald and Shepard - APPLIED ENTOMOLOGY 

Gardner, Bradford, and Ilojkcr FRUIT PRODUCTION 

Gustafson - CONSERVATION OF THE SOIL 

Gustafson SOILS AND SOIL MANAGEMENT 

Hayes and Garber - BREEDING CROP PLANTS 

Hayes and Immer - METHODS OF PLANT BREEDING 

Heald - MANUAL OF PLANT DISEASES 

Ileald INTRODUCTION TO PLANT PATHOLOGY 

Hutcheson, Wolfe, and Kipps FIELD CROPS 

Jenny - FACTORS OF SOIL FORMATION 

Jull - POULTRY HUSBANDRY 

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Leach INSECT TRANSMISSION OF PLANT DISEASES 

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Rather FIELD CROPS 

Rice - BREEDING AND IMPROVEMENT OF FARM ANIMALS 

Roadhouse and Henderson THE MARKET-MILK INDUSTRY 

Robbins, Crafts, and Raynor WEED CONTROL 

Schillctter and Richey TEXTBOOK OF GENERAL HORTICULTURE 

Thompson - VEGETABLE CROPS 

Waite POULTRY SCIENCE AND PRACTICE 

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published in these series in the period 1917 to 1937. 



METHODS 

of 
PLANT BREEDING 



BY 

HERBERT KENDALL HAYES 

Professor and Chief of Division of Agronomy and 

Plant Genetics, College of Agriculture, 

University of Minnesota 

AND 

FORREST RHINEHART IMMER 

Professor of Agronomy and Plant Genetics, 
College of Agriculture, University of Minnesota 



FIRST EDITION 
FIFTH IMPRESSION 



McGRAW-HILL BOOK COMPANY, INC. 

NEW YORK AND LONDON 



METHODS OF PLANT BREEDING 

COPYRIGHT, 1942, BY THE 
McGRAW-HiLL BOOK COMPANY, INC. 



PB1NTED IN THE UNITED STATES OF AMEK1CA 

All rights reserved. This book, or 

parts thereof, may not be reproduced 

in any form without permission of 

the publishers. 



COMPOSITION BY THE MAPLE PRESS COMPANY, YORK, PA, 
PRINTED AND BOUND BY COMAC PRESS, INC., BROOKLYN, N. Y, 



PREFACE 

Plant breeding is an applied science that is carried out effici- 
ently only through the application of other basic plant sciences. 
The rapid increase in knowledge of genetics since the rediscovery 
of Mendel's laws of heredity in 1900 and the application of these 
laws to plant breeding were essential steps in the development of 
plant breeding as a science. The contributions of cytogenetics 
in recent years have furnished, in many cases, a clear picture of 
genetic relationships based upon differences and similarities of 
chromosome morphology, structure, arid function. Many eco- 
nomic plants are polyploids, and a knowledge of chromosome 
numbers, pairing behavior in crosses, and gene differences among 
related species and varieties is essential in building new varieties 
of plants with the characters desired by the grower and con- 
sumer. Physical and chemical methods of inducing changes in 
chromosome number and structure and of inducing gene changes 
are being developed. Satisfactory technics for inducing poly- 
ploidy in species and hybrids are available for certain types of 
plant breeding problems. 

In order to evaluate a variety, it is necessary to compare it 
with varieties of known performance. The comparisons made 
by the plant breeder are extensive, and frequently only a few 
replications can be grown. The development of adequate 
statistical methods has aided greatly in making reliable com- 
parative trials. Experimental methods of making reliable 
comparisons are one of the tools of the plant breeder. 

Methods have been devised in many cases for differentiating 
quality, for a determination of the relative value of different 
characters, including chemical properties, that make it possible 
, under conditions of controljjadf* pollination to select for the 
characters desired. In problems of breeding for disease resis- 
tance, a knowledge of the genetics of the pathogen is as essential 
as that of the crop plant itself. With each individual plant, 
information regarding available varieties, their characters, and 



vi PREFACE 

their wild relatives furnishes a basis for the combination of genes 
desired by the breeder. For diseases caused by pathogens it is 
equally important to know the probable mode of origin of new 
strains of the organism, and the number, distribution, and genetic 
nature of the strains present in the region where the crop plant 
is to be grown. 

The subject matter presented in " Methods of Plant Breed- 
ing" has been used in both undergraduate and graduate courses 
at the University of Minnesota. The undergraduate course is 
taught only to junior and senior students. The graduate courses 
are given for the purpose of teaching standardized methods of 
breeding for particular categories of breeding problems and to 
present the current viewpoint when the most desirable method 
of breeding is not so well known. This is with the belief that 
each of the various methods of hybridization, including the 
pedigree method of selecting during the segregating generations, 
the bulk method with self-pollinated plants, the backcross 
method and convergent improvement, has certain advantages and 
disadvantages that make it desirable under some conditions 
and less desirable for other breeding problems. 

A great deal of information is available regarding the genetics 
of many crop plants, and added information is being obtained 
very rapidly. It seems unwise to attempt a complete review 
of the present status of the genetics of many crop plants, since 
the information available is very extensive and such a review 
would be out of date almost as soon as it was published. Concise 
reviews of the mode of inheritance of important characters of the 
small grains, flax, and corn have been included to illustrate the 
value to the breeder of a knowiedgc of inheritance as an aid in 
planning the breeding program. These should be supplemented 
by similar reviews of inheritance for those crop plants that are 
of greatest value for each class of students who use the book. 

The present status of corn breeding, a rather typical cross- 
pollinated plant, has been reviewed in considerable detail, since 
many of the studies made with corn and the results obtained are 
basic to an understanding of principles of breeding other cross- 
pollinated plants. 

Methods of field-plot technic, experimental design, and statis- 
tical analysis with particular reference to plant-breeding problems 
have been discussed, including some of the newer methods. The 



PREFACE vii 

necessary statistical tables have been included with the permis- 
sion of the original publishers. 

The authors are indebted to Professor R. A. Fisher and to 
Messrs. Oliver and Boyd, of Edinburgh, for permission to reprint 
completely or in abridged form Appendix Tables I ? III, and IV 
from their book " Statistical Methods for Research Workers," 
7th Ed. (1-938) and to Professor George W. Siiedecor and his 
publishers, Iowa State College Press, for permission to reprint 
Appendix Table II from their book "Statistical Methods/' 3d 
Ed. (1940). Professor Snedecor has given permission to reprint 
Appendix Table V, and Dr. C. I. Bliss has given permission to 
reprint Appendix Table VI. 

Various co workers have read particular chapters and have 
made helpful suggestions. Particular thanks are due to Dr. 
0. R. Burnham for suggestions regarding the chapters on Gen- 
etics and on Inheritance in Maize; to Dr. E. R. Ausemus for 
suggestions regarding the chapter on Inheritance in Wheat; 
to Dr. F. A. Krantz for helpful suggestions regarding potato 
improvement; to A. G. Tolaas for information regarding potato- 
seed certification; and to Dr. C. H. Goulden for reviewing the 
chapters on Field-plot Technic and on Statistical Methods. Dr. 
H. M. Tysdal kindly furnished unpublished information regarding 
the effects of self-pollination in alfalfa. In problems relating to 
disease resistance, suggestions by Dr. J. J. Christensen and M. B. 
Moore have been specially helpful. " Breeding Crop Plants/' by 
Hayes and Garber, has been used freely. The writers, however, 
accept full responsibility for the viewpoints presented. 

H. K. HAYES, 
F. R. IMMER. 

UNIVERSITY or MINNESOTA, 
February, 1942. 



CONTENTS 

PAGE 
PREFACE: v 

CHAPTER I 

THE ROLE OF PLANT BREEDING , 1 

The value of plant breeding -Genetic principles are the basis of 
scientific breeding Breeding spring wheat resistant to stem rust > 
Corn breeding Potato improvement. 

CHAPTER II 

THE GENETIC AND CYTOGENETIC BASIS OF PLANT BREEDING 11 

Chromosome number (haploid) in common crop plants Polyploids 
in relation to plant breeding Some applications of genetics to 
plant breeding Colchicine as a polyploidizing agent. 

CHAPTER III 

MODE OF REPRODUCTION IN RELATION TO BREEDING METHODS. ... 39 
The asexual group The sexual group Self-pollination leads to 
homozygosis The effects of self-pollination in the often cross- 
pollinated group. Effects of self-fertilization in cross-pollinated 
plants Heterosis and its explanation A classification of methods 
of breeding sexually propagated plants. 

CHAPTER IV 

TECHNICS IN SELFING AND CROSSING 60 

Corn Wheat, oats, and barley Rye Flax Cotton Sorghum 
Rice Potato Pumpkin and squash Onion Red Clover Al- 
falfa and sweet clover Grasses. 

CHAPTER V 
THE PURE-LINE METHOD OF BREEDING NATURALLY SELF-POLLINATED 

PLANTS 74 

Early studies The pure-line theory The pure-line theory in its 
application Methods of improving self-fertilized plants by indi- 
vidual-plant selection Utilization of introductions- Pedigree 
selection within adapted varieties Cooperative tests and dis- 
tribution of promising lines Illustrations of valuable varieties of 
self-pollinated plants produced by application of the pure-line 
theory. 

CHAPTER VI 

HYBRIDIZATION AS A METHOD OF IMPROVING SELF^POLLINATKD PLANTS 86 
Some studies before 1900 Development of methods since 1900 
Breeding improved varieties of barley Breeding by hybridization 

ix 



X CONTENTS 

PAGE 

Object of crowing Selection of parental material Technic of 
crossing Handling the hybrid material Methods of breeding 
Pedigree method Bulk method Backcross method Multiple 
crosses Combining ability. 

CHAPTER VII 

THE BACKCROSS METHOD OF PLANT BREEDING 101 

Genetic expectations from backcrossmg Cantaloupes resistant to 
powdery mildew, Erysiphe cichoracearum Breeding bunt-resistant 
wheats Breeding rust-resistant snapdragons Studies at the 
Minnesota station Disease resistance in wheat Illustrations with 
corn. 

CHAPTER VIII 

BREEDING FOR DISEASE AND INSECT RESISTANCE 113 

The importance of disease resistance Methods of breeding for 
disease and insect resistance The search for resistant material 
Artificial production of ephiphytotics Black stem rust of wheat, 
oats, and barley (Puctinia graminis) Leaf rust of wheat (P. 
triticina) and crown rust of oats (P. coronata) Bunt of wheat 
(Tilletia tritici) Loose smut of oats (Ustilago avenae); covered 
smut of oats (U. levis) Covered smut of barley (U. hordei) and 
intermediate smut of barley (U. medians) Flax rust (Melamp- 
sora lini) Flax wilt (Fusarium lini) Fusarial head blight (scab) 
of wheat and barley Corn smut (17. zeae) Loose smut of sor- 
ghum (Sphacelotheca cruenta) and covered smut of sorghum ($. 
sorghi) Head smut of sorghum and corn (S. reilianum) Hessian- 
fly injury of wheat Methods of breeding Study of fundamental 
problems, 

CHAPTER IX 

INHERITANCE IN WHEAT 129 

Glume shape Awnedness Chaff characters Seed characters 
Spike density Spring and winter habit Stem-rust reaction 
Bunt resistance Other problems of disease resistance Quanti- 
tative characters. 

CHAPTER X 

INHERITANCE IN OATS 141 

Species groups Inheritance of characters in crosses between 42 
chromosome species Differences in awn development Color of 
grain Hulled vs. hull-less Spreading vs. side panicle Pubes- 
cence Disease reactions (Stem rust Crown rust Correlated 
inheritance of reaction to ' three diseases Smuts Quantitative 
characters. 

CHAPTER XI 

INHERITANCE IN BARLEY " . . . . 152 

Classification and genetics of barley species Chromosome number 
in genus Hordeum Linkage groups Internode length in the 



CONTENTS xi 

PAGE 

rachis of the spike Reaction to Helminthosporium sativum 
Reaction to stem rust Resistance to mildew Interaction of 
factors affecting quantitative characters. 

CHAPTER XII 

INHERITANCE IN FLAX 165 

Factors for flower and seed color in common flax Dehiscence of 
the bolls Smooth vs. ciliate septa Weight of seed and oil content 
Inheritance of quality of oil Disease resistance Wilt resis- 
tance Resistance to rust. 

CHAPTER XIII 
METHODS OF SELECTION FOR SPECIAL CHARACTERS ......... 175 

Quality tests in wheat Wheat-meal fermentation time test 
Cold-resistance tests with wheat Shattering in wheat Dor* 
mancy in relation to breeding Lodging in small grains and corn 
Drought studies with corn Inducing biennial sweet clover to 
flower the first year Determination of coumarin content in sweet 
clover Method of determining hydrocyanic acid content of 
single plants of sudan grass. 

\ CHAPTER XIV 

DEVELOPMENT OF METHODS OF CORN BREEDING 187 

Selection without controlled pollination Early studies of self- 
and cross-fertilization with com Controlled pollination methods 
Breeding improved inbred lines The pedigree method of selection 
in the segregating generations after crossing inbreds Genetic 
diversity The backcross Convergent improvement. 

CHAPTER XV 

INHERITANCE IN MAIZE 215 

Origin and classification The pod corns The flint corns The 
popcorns The dent corns The flour corns The sweet corns 
The waxy corns Endosperm characters Chlorophyll variations 
Plant color Glossy seedlings Linkage studies with maize 
Inheritance of quantitative characters Linkage of factors for 
row number with genes at known loci Inheritance of smut reac- 
tion Inheritance of combining ability Inheritance of other 
important characters. 

CHAPTER XVI 
CONTROLLED POLLINATION METHODS OF BREEDING CROSS-POLLINATED 

PLANTS 242 

Effects of self-fertilization Inheritance of self-incompatibility * 
Methods of breeding Outline for improvement of cross^poUinated 
plants by controlled pollination methods. 



xii CONTENTS 

PAGE 

y CHAPTER XVII 

SEED PRODUCTION 263 

Selecting the variety First increase of seed of a new variety 
Seed certification and registration The Canadian Seed Growers' 
Association The International Crop Improvement Association 
Description of seed classes The Minnesota plan for certain crops 
Seed (tubers) certification for potatoes. 

CHAPTER XVIII 

SOME COMMONLY USED MEASURES OF TYPE AND VARIABILITY .... 280 
Definition of statistical constants Calculation of mean Standard 
error, variance, and coefficient of variability Correlation coef- 
ficient Comparison of differences by the t test. 

CHAPTER XIX 

FIELD-PLOT TECHNIC 289 

Crop rotation for experimental fields Soil heterogeneity Com- 
petition Size and shape of plots Replication Methods of 
making yield trials used in Minnesota. 

CHAPTER XX 

RANDOMIZED BLOCKS, LATIN SQUARES, AND x 2 TESTS 307 

Tests in randomized blocks Latin squares Estimating the yield 
of a missing plot Split-plot experiments Chi square (x 2 ) tests. 

CHAPTER XXI 

CORRELATION AND REGRESSION IN RELATION TO PLANT BREEDING . . . 325 
Simple correlation Linear regression Means and differences of 
correlation coefficients Partial correlation Multiple correlation. 

CHAPTER XXII 

MULTIPLE EXPERIMENTS, METHODS OF TESTING A LARGE NUMBER OF 
VARIETIES, AND THE ANALYSIS OF DATA EXPRESSED AS PERCENTAGES 339 
Multiple experiments in randomized blocks Comparison of varie- 
ties in different experiments where the same check varieties are 
grown Simple lattice experiments Triple lattice experiments 
Analysis of data expressed as percentages. 

LITERATURE CITATIONS 3H1 

if 
GLOSSARY 401 

APPENDIX 411 

INDEX 421 



METHODS OF PLANT BREEDING 

CHAPTER I 
THE ROLE OF PLANT BREEDING 

There is a growing appreciation of the value of plant breeding 
as<a means of obtaining new or improved plant forms adapted to a 
wide variety of uses. Although most important food plants had 
been brought under cultivation before the dawn of recorded 
history, there remains at present almost an unlimited opportunity 
to improve the varieties of plants available for various agricul- 
tural uses and in some cases greatly to modify their characters. 
The primary purpose is to obtain or produce varieties or hybrids 
that are efficient in their use of plant nutrients, that give the 
greatest return of high-quality products per acre or unit area in 
relation to cost and ease of production, and that are adapted to 
the needs of the grower and consumer. It is of great importance 
also to obtain varieties that are able to withstand extreme 
conditions of cold or drought or that have resistance to patho- 
genic diseases or insect pests. Such qualities help materially to 
stabilize yields by controlling extreme fluctuations. 

Although the art of plant breeding, i.e., the ability to discern 
fundamental differences of importance in the plant material 
available and to select and increase the more desirable types, is a 
great asset to the breeder, there is general appreciation that plant 
breeding, efficiently carried out, is to a large extent dependent on 
fundamental training in the biological sciences. 

Some of the more important phases of this training may be 
summarized as follows: 

1. A knowledge of genetic and cytogenetic principles. 

2. A knowledge of the characteristics of the crop to be 
improved, including its wild relatives. 

3. Information regarding the needs of the grower. 

4. A knowledge of special technics adapted to the solution of 
particular problems. 

1 



2 METHODS OF PLANT BREEDING 

5. A knowledge of the principles of field-plot technic. 

6. A knowledge of the principles involved in the design of 
experiments and the statistical reduction of data. 

The purpose of this book is to summarize the methods of breed- 
ing that have been developed for particular categories of crop 
plants, to explain the reason why particular methods are chosen 
for certain types of crop-improvement problems, and to give 
methods of field-plot technic and of statistical analysis that are 
adapted for particular uses. Although individual crop problems 
will be used for illustration, there will be no attempt to summarize 
the work that has been done or that needs to be done with 
individual crop plants except as these facts may aid in under- 
standing types of problems. Emphasis will be placed on methods 
of breeding and principles underlying their use. 

THE VALUE OF PLANT BREEDING 

E. F. Gaines (1934), of the Washington Agricultural Experi- 
ment Station, has made the statement that the practical results of 
genetic research on disease resistance in plants has helped to 
popularize genetics with the general public. The illustration of 
breeding stem-rust-resistant wheat given later in the chapter 
emphasizes the value of cooperation in research and the need of 
intensive study in order to solve underlying principles and thus 
make possible the solution of complex problems and the develop- 
ment of the desired varieties. 

In discussing the importance of a knowledge of genes and their 
control, the following statements have been made by Muller: 

Organisms are found to be far more plastic in their hereditary basis 
than has been believed, and we may confidently look forward to a future 
in which if synthetic chemistry shall not have displaced agriculture 
the surface of the earth will be overlaid with luxuriant crops, at once 
easy to raise and to gather, resistant to natural enemies and climate, 
and readily useful in all their parts. 

This work is a far vaster one th^n the layman ordinarily realizes, for 
there are many thousands of wild species of plants whose varied potenti- 
alities must be tested, and many species both wild and cultivated already 
contain hundreds of varieties and thousands of individual differences. 
By means of laborious crossing methods, these diverse types may be 
combined and recombined within wider limits, and so a virtually endless 
succession of specialized hybrid forms may be produced, differentiated 



THE ROLE OF PLANT BREEDING 3 

into local geographical races each having characteristics especially suited 
to its peculiar conditions of cultivation and to the needs of the district. 
When to the potentialities of hybridization are added those that will 
appear as new hereditary types arising by mutation, the path of change 
and adaptation is seen to be indeed limitless. 

GENETIC PRINCIPLES ARE THE BASIS OF SCIENTIFIC BREEDING 

Many years ago Raymond Pearl emphasized the fact that with 
self-pollinated crop plants the plant breeder was using Mendel's 
laws as a direct working gilide. Illustrations by the score could 
be given to show how particular types of genetic knowledge have 
been and are being used as a basis for a planned crop-improve- 
ment program. A few illustrations will be given to show the 
extent to which a knowledge of the genetics of a particular crop is- 
essential in the development of a logical breeding program. 

Breeding Spring Wheat Resistant to Stem Rust. One of the 
principal cooperative projects at Minnesota since 1915, in which 
agronomists, plant geneticists, cereal chemists, and plant path- 
ologists have all played their parts, has been the development of 
rust-resistant varieties of spring wheat of desirable agronomic 
type and of satisfactory milling and baking quality. This 
research program has been carried on through cooperation 
between workers in the Minnesota Experiment Station and the 
U. S. Department of Agriculture. 

In these studies, artificial epidemics of stem rust have been 
developed both under field conditions and in the greenhouse. 
The rust nursery in the field has consisted of several thousand 
rows yearly. During the early period of this study, resistant 
vulgare wheats were unknown. The present nursery has sudi a 
preponderance of strains of vulgare wheats highly resistant to 
stem rust that it is necessary to plant a considerable amount of 
susceptible host material throughout the nursery in order that 
rust may develop sufficiently so that a satisfactory spread of the 
disease may be made possible. The development of rust- 
resistant strains has been accomplished by obtaining resistance 
from the Emmer group and by combining this resistance with the 
desirable agronomic characters of vulgare wheats through a series 
of crosses and selections. 

At the present time much remains to be known about various 
phases of stem-rust resistance in wheat, but many problems have 



4 METHODS OF PLANT BREEDING 

been solved. Some of the steps leading to our present position 
may be mentioned. 

1. The mode of inheritance of particular types of reaction to 
stem rust has been determined in both the greenhouse and field. 
The most important practical result of these studies is the con- 
clusion that resistance to all races of stem rust of wheat in the 
stage from heading to maturity may be dependent upon only a 
single or a few genetic factors. 

2. The pathogene causing the disease Puccinia graminis tritici 
Eriks. & Henn. is composed of numerous forms, called physiologic 
races, that can be differentiated by their manner of reaction 
with a series of wheat varieties and species known as differential 
hosts, this separation being made primarily on the basis of 
seedling reaction. A wheat variety resistant to a particular race 
of rust in the seedling stage is resistant to the same race in all 
stages of plant growth under field conditions. Physiological 
resistance in the seedling stage is of such a nature that a wheat 
may be immune from one race of rust and susceptible to another. 
As an illustration, Kanred winter wheat and some hybrid deriva- 
tives having Kanred as an ancestor are immune from certain races 
and highly susceptible to others. This knowledge explains the 
reason why Kanred winter wheat and derivatives may be highly 
resistant in one season and highly susceptible in another. 

3. A knowledge of the causes of resistance has been of major 
importance. Thus, the resistance of Kanred is physiological and 
acts only against particular races of rust. A second type of 
resistance under field conditions to many races of rust as the 
plants approach maturity, called mature-plant resistance, appears 
to be simply inherited. The exact cause of this type of resistance 
is unknown. Some have suggested that morphological and func- 
tional causes may be responsible. Others have given evidence 
indicating that this does not seem to be the explanation. Mature- 
plant resistance is inherited, in some cases, in a simple Mendelian 
manner, especially where the varieties Hope and H44 are used as 
the resistant parents. f ; 

4. It has been learned also that extreme conditions of environ- 
ment may cause an apparent breaking down of resistance to a 
particular disease. For example, a plant genotypically resistant 
to stem rust, if infected with loose smut, may be completely 
susceptible to rust. This conclusion seems essential in a logical 



THE ROLE OF PLANT BREEDING 5 

viewpoint of disease resistance in plants. No one expects that a 
potentially high-yielding variety will give high yields under 
unfavorable conditions. Extreme conditions of environment 
may strongly modify reaction to disease by modifying the charac- 
ter that, under normal conditions, is responsible for the resistance 
to that particular disease. 




FIG. 1. Thatcher wheat was first released in Minnesota in the spring of 
1934. There were approximately 12,000,000 acres grown in Canada in 1940 arid 
5,500,000 acres in the United States. The estimate has been made that Thatcher 
has given an annual increase in farm income to the Minnesota farmer of 2 million 
dollars. 

Thatcher wheat (Hayes et al. 1936), first introduced in the 
spring of 1934 in Minnesota, is now the most widely grown stem- 
rust-resistant wheat, being the major spring wheat grown in 1939 
in the United States in the eastern and central sections of the 
spring-wheat area. Thatcher is grown extensively also in 
Canadian provinces where stem rust is most severe. It withstood 
the stem-rust epidemics of 1935, 1937, and 1938 when susceptible 
varieties of spring wheats were very severely injured. Thatcher 
excels in yielding ability, strength of straw, and milling and 
baking quality but is somewhat less satisfactory in weight per 



6 METHODS OF PLANT BREEDING 

bushel than some other varieties, partly because of its small 
size of seed and its susceptibility to scab and leaf rust. The 
latter disease was epidemic in 1938 in the spring-wheat area. 

Thatcher is the product of a double cross between (lumillo 
durum X Marquis) X (Marquis X Kanred). From the first 
cross of lumillo X Marquis and selection during F% to F^ 4 related 
.strains were obtained with 21 pairs of chromosomes, vulgare type 
of plant, and resistance to stem rust. It is of interest that no 
plants were obtained in F% that had this combination of characters 
but that from over one thousand F 3 lines there was one line that 
contained several plants that were of vulgare type that were 
resistant to stem rust. From the cross of Marquis X Kanred, a 
considerable number of spring wheats were selected that were 
homozygous for the immunity of Kanred to several rust races. 
Thatcher was selected from a cross between the more promising 
strains of these two single crosses. The Thatcher variety com- 
bines field resistance to many physiologic races of stem rust 
with seedling resistance to the races to which Kanred is immune. 
It was the first successful attempt to transfer rust resistance from 
the Emmer group with a haploid chromosome number of 14 to the 
vulgare group (n = 21). 

McFadden (1930) was the first to develop vulgare wheats 
with near immunity to stem rust from crosses of Marquis with 
Yaroslav emmer. He produced two wheats, Hope and H44, with 
42 chromosomes that in the mature-plant stage are highly resist- 
ant to stem rust. Neither of these wheats is entirely satisfactory 
in other characters. The resistance of Hope and H44 to all rust 
races in the field under normal conditions in North America is 
dependent upon one or two major genetic factors for resistance. 
Most of the more promising new spring wheats have Hope or H44 
somewhere in their parentage. 

Corn Breeding, The viewpoint . has been expressed by various 
writers that the production of adapted corn hybrids for different 
regions of the corn belt will have the most far-reaching effect of 
any phase of work in crop improvement of the present generation. 
The hybrid Burr-Learning was first distributed in Connecticut in 
1922, but the acreage grown of this hybrid has been very small. 
The first distribution of hybrids in the corn belt occurred from 
1932 to 1934, and in 1938 and 1939 from 15 to 25 million acres 
were planted to hybrid corn, leading to an increased production 



THE ROLE OF PLANT BREEDING 7 

of from 100 to 150 million bu. of corn over what would have been 
obtained if hybrid corn had not been available. Many agrono- 
mists believe that there will continue to be a rapid increase in the 
use of hybrid corn in the years to come until the greater part of 
the acreage of corn in the United States is planted to hybrid 
varieties. 

The widespread interest in hybrid corn is due primarily to the 
superiority of hybrids over normal varieties in a number of char- 
acters. Although higher yields per acre are important, other 
improvements are of equal and perhaps greater value. Ability to 
withstand lodging and resistance to smut and to ear and stalk rots 
are of major importance. The development of drought-resistant 
and frost-resistant hybrids has been studied also, although much 
remains to be accomplished in these fields. 

In the development of hybrid corn, Mendelian principles have 
been used directly. A standardized technic of breeding has been 
developed based on the direct application of principles of genetics. 

Intensive studies of inbreeding and crossbreeding corn were 
started by E. M. East at the Connecticut Agricultural Experi- 
ment Station and G. H. Shull at Cold Spring Harbor in 1905. 
Many investigators have taken part in studies of inheritance in 
maize. The fundamental principles elucidated have led to a 
sound basis for scientific improvement in corn, a field in which a 
considerable number of investigators devote all or part of their 
research efforts. Some of the more important principles leading 
to the present methods will be mentioned, although corn breeding 
will be outlined in detail in a later chapter. 

1. Continued self-pollination in corn leads to the production of 
relatively homozygous types that are in general less vigorous than 
normal corn. Crossing inbreds restores vigor. Some FI crosses 
are more vigorous than normal corn; others, less so. 

2. Crosses between inbreds are difficult to use in commercial 
seed production, since the yield of seed per acre is low. This 
difficulty has been overcome by using for commercial production 
crosses between single crosses. 

3. Hybrid vigor in corn and in other crop plants has been 
placed on a definite Mendelian basis. It is a result of partially 
dominant growth factors. Many genes are involved in growth 
vigor, and consequently linkage makes it difficult to combine all 
important genes in a single inbred line. 



8 METHODS OF PLANT BREEDING 

4. Some inbred lines have much better combining ability than 
others when tested in comparable crosses. By crossing a group of 
inbreds to be used in a definite breeding program with a variety 
and by testing the inbred-variety crosses in yield trials, the 
better combining inbreds can be isolated and the less desirable 
discarded. 

5. The combining value of inbred lines in a double cross can be 
predicted from yield trials of the appropriate single crosses. 
From each of four inbred lines, six single crosses and three double 
crosses can be made. Yields of any particular double cross can 
be predicted from the average yield of the four single crosses not 
used in making the double cross. These results may be under- 
stood on the basis that a double cross produced from advanced 
generations of two single crosses behaves approximately the same 
as the double cross between the two single crosses. 

6. The ease of commercial production of double-crossed seed is 
dependent to a considerable extent upon the vigor of the inbred 
lines as well as the yielding ability of the single crosses used in 
the double cross. Improved inbred lines of corn can be bred by 
the same breeding methods as used in the production of improved 
varieties of self-pollinated plants, although it is necessary to 
control pollination by appropriate selfirig and crossing in carrying 
out the program. 

7. The principles of corn breeding that make possible the 
utilization of hybrid vigor are dependent upon an understanding 
of genetic principles and their application to corn breeding. This 
knowledge has made possible to a considerable extent the stand- 
ardization of corn-breeding technics. 

Potato Improvement. Since commercial varieties of potatoes 
are highly heterozygous, plants grown from seed will vary greatly. 
The selection and clonal increase of plants developed from seed 
was naturally the first breeding method used and led to the 
production of the old standard varieties. During the early 
period of the present century, selection within clones was used as 
a method of potato improvement. Although of little value in 
breeding, clonal selection was an aid in isolating plants free from 
virus diseases. This led to the use of the tuber-unit method in the 
diagnosis for and eliminating of plants affected by virus diseases. 

Most varieties of the potato are nonself-fruitful, but strains 
have been isolated that are highly self -fruitful, Clones of the 



THE ROLE OF PLANT BREEDING 9 

latter type produce an appreciable amount of stainable pollen. 
The partial pollen sterility found in the self-fruitful clones appears 
to be due to abortion of the pollen grains after regular meiotic 
division. In the nonself-fruitful clones very little stainable 
pollen is produced because of irregular meiotic division. In 
crosses between self- and nonself-fruitful clones, the progeny are 
usually highly nonself-fruitful. 

Improvement of self-fruitful clones may be accomplished 
through selfing and selection withiii clones and crosses between 
clones, with the use of the breeding methods applicable to self- 
fertile crops. By the use of such methods clones resistant to late 
blight, scab, and specific virus diseases have been produced. The 
breeding value of selections in self-fruitful clones may be deter- 
mined by tests of clonal progenies or, preferably, by tests of the 
selfed progeny. Thus, two clones may appear to produce the 
same amount of disease but be found to differ in genotype when 
selfed progenies of these clones are compared. The genotype of 
clones that are pollen-sterile may be determined from crosses with 
pollen-fertile clones of known genotypes by the use of the pollen- 
sterile clones as females. 

The use of inbreeding methods, supplemented by planned 
crosses, has resulted in a rapid increase in knowledge of the 
genetics of the potato and the isolation of superior germ plasm in 
this crop. In the utilization of this superior germ plasm, some 
modifications in the ordinary breeding, however, must be made in 
the methods applicable to self-fertile crops. 

Although self -fertility is of value in the isolation and synthesis 
of strains that are resistant to disease or insect attack and have 
desirable agronomic characters, self-fruitfulness in itself leads to a 
loss in yield of tubers. Plants that produce flowers and fruits 
yield less than plants that do not, the reduction in yield being 
proportional to the number of flowers or fruits produced. Conse- 
quently, the character of self-fruitfulness, after being utilized 
during the production of superior strains, must be eliminated in 
the breeding of commercial varieties. This may be accom- 
plished through crosses between nonself-fruitful commercial 
varieties possessing high yielding capacity and certain plant and 
tuber types with self -fruitful clones that possess the characters to 
be added, with the use of the self-fruitful clones as pollen parents. 
The FI progeny of such crosses are highly nonself-fruitful. 



10 METHODS OF PLANT BREEDING 

Selection of nonfruiting types in these progenies may be expected 
to result in improved varieties into which have been synthesized 
the characters desired. 

The use of such methods of breeding has resulted in the develop- 
ment and release to the growers of more than a dozen new varie- 
ties during the past six years. All these have as one parent at 
least a superior pollen parent developed at the Minnesota Agricul- 
tural Experiment Station or by the U, S. Department of Agricul- 
ture. Some of these varieties are resistant to late blight; others 
are resistant to specific viruses, common scab, or insect attack. 
Warba is a newly developed early maturing variety that is 
resistant to mosaic and possesses high-yielding ability. The 
Sebago variety withstood the severe late blight epidemic of 1938 
remarkably well. Katahdin, with its viable pollen, provides the 
plant breeder with a high-yielding commercial variety that can be 
used as a pollen parent in further breeding. The synthesis of 
commercial varieties that have resistance to several diseases, as 
well as many desirable agronomic characters, is preceeding 
rapidly. 



CHAPTER II 

THE GENETIC AND CYTOGENETIC BASIS OF 
PLANT BREEDING 

A knowledge of the chromosome basis of heredity is essential to 
the breeder. The characters of a plant are the end result of the 
interaction of genes, carried in the chromosomes, under particular 
environmental conditions. What is inherited is the manner of 
reaction and not the character itself. 

Diploid organisms result from the union of male with female 
reproductive cells, the chromosome number in the zygote nor- 
mally being twice that of the gamete. With self-pollinated 
organisms, homozygosis is obtained automatically, and perma- 
nence of characters under uniform conditions of environment is 
obtained as a result of equational division of each chromosome 
and gene during somatic mitosis, the diploid conditions of the 
chromosomes in the body and the pairing during reduction divi- 
sion of like chromosomes, two by two, leading to the production 
of a single genetic type of gamete. 

The linear arrangement of genes in the chromosome has been 
generally accepted, and the division of the gene in mitosis and its 
segregation in meiosis have furnished the mechanism for the 
transfer of the unit of inheritance, the gene, from cell to cell. A 
knowledge of the number and nature of the chromosomes in each 
crop plant and their behavior in cell division is fundamental to the 
study of plant breeding. Mendel contributed the law of inde- 
pendent inheritance, and Bateson and Punnett in 1906 gave the 
first case of linkage in sweet peas in a cross between a purple- 
flowered variety with long pollen and a red-flowered variety with 
round pollen. The phenotypic condition in the backcross of 
50 purple long, 7 purple round, 8 red long, and 47 red round plants 
was explained on the basis of gametic production in the ratio of 
7 purple long, 1 purple round, 1 red long, and 7 red round Instead 
of by the usual gametic ratio of 1:1:1:1. The parental com- 
binations were formed seven times as frequently a# the new 
combinations, 

11 



12 



METHODS OF PLANT BREEDING 



TABLE 1. CHROMOSOME NUMBER (HAPLOID) IN THE COMMON 
CROI PLANTS 



Scientific name 


Common name 


Number of 
chromosomes 
(n) 



Cereal Crop Plants and Relatives 



Triticum monococcum 


Wheat: 
ICinkorn 


7 


Triticum dicoccum 


Emmer 


14 


Triticum durum 


Durum 


14 


Triticum spelta 


Speltz 


21 


Triticum vulgare . . 


Bread 


21 


Avena brevis 


Oats: 


7 


Avena strigosa 




7 


Avena barbata 




14 


A vena fatua 


Wild 


21 


Avena sativa 


Cultivated 


21 


Avena byzantina 


Red cultivated 


21 


Avena nuda 


Hull-less 


21 


Hordeum distichon. . .... 


Barley : 
2-row barley 


7 


Hordeum deficiens 


2-row barley 


7 


Hordeum vulgare 


6-row barley 


7 


Hordeum jubatum 


Squirrel tail 


14 


Hordeum nodosum 




21 


Secede cereale 


Rve 


7 


Fagopyrum esculentum 


Buckwheat 


8 


Oryzo, sativa 


Rice 


12 


Zea mays 


Corn 


10 


Sorghum halepensis . . . 


Johnson grass 


20 


Sorghum vulgare 


Milo, Kafir, 


10 


Sorghum vulgare, var. sudanensis 


Feterita, Kaoliang 
Sudan grass 


10 



Forage Grasses 


Agropyron cristatum 
Agropyron pauciflorum. . 


Crested wheat 
Slender wheat 
Red top 
Meadow foxtail 
Big bluesteni 
Little bluestem 
Brome grass 
Orchard grass 
Wild rye 
Meadow fescue 
Italian rve err ass 


7, 14 
14 
21 
14 
35 
20 
21, 28 
14 
14 
7, 14, 21, 35 
7 


Agrostis alba 


Alopecurus pratensis 


Andropogon furcatus 


Andropogon scoparius 


Bromus inermis 


Dactylis glomerata 


Elymus canadensis 


Festuca elatior 


Lolium italicum 



THE GENETIC AND CYTOGENETIC BASIS 



13 



TABLE 1, CHROMOSOME NUMBER (HAPLOID) IN THE COMMON 
CROP PLANTS. (Continued) 



Scientific name 



Common name 



Number of 
chromosomes 

(n) 



Forage Grasses (Continued) 



Lolium perenne Perennial rye grass 7 

Panicum miliaceum Proso millet 18, 21 

Phalaris arundinaceae Reed canary 7, 14 

Phleum pratense Timothy (American) 21 

Phleum pratense Timothy (British) 7 

Poa compressa Canada blue 7, 21, 28 

Poa pratensis Kentucky blue 14-49 

Legumes 

Glycine soja Soybean 20 

Lespedeza sp Japan clover 9, 10, 18 

Medicago falcata Alfalfa 8, 16 

Medicago sativa Alfalfa 16 

Melilotus alba Sweet clover (white) 8 

Melilotus officinalis Sweet clover (yellow) 8 

Pisum sativum Pea 7 

Trifolium hybridum Alsike clover 8 

TrifoUum pratense Red clover 7, 12 ^ 

Trifolium repens White Dutch clover 8, 12, 14, 16 

Vigna sinensis Cowpea 12 

Fiber Plants 

Cannabis sativa Hemp 10 

Gossypium sp Cotton (Asiatic) 13 

Gossypium sp Cotton (American) 26 

Linum usitatissimum Flax 15, 16 

Sugar Plants 

Beta vulgaris Sugar beet 9 

Saccharum offidnarum Sugar cane 40-63 

Stimulants 

Coffea sp Coffee 11, 22, 33, 44 

Nicotiana tabacum Tobacco 24 

Thea sinensis Tea 12-13, 15, 22-23 

Oil Plants 

Aleurites sp Tung oil 11 

Arachis hypogaea Peanut 10, 20 

Linum usitatissimum Flax 15, 16 

Sesamum indicum .... Sesame 26 



14 



METHODS OF PLANT BREEDING 



TABLE 1. CHROMOSOME NUMBER (HAPLOID) IN THE COMMON 
CROP PLANTS. (Continued) 



Scientific name 


Common name 


Number of 
chromosomes 

(n) 



Vegetables 



Allium cepa 


Onion 


8 


Asparagus officinalis .... 


Asparagus 


10 


Beta vulgaris . 


Beet 


9 


Beta vulgaris var. cicla. . . . 


Chard 


9 


Brassica oleracea 


Cabbage, cauliflower, 


9 


Brassica rapa 


kohlrabi 
Turnip 


10 


Capsicum annuum 


PeDDer 


12 


Citrullus vulgaris . . . 


Watermelon 


11 


Cucumis melo 


Muskmelon 


12 


Cucumis sativus 


Cucumber 


7 


Cucurbita moschata 


Squash 


20 


Cucurbita pepo 


Pumpkin 


20 


Lactuca saliva 


Lettuce 


9 


Lycopersicum esculentum 


Tomato 


12 


Phaseolus lunatus 


Bean (lima) 


11 


Phaseolus vulgaris 


Bean (kidney) 


11 


Pisum sativum 


Pea 


7 


Raphanus sativus 


Radish 


9 


Rheum rhaponticum 


Rhubarb 


22 


Solanum melongena 


Eggplant 


12 


Solanuin tuberosum 


Potato 


24 


Svinacia oleracea 


Spinach 


6 



Fruits 



Citrus grandis , 


Grapefruit 


9 


Citrus limonia 


Lemon 


9 


Citrus sinensis 


Common orange 


9, 18 


Fragaria grandijlora 


Strawberry (cultivated) 


28 


Malus malus 


Apple 


17, 5 H 


Prunus americana 


Plum (American) 


8 


Prunus domestica 


Plum (European) 


24 


Prunus avium 


Cherry (sweet) 


8 


Prunus cerasus 


Cherry (sour) 


16 


Prunus persica 


Peach 


8 


Pyrus communis . 


Pear 


17, 5 Ji 


Ribes sp 


Currant 


8 


Rubus idaeus 


Red raspberry (Euro- 


7, 14 


Rubus strigosus 


pean) 
Red raspberry (Ameri- 


7 


Yitis sp 


can) 
Grape (cultivated) 


19, 20, 38 



THE GENETIC AND CYTOGENETIC BASIS 15 

The frequencies of new combinations of factor pairs lying in 
homologous chromosomes are dependent to a great extent upon 
the distance apart of the genes in the chromosome. The spindle 
fiber apparently reduces crossing over in adj acent regions. There 
is no interference between crossovers on opposite sides of the 
spindle fiber. Many studies of genetic linkages have shown wide 
differences between genetic maps and physical-map distances as 
determined by cytogenetic study of induced breaks in chromo- 
somes. These studies have given added evidence, however, of 
the linear order of the genes in the chromosome. There are also 
other types of cytological aberrations, such as inversions and 
translocations that lead to new genetic maps. In crosses between 
the new types with standard types, genetic ratios may be greatly 
modified. 

Qualitative and quantitative differences in chromosomes have 
been extensively studied in recent years, and the field of cyto- 
genetics is being constantly developed. Information regarding 
the number and nature of chromosome differences is being 
obtained rather rapidly for many crop plants. The present 
chapter will summarize the usual chromosome numbers in 
important crop plants arid illustrate how genetic and cytogenetic 
principles are being used by the plant breeder. Chromosome 
numbers in the common crop plants, taken largely from the 1936 
and 1937 U. S. Department of Agriculture Yearbooks, are given in 
Table 1. 

POLYPLOIDS IN RELATION TO PLANT BREEDING 

A study of chromosome numbers in related species of economic 
plants shows many multiple series. A common haploid number 
in the Gramineae is 7. Species of Triticunij Avena, and Hordeum 
with haploid numbers of 7, 14, and 21 are common and illustrate a 
type of variation in polyploids, i.e., multiples of a fundamental 
number, often referred to as a euploid series. Aneuploidy, or 
variation in chromosome numbers not multiples of a fundamental 
number, is frequent in some species. Poa pratensis, for example, 
varies from 28 to over 100 somatic chromosomes, Aneuploid 
chromosome numbers are of more frequent occurrence in species 
that have apomictic development than under conditions of sexual 
reproduction. 



16 



METHODS OF PLANT BREEDING 



-There are two main types of euploids, namely, allopolyploids 
and autopolyploids. These two types are illustrated in Fig. 2. 
In this illustration the autopolyploid is of the autotetraploid type 
and has four sets of like or homologous chromosomes. There 
may be random pairing or mating between each group of the four 
homologous chromosomes. An allopolyploid has chromosome 
sets from different sources. In the illustration a haploid set from 




doubling 




F,hybrid, no pairing 
doubling 



JUUUQQOO 




Autotetraoloid, n?4 Amphidiploid ,n =4 

FIG. 2. Schematic diagram of development of autotraploid due to doubling 
of chromosome number in the zygote and the production of an arnphidiploid 
from a cross between related species due to doubling of chromosome number in 
the gametes or zygotes when chromosomes are so unlike that pairing is not 
obtained in the Fi cross. 

species A is so different from that of species B that pairing does 
not take place. Doubling of the chromosome number will result 
in an allopolyploid of the amphidiploid type. 

One of the best known cases pf triplicate factors in a polyploid 
of the amphidiploid type is in ^riticum vulfftire, where there may 
be three pairs of factors for brownish red color of the kernel, any 
one of the three in a dominant condition leading to the develop- 
ment of color. This case was given originally by Nilsson-Ehle as 
the basis for the multiple-factor theory of quantitative inherit- 



THE GENETIC AND CYTOOENETIC BASIS 



17 



ance, without a knowledge of the fact that T. vulgare is a 
polyploid of the hexaploid type with the amphidiploid type of 
chromosome pairing, i.e., contains three sets or genoms of seven 
bivalents (7 n ) each, or 42 somatic chromosomes. These three 
factor pairs for red kernel color may be designated jRifi, Rzr% f 
72sr 3 . An illustration of the mode of inheritance of red vs, color- 
less kernels may be given where only two of the three factor pairs 
are concerned and the parents and Fi produced red kernels. 

Variety A 
Parental phenotype ................... red * 

Parental genotype .................... .Ri-Ri r^rz T%r% 

Fi phenotype ......................... red 

Fi genotype .......................... 



Variety B 
red 



Since the r 8 r 8 factor pair is in the homozygous recessive condition, 
it will have no effect on kernel color and may be disregarded. 

The following summary gives the genotype and kernel color of 
jP 2 plants and F 3 breeding behavior : 



F, 


F* 








Genotype 


color 


Breeding behavior 


1 /ki/Li/fc2*fc2 


Red 


Breeds true for red kernel color 


2 RiriRzRz 


Red 


Breeds true for red kernel color 


2 RiRiR%r% 


Red 


Breeds true for red kernel color 


4 RiTiR*tr z 


Red 


Segregates; 15 plants red kernels: 1 plant colorless 


1 RiRiTzTz 


Red 


Breeds true for red kernel color 


2 RiTiTzTz 


Red 


Segregates; 3 plants red: 1 plant colorless 


1 TiTiR^Rz 


Red 


Breeds true for red kernel color 


2 TiTijtltzTz 


Red 


Segregates; 3 plants red:l plant colorless 


1 fiTirzrz 


Colorless 


Breeds true for colorless kernels 



Genotypes RiriR^R^ and RiRiR^r^ are illustrations of poly-* 
ploids with genetic segregation that has no definite phenotypic 
effect. There is a general relation between intensity of color and 
number of dominant factors, but the relation is so indefinite that 
the number cannot be estimated by visual inspection. 

The segregation in F 2 of 15 plants with red kernel color to 1 
with colorless kernels results from crossing two varieties, the one 
homozygous for RiRir^r^ and ,the other r.iTiRJR^ Of the 15 
plants with red kernel color in Fg, 7 breed true in F for red color, 



18 METHODS OF PLANT BREEDING 

4 segregate in a 15: 1 ratio, and 4 segregate in a 3: 1 ratio. The 
plants with colorless kernels in F 2 breed true for this color in F$. 

Contrasted with the foregoing allopolyploid type is the auto- 
polyploid, such as is obtained in Datura stramonium resulting 
from doubling of the diploid chromosome number. The chromo- 
some constitution may consist of four identical sets of chromo- 
somes. If we take the case where the diploid was heterozygous 
for a single factor pair Dd, the autotetraploid will have the geno- 
type DDdd. Such a polyploid has a high frequency of quadri- 
valent association, and random chiasma formation occurs among 
the four homologous chromosomes. 

In an autotetraploid for any dominant factor, there may be a 
series of genotypes such as DDDD, DDDd, DDdd, Dddd, dddd, 
also written Z>4, Dsd, D^d^ etc., respectively. In an autopoly- 
ploid there may be chromosome segregation or random chromatid 
segregation. Random chromatid segregation occurs only when 
the factors concerned are somewhat more than 50 crossover units 
from the spindle-fiber attachment. For closer distances the 
ratios are intermediate between those expected from chromosome 
and chromatid segregation, approaching chromosome segrega- 
tion as the genes become closer to the spindle fiber. This 
naturally modifies the ratios obtained from particular types of 
heterozygotes. 

A convenient method of calculating gametic expectation is 
illustrated as follows in an autotetraploid of the D%d (DDDd) 
type. The number of combinations of n things taken r at a 

n\ 

time = 7 - rj ,- 
(n r)!r! 

For chromosome segregation, the gametic expectation may be 
calculated in the following manner. Two types of gametes would 
be obtained, DD and Dd. The gametic ratio expected is as 
follows; 

For gamete DD, or the number of different ways of taking two 

3! 

things out of three, n = 3 and r = 2, and yy^j = 3DD. 



For diploid gametes containing a dominant and recessive factor, 
Dd, for example, it is unnecessary to use the formula. The D 
factor can be taken in three ways from D 8 , whereas d can be 
taken in only one. The gametic expectation then will be 
3D X Id w Wd. This is the result that would be obtained if the 



THE GENETIC AND CYTOGENETIC BASIS 19 

formula was used to calculate the number of combinations and if 
it is remembered that factorial zero (0!) equals 1. 

With random chromatid segregation, however, the condition 
would be entirely different. The chromatid condition would be 



The number of different ways of obtaining a combination of 
DD can be calculated by substituting, where n = 6 and r = 2 
in the formula, The frequency of gametes of the DD type will 

= 15DD. Gametes of the Dd type 





& ' $ * 4: * & 

can be obtained by finding how many times one D can be taken 
from D 6 , which equals 6D, and this multiplied by 2d would give 
l2Dd. One gamete of the dd type can be obtained, and the 
gametic ratio then will be 15DD: 12Dd: Idd. Thus, from selfing 
DDDd, where the percentage recombination between the D locus 
and the spindle fiber approaches 50 per cent, the phenotypic 
expectation in Fz is 783D : Id. Such peculiar ratios cannot easily 
be differentiated from mutations without studying second-genera- 
tion selfed progeny rather extensively. 

In a similar manner, the student can calculate expectation for 
other genetic types of polyploids. Linkage relations are greatly 
complicated in polyploids. The student of plant breeding will be 
able to determine logical explanations for the results obtained 
only when a knowledge is available of the chromosome mechanism 
for the particular plant under study. 

There are two general types of euploids, but probably, in many 
cases, there are also intermediates that behave as amphidiploids in 
some cases and for some chromosome pairs and autopolyploids 
under other conditions or for other chromosome pairs. Wheat is 
a good example of a hexaploid that generally gives an amphi- 
diploid type of inheritance. Ordinary bread wheat contains 
three sets, or genoms, of 7 chromosomes each, and, as a rule, the 
pairing behavior is of the diploid type. Based upon Winge'p 
original explanation, doubling could occur from crosses between 
two closely related species each with a chromosome number of 
n = 7 } which, through geographical isolation, gene mutations, 
and chromosomal changes, had become so differentiated in tfceir 
chromosome mechanism that crossing was possible but pairing did 
not occur in meiosis. This may have led to the inclusion of 
28 chromosomes in a single cell, resulting from equational division 



20 



METHODS OF PLANT BREEDING 



of 14 unpaired chromosomes, 7 being obtained from each parental 
species. A further cross between this species with another 
closely related form with n = 7 chromosomes would furnish the 
type basis for an amphidiploid form with n = 21 chromosomes. 
Doubling has occurred in eKperimental material of this nature 
both in the zygote and in the gamete. 

There are many illustrations in the literature of pairing of the 
autopolyploid type in a polyploid that usually pairs as an amphi- 
diploid. Breeders of crop plants with the amphidiploid-chromo- 
some condition obtain variations in breeding behavior that seem 
most logically explained on the basis of changes in the type of 
chromosome pairing. 

Genom analyses based on types of chromosome pairing have 
been made extensively with Triticum and related genera by 
numerous investigators. One of the first summaries was that 
given by Gaines and Aase (1926), illustrated by Fig. 3. 



TRITICUM TURGIDUM TRITICUM VULGARC AEGlLOPS CYLIKDRICA 




FIG. 3. Diagram illustrating hypothetical relationships of chromosomes. 
The 7 chromosomes in set a and the 7 chromosomes in set 6 are present in both 
Triticum vulgare (21 chromosomes as the hapioid number) and in T. turgidum 
(14 chromosomes). The 7 chromosomes in set c are present in T. vulgare and 
in Avgilops cylindrica but not in Triticum turgidum. The 7 chromosomes in 
set d are present in Aegilops but liot in either T. vulgare or T, turgidum. A 
21-chromosome wheat X a 14-chromosome wheat gives rise to sporocytes with 
14 paired and 7 unpaired chromosomes (lower left). A 21-chromosome wheat 
X Aegilops cylindrica gives rise to sporocytes with 7 paired and 21 unpaired 
chromosomes (lower center). Aegilops cylindrica X Triticum turgidum gives 
rise to sporocytes with 28 unpaired chromosomes (lower right). 

The present status of the problem may be summarized as 
follows: 



THE GENETIC AND CYTOGENET1C BASIS 



21 



EINKORN SERIES 

(n-7) 
AA 

Triticum aegilopoides 
Triticum monococcum 

TIMOPHEEVI SERIES 

(n - 14) 
AAGG 
Triticum timopheevi 



EMMER SERIES 

(n - 14) 
AABB 

Triticum dicoccoides 
Triticum dicoccum 
Triticum durum 
Triticum turgidum 
Triticum pyramidak 
Triticum polonicum 



SPELT SERIES 

(n - 21) 
AABBCC 
Triticum speUa 
Triticum vulgare 
Triticum compactum 



SECALE SERIES 
(n-7) 

EE 

Secale cereak 



AEGILOPS SERIES 

(n - 14) 
CCDD 
Aegilops cylindrica 

The species of Triticum, Secale, and Aegilops are seen to be 
made up of one or more sets (genoms) of seven chromosomes 
each, designated A, J3, C, D, JB, and G (Lilienfeld and Kihara 1934, 
Kostoff 1937). In crosses between the Emmer and Spelt series, 
for example, the pairing behavior in F\ most commonly consists 
of 14n and 7i, although in some cases a few trivalents and quadri- 
valents may be obtained because of the fact that chromosomes of 
one genom have some homology with those of a different genom. 
One of the genoms of timopheevi is similar to the A genom, the 
other (GG) resembles B more closely than C but differs rather 
widely from jB, forming from two to seven loose conjugations 
with it. 

Stadler (1928, 1929) studied rate of induced mutation per r unit 
in barley, oats, and wheat in relation to chromosome numbers. 
Results are as follows: 



Species 


Number of 
chromosomes (n) 


Rate of 
mutation 


Hordeum vulgare . 


7 


4.9 09 


Avend br&vis 


7 


4.1 1.2 


Avena strigosa 


14 


2.6 0.6 


Avena s&tiva 


21 





Triticum monococcum 


7 


10.4 3.4 


Triticum dicoccum 


14 


2.0 13 


Triticum durum . 


14 


1 9 5 


Triticum vulgare 


21 












22 ' METHODS OF^ PLANT BREEDING 

In general, as has been mentioned, there may be three sets of 
factors in hexaploid wheat and oats but o,nly a single factor pair in 
each locus for diploid species. A mutation in a homozygous form 
A A in barley, giving A a, would produce progeny containing 
25 per cent of recessives. In a tetraploid of the amphidiploid 
type, two such simultaneous mutations would be necessary in 
order than an induced mutation for a character that was doubly 
dominant could show up in the immediate progeny. 

Variation in pairing whereby one chromosome pair of a genom 
shows some homology with a member of a different set would lead 
to abnormal segregation. In polyploids of the amphidiploid 
type, such results are probably of relatively frequent occurrence. 

Powers (1932) and Myers and Powers (1938) have studied 
variability in strains of wheat due to various types of chromosome 
abnormalities or to gene differences. In a study of Marquillo, a 
variety belonging to the spelt series with a haploid chromosome 
complement of 21 but derived from a cross between varieties of 
Triticum durum and T. vulgare with 14 and 21 haploid chromo- 
somes, respectively, Powers (1932) found that germinal instability 
in Marquillo was greater than in Marquis or Thatcher. Thatcher 
is a variety produced by crossing a sister selection of Marquillo 
with a purified hybrid of Marquis X Kanred. 

In these studies, the easiest method of estimating the percent- 
age of germinal instability was to measure the occurrence of 
chromatin loss, measured by the frequency of occurrence 
of microspores showing micronuclei. The mean percentage of 
micronuclei in four varieties is \given in the following summary, 
taken from Myers and Powers: 



Variety 


Total plants 


Mean percentage 
of micronuclei 


Thatcher 


25 


8 


Marquis .... 


26 


0.9 


H44 


20 


4.1 


Supreme 


9 


8.3 









H44 is a variety of wheat produced by McFadden from a cross 
of Yaroslav emmer X Marquis, It has the chromosome number 
of the spelt group. Supreme is a variety of T. vulgare produced 
by selection from Red Robs. 



THE GENETIC AND CYTOGENETIC BASIS 23 

Although it seems probable that a wheat of recent origin such 
as Marquillo may show greater germinal instability than old 
established varieties such as Marquis, as has been pointed out by 
Powers and also by Love (1938), it seems of interest that Supreme, 
a variety of T. vulgare, selected from a variety not of recent 
origin, is equally instable, although there is the possibility that its 
origin may be also the result of a natural cross between species. 
Myers and Powers showed germinal instability to be inherited, 
and the isolation of apparently homozygous lines with different 
percentages of micronuclei was considered to indicate that genetic 
factors were involved in conditioning meiotic instability. 

In the studies of Marquillo, Powers found evidence for 7.2 per 
cent of natural crossing. This is higher than has been usually 
observed with other varieties of wheat at the Minnesota station. 
Thirty-two plants of Marquillo were studied, two of these having 
only 41 chromosomes. An average of 23.4 0.24 per cent of the 
mierospores of the 41 chromosome plants showed micronuclei, 
whereas only 2.8 0.16 per cent of the 42 chromosome plants 
showed micronuclei. 

In a recent cross in oats by Hayes, Moore, and Stakman (1939) 
between Bond, Avena byzantina, and standard varieties of A. 
sativa, segregation in F% for type of base on the lower floret 
occurred in a 3 : 1 ratio of sativa to byzantina types. Several F 3 
families from F% plants showed wide deviations from the type of 
segregation in F% and an intermediate type of base bred true in 
later generations. The hypothesis that these results were due to 
change in chromosome pairing was used, although further studies 
are necessary to prove the hypothesis. 

Hope and H44 are vulgare wheats with n = 21 chromosomes 
that descended from crosses of Triticum dicoccum X Marquis 
(T. vulgare). In many studies of stem-rust reaction, when Hope 
and H44 are crossed with other varieties of vulgare wheats, wide 
deviations from the usual type of F% segregation have been 
observed in F$ families. In such crosses, however, it has been 
relatively easy to obtain homozygous types with stem-rust 
resistance similar to that of the Hope and H44 parents. Changes 
in the manner of chromosome pairing in complex polyploids of 
the amphidiploid type seem to occur rather frequently. This 
tends to complicate breeding behavior and necessitates that 
greater care be used to ensure the selections of greatest promise 



24 METHODS OF PLANT BREEDING 

are breeding true before they are increased for distribution. A 
tendency for a modified type of segregation in jP 8 in some families 
does not necessarily greatly complicate the breeder's problem of 
selecting desirable homozygous types. 

Speltoid wheats and fatuoid oats have occurred in T. vulgare 
(2n = 42) and A. saliva (2n 42) as a result of chromosomal 
variations due very probably to a change in chromosome pairing. 
The review of Sansome and Philp (1939) has been used in this 
summary. Speltoid wheats resemble T. spelta and fatuoid, or 
false wild oats, resemble A. Jatua. Three types have been 
observed: Type A, with no change in chromosome numbers, 
Type B, with a chromosome deficiency, and Type C, with a 
chromosome excess. 

The A type, when heterozygous, gives three types of progeny: 
homozygous fatuoid or speltoid, heterozygous, and normals in a 
ratio of 1:2:1. 

An explanation that has been given by Winge and Huskins is 
on the basis of a change in pairing due to the similarity of a 
chromosome of one genom with that of another. If we designate 
the three chromosome pairs concerned, as A, B, and C, one 
chromosome belonging to each of the three genoms, and suppose 
the B chromosome carries the speltoid factors and C the normal 

ABC 
factors epistatic to the speltoid, then the normal type 



would breed true, as a rule, for absence of speltoid characters. 
If one supposes that B has sufficient homology with (7, so that 

occasional pairing occurs between B and C, giving rise to 

then gametes ABB and A CC would be obtained. If gamete 

ABC 
ABB mated with ABC, the heterozygous speltoid form 



would be obtained. On selfing, three types of progeny would 
result normals, -3-575, heterozygous speltoids, -r^ and homo- 



ABB 
zygous speltoids, -rg|> ia a ratio of 1 : 2 : 1. Such a homozygous 

speltoid would give some quadrivalent associations, as was 
observed by Winge, whereas the heterozygous speltoid would 
show trivalent and univalent associations that were observed 



THE GENETIC AND CYTQGEtfETIC BASIS 25 

also. The old hypothesis that fatuoids arise through natural 
crosses between Avena sativa and A. fatua is seen to be 
untenable. 

Winge gave formulas for the B and C types of speltoids where 
stands for the loss of a chromosome, consisting of the heterozy- 

gous type -r77 and two sorts of homozygotes, one -rw with the 



loss of a chromosome, and the other .......... : ..... pp-> with the duplication 

of the chromosome B. 

Huskins studied breeding behavior, variations in pairing, and 
chromosome numbers in fatuoids or false wild oats, obtaining 
the same sort of results that have been outlined for speltoids. 

These types of results have been presented briefly to emphasize 
the difficulties of studying genetics in polyploids. The plant 
breeder must deal with polyploids in economic plants, and a. 
knowledge of the causes of variability may aid greatly in the 
breeding program. Selection for types with chromosome pairing 
that will give normal disjunction will aid in establishing uniform 
breeding strains. Wide deviations from normal types of segrega- 
tion may be expected in some progenies. There is, however, 
considerable evidence that by selection for germinal stability, in 
many cases, the variability resulting from abnormal pairing may 
be overcome. Such selection will often be of great economic 
importance, since germinal instability often leads to the produc- 
tion of undesirable characters. The loss or gain of one or more 
chromosomes in polyploids may lead to the production of an 
undesirable type of abnormality, such as speltoid wheat or 
fatuoid oats. 

SOME APPLICATIONS OF GENETICS TO PLANT BREEDING 

The value to the plant breeder of a knowledge of the mode of 
inheritance of important characters and the application of genetic 
principles to methods of breeding will be illustrated by specific 
examples. A problem in oat improvement recently investigated 
at the Minnesota Experiment Station illustrates the use of 
genetics in a practical breeding problem. The parent varieties 
and character differences are summarized here, 



26 METHODS OF PLANT BREEDING 

Anthony, logold, Rainbow Bond 

1. Good yield* Fair yield 

2. Good-quality grain Excellent quality grain* 

3. Fair straw strength Excellent standing ability* 

4. Stem-rust resistance* Stem-rust susceptibility 

5. Susceptibility to crown rust Crown-rust resistance* 

6. Susceptibility to smuts Smut resistance * 

7. Sativa type* Byzantina type 

* Characters desired in the hybrid. 

Frequently certain crosses give a larger proportion of desirable 
offspring than others, probably because of the fact that the geno- 
type of the one parent supplements that of the other in a more 
satisfactory manner, although the reason why certain crosses give 
a greater proportion of desirable progeny than others, in many 
cases, cannot be placed on a definite genetic basis. These facts 
have led the plant breeder to use several crosses for a specific 
problem rather than a single cross. 

Anthony, logold, and Rainbow were three recommended 
varieties of Avena sativa grown by Minnesota farmers. logold, 
because of early maturity, is adapted to southern Minnesota; 
the midseason varieties Antony and Rainbow usually yield better 
than logold in north central and northern Minnesota. Double 
Cross A, also crossed with Bond, was a selection from (Minota X 
White Russian) X Black Mesdag, homozygous resistant for the 
White Russian type of stem-rust reaction and the Black Mesdag 
type of resistance to smut. Although not particularly desirable 
in type of kernel, it was outstanding in yielding ability. 

Anthony, logold, and Rainbow were selected because they 
produced good yields of grain, were resistant to stem rust, caused 
by Puccinia graminis avenae Eriks. & Henn., and were of the 
sativa type. Cultivated varieties of Avena sativa have proved 
more desirable in Minnesota. Bond, a variety of A. byzantina, is 
highly resistant to crown rust, Puccinia coronata Corda, and to the 
smuts prevalent in Minnesota, Ustilago avenae (Pers.) Jens, and 
Ustilago levis (Kellermann & Swingle) Magn. Bond excels also 
in ability to withstand lodging and in grain quality, producing 
plumper kernels with a higher weight per bushel than the recom- 
mended varieties of A. sativa. 

A summary of the mode of inheritance of the characters will 
help to explain the way that genetic principles can be used in a 
breeding program. 



THE GENETIC AND CYTOGENETIC BASIS 27 

MODE OF INHERITANCE OF CHAKACTBRS IN OAT CROSSES 
(ANTHONY, IOGOLD, RAINBOW x BOND) 

1. Crown rust. F\ resistant; Fg 9 resistant:? susceptible or 3 resistant:! 

susceptible. 

2. Stem rust. F\ resistant; F 2 3 resistant: 1 susceptible. 

3. Smuts. Using a mixture of races of the two smut species, F\ resistant; 

^2 segregation 1 to 3 pairs of genes, 

4. Sativa vs. byzantina characters. 

a. Spikelet disarticulation. F\ sativa base; Fa 3 sativa base: 1 byzantina 

base. 

h. Floret disjunction. F\ byzantina type; F 2 1 or 2 pairs of factors, 
c. Basal hairs. FI sativa type; F 2 3 sativa: 1 byzantina. 

5. Yield. Multiple factors. 

6. Time of maturity. Multiple factors, 

7. Plumpness of grain. Multiple factors. 

The purpose of the crosses was to combine in a single variety 
the desirable agronomic characters with resistance to three major 
oat diseases, stem rust, crown rust, and smuts. In these studies 
the pedigree method of breeding was used. It consisted of grow- 
ing the segregating generations as progenies so that individual 
plant study was possible, each progency consisting of approxi- 
mately 50 plants from a single plant of the previous generation. 
Selection was continued until homozygous lines were obtained 
that appeared desirable. Then the best lines were determined 
from replicated yield trials. 

Crown Rust. In the cross of Rainbow X Bond, only a single 
factor pair was involved. In F 2 in the other crosses, there were 
approximately 9 crown-rust-resistant to 7 susceptible plants. 
The Bond type of resistance appeared to be due to the com- 
plementary action of two factors. Resistance to each physiologic 
race to which Bond was resistant seems to be due to the same 
genetic factors. 

The illustration shown at the top of page 28 is given where 
two factor pairs were necessary to explain the results. F% geno- 
types and phehotypes and F 3 breeding behavior ar& summarized. 

^2 plants resistant to crown rust were selected. On the 
average 1 out of 9 may be expected to breed true for resistance in 
Fa. Two types of segregating progenies are expected in Fg, one 
segregating on a 3 : 1 basis and the other on a 9 : 7 basis. 

Progenies breeding true for resistance to crown rust can be 
determined by seedling inoculation in the greenhouse. By grow- 
ing from 20 to 30 seedlings from each plant selected and by 



28 



METHODS OF PLANT BREEDING 



^ genotype 



1 AABB 
2AaBB 
2AABb 
4AaBb 

lAAbb 
2Aabb 
1 aaBB 
ZaaBb 
I aabb 



phenotype 



Resistant to crown rust 
Resistant to crown rust 
Resistant to crown rust 
Resistant to crown rust 

Susceptible to crown rust 
Susceptible to crown rust 
Susceptible to crown rust 
Susceptible to crown rust 
Susceptible to crown rust 



breeding behavior 



Breeds true for crown-rust resist- 
ance 

Segregates, 3 resistant : 1 suscepti- 
ble 

Segregates, 3 resistant : 1 suscepti- 
ble 

Segregates, 9 resistant : 7 suscepti- 
ble 

Breeds true for susceptibility 
Breeds true for susceptibility 
Breeds true for susceptibility 
Breeds true for susceptibility 
Breeds true for susceptibility 



inoculation with crown rust, the progenies from F* to Ff> that are 
homozygous for crown-rust reaction can be isolated. These 
breed true for resistance under field conditions. 

Stem Rust. Stem-rust reaction is handled in the same manner. 
By the use of a single factor pair, the results can be illustrated as 
follows, where R stands for resistance and r for susceptibility. 



logold, Resistant (RR) 



Bond, Susceptible (rr) 



i, Resistant (Rr) 



F z genotype 


F% phenotype 


F s breeding behavior 


IRR 
2Rr 

Irr 


Resistant 
Resistant 
Susceptible 


Breeds true for resistance 
Segregates, 3 resistant:! susceptible 
Breeds true for susceptibility 



As will be discussed in some detail later, many pathogenic 
organisms are mixtures of raceff that can be differentiated only by 
their manner of reaction on a series of varieties used as differential 
hosts. It has been learned that logold and Rainbow are resistant 
to races of stem rust 1, 2, 3, 5 and 7, that Anthony and Double 
Cross A are resistant to races 1, 2, and 5, whereas Bond is suscep- 
tible to all five races. In this case, there is a series of three alleles. 



THE GENETIC AND CYTOOENETIC BASIS 29 

for resistance and susceptibility to stem rust that may be called 
Ri for resistance to five races; #2 for resistance to races 1, 2, and 
5; and r for susceptibility to all races. 

Crosses of Bond X Anthony or Double Cross A segregate on a 
3 : 1 basis in F 2 , and the only two homozygous types that can be 
obtained will be those that are resistant and susceptible, respec- 
tively, to the three races 1, 2, and 5. 

Crosses of Bond with logold and Rainbow segregate also on a 
3 : 1 basis, in the presence of inoculum of races 3 and 7, whether 
races 1, 2, and 5 are present or absent, and the two homozygous 
types that can be obtained will be resistant and susceptible, 
respectively, to the five races 1, 2, 3, 5, and 7. A consideration of 
these facts will show that, in crosses of Bond with Anthony, 
logold, Rainbow, or Double Cross A, infection only with race 
I furnishes a satisfactory basis for isolation of the parental type of 
resistance. 

If Anthony or Double Cross A are crossed with logold or 
Rainbow, all offspring are resistant to races 1, 2, and 5, but 
segregation in Fz for reaction to races 3 and 7 will occur, giving a 
3 : 1 ratio of resistant to susceptible. 

From any cross, therefore, between homozygous members of a 
multiple allelic series the only homozygous types for the character 
difference that can be recovered will be the parental types. 

There is agreement between seedling and mature-plant reaction 
for stem-rust and seedling studies can be used in the same general 
manner for stem-rust reaction as has been outlined for crown rust. 

Several races of stem rust can attack the parental varieties 
Anthony or logold, but neither of these varieties has been severely 
and widely injured by stem rust in farmers' fields under field 
conditions since their introduction, and Anthony has been grown 
widely for over 10 years. 

Reaction to Smuts. It was somewhat difficult to determine 
the genetics of smut reaction. Resistance was dominant over 
susceptibility, and segregating progenies may be expected to con- 
tain fewer susceptible plants than a homozygous susceptible line. 
Parent rows were included approximately every 20 rows through- 
out the nursery. In crosses of Bond with Anthony, logold, and 
Rainbow, the results in F$ indicated a single major-factor pair for 
smut reaction. In the crosses between Double Cross A with 
Bond, where both parents were resistant to smut, a few highly 



30 METHODS OF PLANT BREEDING 

susceptible progenies were obtained in F&. From previous 
studies, the resistance of Double Cross A was explained on the 
basis of two major-factor pairs. The results in the present cross 
were explained on the basis that the resistance to smuts of the 
Bond parent was independent in inheritance of the two factors 
for smut resistance carried by Double Cross A. When all three 
factor pairs were recessive, susceptibility resulted. 

The methods used in selecting for disease-resistant plants were 
based on a knowledge of the mode of inheritance. An epidemic of 
crown rust, stem rust, and smut was induced by methods that will 
be outlined later. Crown rust appears first, and resistant, 
desirable-appearing plants were selected and tagged about 10 
days after heading. Stem rust can be determined at maturity. 
Plants resistant to stem and crown rust were selected in progenies 
that were free from smut, and smut-free plants were selected also 
in progenies that had a lower percentage of smut than the suscep- 
tible parents. By these methods it was relatively easy to obtain 
a large number of progenies resistant to all three diseases. 

Sativa vs. Byzantina Characters. Three pairs of contrasting 
characters have been used to differentiate byzantina and sativa 
oats. These may be illustrated by Fig. 4, in which are shown the 
upper and lower florets of Anthony belonging to Avcna sativa and 
Bond, a variety of A. byzantina. The characters may be 
explained briefly. 

1. Spikelet disarticulation has been defined as the separation of 
the lower floret of the oat spikelet from the axis of the spikelet. 
Three classes were used to describe the segregating generations: 
(a) abscission, typical of Bond, at the right of the figure, leaving a 
well-defined, deep oval cavity or " sucker mouth" on the face of 
the callus on the base of the lemma of the lower grain; (6) dis- 
articulation by fracture, leaving a rough, fractured surface with 
little or no cavity at the base of the lemma, characteristic of 
A. sativa as illustrated by Anthony in the figure; and (c) dis- 
articulation by semiabscission, intermediate between a and 6. 

2. Basal hairs, conspicuoijs bristles on the base of the lower 
floret. The Bond parent had long abundant hairs, and the A. 
sativa parents had short hairs that were abundant, few, or absent, 
depending on the sativa parent used. 

3. Floret disjunction, defined as the method of separation of the 
second floret from the first floret. 



THE GENETIC AND CYTOGENETIC BASIS 31 

The method shown by Bond in Fig. 4, called disjunction by 
basifracture, is characterized by the rachilla segment breaking 
near its base and remaining firmly attached to the base of the 
upper floret, as contrasted with that in Anthony, which has dis- 
junction by disarticulation at the apex of the rachilla segment, the 
rachilla segment remaining attached to the lower floret. In 
hybrids, many plants seemed intermediate and were characterized 
by disjunction by heterofracture, the rachilla segment breaking 




FIG. 4. At left, tipper and lower florets of Anthony; at right, upper and lower 
florets of Bond; showing the characteristics of these varieties. 

transversely in the middle portion. The Double Cross A parent 
was homozygous for an intermediate type of floret disjunction of 
the heterofracture type. 

The type of spikelet disarticulation of Anthony and the absence 
of long bristles or basal hairs were dominant in f\ y and segregation 
for each pair of characters approached 3:1 in F^. There were a 
few intermediate types in P\ with fewer long hairs and smaller 
base than is characterized by Bond. In general, the type with 
Bond base and long basal hairs bred true in F 3 . Progenies were 
obtained, also, in F 3 that bred true for the sativa type; others 
segregated as in F 2 . Some F 8 lines were obtained that showed 



32 METHODS OF PLANT BREEDING 

unusual types of segregation in F&. These may be illustrated 
by four lines, the progenies of two F 2 plants of the byzantina 
type of base and two of the sativa type. 



F 8 line 


Type of base F 2 


Segregation in F 9 


1 
2 
3 

4 


Byzantina base 
Byzantina base 
Sativa base 
Sativa base 


285:1 1:1 S 
13B-.17S 
2S:23I:SB 
11S:9I:9 



B == byzantina base, I = intermediate, 8 = sativa, 

A large percentage of F% plants of the byzantina type of base 
bred true for byzantina base in F 3 , and approximately one-third of 
those with a sativa type of base bred true for sativa base in ^3. 
By studying the type of breeding behavior in F 3 and later genera- 
tions, it was possible to select those that were homozygous for 
type of base. Variations in type of segregation very probably 
may be correlated with variation in pairing of the chromosomes, 
since both sativa and byzantina oats are amphidiploids of the 
hexaploid type. A knowledge of genetics aids the breeder in 
obtaining pure breeding types and suggests the discard of those 
that show unusual types of segregation. After all, deviations 
from a 3:1 ratio are fairly common. It seems desirable to 
emphasize the probability that two pairs of factors are involved 
that are rather closely linked. Using F% data and placing / and B 
types of spikelet disarticulation together and separating for basal 
hairs on the basis of length of hair gave a dihybrid ratio of sativa 
base and short hairs, sativa base and long hairs, byzantina 
base and short hairs, and byzantina base and long hairs of 
2118:19:81:727, By the product method, this gave a recom- 
bination percentage of 2.7 0.3. It seems probable that the 
wide deviation from expectation of the two middle classes may 
be a result of abnormal chromosomal pairing or other abnormal- 
ity. In the absence of long basal hairs, the type of base seemed 
to be a little less well developed than where the factors for 
byzantina base and those for long basal hairs were both present 
in a homozygous condition. 

The sativa type of base seems more desirable than the byzan- 
tina typQ, because there was a definite tendency for correlation 
between shattering and the byzantina base. 



THE GENETIC AND CYTOOENETIC BASIS 



33 



Floret disjunction in the crosses, except where Double Cross A 
was one of the parents, was dependent upon at least two pairs of 
factors. Double Cross A, when crossed with Bond, gave segrega- 
tion that was relatively well explained by a single factor pair, 
This factor pair was linked in inheritance with the factor pair for 
spikelet disarticulation and also with the factor pair for basal 
hairs. A knowledge of inheritance of these three pairs of factors 
was an aid in selecting the types that bred true. In this case, the 
sativa type was desired with spikelet disarticulation by fracture, 
short basal hairs, and sativa type of floret disjunction, the rather 
strong linkage aiding in obtaining pure breeding types, since more 
of the parental types for all three characters were obtained than 
would have been secured in the absence of linkage. 

Quantitative Characters. The type of results often obtained 
from characters that fluctuate greatly may be illustrated by 
plumpness of grain. When sufficient seed is available, weight per 
bushel is an easy character to work with. In the small grains, as 
studied in Minnesota, there is usually a high correlation between 
plumpness of grain and yield, hybrids with well-developed seeds, 
relatively free from shriveling, generally yielding much better, 
on the average, than those that show a lower degree of plumpness. 
Selection during the segregating generations, therefore, is made 
for plants with plump seeds; this is done by visual examination. 
Behavior in a cross between Double Cross A and Bond is used for 
illustration. 



Parent variety or F z 


Plumpness of grain classes, per cent 


0-25 


26-50 


51-75 


76-100 


Number of plants in class 


Bond 


1 
5 

48 


6 
28 
102 


54 
26 
534 


61 
381 


Double Cross A 


F 2 





Plumpness of grain is without doubt an inherited character, 
dependent upon reaction to diseases and physiological characters 
that may influence the metabolism of the plant. By selection 
during the segregation generations for freedom from disease and 



34 METHODS OF PLANT BREEDING 

for plump grain, itVas possible to obtain hybrids that were resist- 
ant to all three diseases that were of the sativa type and that had 
plumper grain, with higher weight per bushel, than the sativa 
parental varieties. 

Selection for yield on the individual plant basis seems of little 
value, since environmental conditions seem the major cause for 
variations. This is shown by the extreme variation in yield per 
plant within the parental varieties. All that can be accomplished 
during the segregating generations seems to be the selection for 
the combination of characters desired. Selection of progenies of 
desirable agronomic type seems a desirable practice, with the use 
of visual examination rather than intensive study. When 
homozygous lines are available, those that yield most satisfac- 
torily can be isolated through actual comparative-yield trials. 

COLCHICINE AS A POLYPLOIDIZHNTG AGENT 

Dermen (1940), in a recent review, has summarized the rather 
extensive literature on the methods of producing polyploids 
through the use of colchicine. This summary has been used 
freely. Heat and cold, X rays and radium, as well as ultraviolet 
rays, have been used by various workers to induce chromosomal 
aberrations. The discovery that colchicine was a satisfactory 
medium for inducing chromosome doubling has made its use 
extremely popular and has given the plant breeder a relatively 
efficient tcchnic that may be used in the production of polyploid 
species and varieties. The technic first became available in 1937. 
Although there are 179 literature citations in Dermen's review, 
the subject of induced ploidy is of such recent origin that it is 
rather difficult accurately to evaluate its practical possibilities. 
Dermen quotes Blakeslee (1939) as follows: "We now have an 
opportunity to make new species to order/ 7 and " . . . thepossi- 
bilities in the way of new forms of economic value seem very 
great." He quotes Vavilov (1939), who has said: "The possibili- 
ties opened up by the artificial induction of amphidiploidy, i.e., 
of chromosome doubling in hybrids, are immense. Genetics is 
entering a new era of extensive "application of distant hybridiza- 
tion, at least in the case of plants." 

The information already available indicates that polyploids in 
horticultural species that can be propagated asexually may be 
expected to be of considerable economic value. Autopolyploids 



THE GENETIC AND CYTOGENETIC BASIS 



35 



are frequently larger in size and have more showy flowers than 
their diploid ancestors. Emsweller and Brierley (1940) present 
results with Lilium formosanum to show the relative ease of 
doubling chromosome number. They used 20 one-year-old 
plants, trimmed off the tip leaves when the flowering stalk was 
6 or 8 in. high, and treated the apical meristem with colchicine 
solution for a 2-hr, period. From 3.1. aerial bulblets produced in 




FIG. 5. Types of snapdragons. (A) Tetraploid hybrid between tetraploid 
Velvet Beauty and tetraploid Red Shades. Note the large ruffled flowers and 
very deep color, also the heavier stem. The tetraploid hybrid is setting an 
abundance of seed, whereas the parents are highly sterile. (B) Triploid Velvet 
Beauty produced by crossing tetraploid Velvet Beauty X diploid Velvet Beauty. 
This plant is partially fertile. (C) Diploid Red Shades X Velvet Beauty. 
Compared with A, the flowers are smaller, less ruffled, and less deep in color. 
(Courtesy of Nebel and Ruttle.} 

the axils of the old leaf stubs on the thickened stem apex, 22 
polyploids were obtained. They state that polyploids had larger 
flowers, pollen grains, and stomata than diploids. 

Seeds of crimson flowering tobacco, Nicotiana sandarae, which 
has nine pairs of chromosomes, were treated with colchicine, and 
autotetraploids were obtained by Warmke and Blakeslee (1939). 
The autotetraploids obtained had thicker and broader leaves than 
their diploid parents and grew to a larger size and produced larger 



36 METHODS OF PLANT BREEDING 

and more showy flowers. When octoploids of Nicotiana tabacum 
and JV. rustica, which themselves are amphidiploids, were pro- 
duced (Smith 1939), the resulting plants showed a general lack 
of vigor. 

Nebel and Ruttle (1938) have pointed out the value of tetra- 
ploid marigolds, petunias, and snapdragons that were developed 
by the use of colchicine. In several cases, plants were obtained 
that were of sturdier growth and produced larger, sturdier flowers 
(see Fig. 5). 

In the brief review given here, it is impossible to cover all 
phases of the economic importance of induced polyploidy. It is 
well known that wide crosses are sometimes possible between 
species and genera of grasses, although such crosses, in F^ fre- 
quently are highly self-sterile. The development of perennial 
grasses of the amphidiploid type, with larger seed size, desirable 
for forage and range cover, through crosses between Triticum 
and Agropyron species is now being investigated by several 
workers. 

In a little over a year Blakeslee and coworkers (Blakeslee 1939) 
succeeded in doubling the chromosome numbers of 65 different 
species and varieties of plants. They report doubling in the 
following families : Caryophyllaceae, Chenopodiaceae, Coni- 
positae, Cruciferae, Cucurbitaceae, Euphorbiaceae, Malvaceae, 
Moraceae, Oxalidaceae, Plantaginaceae, Polemoniacea, Portu- 
lacaceae, Solonaceae and Violaceae. 

Colchicine occurs in the corm of Colchicum autumnale, which 
may contain as much as 0.4 per cent by dry weight. A solution 
of 0.4 per cent in water may induce doubling in Datura, and one- 
thousandth of this concentration causes doubling in Portulaca. 
Colchicine in solution is diffusible into plant tissues, exerting its 
effect only on cells undergoing cell division. Colchicine prevents 
the formation of the mitotic spindle figure and the development 
of the cell wall. Cell division into sister cells is prevented, and 
the chromosomes continue to divide. The process of chromo- 
some division may continue as long as the tissue is exposed to 
colchicine. A summary of the technics of colchicine application 
may be of interest. 

1. Colchicine in aqueous solution diffuses through plant tissues, 
causing internal changes in meristematic tissues as a result of 
surface application. 



- THE GENETIC AND CYTO&ENETlC BASIS 37 

2. Dormant tissues are not affected; only active tissues are 
affected by colchicine. Treatment is of value from the practical 
standpoint only to tissues that will develop into vegetative, 
sexual, or into both types of plant parts. 

3. Optimum cultural conditions should be maintained during 
treatment so that cell divisfon may be favored. 

4. The duration of treatment must be determined for each type 
of material. In general, the length of treatment is dependent 
upon the time required to complete the cycle of cell division in the 
material worked with. 

5. Concentration of the colchicine solution should not fall 
below an effective minimum and should not be sufficiently high to 
be fatal. A satisfactory concentration must be determined for 
each material. 

Material that has been used with success in colchicine treat- 
ment includes seeds, seedlings, growing tips of twigs or buds or 
bud scales. Successful applications have been made in the 
following media aqueous solution, weak alcohol, a suitable 
emulsion, lanolin paste, agar solution, glycerine and water, or 
glycerine and alcohol. The range of successful concentration 
that has been used varied from 0.0006 per cent to 1 per cent. 
Duration of treatment that has proved successful ranges from 
merely wetting to 24 hr. 

Three methods of treatment that have proved successful will be 
outlined briefly. 

1. Seed treatment. Seeds of Datura, Cosmos, Portulaca, and 
Nicotiana have been soaked in 0.2 to 1.6 per cent aqueous solution 
of colchicine. This treatment has been applied successfully to 
seeds that will germinate in a few days. Seeds may be planted 
after treatment and before germination. 

2. Seedling treatment. Germinating seedlings may be im- 
mersed in colchicine solution in a shallow container or placed 
on filter paper thoroughly wetted with the solution for from 3 to 
24 hr. In Cosmos, polyploidy was induced by moistening the 
soil over and around the seedlings with a 0.02 to 0.1 per cent 
aqueous solution after germination and before the seedlings had 
emerged. 

3. Treating young shoots or bu$s. Tips of young seedlings of 
both woody and herbaceous plants may be treated by brushing 
the solution over partially exposed tips once or several times or by 



38 METHODS OF PLANT BREEDING 

immersing such material in a vessel containing the solution for 
the length of time necessary. 

Successful treatment has bean obtained by the use of 0.5 to 
1.0 per cent colchicine in lanolin smeared on growing portions of 
young shoots and on expanding branch buds. Treatment of 
young seedlings of flax and petunia has been successful by brush- 
ing tepid 1 per cent colchicine agar solution (I part 2 per cent 
colchicine to 1 part 3 per cent agar) over the growing tips. 



CHAPTER III 

MODE OF REPRODUCTION IN RELATION TO 
BREEDING METHODS 

It is recognized that there is a close relation between mode of 
reproduction and methods of breeding. These facts have been 
emphasized by Hayes and Garber (1927). Crop plants may be 
placed in two groups according to mode of reproduction. These 
are (1) asexual and (2) sexual. 

THE ASEXUAL GROUP 

The most important crop plants belonging to the asexual group 
are potatoes, sugar cane, and many fruits. Many of the horticul- 
tural plants grown as ornamentals are members of this group also. 
Plants belonging to the asexual group are propagated by grafting, 
cuttings, layering, or other asexual means. Although this is the 
normal method of commercial propagation, reproduction by 
sexual means hgfe occurred in asexually propagated varieties or 
strains of crop plants at some time in the history of their develop- 
ment. Vigor of growth, yielding ability, and other quantitative 
characters may be explained genetically, in general, as the result 
of the interaction of favorable, partially dominant, growth 
factors. With most normal quantitative characters, the number 
of these factors is large, and linkage is involved. These factors 
account for the reason that it is difficult to obtain all the desirable 
growth factors in any one plant in a homozygous condition. If 
the more promising plants are selected for propagation, it seems 
reasonable to expect these plants to be in a highly heterozygous 
condition, and the experience of breeders has shown this to be the* 
usual case. 

Clonal propagation leads usually to the perpetuation of a 
uniform progeny, i.e., to the reproduction of the biotype, but it is 
recognized that gene changes or chromosomal aberrations do 
occur, although there is some difference of opinion regarding their 
frequency. Shamel, Scott, and Pomeroy (1918a,6,c), ia Cali- 

39 



40 METHODS OF PLANT BREEDING 

forma, experimenting with citrus fruits, have based a system of 
breeding on selection and propagation from bud sports. The 
frequency of bud sports has been emphasized by Shamel and 
Pomeroy (1932), who have listed 173 cases of important bud 
sports in apples. 

Collins and Kerns (1938) discuss mutations in the Cayenne 
variety of pineapple. This variety presumably originated as a 
vegetatively reproduced progeny of a single plant about 100 years 
ago. Thirty mutant types have been shown by progeny trials to 
reproduce themselves vegetatively; 8 types have been reproduced 
through sexual propagation, and 5 of these proved to be dominant 
characters. Collins and Kerns state, "The accumulation of 
mutations in asexually propagated forms may conceivably play a , 
role in the running out and acclimatization of varieties. The 
parade of agricultural varieties during the past years is a demon- 
stration of the chdSiges going on, some of which is known to be 
due to progressive or regressive mutations." 

Methods of breeding the asexual group may be summarized as 
follows: 

1. Systematic survey of material. 

This is an important step in any breeding program. Such a survey 
includes a study of material that is already available and that can be 
obtained from any source whatsoever. In most breeding problems, the 
wild relatives deserve study also. The various steps in such a survey 
may be summarized as follows: 
a. Collect and grow a short row, small plot, or several individuals of the 

varieties of interest. Classify according to plant characters, both 

qualitative and quantitative. 

6. Make a systematic study of chromosome numbers and relationships. 
c. Study relationships by means of controlled crosses, using both genetic 

and cytologic technics. 

2. Improvement by clonal selection. 

In tree fruits, a careful study of variations that appear as individual 
trees, or branches, is of value. A study of the transmission of these 
variations must be made by means of a progeny trial. All that is neces- 
sary is to compare the performance of selected variations with the normal 
variety. This can be accomplished rather quickly by grafting com- 
parable trees with the selected variations and with normal budwood and 
making a test of the desirability of the two sources of cions. Important 
varieties have been selected in the past by these methods. The extent 
to which such selection can be made the basis of a standardized breeding 
program will depend upon the frequency of such mutations. The selec- 
tion of budwood from healthy stock deserves consideration by all who use 
this method of propagation as a means of varietal increase. 



MODE OF REPRODUCTION 41 

In potatoes the tuber-unit or hill-selection method has been used 
widely. This method is of value chiefly as a means of keeping the variety 
free from degeneration diseases such as the various types of mosaic. It 
consists of studying the progeny of selected tubers or hills, selecting the 
most desirable clonal lines, and using these as a basis for the commercial 
variety. It should be recognized that bud sports do occur occasionally, 
and when such are observed that have selection value, they can be used 
as a basis for an improved variety. Blodgett and Fernow (1921) origi- 
nated the tuber-index method with potatoes as a means of testing for 
freedom from disease. The purpose was to test by means of a tuber for 
the disease reaction of parent hills and eliminate the diseased hills, the 
test being made under greenhouse conditions during the winter months. 
This method is now used widely in potato-tuber selection for degeneration 
diseases such as mosaic. 
3. Breeding plants normally propagated asexually by sexual methods. 

Sexual methods of breeding plants belonging to the asexually propa- 
gated group are not widely different from those used with other crop 
plants. Since asexually propagated varieties are highly heterozygous, 
selection in self-fertilized lines is being tried as a means of obtaining 
parental varieties with certain desired characters in a homozygous con- 
dition. When varietal crosses are used it is of value to determine the 
suitability of a particular heterozygous parent variety on the basis of 
the characters of its progeny. Crosses between an inbred line that is 
relatively homozygous for certain desirable characters, with outstanding 
commercial varieties, often furnish the most satisfactory basis for selec- 
tion of new and improved asexual varieties. 

THE SEXUAL GROUP 

Plants belonging to this group may be placed in several subdivi- 
sions according to their normal mode of pollination. It should be 
recognized that varietal differences of a genotypic nature, as well 
as environmental influences, are the major causes of the rather 
wide differences that are observed when the normal mode of 
pollination of plants of economic importance is studied. The 
following subdivisions are those of major importance: naturally 
self-pollinated, often cross-pollinated, naturally cross-pollinated, 
and dioecious. 



Self -pollinated Group. 

As a rule, less than 4 per cent of cross-pollination. The 
crops generally placed here are barley, wheat, oats, tobacco, 
potatoes, flax, rice, peas, beans, soybeans, cowpeas, slender 
wheat grass, and tomatoes. 

There is a gradual variation in amount of cross-pollination 
from this group to that of the often cross-pollinated group and nQ 



42 



METHODS OF PLANT BREEDING 



very clear line of demarcation between the groups. The varia- 
tions that occur are a result of either environmental influences, 
varietal differences, or a combination of the two causes. As wide 
variations in the frequency of natural crosses occur from one 
locality to another, it seems unnecessary to summarize the many 
detailed studies that have been made. It is important for the 
breeder to learn the extent of natural crossing of the crops he is 
working with under his own conditions. 

Methods of learning the extent of normal cross-pollination are 
relatively simple. With tomatoes, at the Connecticut Agricul- 
tural Experiment Station, Jones (1916) interplanted alternate 
plants of dwarf and standard tomatoes, at the usual spacing, in 
rows in the field. Seed from the dwarf plants was harvested and 
sown. From 2170 plants that resulted, 43, or approximately 
2 per cent, proved to be of standard habit. The extent of natural 
cross-pollination would be therefore between 2 and 4 per cent. 

Stevenson (1928) studied the extent of cross-pollination in 
barley under normal conditions in Minnesota, using Consul and 
Gatami as the parental varieties. The type characters and 
period of heading of these varieties are as follows: 



Variety 


Type 
character 


Date heading 


1924 


1925 


1926 


Consul 


White 


6-27 


6-12 


6-12 


Gatami 


Black 


6-26 


6-12 


6-15 



Seed of the two varieties was sown alternately in rows spaced 
1 ft. apart. Black is dominant over white, and the extent of 
natural crossing was determined by sowing seed of the white 
glumed variety, collected under the conditions described, and 
determining the number of natural crosses. Results from the 
3 years are as follows: 



Year 


White glumed 
plants 


Black glumed 
plants 


Per cent off 
type 


1024 


2878 


1 


0.04 


1925 


1600 


2 


0.12 


1926 


2012 


3 


0.15 



MODS OF REPRODUCTION 43 

From similar studies, no natural crosses occurred between 
Hanna and Jet, Oderbrucker and Lion, and Manchuria and 
Nepal. 

Natural crossing has been studied extensively in wheat. There 
is a rather wide range in the amount of natural crossing as reported 
by investigators located in various parts of the world where 
wheat improvement has been carried on, Early investigators, 
including DeVries, Biffin, and Fruwirth, considered that natural 
crossing was very infrequent. Nilsson-Ehle, in Sweden, stated 
that some varieties are cross-pollinated much more frequently 
than others. Natural crossing at University Farm, St. Paul, 
Minnesota, of at least 2 to 3 per cent, on the average, has been 
observed. Powers (1932) studied natural crossing in Marquillo 
spring wheat, derived from a cross of lumillo durum with 
Marquis. Marquillo was grown in alternate rows with Ceres, 
and the percentage of natural crosses determined by inoculation 
in the seedling stage with physiologic race 21 of black-stem rust, 
Puccinia graminis tritici, to which Marquillo normally is resistant 
and Ceres susceptible. Seedlings from seed produced on non- 
covered spikes of Marquillo showed 3.6 0.50 per cent of 
susceptible plants. Since susceptibility is dominant over resist- 
ance to form 21 in crosses of Ceres X Marquillo, it is fair to 
conclude that natural crossing to the extent of 7.2 per cent 
occurred in Marquillo wheat during the year that the study was 
conducted. 

K Often Cross-pollinated Group. 

In this group, self-pollination is more frequent, as a rule, 
than cross-pollination, although cross-pollination may occur 
so frequently that some method of preventing cross-pollina- 
tion between varieties and strains of different genotypic 
constitution must be followed throughout the breeding and 
seed-distribution program. Crops belonging to this group 
are cotton, sorghums, and some strains of sweet clover. 

Except for the necessity of controlling pollination in seed plots 
to a greater extent than with the self-pollinated group, it seems 
probable that methods of breeding are not greatly different than 
for the self -pollinated group. 

Before starting a hybridization program of improvement, it 
may be desirable to practice self-pollination and selection in order 



44 METHODS OF PLANT BREEDING 

to isolate the more desirable hoinozygous types as parents and 
eliminate the less desirable variations. 

f. Naturally Cross-pollinated Group. 

Important crop plants placed in this group include maize, 
rye, clovers, sunflowers, sugar beets, many fruits, some 
annual and most perennial grasses, cucurbits, Brassica 
species, most root vegetables. 

This group is composed of plants of widely different habit in 
relation to mode of pollination. It includes such plants as maize, 
with which cross-fertilization is the rule and which sets seed freely 
when artificial self-pollination is practiced. The wind-pollina- 
tion habit and the large amount of pollen produced tend to cause 
cross-pollination that approaches 100 per cent. Then there are 
many plants adapted to insect pollination, in which cross-pollina- 
tion, under normal conditions, is essential to seed production, and 
many plants that are partially or wholly self-incompatible, in 
which case cross-pollination is essential to seed production 
because of self-sterility. 

Self-sterility and other causes of self-unfruitfulness will be 
discussed in much greater detail in connection with the presenta- 
tion of methods of breeding crop plants that normally do not set 
seed by self-pollination. 

It is apparent that many crop plants contain genotypes that 
carry factors both for self-fertility and sterility. Where self- 
sterility is the rule, methods of breeding are not widely different 
than in dioecious plants, since two parent plants must be selected 
in order to obtain a progeny. 

L Dioecious Plants. 

Important crop plants of this group are hops, hemp, date 
palm, spinach, and asparagus. 

In breeding plants belonging to this group, it is necessary to 
select both male and female plants with the characters desired 
and test their progeny to determine the breeding value of particu- 
.ar parents. By this means varieties of superior type may be 
synthesized. 

SELF-POLLINATION LEADS TO HOMOZYGOSIS 

Even though only an occasional natural cross occurs in a 
lormally self-pollinated crop, this may lead to a new combination 



MODE OF REPRODUCTION 45 

of characters and thus be a source of material for selection. It 
will be of interest to show what will happen in later generations of 
self-fertilization as a result of a cross between varieties differing 
by one or more genetic factor pairs. Two somewhat different 
formulas have been used to express the expectations (East & 
Jones 1919). 

Suppose that the two parent varieties differ by several factor 
pairs. The following formula, [1 + (2 r l)] w , may be used 
where r equals the number of segregating generations after a cross 
and n equals the number of independently inherited factor pairs 
involved and the first and second terms of the binomial are 1 and 
2 r 1, respectively. The exponent of the first term gives the 
number of heterozygous factor pairs and the exponent of the 
second term, the number of homozygous factor pairs. Supposing 
the number of factor pairs is 3, i.e.j n = 3, and the progeny 
is in the fifth segregating generation, or F$, i.e., r = 5 and 
2' - 1 == 31. The results will be I 8 + 3(1) 2 31 + 3(1)(31) 2 + 
31 s , giving: 

1 individual with all three factor pairs heterozygous. 

93 individuals with two factor pairs heterozygous and one 
homozygous. 

2883 individuals with one factor pair heterozygous and two 
homozygous. 

29,791 individuals with all three factor pairs homozygous. 

Another formula that has been used to express the percentage 
of homozygous individuals in any generation following a cross 

between different forms is ( ^ J ; where n and r have the 

same meaning as in the previous formula. In actual practice, the 
calculated expectation would not hold unless all the progeny of 
each genotype were equally productive and the factor pairs were 
independently inherited. If linkage is involved, this changes the 
percentage of homozygous individuals but does not change the 
percentage of homozygosis, as has been shown by Wright (1921). 
The percentage of homozygosis in any segregating generation, r, 
can be obtained by the foregoing formula for a single factor pair. 
Under conditions of self-pollination, linkage increases the rapidity 
of obtaining homozygous individuals over that expected for 
independent Mendelian inheritance. 

The results of applying this formula, with 1, 5, 10, and 15 factor 
pairs for from 1 to 10 generations of self-fertilization have been 



46 



METHODS OF PLANT BREEDING 



expressed in the form of curves by Jones (1918). The results 
(Fig. 6) are given on the basis of the percentage of heterozygous 
individuals in each selfed generation and the percentage of 
heterozygous pairs, i.e.j the percentage of heterozygosis. 

These graphs show that self-fertilization leads rapidly to homo- 
zygosis and that the progeny of individual plants of a self- 
fertilized crop may be expected to breed true for the most part. 



100 * 



Percentage of Heterozygous 
Individuals in each Selfed 
Generation when the Number 
of Alleles Concerned 
Are: 1,5 10,15. 




1 



8 



9 10 



3456 
Segreating Generations 

FIG. 6. The percentage of heterozygous individuals in each selfed generation 
when the number of independently inherited factor pairs are 1, 5, 10, and 15. 
The percentage of heterozygosis in any selfed generation is given by the curve for 
one factor pair. 

The principles outlined show why breeding methods have been 
standardized to a considerable extent with self-pollinated crop 
plants. 

THE EFFECTS OF SELF POLLINATION IN THE OFTEN 
CROSS-POLLINATED GROUP 

It has been stated that except for the necessity of greater 
care in controlling pollination the breeding of the often cross^ 
pollinated group can be carried on in much the same manner as 
with plants belonging to the naturally self-pollinated group. 



MODE OF REPRODUCTION 



47 



Kearney (1923), with Pima cotton, studied the effects of 
controlled self-fertilization during successive generations. Some 
of the results presented by him are summarized here. 

TABLE 2. RANDOM SAMPLE OF COMMEBCIAL STOCK OF PIMA COTTON 
COMPARED WITH STOCK INBRED FOR SEVEN SUCCESSIVE GENERATIONS 









Ivtean 






Population 


Flowers 
tagged 


Percentage 
of bolls 
shed 


number of 
seeds 
matured 


Mean 
weight of 
1000 seed, 


Percentage 
of germi- 
nation of 










g- 


seeds 








per boll 






Inbred 


296 


11.8 1.3 


17.2 + 0.12 


13.6 0.04 


90.8 + 0.8 


Open pollinated 


367 


8.4 1.0 


17.1 0.12 


13.4 0.03 


90.2 0.9 


Difference . . 




3 4 1.6 


0.1 17 


0.2 0.05 


0.6 1.2 



Boll Weight and Lint Index 



Population 


Number of bolls 


Seed cotton 


Lint index 


Inbred 


105 


3.22 + 0.21 


4.90 0.27 


Open pollinated 


115 


3 04 + 06 


5 12 03 


Difference 




0.18 4- 0.22 


0.22 27 











Boll Dimensions 



Population 


Number of bolls 


Length, mm. 


Diameter, mm. 


Inbred 


25 


46.6 4- 56 


26 8 -f 19 


Open pollinated 


25 


45 7 + 80 


26 1 19 


Difference 




9 + 97 


7 27 











There was no harmful effect of continued self-pollination in this 
variety of cotton. It may be concluded that controlled self- 
pollination can be used, when desired, with plants belonging to 
this group without leading to a great reduction in vigor. 

Humphrey (1940) has emphasized the desirability of inbreeding 
cotton in order to obtain uniformity in fiber characters. Com- 
parison of lines that had been self -pollinated for 2 and 7 years 
indicated that inbred lines were much more uniform than the 
variety from which they arose, but little increase in uniformity 
was obtained after 2 years of self-pollination. Humphrey's data 
lead to the conclusion that vigorous self -pollinated lines can be 



48 



METHODS OF PLANT BREEDING 



obtained in cotton, and, as would be expected, there seem to be no 
harmful effects of continued self-pollination. 

EFFECTS OF SELF-FERTILIZATION 
IN CROSS-POLLINATED PLANTS 

From the genetic standpoint, artificial self-pollination in a 
normally cross-pollinated crop leads to the production of homo- 
zygous lines. In many crops, notably corn, there is a rapid reduc- 
tion in vigor when self-pollination is practiced. The extent that 
vigor of growth is reduced is not the same in all lines, and some 
inbred lines of corn have been obtained that appear relatively 
homozygous and are rather vigorous. In general, in corn, no 
inbred lines that approach homozygosis have been obtained that 
are as vigorous as normal corn. Studies of the effects of self- 
fertilization have been made with many crop plants. Extensive 
studies of squashes have been made, and much of the improve- 
ment in recent years has resulted from the isolation of desirable 
selfed lines and their use as commercial varieties. Both high- 
yielding and low-yielding selfed lines have been isolated. Cum- 
mings and Jenkins (1928) studied a high-yielding line that had 
been selfed for 10 generations without harmful effect. 

It is apparent that the extent to which a crop can be inbred 
without leading to a great reduction in vigor will be the main 
factor in deciding how extensively controlled self-pollination can 

TABLE 3. THE EFFECT OF 30 GENERATIONS OF SELF-FERTILIZATION WITH 

THREE INBRED LINES OF MAIZE UPON THE HEIGHT OF PLANT AND 

YIELD OF GRAIN 





Line 1-6 


Line 1-7 


Line 1-9 


Number of 




















generations 
selfed 


Height, 
in. 


Yield, 
bu. per 


Height, 
in. 


Yield, 
bu. per 


Height, 
in. 


Yield, 
bu. per 






acre 




acre 




acre 





117 


81 7 


117 


81 7 


117 


81 7 


1-5 


87 


64 11 


81 


51+7 


77 


41+5 


6-10 


97 1* 


45 12 


84 1 


36+5 


82 2 


34 4 


11-15 


97 3 


38+4 


84 + 2 


34 3 


83 + 2 


26 2 


16-20 


88+4 


22+4 


85 + 3 


24 3 


75 4 


14 3 


21-25 


81 2 


20 6 


75 3 


21 3 


71 3 


13 2 


26-30 


92 3 


24 9 


80 2 


18 4 


77 3 


9 4 



* Standard errors. 



MODE OF REPRODUCTION 



49 



be used in breeding cross-pollinated plants. Studies of controlled 
cross- and self-pollination with each of the important crop plants 
are essential in the establishment of breeding methods. 

Jones (1939) has summarized the effects of continued inbreed- 
ing with maize for three inbred lines started by East in 1905 and 
discussed by East and Hayes (1912). Yield in bushels per acre 
and height of plant in inches given in Table 3 were presented by 
Jones (1939). The data were given as averages for 5-year 
periods to overcome seasonal fluctuations. 

I2C 




2.5 



22.5 



27.5 



J.5 12,5 17.5 

Number of generations sefffed 

FIG. 7. A comparison of three maize lines, derived from the same variety, 
self-fertilized for 30 generations. Height of stalk is measured in inches and yield 
of grain in bushels per acre, both plotted on the same scale. The broken lines 
are the theoretical curves of inbreeding. (Adapted from Jones.) 

The results are presented also in the form of curves in Fig. 7. 

The theoretical curves were calculated by subtracting the 
average height and average yield of the three inbred lines at the 
end of the 30 generations of self-pollination from the figures at 
the start. The difference was halved in each generation and 
subtracted from the initial yield. Theoretical yields at the end 
of the fifth generation of inbreeding were obtained by averaging 
the theoretical yields at the end of each generation from 1 to 5, 
with the use of the following calculations, where the original yield 
was 81 bu. and the average yield at the end of 30 years of selfing 
was an average of 24, 18, and 9, or 17 bu. Subtracting from 81, 



50 



METHODS OF PLANT BREEDING 



one obtains 81 17 = 64. This value is halved for each succes- 
sive generation of selfing and subtracted from 81. On this basis, 
theoretical yields for each of the first five generations of selfing 
can be computed as follows: 



Generation 
of selfing 


Calculation 


Theoretical 
yield 


1 


81 - (}i X 64) 


49 


2 


81 - (% X 64) 


33 


3 


81 - (H X 64) 


25 


4 


81 - OJie X 64) 


21 


5 


81 - (% X 64) 


19 




Average . . . 


29.4 




i 



The calculations are based on the hypothesis that the effects 
of inbreeding are dependent upon the extent of heterozygosity, 
the number of heterozygous pairs of factors being reduced one- 
half for each successive generation of self-fertilization. The 
average theoretical yield of the three inbred lines, for generations 
1 to 5, of 29.4 bu., was less than the actual yield obtained, which 
indicates that selection was practiced. 

Comparing the actual and theoretical curves indicates that the 
three inbred lines were homozygous for factors influencing height 
after 5 generation of selfing and for yield after approximately 
20 generations of selfing. Besides these lines that can be propa- 
gated by continued self-pollination, there are other inbred strains 
that are so weak that they cannot be propagated and still others 
that can be perpetuated only with difficulty. 

HETEROSIS AND ITS EXPLANATION 

Early plant hybridists, including Kolreuter, in the eighteenth 
century, Gartner and Weigmann, in the nineteenth, noted the 
increased vigor of hybrids. Although many others in the last 
century observed hybrid vigor, a clear understanding of the 
effects of self-fertilization in cross-pollinated plants and of the 
effects of crossing self-pollinated plants was obtained only as a 
result of genetic research. East and Hayes (1912) pointed out 
the value of hybrid vigor both in evolution and in plant breeding 
and Shull (1914) suggested the term heterosis in the following 
words: " 



MODE OF REPRODUCTION 51 

To avoid the implication that all the genotypic differences which 
stimulate cell division, growth and other physiological causes are 
Mendelian in their inheritance and also to gain brevity of expression, I 
suggest that instead of the phrases, "stimulus of heterozygosis," 
" heterozygotic stimulation," . . . , that the word heterosi^ be adopted. 

Because of the importance to the plant breeder of heterosis, it 
seems desirable to summarize the suggestions for an explanation 
of heterosis in the light of present-day knowledge. 

Keeble and Pellew (1910) explained hybrid vigor in peas from 
a cross between two half-dwarf varieties, Autocrat and Bountiful, 
on a dihybrid basis with dominance in the FI of the thick stem of 
one parent and long internode of the other. 

This explanation was not considered generally applicable by 
East and Shull, since other cases of hybrid vigor could not be 
placed on an equally simple basis. At this time (around 1910) 
there was a lack of appreciation by most workers that for many 
characters large numbers of factor pairs were involved. Brief 
quotations from East and Hayes (1912) serve to summarize the 
viewpoints of East and Shull, who, in general, were in close 
agreement. 

One can say that greater development stimulus is evolved when the 
mate of an allelomorphic pair is lacking than when both are present in 
the zygote. In other words, development stimulus is less when like 
genes are received from both parents. 

The decrease in vigor due to inbreeding naturally cross-fertilized 
species and the increase in vigor due to crossing of naturally self- 
fertilized species are manifestations of the same phenomenon. This 
phenomenon is heterozygosis. Crossing produces heterozygosis in all 
characters by which the parent plants differ. Inbreeding tends to 
produce homozygosis automatically. 

Inbreeding is not injurious in itself but weak types kept in existence 
in a cross-fertilized species through heterozygosis may be isolated by this 
means. Weak types appear in self-fertilized species, but are eliminated 
because they must stand or fall on their own merits. 

The selfed lines of corn first grown by East at the Connecticut 
station in 1906 and carried on by Hayes from 1910 to 1914 were a 
part of the long-time selfed material used by Jones (1918) in 
studies of selfing and crossing. 

Studies of size inheritance in tobacco and corn furnished a 
considerable part of the necessary evidence that many quantita- 



52 METHODS OF PLANT BREEDING 

tive characters were dependent upon the interaction of many 
factors for their full expression. If such is the case, it is evident 
from any particular cross that it is difficult to obtain all factors in 
a homozygous condition that have an influence on hybrid vigor. 
The explanation of heterosis given by Jones (1917) is well known 
to all students of genetics. He supposed that the vigor of an FI 
cross was dependent upon the interaction of dominant, favorable 
growth factors, part of which were obtained from each of the two 
parents. If large numbers of factors are involved, linkage is 
bound to occur, and this makes it extremely difficult to obtain all 
necessary growth factors in a homozygous dominant condition in 
later segregating generations. 

To the breeder who has had much experience with quantitative 
inheritance the explanation seems entirely logical. It is difficult 
to prove the truth or falsity of the explanation. To the breeder 
of economic crop plants the dominance of linked growth factors in 
relation to heterosis furnishes a basis for methods of breeding 
cross-pollinated plants and the perpetuation of hybrid vigor to 
the extent possible with each particular category of crop plant. 

Collins (1921) raised certain objections to Jones's explanation. 
He emphasized the importance of deleterious recessives that so 
frequently show up as a result of inbreeding maize. He pointed 
out also that the effect of a genetic factor was dependent upon the 
size of an organism and that skewness of the P\ distributions 
would not be evident if as many as 20 pairs of factors were 
involved, with complete dominance of each and a cumulative 
effect of one on the other. With more pairs of factors involved, 
linkage would result, however, and add to the difficulty. 

Richey (1927) and Richey and Sprague (1931) have presented 
data on convergent improvement that gives some support to 
Jones's explanation of hybrid vigor. The method of convergent 
improvement will be presented in much greater detail in relation 
to corn breeding. It is equivalent to double backcrossing and 
furnishes a method for improving each of two inbred lines without 
interfering with their combining ability. If the selfed lines A and 
B combine to give a vigorous FI cross, (A X -B), two series of 
backcrosses are carried on, (A X B}A and (A X B)B. In the 
cross of (A X B) A and subsequent backcrosses to A, it is hoped 
to retain the favorable dominant growth factors from A and add a 
part of B. In the cross of (A X B)B y etc., the favorable domi- 



MODE OF REPRODUCTION 58 

nant growth factors of B will be retained, and a part of these 
from A will be added. After backcrossing, selfing is necessary 
until the heterozygous dominant growth factors become homo- 
zygous. The Fi cross of A(/?i), containing the growth factors of 
A with a part of those obtained from B, with B(Ai) 7 or [A(Bi) X 
B(Ai)], should yield as much as A X B if the partially dominant 
linked-growth-factor theory of hybrid vigor is the correct one. 
Greater yields seem possible if dominance is not complete. 

Richey and Sprague (1931) presented data from six crosses 
where N = nonrecurring parent, R = recurring parent, and 
(N X R*) refers to four generations of backcrossing of (N X R) X 
R. All combinations of new crosses [A(Bi) X B(Ai)] should not 
be expected to yield equally as well as A X B, and in practice it is 
necessary to determine the number of generations to backcross 
before selfing. One of the crosses studied by Richey and Sprague 
indicates the possibility of increasing the yield of selfed lines and 
of the Fi cross over the original selfed lines and FI cross, respec- 
tively, by the process of convergent improvement. In a repli- 
cated trial, N X R yielded 17.8 0.20 Ib. of ear corn per plot, 
N X (N X R*), an Fi cross of a fourth generation backcross of 
(N X K)R 9 when crossed with N, yielded 19.0 0.30, or 
significantly more than N X R. The yield of R selfed was 
5.5 0.22, which is significantly lower than the yield of 
(N X RA} of 8.3 0.24. 

The writers say, " Convergent improvement, suggested 
originally from theoretical considerations as a means of improving 
selfed lines of corn without interfering with their behavior in 
hybrid combination, so far has been found successful. Further- 
more, the results suggest that this method may also provide a 
means by which the yields of F\ crosses between selfed lines can 
be raised to an even higher level." 

More recently East (1936?;) has presented a genetic explanation 
for heterosis that emphasizes the importance of linkage and 
makes the suggestion that multiple alleles are concerned also in 
heterosis. The genetic factors involved are not those used 
normally in genetic experiments, called physiologic defectives 
by East, but the factors with small effects and more difficult to 
study are considered to be of greater importance in evolution and 
in plant breeding. It is suggested by East that these factors, 
which have a cumulative effect and for which dominance is 



54 METHODS OF PLANT BREEDING 

virtually absent, occur in series of multiple alleles. Each mem- 
ber of a series may be considered to have the ability of affecting 
a different physiological process. Thus, if A\, A%, and A$ are 
three such alleles, AiA% or any other combination of two of the 
three factors would have a greater effect than the homozygous 
condition for one, i.e., A\Ai, A 2^2, or A^A^. Although there is 
nothing inconsistent in such a hypothesis in the light of the 
numerous series of multiple alleles for qualitative characters, there 
seems no reason to suppose that multiple alleles are of greater 
importance for quantitative than for qualitative characters. 

Studies of corn breeding have given further evidence regarding 
hybrid vigor, although the problem of heterosis needs further 
study, both on a genetic and physiological basis. It is now 
generally accepted by students of corn breeding that combining 
ability is a genetic character. Recent rather extensive studies 
of Hayes and Johnson (1939) showed the extent to which com- 
bining ability is an inherited character. When selfed lines were 
selected from a cross between inbreds with high combining ability, 
most of the selfed lines obtained from the cross were of high com- 
bining ability also, as tested in inbred-variety crosses. Con- 
versely, when selfed lines were selected from a cross of low 
combiners, the greater proportion of lines obtained were of low 
combining ability. Data were given to show that the characters 
of selfed lines that measure vigor of growth were responsible for 
approximately 45 per cent of the variance in yield of the inbred- 
variety crosses. 

Heterosis, then, is a general term for hybrid vigor. It is a 
phase of quantitative inheritance, and if quantitative inheritance 
is Mendelian it seems equally reasonable to place heterosis in a 
similar category. If the growth characters of self-pollinated 
plants are inherited in the same manner as in cross-pollinated 
plants, it seems evident that nature and man have obtained 
vigorous self-pollinated plants by selection of the fittest. It is 
evident that similar selection in selfed lines of cross-pollinated 
plants will, in many cases, lead to the isolation of inbred lines 
that are progressively more vigorous than those now available. 
The extent of improvement obtainable can be determined only 
by actual study. 

In recent years, physiological studies of the manifestations of 
heterosis have been made with several different crops by Ashby 



MODE OF REPRODUCTION 

(1930, -1932, 1937), Sprague (1936), Lindstrom (1935), Luckwill 
(1937), et al. In general, three stages of development may be 
differentiated: (1) fertilization to maturity of seed; (2) from 
germination to first flowering; (3) subsequent growth. The 
efficiency of the FI crosses was studied for various physiological 
characters. The hybrids during the stages of development 
designated as (2) and (3) did not excel the better inbred 
parent in relative growth rate, respiration rate, or assimilation 
rate. Ashby attributes the greater development of the hybrid 
to "greater initial capital/' i.e., greater embryo size. Although 
Ashby's data were in agreement with this hypothesis, no such 
relation is universally present. Sprague (1936) concluded that 
growth rate of the hybrids was greater than that of the inbreds 
during the first stage and in the early seedling stage but could 
not demonstrate a higher growth rate for the hybrids from the 
late seedling stage to maturity. 

Kiesselbach (1922) studied external and internal expressions 
of hybrid vigor in maize crosses. The increased weight of kernel 
due to crossing showed the following percentage of increase of 
parts of the hybrid kernel over the kernels of the inbreds: total 
kernel, 11.1 per cent; embryo, 20.2 per cent; endosperm, 10.4 
per cent; and seed coat, 5.4 per cent. 

Some measurements of the causes of increased vigor given by 
Kiesselbach are of interest. 

Increase of hybrids over their pure-line parents: 

Stalk diameter at base, 48 per cent. 

Number of fibro-vascular bundles in cross section of stalk, 
43 per cent. 

Number of fibro-vascular bundles in 1 sq. cm. of cross section, 
38 per cent. 

Average diameter of one pith cell in stalk, 6 per cent. 

Average length of one pith cell in stalk, 10 per cent. 

Number of pith cells along one diameter in cross section, 
38 per cent. 

Increase in size of the hybrid over the parents in pith cells in 
the stalk and epidermal cells of the leaf was studied in relation to 
cell number and cell size. The total increase of the hybrid over 
its parents was due to 10.6 per cent increase in cell size and 89.4 
per cent to an increase in cell number. 



56 METHODS OF PLANT BREEDING 

Bindloss (1938), Whaley (1939a,6), and Wang (1939) studied 
the apical meristem of inbreds and FI hybrids without finding 
any one characteristic uniformly correlated with hybrid vigor. 
Bindloss observed a positive correlation between nuclear size 
and heterosis in one maize pedigree but no such relation in two 
others studied. Her data indicate significantly larger nuclei for 
the hybrid than for either parent in one cross, but in another 
hybrid the nuclei in the meristem were intermediate between the 
two inbred parents. Whaley found that cell and nuclear size 
in the plumular meristem of Lycopersicum decreases during 
development but less rapidly in the hybrids than in their parents. 
The differences observed indicate a fundamental metabolic dif- 
ference between the hybrids and their parents. Wang studied 
four inbred lines of corn and all six possible F\ crosses between 
them, using the apical meristem of the growing shoot. He found 
some evidence of heterosis in the volume of the plumular meri- 
stem and within the hybrids or within the selfed lines a positive 
correlation between cytonuclear ratio of the cells of the growing 
shoot and vigor of growth. This ratio, however, did not hold 
when comparisons of hybrids and selfed lines were made. 

From these physiological studies, there is an indication that 
the hybrid approaches the better parent in measures of physio- 
logic efficiency. The lack of agreement among the various 
studies indicates that heterosis is manifested in various ways in 
different hybrids and that it may be due to various causes. The 
hypothesis of the complementary action of growth genes seems 
the best genetic explanation now available. For the plant 
breeder, the explanation of Jones for heterosis on the basis of the 
partial dominance of linked growth factors furnishes, at any 
rate, a working basis that aids in an attack on improvement 
problems. Considering heterosis as a phase of quantitative 
inheritance furnishes a basis for an outline of methods of breeding 
that aim to obtain, as far as possible, the full benefits of hybrid 
vigor to the grower and producer of crop plants. 

A CLASSIFICATION OF METHODS OF BREEDING SEXUALLY 
PROPAGATED PLANTS 

A brief outline of methods of breeding will help to illustrate 
the close relation between methods of breeding and mode of pol- 
lination, The major groups are as follows: 



MODE OF REPRODUCTION 57 

I. Introductions. 
II. Selections. 

A. Mass selection. 

1. In self-pollinated crops. 

2. In cross-pollinated crops. 

3. In dioecious crops. Selection of both male and female plants for 
the characters desired. 

B, Individual plant selection. 

1. In self-pollinated crops. 

2. In cross-pollinated crops without control of pollination. 

3. In controlled self-pollinated lines of cross-pollinated plants. 

4. In dioecious crops. 

5. In crops normally clonally propagated. 
III. Hybridization. 

A . Crosses in self-pollinated e> ops. 

1. The pedigree and bulk methods. 

2. Backcrossing. 

B. Crosses of self-pollinated lines and the use of the FI generation for 
the commercial crop. 

C. Convergent improvement. 

These various methods will be outlined in greater detail later. 
At this time it will be sufficient to discuss them briefly. 

Introduction is not a method of breeding in itself but a means 
of securing material from other workers and from foreign coun- 
tries. Many species and varieties of crop plants now grown in 
one country were introduced originally from foreign countries. 
For example, the soybean, introduced into the United States 
from the Orient in the present century, is becoming of out- 
standing value to American agriculture. 

Mass selection as now practiced in self -pollinated crops is 
chiefly a matter of roguing or of selecting individual plants or 
heads from a commercial standard variety for seed-plot pur- 
poses. In cross-pollinated plants, mass selection is of great value 
as a means of selecting and developing ecotypes that through 
years of natural selection have become adapted to particular 
environmental conditions. Grimm alfalfa, selected in Carver 
County, Minnesota, many years ago, was a product of mass 
selection. 

More varieties of self-pollinated crops have been obtained 
from the individual-plant method of selection than by other 
methods. Some of the results of these and other methods of 
breeding have been summarized by Hunter and Leake (1933). 
Most commercial varieties are mixtures of different biotypes that 



58 METHODS OF PLANT BREEDING 

can be isolated by the individual-plant-selection method. These 
mixtures result from natural crossing, mutation, or from mechani- 
cal mixtures. They have furnished a logical basis for the 
selection of pure-line strains of greatest promise. Several 
varieties of oats, Gold Rain and Victory at Svalof, Sweden, 
Gopher in Minnesota, Richland, lowar, and logold from Iowa, 
and Rusota from North Dakota are illustrations of valuable 
varieties obtained by this method of breeding. 

With cross-pollinated crops one of the best known illustrations 
of individual-plant methods of selection is the ear-to-row- 
selection method with corn outlined by Hopkins about 1900. 
This method has been used rather widely as a means of develop- 
ing adapted varieties of corn. Most of the improvement in 
sugar content and quality, of a heritable nature, with sugar 
beets was a result of individual-plant selection without control 
of pollination. 

With cross-pollinated plants like corn, selection in self- 
fertilized lines has been used during the last 15-year period as 
one of the steps in the modern corn-breeding program. It has 
been used also with potatoes as a means of developing better 
breeding stock. 

With dioecious plants, a good illustration of the individual- 
plant methods of selection that led to the development of an 
improved variety is the Washington asparagus listed in many 
seed catalogues. In this case, both male and female parent 
plants were selected and their combining ability determined. 

Hybridization is a means of combining the desirable char- 
acters of two or more varieties. Two smooth-awn varieties of 
barley Velvet, developed at the Minnesota Agricultural Experi- 
ment Station, and Barbless, in Wisconsin and the Little Joss 
and Yeoman varieties of wheat developed in England are illus- 
trations of the many cases in recent years where new varieties of 
crop plants have been developed by combining in a single 
variety the desirable characters of two or more parents. 

The development of a hybrid method of seed-corn production 
was predicted by Shull in 1909. Some of the results of this 
method of breeding have been emphasized in the first chapter. 

As a result of combined genetic and plant-breeding studies, 
the value of backcrossing in plant breeding is becoming generally 
recognized. When it is desired to add one or two characters to 



MODE OF REPRODUCTION 59 

an otherwise desirable variety and the technic of crossing is 
relatively easy, the method seems almost to be made to order. 

Convergent improvement or double backcrossing is a method 
of improving each of two inbred lines of corn or other crop plant 
without modifying their combining ability. 

These and other methods of plant breeding will be discussed in 
greater detail in later chapters, when the relative desirability of 
various methods of breeding for different types of improvement 
problems will be emphasized. 



CHAPTER IV 
TECHNICS IN SELFING AND CROSSING 

Two general methods for the exclusion of foreign pollen may 
be used in controlled self-pollination. One method is the use of 
space isolation, spacing single plants far enough apart from other 
plants with which they might cross so that selfing is ensured. 
The distance needed for complete isolation will vary with the 
crop, weather conditions, and natural barriers to the spread of 
pollen. This method has been employed rather extensively in 
selfing sugar beets. The other method is the use of some type 
of bag, either paper, vegetable parchment, or cloth, to enclose 
the inflorescences and ensure self-pollination. 

Crossing different strains usually involves the use of some 
special technic appropriate for the crop and environmental con- 
ditions prevailing. A knowledge of flower structure of the 
species or variety to be worked with is essential before crossing 
is undertaken. Some important features of the technic of cross- 
ing have been summarized by Hayes and Garber (1927) as 
follows: 

/ 1. Make a careful study of the structure of the flower before 
commencing operations. This may be with, or without, the 
aid of a dissecting microscope. 

/ 2. Determine which flowers produce the larger, healthier 
seeds and which set seed most freely. 

3. Learn the normal time and method of blooming of the 
flowers and the length of time that the pistil will remain recep- 
tive and the pollen grains capable of functioning. 

4. Procure the necessary instruments, and see that these are 
of an efficient kind for the work to be undertaken. 

5. Be careful not to injure the flowering parts any more than 
is necessary. Do not remove the surrounding flower parts, i.e., 
petals, glumes, etc., unless necessary. 

6. A few crosses carefully made are of much greater value than 
many pollinations carelessly executed. 

60 



TECHNICS IN SELFING AND CROSSING 61 

Some of the common methods employed in selfing and crossing 
different crops will be outlined. 

Corn. In selfing and crossing individual plants of corn, vege- 
table parchment and paper bags are commonly used to cover the 
ears and tassels. At Minnesota, ear bags made of 40-lb. vege- 
table parchment paper, 4 by 2J^ by 11 in. in size, with round 
bottom, 1-in. lip, and 1-in. bottom fold, sealed with a double 
strip of casein glue, have proved very satisfactory. These bags 
are placed over the ears before the silks emerge and are clipped 
with a collette paper clip to the stalk. After emergence of the 
silks, another bag, made of extra-heavy kraft paper, 7 by 4^ by 
16 in., with round bottom and 1-in. lip, is placed over the tassel. 
The end of the bag is folded tightly around the stalk and held 
in place with a paper clip. The next day the ear bag is removed, 
and the pollen that has collected in the tassel bag is poured over 
the silks of the ear to be selfed or crossed. In some cases, it is 
desirable to clip off the young silks at about the time that the 
tassel bag is placed over the tassel. This ensures a tuft of silks 
of similar length at pollination time. After pollination, the 
parchment ear bag is replaced and tied to the stalk with a string. 
This bag is left on until harvest. The used tassel bag is discarded. 

A method used commonly is to cover the ear shoot with a 
glassine bag, approximately 6^ by 2^ in., before the silks 
appear. These bags are placed over the ear shoot but are not 
clipped or tied to the plant. This method works satisfactorily 
when the ear shoot is large enough to support the bag. In some 
early varieties and inbreds of field corn and some strains of 
sweet corn and popcorn, the ear shoot is not sufficiently well 
developed to hold a glassine bag in place. After the silks 
appear, a specially treated tassel bag that is resistant to moisture 
and weathering is placed over the tassel and held in place with a 
clip. At pollination, the bottom of the glassine bag is clipped off, 
the silks are pollinated, and the ear shoot, after pollination, is 
covered with the tassel bag that is clipped in place. 

Another method used in selfing is the " bottle method" 
developed by Jenkins (1936). Small glassine bags are placed 
over the ear before any silks appear. After emergence of the 
silks has begun, a 2 oz. bottle of water is hung on the stalk at 
the ear-bearing node with a bent wire. The tassel is cut from 
the stalk, its shank is inserted in the bottle of water, and tasseJ 



62 METHODS OF PLANT BREEDING 

and shoot are enclosed in a large paper bag. The tassel should 




FIG. 8. Details of wheat inflorescence. 

Upper left, normal spikes; lower right, emasculated spike; 2, spikelet natural size; / and 
g, flowerless glumes; k and r, florets; 3, a single flower closed just after flowering, 3X;4A, 
longitudinal diagram before flowering, 1 x 2.5 X, a ** anthers, o = ovary, a = stigma, / = 
filament; 4B diagram after flowering; 5 = transverse floral diagram, 6X, fff "* lemma, 
p = palea, a = anthers, s = stigma; 6, flowerless glume, 7, lemma, 8, palea, slightly 
reduced; 9, lodicule, 4X; 10, cross-section anther, 26 X: 11, pollen grains; 12, ovary and 
stigma just prior to flowering; 13, at flowering; and 14, shortly after; 15, 16, 17, the mature 
seed. (After Babcock and Clausen, 1918, after Hays and Boss.) 

be arranged directly above the ear shoot. The bottle of water 
seems to keep the tassel alive and shedding pollen as new silks 



TECHNICS TN SELFING AND CROSSING 63 

emerge. After 48 to 72 hr,, the tassels may be removed and 
the bottles collected. 

When large quantities of seed are required, as in sib pollina- 
tions or crossing, it is usual to mix the pollen collected from 
several plants of one line and apply the mixture to the silks of the 
desired number of plants in the female line. For this purpose, a 
small " pollen gun" or small insect duster may be used to apply 
the pollen, the anthers first being screened out. 

Large-scale production of crossed seed is accomplished by 
planting the lines to be crossed in alternate blocks in a field 
isolated from other corn and removing the tassels of the female 
line before pollen sheds or before the silks appear. The seed 
produced on the detasseled line is hybrid seed. The ratio of 
pollen-parent rows to detasseled rows varies from, 1:2 to 1:4, 
depending on the pollen-producing ability of the male line. 

Wheat, Oats, and Barley. Hayes and Garber reviewed 
studies of blooming with wheat that emphasize the importance 
of this knowledge in relation to time of emasculation. The 
period from about 5 p.m. to 7 a.m. was referred to as night. 
Of 2,977 flowers studied on 69 spikes, 1,492 bloomed at night 
and 1,485 during the day. These data show that with wheat 
it is equally satisfactory to pollinate during the day as in the 
very early morning. 

The same writers reviewed studies that have been made to 
determine whether it was necessary to cover emasculated spikes 
of wheat. All results showed that emasculated spikes when left 
uncovered without hand pollination set a high proportion of seed. 

Crosses in the self-pollinated cereal grains may be made 
either in the field or greenhouse. All but about 8 to 15 of 
the florets on a spike or panicle arc removed, before anthesis, 
from the heads of each plant to be used as a female parent. 
The stamens are then removed from these remaining flowers 
with small forceps before the anthers dehisce, and the head 
is enclosed in a paper bag. Bags 2% in, wide and 6 in. long, 
made of vegetable parchment paper, are satisfactory. About 
2 days later, ripe anthers are collected from the male plants, 
and pollen is applied to the flowers of the female by breaking 
a mature anther and placing it within the emasculated floret. 
The paper bag is placed over the pollinated head and allowed 
to remain until harvest. Seed from both male and female 



64 METHODS OF PLANT BREEDING 

plants used in the crosses may be harvested also. Direct 
comparisons of the progeny of the two parents with the Fi and 
segregating generations of the crosses are highly desirable when 
genetic studies are to be made. 

Suneson (1937) found that chilling wheat plants for periods of 
15 to 24 hr. at 27 to 36F. resulted in a marked reduction of self- 
fertile florets through killing of the pollen. Different varieties 
varied in tolerance to chilling. 

Since the glumes of self-unfruitful florets are held open by the 
lodicules, rapid application of the desired foreign pollen by dust- 
ing on the exposed stigmas was possible. Self-fertile florets 
tend to remain closed and can be rogued. This method of 
emasculation might be useful if large numbers of hybrid seeds 
were needed. If the female parent possesses a simple recessive 
character and the male the dominant allele, any plants from 
self-fertilized seed can be rogued the year the Fi plants are grown. 

Rye. In self-pollinating rye, several heads of a plant may be 
enclosed in a parchment bag before anthesis. It is desirable to 
place an eyelet in the top of the bag and to tie it to a stake for 
support. Bags of the same size as those used for ear bags with 
corn are satisfactory. These bags are left on the plants until 
harvest. In making controlled crosses between individual 
plants, the same technic used in emasculation and pollination 
with wheat, oats, or barley may be used. In making inbred- 
variety crosses, the flowers of the inbred lines may be emas- 
culated in the usual manner, and when the florets open 1 to 4 
days later a large amount of pollen may be collected by enclosing 
large numbers of heads of the open-pollinated variety in a large 
paper bag and the pollen applied to the emasculated flowers 
with a camePs-hair brush. 

Flax. Emasculations of flax are commonly made in mid-to- 
late afternoon. At this time a little experience will indicate 
which flowers will open the following morning. The petals of the 
flowers may be pulled out and the anthers pushed off with a 
toothpick. The next morning, flowers are collected from the 
male plants, and, by holding them between the thumb and fore- 
finger, the dehiscing anthers may be brushed over the stigma. 
It does not appear to be necessary to bag the flowers. 

Cotton. In hybridizing cotton, it has been found that a short 
section of ordinary soda-fountain straw, closed at the upper end, 



TECHNICS IN SELFING AND CROSSING 65 

may be used to enclose the exposed pistil after emasculation. 
Humphrey and Tuller (1938) described an improvement in the 
use of this technic. They found it unnecessary to remove all 
the anthers in emasculation, since those not removed were cut off 
by the straw when this was inserted over the staminal column. 
The soda straw, before use, was closed at one end and about 
one-fourth of the anthers frotia a male flower scooped into the 
straw. This was then inserted over the pistil of the emasculated 
flower, forced down until it reached the ovary, and the straw 
fastened to the stem with No. 26 copper wire. By the use of 
this technic the flowers were emasculated and pollinated the same 
day, the flowers being worked with only once. 

Sorghum. Stephens and Quinby (1933) suggested the use of 
hot water for bulk emasculation of sorghum. If large amounts of 
hybrid seed were needed or backcross populations desirable, the 
ordinary methods of individual floret emasculation were too slow. 
They found that immersion of the sorghum heads in water, the 
temperature of which was 42 to 48C., for 10 min. resulted in 
killing of the pollen. The equipment consisted of a large rubber 
tube that could be placed over the head to be treated and tied 
to the peduncle of the head at the lower end. A metal container 
was connected to the upper part of the tube, into which the hot 
water was poured. When proper temperature conditions were 
obtained, all pollen in the head was killed. The emasculated 
heads could then be pollinated with pollen of the desired male 
parent. 

Rice. Jodon (1938) found that immersion of the heads of 
rice in water at 40 to 44C. for 10 min. destroyed the viability of 
pollen without injury to other floral organs. Treatment at to 
6C. gave similar but probably less effective results. 

A large-mouthed Thermos jug was used as a water container 
and the treatment applied in the morning prior to normal 
blooming. Emasculation by hot or cold water eliminated injury 
to the glumes, and the florets opened in a normal manner. 
Normal seed, which germinated well, was obtained when florets 
so emasculated were pollinated. 

Another method used in artificial hybridization is ibo emascu- 
late by removal of the anthers with small forceps through a 
. slanting opening made by clipping away a portion of the upper 
part of the lemma. This is done in the evening or morning 



66 



METHODS OF PLANT BREEDING 



prior to blooming, before the anthers will shed pollen on handling. 
The florets are pollinated by breaking mature anthers within the 
emasculated floret. 

Potato. For careful genetic experiments it is probably wise 
to enclose the flower clusters in small cloth bags in selfing the 

potato. Otherwise, bagging 
seems unnecessary. Emascu- 
lation is accomplished by re- 
moving the anthers with a 
small forceps or by scraping off 
the anthers with a small knife. 
Pollination is accomplished by 
tapping a flower of the male 
parent gently so that pollen is 
spilled onto the thumbnail and 
then applied to the stigma of 
the emasculated flower. 

Pumpkin and Squash. Most 
varieties of pumpkins and 
squashes have imperfect flowers, 
some flowers on the plant having 
only male and others only 
female organs. Pulling the 
petals of the female flowers 
together so that they com- 
pletely cover the stigma and 
putting a rubber band around 
them are easy and acceptable 
ways of excluding foreign pollen. 
In selfing, or crossing, the male 
flowers may be collected and 
pollen shaken directly onto the 
stigma or first shaken onto the 
thumbnail and then transferred 
to the stigma. 

Onion. Onions may be selfed by enclosing the head with a 
paper bag before any pollen is shed. Shaking the plant daily 
or tying the bagged head to a stake so that the wind will do the 
shaking was found by Jones and Emsweller (1933) to increase 
the amount of seed set. For seed increases, large cheesecloth 




4 

Fits. 9. Structure of squash flower. 

1. Female flower: (a) corolla; (&) 

calyx; (c) fruit. 

2. Male flower. 

3. Male flower with calyx and corolla 
removed. 

4. Female flower with calyx and 
corolla removed showing: (a) 
stigma; (6) style; (c) point of at- 
tachment of calyx and corolla; (d) 
undeveloped fruit. 

5. 6. Longitudinal and cross sections 
of fruit. 

Size: 1, 2, % X; 3, 4, H X; 5, 6 greatly 
reduced. (After Hayes and Garber.} 



TECHNICS IN SELFING AND CROSSING 67 

cages may be used, several plants being enclosed. The authors 
mentioned above used cloth cages 3 by 3 by 6 ft. in making 
crosses. Fly pupae were introduced into the cages to act as a 
means of transferring pollen from one plant to another. Hybrids 
of some crosses may be distinguished in the seedling stage. In 
other crosses, it was necessary to grow the bulbs before roguing 
out the selfcd plants. If the hybrids are not distinctly different 
from the female parent, it would be necessary to emasculate the 
female-parent flowers. 

Red Clover. In selfing red clover, cloth bags about 4 in. long 
and 2 in. wide may be used to exclude insects. Such bags are 
tied on before the flowers open. Usually a higher amount of 
selfed seed is obtained if the heads are rolled several times during 
the flowering period to aid in tripping the flowers. Cloth bags 
are preferred to paper, since the heads can be rolled without 
removing the bag. These bags may be made of theatrical gauze, 
such bags having a coarse mesh. Controlled cross-pollinations 
may be made by hand or through the use of bees. For hand 
pollination, Williams (193 Ic) states that emasculation is not 
necessary, since most red-clover plants are self-incompatible. 
Under Welsh conditions, the percentage of self-fertility varied 
from 3.45 to 0.17 per cent, with a mean of 0.85 per cent, during an 
8-year period. Partly folded triangular pieces of cardboard 2 in. 
long and about }/% in. wide at the broad end and tapering to a 
point at tho other are used for tripping the flowers and applying 
pollen. One card is used for tripping the flowers and the other 
for collecting pollen from the male parents and applying to the 
stigmas of the female parents. One collection of pollen usually 
will pollinate from 15 to 25 florets. After pollination, the polli- 
nated heads are enclosed in cloth bags. 

In using bumblebees for cross-pollination of red clover, the 
plants to be crossed are grown in pots. The parents to be 
crossed may be placed in insect-proof compartments in a green- 
house or in the field, the former being the more satisfactory. 
The bees are trapped in large test tubes (Williams 1931) and 
washed for about ]^ min. by partly filling the tubes with water 
and shaking, the water being changed several times. The water 
is then poured off and the tubes placed in a rack for 2 or 3 min., 
after which the bees are rinsed two or three times before being 
placed in a wooden box to dry. 



68 



METHODS OF PLANT BREEDING 




1 




For descriptive legend see page 69. 



TECHNICS IN SELFING AND CROSSING 69 

In making paired crosses, the bees are introduced into a com- 
partment containing the plants in about the half-bloom stage. 
After 4 to 7 days, the bees are removed, washed, and used for 
other crosses. When mass crosses are made, one bee to each six 
or eight plants is introduced into the compartment containing 
the plants and left until the flowering period is over. Similar 
methods have been found by Atwood (1940) to be satisfactory 
with white clover. 

Alfalfa and Sweet Clover. Several immature flowering 
branches of sweet clover may be covered with a lightweight 
cheesecloth bag approximately 6 or 8 in. wide and 12 in. long. 
This excludes bees and prevents cross-pollination. There are 
three types of plants of Melilotus alba, according to Kirk and 
Stevenson: (1) those that are spontaneously self -pollinated and 
self -fertile and produce seed without manipulation; (2) those that 
are self -fertile but that are not normally self-pollinated without 
manipulation; (3) self-sterile plants. To ensure self-pollination, 
when the plant is self-fertile, it is desirable to manipulate the 
bag by rubbing gently with the hands every day or two at the 
time of pollination. M. officinalis is not entirely self-sterile, 
and selfed seed can be obtained by the same means (Pieters and 
Hollo well, 1937). 

Kirk (1930) devised the suction method for emasculating 
sweet-clover flowers. If the plants are located near a water 
faucet, a vacuum flask inserted in the hose line will furnish the 
necessary suction. Otherwise, an electric or gasoline-driven 
suction pump must be used. A short piece of glass tubing 
slightly less than 1 mm. in diameter is inserted in the end of the 
hose. The point of this nozzle must be smooth, in order not to 
injure the flower. The amount of suction is of considerable 



FIG. 10. Structure of alfalfa flowers. 

1. Branch showing flowers in position. 

2, Single flower, showing a, standard; 6, sexual column in contact with 
standard; c, keel; d, wings. 

3. Seed pod. 

4. Flower parts in position a, undeveloped pod; 6, ovary; c, filament; 
<i, anther. 

5, Same with all anthers removed except one to show stigma, 

6, Anther. 

Size: 1, about K X; 2, about 2 X; 3, about ^ X; 4, 5, 6, greatly enlarged. 



70 METHODS OF PLANT BREEDING 

importance. All the flowers on a raceme are removed except 
about 20 per cent of the flowers that have most recently opened. 
The petals are next removed with forceps. This ruptures' the 
stamens and scatters the pollen. With the use of the nozzle 
attached to the suction flask or pump, the anthers and adhering 
pollen are sucked off. The stamens should be approached from 
the side of the staminal tube in order not to draw the pistil and 
staminal tube into the end of the nozzle. After the stamens have 
been removed, the end of the nozzle should be passed over the 
surface of each style and stigma, sepals and axis of the rachis. 
If the operator wears a low-powered binocular magnifier on his 
head, he can check on the thoroughness of the emasculation 
while leaving his hands free. The pollen may be applied effec- 
tively with the end of the thumbnail. 

Kirk found the degree of effectiveness of emasculation by suc- 
tion to be 87 per cent but suggested that improvement in technic 
might increase this materially. He used the suction method on 
alfalfa also with good results. 

Tysdal and Garl (1938) found that when suction alone was 
used and no foreign pollen applied to the stigmas, 14.1 per cent 
of the flowers formed pods. If suction plus washing with a 
stream of water was used, the percentage of flowers forming pods 
without application of foreign pollen was reduced to 5.5. 

Tysdal suggested the use of alcohol as an agent for killing 
the pollen on the flowers of the female plants. The standards 
were first clipped from flowers in full bloom with a sharp scissors 
and the flowers tripped, leaving the stigmatic column exposed 
for treatment. All flowers on a raceme to be emasculated were 
treated in a similar manner. The raceme was then immersed 
for 10 min. in a beaker containing 57 per cent ethyl alcohol. 
The raceme was rinsed for a few seconds in another beaker 
containing water, after which the adhering water was blown 
off the stigma with a dentist's syringe or bulb from an atomizer 
and pollinated with the desired pollen. By the use of this 
method, the percentage of flowers forming pods without applica- 
tion of foreign pollen was 0.89. The percentage of flowers 
forming pods when foreign pollen was added was 26.3, as com- 
pared with 60.0 for the suction method. Emasculation by 
the use of alcohol was more complete, faster, and simpler than 
emasculating by suction. 



TECHNICS IN SELFING AND CROSSING 71 

Grasses. Selfing, in greenhouses, may be accomplished by 
enclosing a number of inflorescences in a paper bag prior to 
pollen shedding. Bagging should be done soon enough so that 
stray pollen that fell on the flowering panicle or spikes before 
bagging will not remain viable long enough to effect cross-fer- 
tilization. Glassine or vegetable-parchment-paper bags are 
satisfactory. In closing the mouth of the bag, the stems are 
wrapped with cotton and the bag tied over this cotton. This 
excludes insects, if present, and helps to protect the stems from 
injury. The upper part of the bag is tied to a stake by means of 
a string inserted through an eyelet. 

Bagging in the open requires careful consideration of possible 
damage due to wind and rain, as well as complete exclusion of 




FIG. 11. Studies of the effects of self-fertilization with grasses at the U.S. 
Department of Agriculture Regional Pasture Research Laboratory, State College, 
Pennsylvania. 

foreign pollen. At Minnesota, vegetable-parchment-paper bags 
4 by 2,^2 by 18 in., with round bottoms, sealed with casein glue, 
are used for the larger grasses, such as species of Dactylis, BromuSj 
Phleunij Festuca, Agropyron, and Alopecurus. A number 
of inflorescences are enclosed in a single bag. The leaves 
on the upper part of the stems "are removed, cotton is placed 
around the stems, and the bags are tied around the cotton pad. 
The bottom end of the bag is tied loosely to a stake and the upper 
end tied tightly to the same stake, a string inserted through an 
eyelet put in with a small eyelet machine holding the bag at the 
upper end. Such bags allow for elongation of the stems and 
inflorescences. The bags are left on until harvest. 

At the Welsh Plant Breeding Station, vegetable parchment 
that took the form of a sleeve (topless and bottomless) fitted 



72 METHODS OF PLANT BREEDING 

over a wire spiral was used. The wire spiral provides protection 
against storms. This sleeve was fitted over the inflorescences 
and tied to a stake at both top and bottom, a wad of cotton 
being first wrapped around the stake and the bag tied over this. 

Jenkin (1931) reported that cotton sleeves (seamless), about 
15 in. in diameter and from 3 to 4 ft. long, stretched over a 
frame, have been found to be highly effective in excluding foreign 
pollen, provided the proper type of fabric is used. The fabric 
found to be most satisfactory was a very dense and rather 
heavy fabric, the most closely woven that it was possible to 
procure. This fabric proved highly effective in excluding foreign 
pollen but was not absolutely pollen-proof. Cheesecloth gave 
very little or no protection. The cotton sleeve was tied to a 
stake in a manner similar to the method of fastening vegetable- 
parchment sleeves described above. 

Kirk (1927) enclosed entire plants of brome grass in cotton 
cages about 5J^ ft. high and 3J^ ft. square as a means of effecting 
self-pollination. The bottom of the cotton cage was soaked in 
oil and buried a few inches in the soil. The tops were tightly 
tied. Foreign pollen probably was not absolutely excluded, but 
the method was highly effective when closely woven cloth was 
used. If all plants in the nursery not covered by cages were 
nut off prior to pollen shedding, it would be necessary for pollen 
to blow out through the cloth of one cage and in through the 
cloth of another and onto the flowers before crossing could be 
obtained. The amount of such cross-fertilization probably is 
very small. 

In making crosses by hand-hybridization, Jenkin (1924) grew 
the plants to be crossed in pots and placed these in a cool green- 
house some time before flowering. Emasculation was done a few 
days before flowering. The upper and lower spikelets of an 
inflorescence were removed and the anthers removed from the 
remainder with a flat-pointed, blunt pair of forceps, the upper 
florets being emasculated first. In Phleum, Alopecurus, and 
PhalariSj severe thinning of the florets in an inflorescence is 
necessary. After emasculation, the inflorescence is covered with 
a paper bag. 

Inflorescences of the male parents are covered with paper bags 
prior to flowering. The greenhouse is closed tightly about an 
hour before pollination begins so that any floating pollen may 



TECHNICS IN SELFING AND CROSSING 73 

settle down. The bag on the male plant is inclined so that when 
shaken vigorously the pollen collects in the creases toward the 
mouth. The bag is removed and the pollen poured on a sheet of 
dark, glossy paper, previously folded into a boat shape and cut 
with a sharp point at one end. The pollen is brushed lightly 
over the stigmas of the emasculated flowers and thfe female unit 
rebagged. Since all florets do not open on the same day and 
flowering proceeds progressively downward, pollination is 
repeated every day until no more f^esh stigmas are produced. 
Jenkin (1931c) reported successful crosses, by the foregoing 
method, with species of Lolium, Festuca, Arrhenatherum, Dactylis, 
ij and Alopecurus. 



CHAPTER V 

THE PURE-LINE METHOD OF BREEDING NATURALLY 
SELF-POLLINATED PLANTS 

EARLY STUDIES 

This method has been developed as a result of fundamental 
studies like those of Vilmorin, Mendel, Johannsen, and of numer- 
ous workers in recent times. These studies, together with field 
experience, have led to the conclusion that the progeny of an 
individual plant selection with self-pollinated crops may be 
expected, for the most part, to breed true immediately. 

A brief review of some of the more important of these early 
studies will be of interest. 

Le Couteur, in the early part of the nineteenth century, was a 
farmer on the isle of Jersey who was interested in the problem of 
improving his crops. Professor La Gaska, from the University of 
Madrid, visited Le Couteur and pointed out numerous differ- 
ences in plant type occurring in Le Contour's wheat field. Selec- 
tions were made and the progenies tested. Some proved 
superior to the commercial variety and were of more uniform 
habit of growth; other selections were of little value. Bellevue 
de Talevera, one of these selections, was of commercial value for 
many years. 

Patrick Shirreff, a Scotsman, carried on selection with wheat 
and oats at about the same period as Le Couteur. He used the 
individual-plant method, selecting strong, vigorous plants in his 
wheat and oat fields, keeping the progeny of individual plants 
separate, and increasing the more desirable. Like Le Couteur, he 
proceeded orx the assumption that the selected single plants would 
breed true. New varieties produced by this means were grown 
extensively. 

Hallett began selection with wheat, oats, and barley about 
1857, believing, apparently, that acquired characters were 
inherited and that improvement induced by favorable growing 
conditions would be transmitted to the progeny. He raised his 
plants, therefore, under the most favorable cultural conditions, 

74 



THE PURE-LINE METHOD OF BREEDING 75 

selecting the best seed on the best developed head of the more 
vigorous plants, replanting, and following the same plan of selec- 
tion in subsequent years. New varieties were introduced, the 
best known being Chevalier barley. Although the method 
appears less desirable than that of Shirreff and there is little 
reason to suppose that the continuous selection was of value in 
isolating new heritable variations, it gave an opportunity to study 
progenies during different seasons and in this way to select the 
best. New varieties were introduced that proved of value. 

The Vilmorins, in France, were early leaders in improvement of 
plants by selection. Louis de Vilmorin (1856) developed the 
progeny test with reference to sugar beets. Early wheat selec- 
tions were made also, and the method developed is known as 
Vilmorin's isolation principle. Briefly, this consists of the fact, 
well known today, that the only sure means of knowing the value 
of an individual-plant selection is to grow and examine its prog- 
eny. Methods were developed for the determination of the sugar 
content of individual roots of sugar beets. Louis de Vilmorin 
observed that the progeny of some beets of high sugar content 
gave progenies of high sugar content rather uniformly, whereas 
others gave progeny of both high and low content and still others 
gave progeny that were uniformly of low sugar content. Four 
varieties of wheat were propagated for 50 years by selecting the 
best plants each year. At the end of the selection period they 
were compared with specimens saved at the beginning of the 
experiment, and no change was noted. 

Newman (1912) made an interesting review of plant breeding in 
Scandinavia. The Swedish Seed Association, formed in 1886, 
had a marked influence on the development of plant-breeding 
methods. Hjalmar Nilsson became the director of the associa- 
tion in 1891. From the beginning, careful records were kept, 
individual plants were classified on the basis of minute botanical 
differences, and seed of plants containing the same characteristics 
was combined, the progeny of each separate type being grown in a 
separate plot. Some progenies appeared so uniform that they 
were especially noted by Nilsson. From a study of the records, 
it was learned that in each case these were from seed of an indi- 
vidual plant, there being only one representative of that mor- 
phological group. This led, naturally, to the individual-plant 
method of selection. 



76 METHODS OF PLANT BREEDING 

W. M. Hays started his plant-breeding program in Minnesota 
in 1888 and from the beginning used the individual-plant method 
of selection. Besides making practical studies, he initiated many 
experiments that had as their purpose the formulation of funda- 
mental principles. He developed the centgener plan of plant 
breeding. The first step consisted of selecting individual plants 
of promise, threshing these separately, and making nursery 
trials of their progeny. During the period of study, plots of 100 
plants each were grown from each selection. Besides taking 
notes on yield and other characters on the plot basis, the 10 better 
plants in each plot were selected in the field, threshed individually, 
and the seed of the 5 that were of greatest promise, after labora- 
tory study, was bulked and used for the following year's centgener 
plot. One of the difficulties of the method as a yield trial was 
that when numerous selections were made it took several days 
to plant the nursery and, since only one plot of each selection was 
grown, as a rule, the data obtained were not comparable. The 
types of greatest promise, however, were quickly isolated and 
grown in larger plots. Improved Fife, Minnesota 163, and 
Haynes Bluestem, Minnesota 169, were valuable new varieties 
of spring wheat selected by this method and grown widely in the 
early part of the present century. 

THE PURE-LINE THEORY 

The experiences of plant breeders played their part in develop- 
ing breeding methods, but it remained for Johannsen to place the 
individual-plant method of selection on a firm scientific basis. 

Johannsen (1903, 1909) made his studies with beans, selecting 
this plant because it belongs to the self -pollinated group and con- 
tains characters that are easy to measure. He hoped to control 
heredity by applying Galton's law of regression, i.e., that the f 
progeny of parents above or below the average tend to revert to 
the average type. The tendency to regression toward the aver- 
age could be measured and expressed statistically. By selecting 
extreme parents, continual improvement could be obtained, if 
the same degree of inheritance was obtained in later generations. 
In studying size of beans, Johannsen found a different regression 
value from that obtained by Galton and less progressive improve- 
ment than he expected. This led to a study of the progeny of 
individual plants, each of which varied around its mean. He 



THE PURE-LINE METHOD OF BREEDING 77 

found each of these progenies to be a single hereditary line, 
within which there was complete regression to the mean of the 
line when extreme parents were selected and their- progeny 
studied. These principles are well understood today and have 
had a profound effect on plant-breeding practices. Johannsen 
defined a pure line as the descendants of a single, homozygous, 
self-fertilized organism. Jones gave a definition, which is in 
common use today, by stating that a pure line comprises the 
descendants of one or more individuals of like germinal constitu- 
tion that have undergone no germinal change. 

THE PURE-LINE THEORY IN ITS APPLICATION 

Although many experiments have been carried out that prove 
that continuous selection in self-pollinated crops, as a means of 
obtaining further improvement, is not worth while and there is 
general appreciation of the fact that the initial individual selec- 
tion is of greatest importance, there is a growing body of evidence 
that heritable variations are more frequent than was supposed at 
one time. An illustration may be useful. Several years ago, 
Victory oats, originally produced in Sweden from an individual- 
plant selection, was on the recommended list of the Minnesota 
Agricultural Experiment Station. A large number of individual- 
plant selections were made and their progeny studied by R. J. 
Garber. When these various lines were compared for differences 
of plant-breeding importance, in replicated rod-row trials, no 
new line was obtained that was appreciably superior to the com- 
mercial seed of Victory that had been distributed to Minnesota 
farmers. The different selections showed, however, numerous 
minor, heritable differences of distinct morphological type as well 
as differences in quantitative characters that were more difficult 
to evaluate exactly. 

In this connection, recent papers by East (1935a,6,c, 1936a) 
deserve consideration. He classified gene mutations under two 
categories: " physiological defectives" and nondefective genes. 
The former are the genes that have been used, largely, in genetic 
experiments. An illustration may be given of East's viewpoint 
by reference to the ligule that is characteristic of the entire 
group of Gramineae. Liguleless stocks are known in maize, rye, 
wheat, and oats, and in some cases the difference between liguled 



78 METHODS OF PLANT BREEDING 

and liguleless types behaves as if controlled by a single factor 
pair. East suggests that the ligule " presumably is the result 
of a very large number of non-defective mutations in various 
genes, and, physiologically speaking, is the end product of a 
long chain of reactions." A single mutation breaks this chain, 
and a liguleless plant results. 

East states that he believes every experienced plant breeder 
will agree with the statement that " non-defective gene mutations 
are frequent in Nature, but are difficult to detect." He sum- 
marizes the results with tobacco, where characters of plants in 
self-fertilized lines were evaluated statistically. Although there 
was a rapid approach toward uniformity and gross homozygosis, 
there still remained considerable variability, a part of which was 
proved to be heritable. High mutation frequently is believed to 
be responsible for heritable changes in these small genetic factors 
of the nondefective type. 

East gives an illustration of several cases in which, in attempts 
to produce certain species hybrids, only maternals resulted. The 
plants were ordinary fertile diploids and, presumably, arose from 
mature gametes in which parthenogenesis was induced. The 
plants then would be completely homozygous. In cases in 
Nicotiana rustica, each progeny row was astonishingly alike, more 
so than "any ordinary inbred populations that I had ever exam- 
ined." Several of these lines were continued by self-fertilization 
and within 3 or 4 years were as variable as ordinary inbred 
populations. 

For practical purposes, the pure-line theory furnishes a basis for 
the isolation of types that differ appreciably in heritable char- 
acters, and the progeny of individual plants in self-pollinated 
crops breed relatively true. Mutations do occur, and minor 
mutations of a nondefective type are relatively frequent, although 
often not sufficiently large to be of major selection value. 

Natural crosses are more frequent than is generally appreciated 
and furnish another basis for variation among plants within a 
variety or strain. Mechanical mixtures occur also. These 
various causes emphasize the necessity of constant care to ensure 
the necessary uniformity desired in an improved variety. They 
do not detract from the value of the pure-line concept in its 
application to the improvement of self -pollinated crops by indi- 
vidual-plant selection. 



THE PURE-LINE METHOD OF BREEDING 79 

METHODS OF IMPROVING SELF-FERTILIZED PLAKTS 
BY INDIVIDUAL-PLANT SELECTION 

The following condensed summary of methods will serve as a 
basis for a plan with particular crops. It is stated in general 
terms, for it is recognized that such widely different plants as 
tomatoes, tobacco, rice, and wheat must be grown according to 
their special adaptations. With crops such as tobacco and 
tomatoes, individual plants will be separately spaced in rows or 
plots, whereas with the small grains bulk sowing of seed may be 
practiced from the beginning of the trials. 

Two principal sources of selections are available in the produc- 
tion of new varieties: 

1. The introduction of improved or relatively unimproved 
strains and varieties of crops found in use over a wide range of 
conditions, both foreign and domestic. 

2. Well-adapted local varieties that are found to be variable 
and to contain a composite of a number of biotypes. These may 
have had their origin aajhybrids or .pure lines) which have become 
altered as to general type through mechanical mixtures, natural 

crossing, or mutations. 

/ 

I. UTILIZATION OF INTRODUCTIONS 

A. Source of materials. 

1. A list of introduced crops and varieties with their descriptions may be 
obtained from the U.S. Department of Agriculture, Bureau of Plant 
Industry. It will be desirable to determine through the bureau, 
when possible, the adaptation range of the introductions that appear 
to meet the needs and secure seed from this source. 
! 2. Personal contacts with foreign and domestic visitors is a natural 
source of introductions for crops that are developed along special lines 
but that frequently do not arrive through the channels of the Bureau 
of Plant Industry. The visits of staff members to foreign and 
domestic stations likewise may occasionally bring to attention special- 
purpose crops and their varieties. 

3. Mutual exchange of crops with domestic stations is a desirable 
practice. Station publications afford a description of crops in use. 

t 4. A survey of farm varieties is desirable. Native species^ especially 
with forage crops, may yield a source of new material. 

B. History and records of all introductions. 

It will be desirable to keep a record book or card file recording as follows: 

1, History of each introduction. 

2, Description of same. 

3, Year introduced. 



80 METHODS OP PLANT BREEDING 

<7. System of records. 

A system of numbering new varieties that ensures ease of interpretation 
and accuracy of record is desirable. 

1. The Minnesota method is presented here and, for comparison, nota- 
tions for introductions, selections, and hybrids are included. 

Minnesota Records 

1-20-1 Selections 

11-20- 1 Crosses 

III-20-1 New introductions 

In this method, I, II, and III stand for individual-plant selections, 
crosses, and introductions, respectively; 20 represents the year in 
which the selection, cross, or introduction was made; and the final 
number represents the particular selection, cross, or introduction. 
Crosses are given a selection number only after having been shown to 
be homozygous. Parental and F n populations are numbered by 
carrying row numbers for the current and preceding season, until 
homozygosity is reached. When the method of carrying row numbers 
for 2 years is used in the planting plan, a pedigree can be completed 
when desired. The method often used by workers in the U.S. 
Department of Agriculture or in state experiment stations is given 
here where FI = A, F 2 = A-l, A-2, etc., F 3 = A-l-1, A-l-2, etc., 
according to the number of selections grown. 
First year = 11-18, A. 
Second year = 11-18, A-l, A-2, etc. 
Third year = 11-18, A-l-1, A-l-2, etc. 

Selections of crosses, when given series numbers, after reaching 
homozygosity, are designated 11-18- 1, II-18-2, etc., according to the 
number of selections made, 
2. Alberta system modification of method 1. 
/ = introduction. 
S selection. 
H = hybrid. 

Otherwise the method of numbering is similar to that used in Minne- 
sota. 
D. Observation of introductions. 

1. All introductions may be placed under observation in small plantings. 
Some of the original seed should be retained in case of unfavorable 
growing conditions the first season and for later comparison in the 
case of selection. 
a. Plots will consist of single short rows for small grains; other types 

of small plots may be used for other crops. 

6. The first observations will be concerned especially with characters 
of outstanding known value or for adaptability, uniformity, and 
general utility of the crop. The new introductions will be com- 
pared with standard varieties that are sown as frequent checks in 
these observation tests. 



THE PURE-LINE METHOD OF BREEDING 



81 



c. This preliminary planting may serve also as a means of seed 

increase for larger trials. 
2. During the second year, observations will again be based on small 

plantings similar to those of the first year and may serve as a natural 

means of eliminating those that are poorly adapted. These second 

plantings are also a means of seed increase. 

E. Method of testing desirable introductions for further trial (Love and 
Craig 1918o, 1924) (Noll 1927) (Goulden 1931). 

By means of several years of observation, a few introductions may have 
been found that appear to fill a special need. The procedure of testing 
these is outlined under II C. 

II. PEDIGREE SELECTION WITHIN ADAPTED VARIETIES 
A. /Agronomic characters sought according to needs of the regions con- 

/ r 



cerned. 

Some important agronomic characters are given below: 

1. Small grains and other cereals. 
Winter hardiness 

Straw strength 
* Time of maturity 
Drought resistance / 

Quality 
Nonshattering habit 

2. Forage crops. 
Growth habit 
Quality 

Drought resistance 
Straw strength 
Contribution to soil 
content 

3. Root, tuber, and sugar crops. 
Sugar content 

Ratio of roots to tops 
Nutritive value 
Seed production 



Awn characters (barley) 
Presence and absence of awns 
Percentage of hull (barley and oats) 
Seed color 
'Yielding ability 



Leafiness 

Recovery after grazing or cutting 
Cold resistance 

Yielding ability (forage and seed) 
organic " /Palatability 

; Nutritive value 



Palatability 

Quality 

Yielding ability 

Frost resistance 

NOTE: This list is not intended to be exhaustive and may be supplemented 
according to the interests of the individual. 
B. Resistance to diseases and insects. 

1. Selection of strains resistant to diseases that are difficult to control 
except through the production of resistant varieties is of greatest 
importance. The following diseases may be mentioned: 

Rusts Blights Root and stalk rots 

Smuts Wilts Take-all 

Mosaic Scab Anthracnose 

2. Selection of pathogens. 

a. Study the disease reaction in special disease nurseries and in the 
greenhouse with the use. of physiologic races existing in the 
particular locality or over a wider region. 



82 METHODS OF PLANT BREEDING 

b. Grow special disease nurseries in several places in the area in order 
to test for resistance under field conditions to physiologic races 
as they occur naturally. 

3. Disease garden. 

a. Selections should be tested in short rows or in other types of plots, 
6. Disease epidemics. 

(1) Artificial epidemics should be induced on susceptible border 
rows grown throughout the nursery and generously distributed 
through the plots of tested varieties or directly on the varieties 
themselves. 

(2) Natural or artificial epidemics may be obtained by growing the 
particular crops on soil infected by wilt, root rot, etc. 

4. Insect pests. 

a. Grow short-row plots on soil or in regions infested with such 
insects as Hessian fly, jointworms, boll weevils, borers, etc. 

5. Replication frequently is important in testing for resistance to plant 
diseases or insect pests. It is helpful in many cases to plant at 
different periods in order to obtain favorable conditions for producing 
the epidemic. 

C. Technic for selection and testing. 

1. Single-plant basis for selecting lines. 

a. First year. Select approximately 1000 heads from individual 
plants of the type desired. The total number of initial selections 
depends on the crop and the amount of land and funds available 
for subsequent testing. 

b. Second year. Sow 25 to 50 seeds of each selected plant in space- or 
bulk-planted single-plant or head-progeny rows. Discard all 
plant rows that appear of undesirable type, Heterozygous types 
of extreme promise may be rcselected. Continue elimination 
of undesirable types in each successive year. Bulk seed of the 
individuals for test in progeny rows. 

c. Third year. Replication should be started this year for prelimi- 
nary yield trials. Observe lines for uniformity for such agronomic 
characters as date of heading, strength of straw, and height of 
plant. Disease tests may be carried out as described under II B 3. 

d. Fourth to sixth years. The number of years indicated is arbi- 
trarily suggested, and these trials should be continued to the extent 
found desirable. 

(1) Composite seed of the replications of previous year's test and 
grow in single- or three-row plots or in other types of plots 
when desired. Replication is necessary. 

(2) Plant a duplicate test in the disease garden each year, and test 
for resistance to important diseases and insect pests. 

(3) Test for special characters grow replications in a particular 
environment, as on peat, sand, etc. 

(4) Make quality tests on the crop from border rows. 

(5) Select the more desirable lines for more extensive trials. 



THE PURE-LINE METHOD OF BREEDING 83 

e. Seventh to ninth year. Test promising lines in advanced trials, 
i.e.j in J^o-acre plots replicated or in row plots with more repli- 
cations than in earlier years and, when possible, at a number of 
stations. In these yield trials, replicate to the extent found 
necessary. 

III. COOPERATIVE TESTS AND DISTRIBUTION OF PROMISING LINES 

A. Bring information of the proved lines and introductions before the 
farmers through the extension service, agricultural high-school teachers, 
county agents, and crop-improvement associations and by means of 
bulletins. 

B. Select reliable farmers to grow demonstration plots of the improved lines 
in comparison with standard varieties. 

1. Plots, a single drill width, in the center of the farmer's field are used in 
Minnesota. 

2. A replicated trial may be made with a few farmers or local schools 
when desirable. 

C. Arrange these demonstration projects in a number of counties or prov- 
inces, and organize a field day for the community at which the county 
agent can use these plots as part of his program. 

D. Distribute seed to those interested through the farmers' crop-improve- 
ment association. 

ILLUSTRATIONS OF VALUABLE VARIETIES OF SELF-POLLINATED 

PLANTS PRODUCED BY APPLICATION 

OF THE PURE-LINE THEORY 

Selection has played a large part in the production of new 
varieties of wheat, oats, barley, flax, and other self -fertilized crop 
plants. Clark (1936) has given the origin of many of the varie- 
ties of spring and winter wheat. In winter wheat, lobred, 
loturk, and lowin, selected by L. C. Burnett, at Ames, Iowa, 
have been grown extensively. Nittany, selected from the Ful- 
caster variety by Noll, is the principal variety grown in Pennsyl- 
vania. Nebraska 60, selected by Kiesselbach from the Turkey 
variety, is grown widely in Nebraska, and Kanred, selected 
from Crimean by Roberts, with an estimated acreage of 3J^ 
million acres in 1929, has been of great value in the hard red 
winter-wheat region. 

In spring wheat, the early selections, Improved Fife (Minn. 
163) and Haynes Bluestem (Minn. 169) introduced about 1900 
were important varieties in the early part of the present century. 
Mindurn durum, the standard for quality of semolina products 
and the most widely grown durum variety in United States and 



84 METHODS OF PLANT BREEDING 

Canada, was produced by plant selection at the Minnesota 
station. 

In a discussion of superior germ plasm in oats, Stanton (1936) 
described many new varieties that have been developed by plant 
selection. Fulghum oats and its many strains originated from a 
single plant selected from Red Rustproof by J. A. Fulghum. The 
single plant was earlier and taller than the Red Rustproof 
variety. Other important selections from Red Rustproof and 
Fulghum include Kanota, Franklin, Columbia, Nortex, and 
Frazier. 

Varieties of Kherson and Sixty-day oats are grown extensively 
in regions of the corn belt where early oats of the Avvna saliva 
group seem desirable. Gopher, a white-seeded strain of sixty- 
day, has been grown extensively in southern Minnesota and in 
other states where early oats are adapted. It is perhaps the 
stiffest strawed early variety available. Its production empha- 
sizes the ease of improvement in some cases. Only 200 original 
plant selections were made from an early variety with mixed seed 
color. The first year in plant rows, six strains excelled in 
strength of straw, and the remainder were immediately discarded. 
Gopher was the best yielding strain of the six. Richland and 
logold selected by Burnett are both resistant to black-stem rust. 
Nebraska 21, selected in Nebraska, has been grown widely. 
State Pride, a plant selection made in Wisconsin, has been the 
standard early variety in that state. 

Among midseason varieties, Colorado 37 is outstanding in 
strength of straw and suitability for growing under irrigation. 
Cornellian, Ithacan, Upright, and Lenroc, selected by Love, in 
New York, occupy about 50 per cent of the oat acreage in that 
state. Rainbow and Rusota are important varieties selected 
from Green Russian at the North Dakota station. Both are 
resistant to black-stem rust. 

Improved varieties of barley resulting from plant selection have 
been given by Harlan and Martini (1936). A few of the more 
widely grown varieties will be mentioned. Atlas selected from 
the coast variety is the most important variety in California. In 
the Manchuria-Oderbrucker group, Manchuria, Minn. 184, was 
selected at the Minnesota station. Wisconsin Pedigrees 5 and 6 
selected from Oderbrucker are the chief strains selected from 
this variety. Peatland, selected at Minnesota, in cooperation 



THE PURE-LINE METHOD OF BREEDING 85 

with Harlan of the U.S. Department of Agriculture, is especially 
well adapted to peat soils and is valuable also because of its 
resistance to scab and black stem rust. Trebi, selected by 
Harlan, was grown on an estimated acreage of 2,224,000 in 1935, 
the largest acreage devoted to any single variety. It is not a 
desirable malting variety, but in spite of several undesirable 
characters it has high yielding ability and is especially well 
adapted for growing under irrigation. 

Practically all the varieties of rice grown in the United States, 
according to Jones (1936), were developed by selection, although 
not all were obtained by pure-line selection. More recently, 
hybridization has been used as a method of breeding, but to 
date only one variety produced by hybridization is grown 
commercially. 

Dillinan (1936) states that all varieties of seed flax grown in 
the United States were obtained by plant selection. Bison, 
selected by Bolley, at the North Dakota station, from commercial 
seed obtained from Belgium, is the most widely grown variety in 
United States. Buda, selected also by Bolley, has been a popular 
variety. Redwing, selected in Minnesota, is an early-maturing 
variety well adapted to southern Minnesota and Iowa, where it is 
extensively grown. All three varieties are resistant to wilt. 
Without this resistance it would have been impossible to continue 
to grow flax in the hard red spring-wheat belt. 

Individual-plant selection has been of great importance also in 
peas and beans (Wade 1937). Strains of Alaska peas and of other 
varieties have been selected that are resistant to fusarium wilt, 
M.A.C. Robust, selected by Spragg, in Michigan, is resistant to 
mosaic and has been grown extensively in Michigan and New 
York. Among the present varieties of soybeans, Morse and 
Cartter (1937) state that a considerable proportion were obtained 
by selection from the large number of introductions that were 
obtained from the Orient. Individual-plant selection has played 
a large part also in the origin of tobacco varieties, as has been 
pointed out by Garner, Allard, and Clayton (1936). 



CHAPTER VI 

HYBRIDIZATION AS A METHOD OF IMPROVING 
SELF-FERTILIZED PLANTS 

SOME STUDIES BEFORE 1900 

Many studies were made during the eighteenth and nineteenth 
century for the purpose of learning the laws of inheritance in 
hybrids or to develop new and improved varieties. A few of 
the more importar^t of these early studies will be mentioned to 
suggest the extent of the many investigations made before the 
present century, each of which played a part in developing 
principles that have led to the present view of a planned plant 
breeding program. 

Kolreuter, in 1760-1766, made extensive studies of artificial 
hybrids and emphasized especially hybrid vigor in F\ crosses. 
He noted the intermediate condition of the F\ in crosses in tobacco 
and interpreted this as showing the effect of the male parent. 
Thomas Andrew Knight, born in England in 1759, contributed 
greatly to early plant breeding. Much of his work was with 
fruit crops apples, pears, peaches, currants, and grapes. He 
emphasized the value of crosses as a means of obtaining new 
combinations of characters. John Goss, about 1820, studied 
segregation in crosses with peas but did not give an adequate 
explanation of the nature of the segregation. Sargaret, about the 
same period, made crosses between muskmelon and cantaloupe 
and studied fruit characters in F\. He reported the appearance 
of differences in flesh colors, seed color, rough or smooth fruit, 
extent of ribbing and flavor and emphasized the dominance of one 
character over the other. Gartner, in 1849, studied thousands of 
crosses, observing the uniformity and appearance of the Fi 
generation. Naudin, in 1865, just prior to Mendel's report, noted 
the uniformity of the F\ generation and segregation in F 2 , ascrib- 
ing this to the segregation of heritable factors in the formation of 
male and female reproductive gametes. 

Mendel's work need be mentioned only briefly. He studied 
individual characters and placed his results on a definite factor 

86 



HYBRIDIZATION AS A METHOD OF BREEDING 87 

basis. The methods used by him are not widely different from 
those used today. Although the laws of inheritance are much 
more complex than those presented by Mendel and although most 
normal characters are dependent upon the interaction of many 
genetic factors, the methods of work introduced by him have 
found very wide application. These methods have made it 
possible to develop a planned plant-breeding program based on 
the laws of heredity. 

William Farrer, of Australia, during the latter part of the 
nineteenth century, approached present-day plant-breeding 
methods and developed many wheat varieties of great value. He 
selected parents for crosses on the basis of their characters, 
strongly featuring the value of composite crosses as a means of 
inducing maximum variation. Federation, a variety of wheat 
that was early maturing, nonshattering, with stiff, erect, short 
straw, was produced as the result of a definite attempt to obtain 
a variety of wheat suited to gathering with a stripper. 

An illustration of the crosses used in the parentage of Federa- 
tion is given below: 

Improved Fife X Etitwah 

I I 



Yancii 



ilia X Purple Straw 



Federation 

By similar means, he obtained the following varieties: Come- 
back, Ceder, Firbank, Bobs, Cleveland, and Florence, the latter 
being a bunt-resistant variety. 

The work of A. P. and C. P. Saunders in Canada is well known. 
In 1892, A. P. Saunders crossed Hard Red Calcutta with Red 
Fife. C. P. Saunders took over the experimental work at Ottawa 
in 1903 and continued the selections that led to Marquis and 
other varieties, the new variety Marquis being first grown in pure 
form in 1904, 12 years after the original cross was made. He 
used the individual-plant method of selection and determined the 
gluten quality in the progeny of crossbred wheats by the chewing 
test. 

DEVELOPMENT OF METHODS SINCE 1900 

The rediscovery of MendePs l#ws by De Vries, Correns, and 
von Tschermak, in 1900, stimulated the extensive studies of the 



88 METHODS OF PLANT BREEDING 

laws of heredity that have led to the present system of breeding 
crop plants with a definite plan to obtain the combination of 
characters desired. The first step in such a program is a careful 
study of material available and an analysis of the characters 
desired. The necessity of making a collection of all available 
strains and varieties and an analysis of their characters needs 
emphasis. Although there is general appreciation of the desir- 
ability of this step, it is seldom practiced to the extent that would 
seem to be worth while. In recent years, Vavilov and his 
coworkers in Russia have made extensive world-wide collections 
of many crops. The U.S. Department of Agriculture maintains 
very extensive collections of varieties of grains, fruits, and 
vegetables that serve as a potential source of material for breed- 
ing. New strains and varieties are being added constantly 
through the plant-introduction service. The second step is to 
obtain the most desirable strains by selection. When these steps 
have been taken and the necessary background of knowledge 
with respect to disease reaction and agronomic characters of the 
crop has been gained, a crossing program may be undertaken. 
Crosses are made with a definite purpose in mind, i.e., with the 
intention of combining in one variety the characters desired. 
Illustrations will be given from some of the present problems 
being studied at Minnesota. 

BREEDING IMPROVED VARIETIES OF BARLEY 

This work, cooperative between plant geneticists, plant path- 
ologists, and cereal technologists, illustrates the value of a 
cooperative program. 

The first crosses for the Minnesota experiments, designed to 
produce satisfactory smooth-awned barleys, were made in 1912. 
These involved crosses of Lion, a six-rowed, black-glumed, 
smooth-awned variety with good, adapted, six-rowed, white- 
glumed, rough-awned sorts. Strains with white glumes and 
smooth awns were selected and appeared to yield well in rod-row 
tests (Harlan and Hayes 1919). In more extensive tests (Hayes 
1926), it was found that in some seasons these strains were 
reduced in yield because of the "spot-blotch" disease caused by 
Helminthosporium sativum. This led to a cooperative attack on 
the problem by plant geneticists and plant pathologists. It was 



HYBRIDIZATION AS A METHOD OF BREEDING 89 

found that the greater susceptibility of the hybrids appeared to be 
due solely to their greater susceptibility to H. sativum. 

A second series of crosses was made, with the use of one of the 
better white-grained, smooth-awned segregates of the first cross 
with desirable white-grained strains of the Manchuria type that 
were resistant to spot blotch. 

Studies of disease resistance were made in specially prepared 
disease gardens. The mode of inheritance of reaction to Hel- 
minthospormin was studied in the early segregating generations 
(Hayes el al. 1923 and Griff ee 1925), and it was found that at 
least three genetic factors were involved in differentiating reaction 
to the spot-blotch disease. 

Selections of smooth-awned segregates of desirable plant and 
kernel type were made in the plant rows found to be resistant to 
H. sativum. From the cross of a smooth-awned segregate of the 
first cross with Luth was produced the variety Velvet. The 
cross of " smooth awn 7 ' X Manchuria led to the production of 
Glabron. Velvet is grown rather extensively at the present time. 
The most extensively grown smooth-awned variety of the Man- 
churia type is Barbless (Wisconsin 38) produced from a cross of 
lion X Oderbrucker by Leith of the Wisconsin Agricultural 
Experiment Station. 

The smooth-awned varieties Velvet, Glabron, and Barbless 
are susceptible to stem rust and to blight. The variety Peat- 
land, selected at Minnesota from a lot of seed obtained from 
Switzerland, is resistant to both diseases. Studies by Powers 
and Hincs (1933) and by Reid (1938) showed that the stem-rust 
resistance of Peatland was due to a single dominant factor, in 
crosses with susceptible varieties. Brookins (1940) has shown 
that the factor pair conditioning resistance and susceptibility to 
a collection of races of rust in the field in the mature-plant stage 
also controls the same type of reaction to races 19, 36, and 56 in 
the seedling stage in the greenhouse. 

Peatland was crossed with Barbless for the purpose of com- 
bining the good characters of both. The contrasted characters 
are given in the table shown on page 90. 

A large F 2 was grown in a space-planted nursery and only plants 
with smooth awns that were resistant to stem rust and that were 
of desirable plant and seed type were selected. Since smooth 
awns are due to one main recessive factor, the selection of smooth- 



90 



METHODS OF PLANT BREEDING 



awned plants in F% eliminated all rough-awned sorts from subse- 
quent generations. Resistance to stem rust is dominant. 
Consequently, the ^2 resistant plants gave rise to homozygous 
and heterozygous F 3 progenies in a ratio of 1:2. 



Character 


Barbless 


Peatland 


Yield 


Good* 


Fair 


Seed size 


Large * 


Moderately small 


Type of awns 


Smooth* 


Rough 


Strength of straw 


Poor 


Fair* 


Resistance to stem rust 
Resistance to scab and 
blight 


Susceptible 
Susceptible 


Resistant * 
Resistant * 


Resistance to loose smut . . 
Resistance to covered smut 
Resistance to stripe 


Susceptible 
Moderately resistant* 
Moderately resistant* 


Resistant * 
Resistant* 
Susceptible 


Resistance to spot blotch 


Moderately resistant* 


Moderately resistant* 



* Indicates desired character. 

Tests of reaction to blight were begun in F 3 or F in a special 
tent under conditions conducive to the development of a severe 
epidemic. Notes on reaction to blight are taken just before the 
heads ripen. These notes are then used in conjunction with 
notes on reaction to stem rust and smut, date of heading, height 
of plants, and lodging in conjunction with observation of general 
vigor and appearance of the plants in making individual-plant 
selections. Many of these strains are now in rod-row trials and 
appear promising. 

Other crosses are, of course, made also and carried along in a 
parallel manner. One of these involves Velvet X Chevron. 
Chevron is a sister selection of Peatland and has a similar reaction 
to the common barley diseases. If some of the best segregates 
are found to be a distinct improvement over the existing varieties, 
they will be released for distribution to the farmers. The best of 
these, from different crosses, may then be crossed in an effort to 
bring about further improvement. 

Tests of yielding ability begin with rod-row trials at University 
Farm only. The best of these are then tested in replicated yield 
trials in four stations in Minnesota. After a 3-year test in rod 
rows, the most promising strains are then tested in J-^Q -acre-plot 



HYBRIDIZATION AS A METHOD OF BREEDING 91 

trials in six places in Minnesota, usually for a period of 3 years, 
before a final conclusion regarding distribution to the growers is 
made. 

Studies of diastatic activity are made on the material in rod 
rows in cooperation with the Division of Agricultural Biochemistry 
at the University of Minnesota. When the new strains go into 
J<40-acre-plot trials, a complete malting test is made in the cooper- 
ative malting laboratory at the University of Wisconsin. 

BREEDING BY HYBRIDIZATION 

Examples have been given above and in previous chapters of a 
few problems that are being attacked or that have been solved 
through the crossing of different varieties and the combination of 
characters from them. The broad principles involved in a 
hybridization program, the selection of the parental material, 
and a general description of the method of handling the hybrid 
material will be discussed here. The detailed outline of the steps 
to be followed in successive generations following the cross will be 
given under Methods of Breeding. 

Object of Crossing. The object of crossing is to combine in a 
single variety the desirable characters of two or more lines, 
varieties, or species. Occasionally the recombination of genetic 
factors leads to the production of new and desirable characters 
riot found in either parent. In a planned program every effort 
should be made, however, to select parents that have the char- 
acters desired. Frequently transgressive segregation occurs for 
quantitative characters such as yield, height of plant, earliness, 
and resistance to lodging. Selection of parents that are already 
relatively satisfactory for these characters will enhance the 
probability of obtaining the desired end result. 

Selection of Parental Material. The procedure to be followed 
in selecting parental materkl for crosses will depend upon the 
extent to which the station conducting the breeding program has 
previously experimented with the crop in question. A station 
that has conducted extensive variety tests for any given crop will 
in all probability have sufficient data to inaugurate a breeding 
program without further study of the parental material. How- 
ever, a station beginning a breeding program with a crop of which 
it knows relatively little should conduct a thorough study of all 
present varieties (and of species in some cases) of that crop before 



92 



METHODS OF PLANT BREEDING 




FIG. 12. Uton oats was bred in Utah by Tingey, Woodward, and Stanton 
(1941). It combines the large, white kernel of its Swedish Select parent with 
resistance to smuts from its Marktoii parent. 

The upper photograph shows reaction to loose smut and the lower photograph 
to covered smut. The two bundles at the left of the photographs show the 
proportion of smutted and smut-free panicles of Swedish Select, the two at the 
right the smutted and smut-free panicles of Utou. 



HYBRIDIZATION AS A METHOD OF BREEDING 93 

beginning a breeding program. The importance of having a 
thorough knowledge of the parental material cannot be too 
strongly emphasized. 

Technique of Crossing. Crossing may be performed in either 
greenhouse or field. The greenhouse offers better protection 
from the elements and from stray pollen and often provides more 
satisfactory temperature and humidity. Crosses in the green- 
house can be made at almost any time of the year. 

It is advisable to make several dates of planting, particularly 
when the parents differ in time of flowering. The parents should 
be sown in short rows (or in pots), with the seeds individually 
spaced and with sufficient space between the rows so that the 
plants can be worked with easily. 

A study of the structure of the flower will reveal the best 
method of making the crosses. A study of the viability of the 
pollen and the time of receptivity of the stigma will be of material 
aid. An examination of the stigma and anthers sometimes will 
reveal which of the two parents should be used as the female. 
For example, it is known that it is more difficult to obtain crossed 
seed when barley varieties with unbranched stigmas are used 
as females than when varieties with branched stigmas are used as 
females. It is important also to prevent as much injury to the 
flowers as possible. If possible, use as the female the parent with 
a recessive character so that selfs can be discarded when the F\ is 
grown. The details of emasculation and pollination were dis- 
cussed in Chap. IV. 

Handling the Hybrid Material. Sufficient FI plants are neces- 
sary to give the amount of seed required for the F 2. If grown in 
the field, the Fi seeds should be individually space-planted far 
enough apart to give maximum seed production. In the green- 
house the Fi seeds are planted in pots or in the soil of the green- 
house bench. Some artificial light may be necessary in the winter 
time in the northern climate, and frequently a complete fertilizer 
is needed. 

If the pedigree method is used, the F 2 and succeeding genera- 
tions, until bulked, should be grown in spaced planted progeny 
rows with 25 to 50 seeds per row. In certain studies, replication 
is desirable. The parental checks should be sown every 10 to 30 
rows so that frequent comparisons can be made with them in 
selecting plants for further study. 



94 METHODS OF PLANT BREEDING 

Selections for disease resistance, height of plants, date heading, 
and any special characters such as head type, color of glumes, and 
type of awn (in the case of cereals) are made from plant rows in 
jP 3 and later generations. In selecting for leaf rust, the plants 
must be marked several weeks before harvest. Selection for 
stem-rust resistance can be made at harvest time. The general 
vigor and habit of growth of the lines is observed in making selec- 
tion and this observation used in conjunction with notes on 
specific characters. The individual plants harvested are threshed 
separately and the seed examined in the laboratory for type, size, 
shape, color, and plumpness. Seed of plants with inferior grain 
quality is discarded. 

Disease tests usually arc begun in the P\ by subjecting the 
plants to an epidemic and selecting only resistant plants. In F 3 
and later generations, the usual method is to plant separate 
nurseries in order to study reaction to the various diseases for 
which it is hoped to obtain resistant varieties. Resistant plants 
are then selected in these disease nurseries. In breeding for 
resistance to diseases in which the methods used in inducing the 
disease epidemic results in abnormal plant growth, the common 
practice is to grow special disease nurseries but to select plants or 
lines from a duplicate nursery grown under normal conditions, 
lines found to be susceptible in the disease nursery being 
discarded. 

Quality tests are made whenever possible. In some breeding 
programs these can be begun in F z . Usually these tests are made 
in later generations when a greater bulk of seed or plant material 
is available. This is true particularly when the cost of making 
the quality tests is great. The material is then purified, and all 
otherwise undesirable lines are discarded before being tested for 
quality. 

Special characters may be studied by growing the F* and subse- 
quent generations under environmental conditions that will bring 
out the differentiation desired. 

During the segregating generations, it is desirable to grow rows 
of the parents and of the best available standard variety at fre- 
quent intervals throughout the nursery. Only plants and prog- 
eny rows that appear equal to the standards in all respects should 
be selected. 



HYBRIDIZATION AS A METHOD OF BREEDING 95 

^ ' ^'Wiw . , , , , 

METHODS OF BREEDING 

Several methods of breeding self-pollinated crops through the 
use of hybridization have proved satisfactory for particular 
problems. These may be classified as: 

1. The pedigree method. 

2. The bulk method. 

3. The backcross method, 

4. Multiple crosses. 

In these and other problems of a similar nature, the larger the 
populations during the segregating generations the more chances 
there are of obtaining the combination of characters that are 
desired. The more complex the inheritance the greater the need 
for larger numbers. Although the exact combination of char- 
acters desired may not be recovered in F%, there is still the possi- 
bility of obtaining it in F& or later segregating generations. 
When two factors are closely linked, their recombination will be 
obtained infrequently in F% but secured more easily in jF 3 by 
growing the progeny of F% plants that contain one of the two 
desired characters. In most crosses it is a sensible plan to grow 
as large an F 2 population as can be sampled adequately 
in'F 8 . 

Pedigree Method. This method consists of (1) making a cross 
between two parents possessing the characters that it is desired to 
combine in a new variety, (2) growing the material in spaced 
plant rows so that individual plants may be studied, and (3) 
keeping a system of records so as to be able- to trace individuals 
from one generation to the next. A ! Numerous systems of keeping 
progeny records are available and will be chosen to suit the needs 
of the investigator. An outline of some of the methods was given 
in Chap. V. 

The number of seeds sown, length of row or size of plot, and 
number of generations grown before bulking the plants in progeny 
rows will vary considerably with the different crops. For cereal 
crops the following procedure will illustrate the steps involved. 

1. Grow sufficient F\ plants to produce the desired amount of 
seed for .PV Compare the Fi plants with the parent varieties, 
note dominance of characters, and discard selfs. Seed from the 
identical parent plants used in producing each Fi progeny may be 



96 METHODS OF PLANT BREEDING 

grown beside the F\ and, in critical studies, seed from these 
parent plants grown for comparison with F% and later generations. 

2. Grow 2000 to 10,000 individually spaced F 2 plants. In 
F 3 and subsequent generations, grow 1000 or more progeny rows 
each year from seed of individual plants selected the previous 
year. Select on the row basis first, and then select the best plants 
in these rows. Discard any lines found to be undesirable in 
disease nurseries. 

3. Bulk the seed of rows when homozygous. This usually is 
done in F to F Q . At Minnesota, with small grains, pedigree 
selection is continued until F b , when promising apparently homo- 
zygous lines are bulked for the yield trials. Some lines may be 
continued in F$ from selected F& plants before bulking. Lines not 
homozygous in F 6 are discarded unless very promising. Appar- 
ent homozygosity is determined by examination of the individual 
plants of a line, in the field, for observable agronomic or disease 
characters, and then the plants are harvested and threshed 
individually and the seed examined before bulking the seed for 
yield trials. 

4. Conduct yield trials, and release for distribution to the 
growers as described in Chap. V. 

Bulk Method. This method consists of growing the material 
in a bulk plot, usually from the jF 2 to about the FQ generations, 
inclusive, followed by head selection in F 6 . By the F 6 genera- 
tions, a high proportion of the plants will be homozygous for most 
observable characters. The bulk plots can be subjected to 
disease epidemics and special conditions as an aid in selection. 
Natural selection probably will eliminate some of the weaker 
types. The progenies of plants selected in F 6 are tested in the 
manner described for improvement by selection in Chap. V. 

Because of the ease with which crosses can be carried in bulk, a 
greater number can be grown in this way during the segregating 
generations than by the pedigree method. However, in the 
absence of selection through FQ a higher proportion of the popula- 
tion will be undesirable than with the pedigree method, in which 
case careful selection over a period of years would have eliminated 
more of the undesirable types. As a consequence, it would be 
necessary to select more plants in F$ for testing in plant rows than 
would be necessary to test in F& or F 6 with the pedigree 
method. 



HYBRIDIZATION AS A METHOD OF BREEDING 9< 

Harrington (1937) suggested a modification of the bulk method 
called the mass-pedigree method. This involves a combination of 
the two methods. The material is grown in bulk until a favorable 
season provides conditions for efficient selection. Then head 
selections are made and grown the following year in progeny rows 
as described for the pedigree method. The essential feature 
of this method is the growing of the crosses in bulk until a year 
favorable for efficient selection occurs, when single-plant selec- 
tions are made and the pedigree method used from that time 
onward. In order to make selections in bulk plots, selection 
would need to be made on the head rather than plant basis. 

Frequently a great deal can be learned regarding the genetics of 
the material during the segregating generations when the pedigree 
method is followed. Such is impossible with the bulk method. 

Backcross Method. This method is used primarily when it is 
desirable to transfer one or two simply inherited characters of the 
nonrecurrent parent to the recurrent parent, which is usually a 
highly improved variety of a desirable agronomic type. 

An outline is given of the steps to be followed: 

1. Grow the FI and backcross to the recurrent parent. 

2. Grow 50 to 200 individual backcrossed plants in spaced progeny rows. 

3. Select desirable individuals, i.e., those containing the characters to be 
selected from the nonrecurrent parent. 

4. Backcross these selected plants to the recurrent parent. Continue 
backcrossing and selecting from 2 to 6 generations. In some cases, it 
may be necessary to study the progenies of selected plants before making 
the next backcross. 

5. After backcrossing is finished, the material is handled in the same man- 
ner as outlined for the segregating generations by the pedigree method. 
There is, however, this difference. After several generations of back- 
crossing, many of the factors from the recurrent parent will be homo- 
zygous, and fewer generations need be grown in individual plant rows 
before bulking. Only a few years of yield tests will be required also, 
since most of the lines will be similar to the recurrent parent in all but 
the one or two of the characters added from the nonrecurrent parent. 

Multiple Crosses. Harlan and Martini (1940) have suggested 
the use of compound crosses. The method may be illustrated by 
assuming that eight varieties are to be combined. A series of 
bridging crosses is made as follows: a X 6, c X d, e X /, g X h. 
In a second mating, the FI plants will be crossed to produce the 
double crosses (a X b) X (c X d) and (e X /) X (g X h). In 



98 METHODS OF PLANT BREEDING 

the third mating the double crosses will be combined as follows: 
[(a X 6) X (c X d)] X [(e X /) X (g X h)]. As segregation will 
have taken place at the time the second cross is made, a greater 
number of crosses would need to be made than in the first mating. 
In the third cross, a very large number of seeds would be desired, 
since every seed contains essentially a different genotype and will 
result, presumably, in a new combination of characters. This 
procedure offers some promise of obtaining unusual combinations 
of factors, leading to the production of exceptional segregates. 
Its disadvantages would lie in the fact that several of the parent 
varieties probably would be undesirable for certain characters, 
and crosses between them would lead to the production of a 
higher proportion of plants with these undesirable traits. Large 
populations would need to be grown during the segregating 
generations following the compound crosses. These can be 
carried by either the pedigree or bulk method of breeding. 

COMBINING ABILITY 

Plant breeders observe very frequently that more desirable 
segregates are obtained from some crosses than from others. 
Some varieties are good parents, as judged by their ability to 
transmit high yield and quality to their progeny in crosses; others 
are less desirable. In the production of hybrid corn, the fact 
that some inbred lines transmit higher yielding ability to their 
Fi crosses than do others, when crossed with a series of inbreds, 
has been known for many years. The classification of varieties of 
self -pollinated crops as to whether they will transmit high yield in 
crosses has hardly begun. 

Harrington (1932) suggested that an analysis of the characters 
that could be studied in an F% population will provide a means of 
predicting the value of a cross. Harlan and Martini (1940) 
crossed 28 varieties of barley in all possible combinations of two 
each, making 378 crosses. These crosses were each carried in 
bulk plots, without selection, until the eighth generation and then 
space-planted. Plant selections were then made from each cross 
and tested in progeny rows the next year. Since each variety 
was crossed with each of the other 27, the potential value of each 
variety, in crosses, could be determined from the average yield 
of the selections made in crosses involving each parent in turn. 
The varieties Atlas, Club Mariot, Minia, Trebi, and Sandrel 



HYBRIDIZATION AS A METHOD OF BREEDING 



produced an unusually high percentage of superior selections. 
Crosses involving Glabron produced very few. Some varieties 
that had not been sufficiently promising in nursery tests to be 
grown in plots were found to be superior parents. 

Harrington (1940) and Immer (1941) studied the yield of bulk 
crosses in wheat and barley, respectively, in early generations as 
a means of determining the comparative breeding value of differ 
ent crosses. The study by Immer will be reviewed briefly. 

Six barley crosses were compared with one another in JPi, F%, 
F 3 , and jP 4 and with the parents. The yields of FI and parental 
checks were determined from rows of 11 plants per cross or 
variety, spaced 5 in. apart, and replicated six times. The tests 
in F%, FZ, and P\ were made in five replicated rod-row plots, the 
parents being included. The seed for F 3 and F* tests was a 
random sample from F 2 and F 3 , respectively. 

In Table 4 is given the average yield of each pair of parents for 
3 years, expressed in percentage of the mean yield of parents for 
all crosses. The yields in FI to Ft are expressed in percentage 
of the average mean yield of the parents in the six crosses for the 
year or years in which the test was made. 

TABLE 4. YIELD OF PARENT VARIETIES AND F\, F 2 , F s , F '4 CROSSES IN 
BARLEY, EXPRESSED IN PERCENTAGE OF THE AVERAGE YIELD 

OF THE PARTCNTS GROWN THE SAME YEAR AS THE CROSSES 



Cross 


1938 


1939-1940 


1940 


Average 
of 
parents 


Fi 


Parent varieties 


F 


F s 


F 4 


9 


cf 


Average 


Barbless X Chevron 
Barbloss X Minsturdi 


121 
118 
117 
87 
80 
76 


151 
186 
142 
116 
81 
89 


127 
127 
111 
127 
127 
111 


93 
74 
93 
109 
51 
51 


110 
101 
102 
118 
89 
81 


119 
125 
140 
137 
115 
111 


114 
114 
118 
124 
105 
101 
113 


120 
83 
111 
117 
100 
99 


Velvet X Chevron 


Barbless X Olli 


Barbless X C.L 2492 


Velvet X C.I. 2492 


Average 


100 


128 






100 


125 


105 



The crosses of Barbless X Olli and Velvet X Chevron pro- 
duced the highest yields in ^2 and*F 3 and were among the highest 
in F 4 , They were intermediate in yield in FI. The two crosses 



100 METHODS OF PLANT BREEDING 

involving C.I. 2492 were relatively low in yield in all four genera- 
tions tested. 

It appears that tests of bulk crosses in F% or F 3 may be used as a 
means of discarding entire crosses in the early segregating genera- 
tions, and the plant breeder then can make selections only from 
the crosses that promise the greatest proportion of high-yielding 
segregates. Testing in several different localities and for more 
than 1 year would be advisable. 

From the study by Immer, it appeared that the F\ could not be 
used to determine satisfactorily the potential value of a group of 
crosses. Since the amount of seed in FI is very much limited, 
space planting must be resorted to. It was found that some of 
the varieties and crosses responded in a differential manner when 
space-planted 5 in. apart as compared with seeding in rod rows 
at the regular rate for such trials. 

As information on the sources of good germ plasm in crop 
plants accumulates, as measured by combining ability in crosses, 
the outstanding parent varieties will be isolated and used more 
extensively in breeding programs. 

In using the pedigree or bulk methods of breeding, the first 
yield test is obtained usually in F 6 to F 8 . It would be highly 
desirable to know the yielding capacity of different strains 
from a cross and to discard the low-yielding ones before F G 
to FV Although no experimental data are available, it would 
appear that replicated yield trials in F^ from bulked seed of F 3 
lines that themselves were each the progeny of an individual F 2 
plant, should supply information on the relative yielding capacity 
of such strains. A space-planted nursery of the same strains 
could be grown the same year and single-plant selections made. 
In F 5 plant-progeny rows would be grown from the strains found 
to produce high yields in the yield trials. The plant-progeny 
rows could be bulked in ^5 or F$, if homozygous, for regular yield 
trials of pure material. By this procedure, a higher proportion 
of the strains in the regular yield trials would be expected to give 
satisfactory yields. 



CHAPTER VII 
THE BACKCROSS METHOD OF PLANT BREEDING 

Baekerossing, when possible, is the most satisfactory method to 
use in genetic studies to determine linkage relations. It is also 
useful as an aid in developing a factorial hypothesis. Harlan 
and Pope (1922) pointed out its probable value in small-grain 
breeding and stated that it has been " largely if not entirely 
neglected in any definite breeding programs to produce progeny 
of specific types/' They suggested the probability that there 
were many instances in which backcrossing would be of greater 
value than the more common method of selecting during the 
segregating generations after making suitable crosses. Before 
giving some of the results obtained, it seems desirable to discuss 
the principles involved. 

GENETIC EXPECTATIONS FROM BACKCROSSING 

As used in plant breeding, backcrossing seems to be a logical 
procedure when it is advantageous to add one or two characters, 
each of which is conditioned by one or two genetic factors, to an 
otherwise desirable variety. The general plan of study may be 
outlined as follows: 

1. Selection of parents for crossing. 

A variety, A, with desirable characters but lacking one or two characters 

that are dependent upon only a few genetic factors. 

A variety, /?, containing these one or two characters that A lacks. 

2. Backcrossing of the F\ of A X B to A; selection for the one or two 
desirable characters of B, if they are dominant, in each backcross gen- 
eration and again backcrossing of these selected plants to A, 
Repetition of the process as seems necessary. In this illustration, A 

and B are called the recurrent and nonrecurrent parent, respectively. 
Recessive characters of the nonrecurrent parent can be carried along 
by growing sufficient plants in each backcross generation and by making 
sufficient backcrosses to be sure some plants are heterozygous for the 
recessive factors that it is desired to add to the recurrent parent. 

3. Selection in the selfed progeny from plants carrying the factors obtained 
from B until homozygosis for the characters of the B parent is reached. 

101 



102 



METHODS OF PLANT BREEDING 



In self-pollinated plants, the new lines obtained may be compared with 
each other and with parent A in field trials and the strain of greatest 
promise increased and distributed as an improved variety if it per- 
forms satisfactorily. In cross-pollinated plants it seems necessary to 
produce several desirable lines arid recombine these to produce a 
synthetic variety or to use certain of these lines to produce F\ crosses 
for the utilization of hybrid vigor. With a crop like com, hybrid seed 
may be produced by this method. With asexually propagated crops, 
the more desirable crosses may be propagated by asexual methods. 

Richey (1927) has given the percentages of plants homozygous 
for the n factors entering the cross only from the recurring 
homozygous parent in each of r successive generations, calcu- 



in Table 5. 



2* \\ n 

^ J 



These percentages are given 



TABLE 5. PERCENTAGES OF PLANTS HOMOZYGOUS FOR THE n FACTORS 

ENTERING A CROSS ONLY FROM THE HOMOZYGOUS RECURRENT PARENT 

TO WHICH THE ("ROSS AND THE RESULTING PROGENIES ARE 

MATED IN EACH OF r SUCCESSIVE GENERATIONS* 



Number of 



Number of generations of back pollinating, r 



lautui pa-lie , 

n 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


It 


50 


75 


88 


94 


97 


98 


99 


100 


100- 


100- 


5 


3 


24 


51 


72 


85 


92 


96 


98 


99 


100- 


10 




6 


26 


52 


73 


85 


92 


96 


98 


99 


15 




1 


13 


38 


62 


79 


89 


94 


97 


99 


20 






7 


28 


53 


73 


85 


92 


96 


98 


30 






2 


14 


39 


62 


79 


89 


94 


97 


40 








8 


28 


53 


73 


86 


92 


96 


50 








4 


20 


46 


68 


82 


91 


95 


75 










9 


31 


56 


75 


86 


93 


100 










4 


21 


46 


68 


82 


91 



* Subject to eirors incident to the use of 6-place logarithms. 

t The values f or n = 1 give also the percentages of homozygous factor pairs in the entire 
population, regardless of the value of n. 

This formula is the same as that used for finding the percentage 
of homozygous individuals in different segregating generations 
after a cross. In the segregating generations after a cross, only 
one-half of the homozygous individuals are of the desired geno- 
type. For example, the F% generation of the cross between A A 
and aa will consist of 1AA + 2Aa + 100. One-half of the 



THE BACKCROSS METHOD OF PLANT BREEDING 103 

progeny are homozygous, but of these only one-half are of the A A 
genotype. If, instead of selfing the FI, Aa, it is backcrossed to 
AA, IAA to lAa will be obtained. In this case, one-half of the 
total progeny are of the desired genotype A A. 

Richey gave a summary also of the number of plants required 
in F and the first backcross generation to obtain a single indi- 
vidual with the required genotype when one to eight factor pairs 
were involved. These results, which are calculated on the basis 
of independent inheritance, are given in Table 6. 



TABLE 6. PROGENY REQUIRED TO HATE ONE DOMINANT HOMOZYGQUS 

INDIVIDUAL 





Number of factor pairs 


A/T "k ,-! 






1 


2 


3 


4 


5 


6 


7 


8 


FI, selfed 


4 


16 


64 


256 


1024 


4096 


16,384 


65,536 


FI, backcrossed to homo- 


















zygous dominant 


2 


4 


8 


16 


32 


64 


128 


256 



With a difference of five factor pairs in the parents, for example, 
the calculated expectation in F z is only 1 individual out of every 
1024, with all 5 factor pairs in a dominant homozygous condition, 
whereas for the first backcross generation the theoretical expecta- 
tion is 1 out of every 32 that contain all 5 factor pairs in a 
dominant homozygous condition. 

Linkage may be involved between a factor C for one of the 
desirable characters of the recurring parent A and the recessive 
condition of the dominant factor R carried in parent B that it is 
hoped to add to A. Suppose, in addition, that there may be 10 
other factor pairs involved in which the A parent carries the 
desired genotype. 

Parent A carries CC linked with rr and 10 other dominant fac- 
tors, and parent B carries cc linked with RR, the latter being the 
character desired to add to parent A. It may be supposed that C 
and r show 10 per cent recombination. Selection for R in the 
backcross generations will tend to make it difficult to obtain the 
desirable factor C, but as C is brought in from the recurring parent 
in each backcross the chances of a crossover and the desired 



104 METHODS OF PLANT BREEDING 

combination of CCRr seems better in backcrosses than by the 
pedigree plan. The reason for this is that the Rr genotypes are 
selected each year and the C factor brought in from the recurring 
parent. After a crossover takes place, then linkage of C and R 
will tend to make these combinations more frequent than under a 
system of independent inheritance of these 2 factor pairs. The 
10 remaining dominant factors will be recovered according to the 
usual theoretical expectation. 

The value of the backcross method may be better appreciated 
by giving a few illustrations. 

CANTALOUPES RESISTANT TO POWDERY MILDEW, 
ERYSIPHE CICHORACEARUM 

This disease, according to Jones (1932), cannot be controlled 
satisfactorily by spraying or dusting. A mixed lot of seed from 
India produced numerous plants practically free from disease, 
but the melons were of very low quality. These conditions gave 
an ideal setup for a backcross plan of breeding, for resistance 
appeared to be a simple dominant over susceptibility, and desir- 
able melons lacking resistance to powdery mildew were available. 

The method used consisted of crossing the resistance Hindu 
melon with commercial cantaloupes, selecting for resistance in the 
backcross generations, and recrossing these selected resistant 
plants to commercial cantaloupes. After cantaloupes of desired 
quality were obtained, selection was followed until strains were 
obtained that were homozygous for resistance. Seed from several 
strains was combined to give the necessary vigor of growth in the 
new variety. This material should be as uniform for other char- 
acters as the original variety. 

BREEDING BUNT-RESISTANT WHEATS 

Briggs (1930) described a project that was started in 1922 fo:- 
adding the bunt resistance of Martin to important commercial 
varieties of wheat grown in California, Martin being selected for 
one parent because it had proved completely resistant to bunt on 
the Pacific coast and because there appeared to be only one factor 
pair involved in this type of resistance. Subsequent discussions 
of the backcross method by Briggs (1935, 1938) emphasize the 
extensive use of the method by Briggs and coworkers. 



THE BACKCROSS METHOD OF PLANT BREEDING 105 

The plan outlined originally by Briggs is as follows: 

1922. Martin (resistant variety) X Baart (commercial, susceptible 
variety) 

1923. Fi X Baart 

1924. Plants segregated 1 resistant: 1 susceptible 

1 925. Plants segregated 3 resistant : 1 susceptible 

1926. Progeny of resistant plants segregated giving 1 homozygous: 
2 heterozygous rows 

Homozygous resistant plants were crossed with Baart 

1927. Fi X Baait 

It will be noted that the progeny of the first backcross segre- 
gated in a ratio of 1 resistant: 1 susceptible, showing resistance 
to be dominant. The progeny of the resistant plants of the back- 
cross segregated in a ratio of 3 resistant: 1 susceptible, and the 
progeny of these resistant plants gave 1 homozygous resistant 
line : 2 heterozygous, on the average. 

The resistant line was then used for the second backcross. The 
reason for studying the progeny of selfed lines after the first 
backcross, until homozygosis is again obtained, is to eliminate 
the possibility of selecting a plant for backcrossing that did not 
carry factors for resistance, since some plants escaped infection 
even though genotypically susceptible. 

The practical accomplishments of Briggs, 1 in California, demon- 
strate the value of the backcross method. In 1922, a program 
was started to incorporate the bunt resistance of Martin in all 
commercial wheats grown in California, including the varieties 
Baart and White Federation. In 1930, a program was initiated 
to add the stem-rust resistance obtained from Hope to Baart and 
White Federation in addition to bunt resistance. By crossing 
the bunt-resistant Baart and White Federation with rust-resist- 
ant strains of the two varieties, resistances to both diseases were 
combined. From these studies, 11 bunt-resistant varieties, two 
of these being resistant also to stem rust, have been produced. 
The first group of varieties obtained from the program have been 
grown extensively. The improved varieties are practically 
identical with the original varieties except for the character of 
bunt resistance. 

A program has been adopted by Briggs and his coworkers of 
compositing 70 or more backcross lines for each variety. These 

1 Unpublished information kindly furnished by Fred N. Briggs. 



106 METHODS OF PLANT BREEDING 

lines retain the name of their original commercial type, with the 
year of increase appended to designate them from their susceptible 
counterpart. It has been found that the mean yield of all lines 
is almost exactly the same as that of the original parent when 
bunt is not a factor in yielding ability. 




FIG. 13. -Top row: (A) Baart 38; (B) White Federation 38; (C) Big Club 37; 
CD) Poso 41; (#) Sonora 37; (F) Pacific Bluestem 37; (G) Ramona 41; (H) 
Bunyip 41; (/) Escoridido 41; (,/) Federation 41; and (K) Onas 41, all carrying 
the Martin factor for resistance to bunt. Tilletia tritici and the first two, Baart 38 
and White Federation 38, also have resistance to stem rust, Puccinia graminis 
tritici, from Hope. The corresponding heads in the bottom row are from the 
original susceptible parents. 

BREEDING RUST-RESISTANT SNAPDRAGONS 

Emsweller and Jones (1934) have described the development of 
varieties of the cultivated snapdragon resistant to rust, Puccinia 
antirrhini D. & IL, and emphasized the extent to which the 
disease has become of commercial importance. From the progeny 
of seed obtained originally from E. B. Mains, of Indiana, several 
plants were found that under favorable conditions for infection 
proved entirely free from rust. Resistance was found to be 
dominant in crosses and resistance and susceptibility to be con- 
ditioned by a single main factor pair, although minor modifying 
factors that influenced the extent of resistance were present also. 



THE BACKCROSS METHOD OF PLANT BREEDING 107 

These writers describe their experiments in which they used the 
backcross method to combine this resistance with the flower color 
and plant habit of standard commercial varieties and state that 
progress was very encouraging. 

STUDIES AT THE MINNESOTA STATION 

For several years, backcross studies have been carried on at 
Minnesota, where the problems involved appeared to be of such a 
nature that the backcross method seems the most logical plan of 
breeding. Several of these problems will be outlined briefly to 
give further illustrations of the principles involved. 

Disease Resistance in Wheat. In spring and winter wheat, 
desirable commercial varieties are available that are of good 
agronomic habit and of high milling and baking quality. These 
varieties lack one or two characters of outstanding importance, 
notably the high resistance of Hope and H44 wheats to stem and 
leaf rusts. Since resistance to both diseases is relatively simple 
in inheritance, the addition of these types of resistance to desir- 
able varieties available can be most logically and easily accom- 
plished by the backcross method of breeding. 

Its use may be illustrated by the improvement of Thatcher 
through crossing with Hope, primarily to add leaf -rust resistance 
from Hope and increase stem-rust resistance. Thatcher is the 
standard for yielding ability, desirable agronomic characters, 
and milling and baking value. It is not as stem-rust resistant as 
Hope and is very susceptible to leaf rust. The following informa- 
tion was furnished by E. R. Ausemus, of the Division of 
Cereal Crops and Diseases, IT. S. Department of Agriculture, who 
is stationed at University Farm, St. Paul, Minnesota, and who has 
charge of the wheat-breeding program. 

HISTOEY OF BACKCROSS (THATCHER X HOPE) X THATCHER 



Year 


Plan 


Place 


1930 


Original cross 


Field 


1930-1931 


First backcross 


Greenhouse 


1931 


Second backcross 


Field 


1932-1937 


Pedigree selection 


Field 



Leaf-rust epidemics were obtained only in 1932 and 1935. 
Stem-rust epidemics were obtained each year. 



108 



METHODS OF PLANT BREEDING 



Yield in bushels per acre, test weight, and leaf-rust reaction, 
from trials made in 1938, when there was a severe rust epidemic 
in the northwest spring- wheat area, are given in Table 7. 

TABLE 7. YIELD IN BUSHELS PER ACRE AND TEST WEIGHT IN REPLICATED 

ROD-ROW TRIALS AT UNIVERSITY FARM, 1938. LEAF-RUST REACTION 

IN ROD Rows (AGRONOMY) AND IN THE RUST NURSERY (R.N.) 











Rust, p 


>er cent 




Variety 


Yield, 
bu. 


Test 
weight 


Le 


af 


Ste 


m 








Agroii. 


R.N. 


Agron. 


R.N. 


Thatcher 


18 


47 


70 


80 


T 


3 


B.C., II-31-2 


31 


55 


2 


T 


T 


T 


B.C., II-31-6 


30 


54 


T 


5 


T 


T 


B.C., 11-31-14 


32 


54 


3 


T 


T 


T 

















Illustrations with Corn. The backcross method seems well 
adapted to use with cross-pollinated crops that are being bred by 
controlled pollination and selection. In one instance, two inbred 
lines of Crosby sweet corn have been selected that combine well 
together to give a vigorous F\ cross. In common with many 
strains of Crosby sweet corn, these lines have the undesirable 
characteristic of toughness of pericarp. Two linen of Golden 
Bantam have been selected that ex( el in flavor and tenderness of 
pericarp. One of these has been crossed with one of the strains 
of Crosby and the other Golden Bantam line with the second 
strain of Crosby. 

The FI generation is intermediate in tenderness and can be 
differentiated from the tough pericarp parent by puncture tests 
when the canning stage is reached. This can be accomplished by 
stripping back the husk at this stage and puncturing several 
kernels in the middle of the ear and recording the pressure 
required. The backcross method has been used in this problem. 

It is not known how many genes are concerned in tenderness of 
pericarp. Inbred lines are available that give considerable 
ranges in mean values when measured by the puncture test. The 
results in the following summary show that by selection it is 
possible to differentiate heterozygous ears, by means of puncture 
tests, from the homozygous tough parent. Data given in Table 8 
are summarized from the studies of Johnson and Hayes (1938). 



THE BACKCROSS METHOD OF PLANT BREEDING 109 



The major factor or factors for tenderness was retained in the 
heterozygous condition by selection in each of the succeeding 
generations of backcrossing. Plants of the first backcross genera- 
tion, (I X H)I, were pollinated by pollen from the I inbred 
parent, tested for puncture-test values, and those that were 
intermediate for tenderness were selected as parents for the next 
backcross generation. After three generations of backcrossing, 
selection in self-pollinated lines was used to isolate homozygous 
tender pericarp inbreds that resembled the recurrent tough peri- 
carp parent in most other characters, 

TABLE 8. FREQUENCY DISTRIBUTION OF PUNCTURE-TEST VALUES OP EARS 

FROM INDIVIDUAL PLANTS OF THE PROGENY OF BACKCROSSES TO THE 

TOUGH PERICARP PARENT WITH SELECTION FOR TENDERNESS 







Puncture-test values 


f^nltiir^ 


"V 








240 


260 


280 


300 


320 


340 


360 


380 


400 


420 


I 


1935 














11 


40 


37 


4 


I 


1936 














11 


46 


43 




I 


1937 












2 


16 


8 






H 


1936 


14 


28 


33 


6 


1 












H 


1937 


1 


19 


16 


10 


2 












(I X H)I 


1935 






4 


12 


23 


23 


15 


4 


1 




(I X H)I 2 


1936 






5 


14 


36 


40 


26 


13 


2 




(I X H)I 3 


1937 






2 


28 


43 


65 


40 


15 


6 





Recent studies of inheritance of smut reaction in corn show that 
the character is relatively complex from the genetic standpoint. 
Attempts have been made to gain some idea of the number of 
factors involved in crosses of resistant inbred lines with highly 
susceptible lines that have known interchanges for certain 
chromosomes. The interchange plants are semisterile, and the 
point of interchange may be handled in the same manner as a 
dominant factor. To determine what parts of the chromosome 
map are involved in relation to factors for resistance and suscepti- 
bility to smut, studies were made of smut reaction in relation to 
points of interchange. Studies, at Minnesota of crosses of sus- 
ceptible lines carrying interchanges with two different selfed lines 
resistant to smut, one from Minn. 13, and the other from 



110 METHODS OF PLANT BREEDING 

Rustler, were carried on. The FI plants were crossed to the 
resistant parents and in backcross and F% generations the X 2 test 
for independence was used to determine associations between 
smut reaction and points of interchange. In each series of 
crosses, at least three different chromosomal regions carried 
inherited factors for reaction to smut, and the regions from the 
Rustler crosses were entirely different than those for the Minn. 
13 crosses. Similar results have been reported by Burnham 
and Cartledge (1939). 

Various workers have found it relatively easy, however, to 
select inbred lines resistai^t to smut from crosses between resistant 
and susceptible inbreds and from selection in self -pollinated lines 
from commercial varieties. Resistance seems to be relative and 
probably functions under normal conditions against all physi- 
ologic races of smut. The inbred line B164 is used as a male 
parent in producing Minhybrid 301 and also in Pioneer 355, two 
three-way crosses adapted to southern Minnesota. As grown in 
Minnesota, B164 is highly susceptible to smut, and under normal 
conditions as high as 90 per cent of the plants may be infected. 
New lines, resembling B164, have been obtained from a cross 
between B164 and culture 37, a resistant line of Minn. 23. Two 
backcrosses to B164, followed by 3 years of self-pollination, 
isolated several inbred lines that had only 10 per cent of smut 
when grown adjacent to B164 that showed 85 to 90 per cent smut. 

Another illustration may be given with a corn problem now 
being investigated. Seed from one of the double crosses grown 
commercially in Minnesota, known as Minhybrid 401, is of mixed 
color, carrying both yellow and white kernels on the same ear- 
It was obtained by crossing the F\ cross of two inbred lines of 
yellow endosperm corn obtained from Minn. 13, lines 11 and 14, 
with two white endosperm inbr : ed lines of Rustler, 15 and 19. 

t It was desired to change the color of the white endosperm lines 
of Rustler from white to yellow without changing their combining 
ability. These Rustler lines carry the dominant whitecap factor 
We, which, in the presence of yellow endosperm, causes whitecap. 
The yellow lines lack this factor but contain a dominant factor 
for yellow endosperm color Y. The expected results for several 
backcrosses will be given on the basis of independent inheritance 
of Wcwc and Yy, 

Unrelated yellow endosperm lines were selected to cross with 
these white endosperm lines, the problem being to obtain yellow 



THE BACKCROSS METHOD OF PLANT BREEDING 111 

endosperm lines that in other characters resemble the white lines 
of Rustler used in the double crosses. During the backcrossing 
period, selected plants in each backcross generation were crossed 
with particular Rustler inbreds that were used as the recurrent 
parent. In each backcross generation, the gametes of the non- 
recurrent parent will be given, and the percentage of seeds 
heterozygous for We and Y will be given also. 

In each backcross generation, whitecap, yellow-endosperm 
kernels were selected. Some of these will be homozygous for 
whitecap and will be of no value. Others will be heterozygous 
for both the whitecap and yellow-endosperm factors. These are 
the combinations desired, and the proportions of such combina- 
tions are given for each backcross generation. 

1. Parent genotypes, WcWcyy and wcwcYY. 
Fi genotype WcwcYy* 

FI gametes WcY, wcY, Wcy, wcy. 

2. First backcross genotypes and phenotypes. 

a. 1 WcWcYy whitecap, yellow endosperm. 
1 WcwcYy whitecap, yellow endosperm. 
1 WcWcyy white endosperm. 

1 Wcwcyy white endosperm. 

b. Per cent heterozygous for F, 50. 
Per cent heterozygous for We, 50. 

Per cent heterozygous for We and F, 25. 

c. Select to backcross to the Rustler inbred line. 
Genotypes: WcWcYy, WcwcYy. 

Gametes: 3 WcY, 1 wcY, 3 Wcy, 1 wcy. 

3. Second backcross genotypes and phenotypes. 
a. 3 WcWcYy whitecap, yellow endosperm. 

1 WcwcYy whitecap, yellow endosperm. 

3 WcWcyy white endosperm. 

1 Wcwcyy white endosperm. 
6. Per cent heterozygous for F, 50. 

Per cent heterozygous for We, 25. 

Per cent heterozygous for F and We, 12.5. 
c. Select to backcross to the Rustler inbred line. 

Genotypes: 3 WcWcYyj 1 WcwcYy. 

Gametes: 7 WcF, 1 wcY, 7 Wcy, 1 wcy. 

4. Third backcross genotypes and phenotypes. 
a. 7 WcWcYy whitecap, yellow endosperm. 

1 WcwcYy whitecap, yellow endosperm. 
7 WcWcyy white endosperm. 
1 Wcwcyy white endosperm. 
6. Per cent heterozygous for F, 50. 
Per cent heterozygous for TFc, 12.5. 
Per cent heterozygous for F and TFc, 6.25. 



112 METHODS OF PLANT BREEDING 

In most problems of this kind, three backcrosses will probably 
be all that are necessary. At the end of this period, in the 
absence of linkage, seven-eighths of the genotype of the Rustler 
inbred line will be recovered, according to theory, and if the 
whitecap, yellow-endosperm seeds are selected, one out of every 
eight will be heterozygous for both We and F. When planted 
and self-pollinated, segregation will occur for both We and F. 
From selfed ears, yellow seeds that do not carry the dominant 
whitecap factor should be planted the following year, and of these 
one plant out of every three, on the average, when self-pollinated, 
will breed true for yellow color. In backcross studies with inbred 
lines of corn, it is generally agreed that after three backcrosses the 
progeny very closely resemble the recurrent parent in general 
habit of growth. 

From the breeding results with corn, some general conclusions 
may be emphasized. When it is desired to add certain definite 
characters to an otherwise desirable inbred, selection may be 
practiced for these characters during the generations of backcross- 
ing when the character is a dominant one. Backcrossing is 
followed by selection in self-pollinated lines. If the character is 
recessive, selection may be made after each backcross by self- 
pollination and selection for the homozygous recessive before 
making further backcrosses, or selection may be made for the 
recessive character obtained from the nonrecurrent parent during 
the segregating generations when selfing is practiced. 

In certain corn crosses, one of the selfed parents excelled in 
most easily observed characters, such as resistance to smut, good 
root system, and ability to withstand lodging and in general 
vigor. The other parent was less desirable in most easily 
observed characters. The FI crosses were vigorous and far 
superior to either of their inbred parents. It seemed relatively 
easy by backcrossing and selection to obtain inbred lines with 
marked improvement over the more undesirable parent but 
rather difficult to obtain lines better than the more desirable 
inbred from backcrosses to this inbred as the recurrent parent. 
A backcross program may be most advantageously pursued when 
definite characters may be selected for. The problem seems 
more difficult in selecting for such characters as vigor of growth 
that a^e dependent upon the interaction of many factors. 



CHAPTER VIII 
BREEDING FOR DISEASE AND INSECT RESISTANCE 

The principles underlying the breeding for resistance to disease 
or insect attacks are much the same as for other characters. 
There is, however, one important difference. In breeding for 
disease and insect resistance, one is dealing with two series of 
heritable factors: (1) the heritable characters of the host plant 
and (2) the heritable differences in the organism. 

In most cases, the plant breeder is interested primarily in the 
reaction of selected strains, varieties, and hybrids under condi- 
tions to which they will be exposed normally when grown for 
economic purposes. The breeding program should be carried on 
under conditions as similar to those to be encountered by the 
commercial varieties as is feasible. 

It is in breeding for resistance to diseases that the modern 
plant breeder has made some of his greatest contributions. The 
development of special methods for producing artificially induced 
epiphytotics and fundamental studies of the genetics of the host 
and parasite have laid the foundations for the planned breed- 
ing programs of the present. This fundamental information, 
although coming slowly in the beginning, has increased rapidly in 
recent years, leading to a scientific appreciation of the problems 
and, in many instances, to a sound basis for solution. 

THE IMPORTANCE OF DISEASE RESISTANCE 

The development and utilization of disease-resistant varieties 
is one of the important methods of disease control. When the 
required resistance can be obtained in combination with other 
necessary qualities, it seems fair to conclude that the growing of 
disease-resistant varieties is the most desirable method of con- 
trolling diseases. Much has been accomplished already, but 
there is an almost unlimited opportunity for further work. 
Seasonal variations in climatic factors are the major causes of 
seasonal variations in the yielding ability of crops, and to a 
considerable extent these variations cannot be controlled. The 

113 



114 METHODS OF PLANT BREEDING 

development of disease-resistant varieties will help to stabilize 
yields, since disease epidemics are among the more important 
causes of wide fluctuations in the yield of crops from season to 
season. 

With disease resistance, as with other characters, it is important 
to use as large numbers as possible in the breeding program, 
although the source of material is of greater importance. A good 
illustration of these two points is the present plan for breeding 
high-quality European grapes that are resistant to Phylloxera, 
the vine louse, and Peronospora, the vine mildew. According to 
Baur (1931) the cost of attempting to control these pests amounts 
to between 30 and 50 million marks annually. American varie- 
ties of grapes, Vitis rupestris, are resistant to both Phylloxera and 
Peronospora. The American grapes are of low quality, whereas 
the European varieties, V. vitifera, are of high quality but 
susceptible. Baur stated that crosses between these two species 
are fertile, and he had under way large-scale experiments to 
select, from the segregates of hybrids between the two species, 
varieties that excel in both quality and resistance. The tests for 
mildew resistance are made at the plant-breeding station at 
Miincheberg, and those for resistance to vine louse at the 
Institute for Phylloxera Research at Naumberg. In another 
publication (Baur 1933), the statement has been made that from 
5 to 7 million F% seedlings are grown yearly. They are tested for 
reaction to mildew, and only the seedlings resistant to mildew are 
saved and tested for yield and quality. Those that survive are 
then tested for resistance to the vine louse. 

Flax is grown as a cash crop in the United States in the spring- 
wheat region of the central northwest, largely for the oil content 
in the seed. "In earlier years, it was grown chiefly on new break- 
ing, i.e., prairie soil not previously under cultivation. Eventu- 
ally no new soil was available, and it became necessary to grow 
the crop on old land. Serious losses from wilt occurred, and it 
seems very probable that flax could not have continued to be a 
successful crop without the development of resistant varieties, 

In 1901, Bolley grew normal varieties on " wilt-sick soil" and 
isolated the organism Fusarium lini responsible for the disease. 
He observed (1901) the fact that some plants were not seriously 
injured even under epidemic conditions. These and other studies 
continued until the present time have emphasized the value of 



BREEDING FOR DISEASE AND INSECT RESISTANCE 115 

wilt resistance. Today no improved varieties of flax are intro- 
duced unless they have the necessary resistance to wilt. 

In more recent times, wilt-resistant varieties have been devel- 
oped for many plants. In 1915, cabbage growers in Wisconsin 
were 'so discouraged because of the ravages of cabbage yellows 
(F. conglutinans) that they were about to abandon cabbage grow- 
ing. Jones and Gilman (1915) observed a few plants in fields 
infected with the disease that apparently escaped the disease. 
These were selected and proved to be resistant by progeny trial. 
Today cabbage yellows is no longer serious. Wilt-resistant 
strains of all important varieties grown in Wisconsin have been 
developed. 

By similar methods, wilt-resistant varieties of tomatoes have 
been obtained. Edgerton (1918) and others, in Louisiana, have 
developed an improved technic for selection. Seed was planted 
in sterilized soil and then inoculated with a pure culture of the 
wilt-producing organism F. lycopersici. Those seedlings that 
were injured by wilt were pulled up and discarded and the resist- 
ant seedlings transplanted to a field that was known to contain 
infected soil. Lines breeding true for resistance were tested for 
other characters and distributed when satisfactory. 

Orton (1913) developed watermelons resistant to wilt, caused 
by F. niveum, by crossing an inedible, resistant citron with a good- 
quality, susceptible watermelon and selecting for resistance and 
quality. 

About 1920, farmers in western New York were greatly con- 
cerned over the bean-mosaic disease. Emerson and coworkers 
had learned that a variety known as M. A. C. Robust, devel- 
oped by selection in Michigan, was resistant to mosaic. They 
introduced the new variety, planting single rows in the center of 
the farmer's fields, and were greatly pleased with the great 
resistance that this variety exhibited. To quote from Emerson, 
"I have no hesitation in saying that resistance to this disease, 
mosaic, saved the pea-bean industry in Western New York." 

Some of the accomplishments during the last 25 years in the 
production of disease-resistant varieties of vegetables have been 
summarized by Rieman (1939). A study of lists of varieties of 
vegetables offered for sale by the seed trade was made in 1914. 
At that time, less than a dozen resistant varieties were listed by 
two of the leading American vegetable seed houses, and most 



116 METHODS OF PLANT BREEDING 

of these proved of doubtful value. In 1939, over 80 resistant 
varieties were listed, and 20 or more were recognized by the seed 
trade as leading varieties. These 80 disease-resistant varieties 
included 2 varieties of asparagus resistant to rust; 3 varieties of 
snap-bean resistant to mosaic and 2 resistant to bean rust; 10 
varieties of cabbage resistant to cabbage yellows; 1 variety of 
celery resistant to Fusarium wilt; 6 varieties of sweet corn resist- 
ant to Stewart's bacterial wilt and 2 resistant to the corn-ear 
worm; 9 varieties of lettuce resistant to brown blight, 3 resistant 
to downy mildew, and 2 resistant to tip burn; 2 varieties of 
cantaloupe resistant to powdery mildew; 29 varieties of peas 
resistant to Fusarium wilt; 2 varieties of spinach resistant to 
mosaic; and 7 varieties of tomatoes resistant to Fusarium wilt. 

Rieman stated that the method of control through breeding 
disease-resistant varieties involved four important steps: (1) 
the recognition of disease symptoms and the identification of the 
causal organism, (2) the isolation of fertile, resistant breeding 
stocks, (3) the development of true-breeding disease-resistant 
varieties through crossing and selection, and (4) the production 
and distribution of pure high-quality seeds of the resistant varie- 
ties in commercial quantities. 

METHODS OF BREEDING FOR DISEASE AND INSECT RESISTANCE 

The methods of breeding will be discussed under several head- 
ings, namely: (1) the search for resistant materials, (2) the artifi- 
cial production of the disease epidemic, (3) the plan of breeding, 
and (4) a study of fundamental problems that aid in a logical 
attack on the breeding problem. 

THE SEAECH FOR RESISTANT MATERIAL 

The search for resistant varieties or strains is a logical first step. 
It is highly desirable, in beginning an attack on a disease problem, 
to make a collection of local and foreign varieties and to test their 
reaction under epidemic conditions. If reaction to the disease 
has been studied by investigators in other states or other coun- 
tries, varieties found by them to be resistant would, of course, 
be tested first to determine their reaction under the environ- 
mental conditions of the new investigation. 

The methods of breeding varieties with the necessary resistance 
do not differ from those used for other characters. In some 



BREEDING FOR DISEASE AND INSECT RESISTANCE 117 

cases, hybrids between susceptible varieties may give resistant 
plants in the segregating generations. If disease resistance is an 
important problem, at least one of the parents of a hybrid should 
have the desired resistance whenever such resistant varieties 
are available. 

With disease resistance, as with other characters, it is extremely 
important to learn as much as possible regarding the genetic 
factors responsible for resistance. It must be appreciated that 
the organism causing the disease frequently comprises several (or 
many) strains or physiologic races, which in some cases can be 
differentiated only by their manner of reaction to a series of 
varieties known as differential hosts. Almost 200 such phys- 
iologic races have been found in Puccinia graminis tritici. 

For stem rust of oats (P. graminis avenae), there is a complete 
correlation between the manner of reaction of seedlings and the 
reaction of the mature plants to the same physiologic races (Smith 
1934). In barley, Brookins (1940) found the reaction of mature 
plants to a large collection of physiologic races in the field to be 
controlled by the same genetic factor pair controlling reaction to 
races 19, 36, and 56 in the seedling stage. Resistance to stem 
rust in wheat may be placed in two main classes: (1) physiological, 
where the reaction to a specific race of the pathogen is relatively 
the same throughout the life of the plant, and (2) mature-plant 
resistance, in which case the genes concerned produce resistant 
mature plants independently of their reaction in the seedling 
stage. 

It is necessary in most cases to make a survey of the physio- 
logic races normally prevalent in the locality and to breed for 
resistance to all prevalent forms. This is essential in dealing 
with physiological resistance, since a variety may be very resist- 
ant to one physiologic race and highly susceptible to another. 
With mature-plant resistance to stem rust of wheat and smut in 
corn, varieties tend to react in the same manner to all physio- 
logic races of the pathogen. In studies of disease resistance, it is 
very helpful to have the definite cooperation of the plant pathol- 
ogist, who will lead in the studies of the organism and in 
methods of creating artificial epidemics. After -these problems 
have been solved, the breeding of disease-resistant varieties 
is not greatly different from that of breeding for any other 
character. 



118 METHODS OF PLANT BREEDING 

ARTIFICIAL PRODUCTION OF EPIPHYTOTICS 

It is not within the scope of this book to describe methods of 
inducing disease or insect epidemics for all crops in which breed- 
ing for resistance is being undertaken. A brief description will 
be given for some of the major diseases of the common field crops 
grown in the northern United States and Canada. These will be 
described for the crop and disease, or insect pest, involved. 

Black-stem rust of wheat, oats, and barley (Puccinia graminis). 

1. Field. 

a. Plant susceptible varieties as borders around the outside of the plot 
and through the alleys. 

b. Obtain as many physiologic races as possible that have been found 
in the region . Increase these races on seedlings of susceptible varieties 
in the greenhouse, arid use a mixture of races for inoculations in the 
field. 

c. Transfer rusted plants from the greenhouse to the border rows in the 
field. 

d. Hypodermically inoculate the border rows with a mixture of uredo- 
spores of all the races increased in the greenhouse. A mixture of 
about 30 races has been used at Minnesota in recent years. 

e. Spray the plants with an aqueous spore suspension late in the evening, 
when there is probability of dew, or just before or after a rain. 

/. Keep the soil moist in a dry season to delay premature ripening and 
prolong the length of the susceptible period. 

2. Greenhouse. 

When there is correlation between seedling reaction in the greenhouse and 
reaction in the field from heading to maturity, it is of advantage to study 
the progeny of selected plants in the greenhouse as an aid in discarding 
susceptible material, 
a. Grow from 15 to 20 seedlings from selected plants in small pots until 

first leaves are well developed. 
6. Spray seedlings with water, and inoculate by brushing with leaves of 

infected seedlings, or apply the spores with a scalpel. 

c. Place the pots in an incubation chamber under high humidity for 
48 hr. The chamber may have a glass top to admit light. 

d. Transfer pots to greenhouse bench, and observe the reaction when 
rust has developed to the point where maximum differentiation is 
obtained. 

Leaf rust of wheat (Puccinia triticina] and crown rust of oats (P. coronata). 

1. Increase rust of the races to be used on seedlings in the greenhouse. 

2. Plant susceptible varieties as border rows around and through the field- 
rust nursery. 



BREEDING FOR DISEASE AND INSECT RESISTANCE 119 

3. Spray the plots with an aqueous suspension of all races usually prevalent 
' in the locality. The plants should be inoculated on a still night, when 

the humidity is high. Seedlings may be inoculated in the field when 
about 8 in. high. 

4. Irrigate, if necessary, to maintain susceptibility over a period of time. 

5. Tag resistant plants, if the lines are segregating. Final selections are 
made at harvest time from these resistant plants. 




__ 

FIG. 14. Hypodermic inoculation of border rows of susceptible plants with 
a spore suspension of a collection of races of stem rust. 

Bunt of wheat (Tilletia tritici). 

1. Obtain as many collections of smut as possible from a wide area in 
order to obtain a large number of races. Do not use collections of smut 
from too wide an area or from foreign countries, for there is danger in 
introducing more virulent forms of the pathogen. 

2. Dust the seed of varieties or hybrids to be tested with a mixture of spores 
from all the collections, using about 1 g. of smut per 100 cc. of grain. 

3. Plant the seed as early as possible, if spring wheat, or when the soil is 
sufficiently cool and relatively dry. The optimum temperature for 
infection is approximately 12G, 



120 METHODS OF PLANT BREEDING 

Loose smut of oats (Ustilago avenae), covered smut of oats (U. levis), covered 
smut of barley (U. hordei), and intermediate smut of barley (U. medians). 

1. Obtain as many collections as possible in the area in which the variety 
may be grown ultimately. 

2. Make an aqueous suspension of the spores at the rate of J/ g. of spores 
to 100 cc. of water. 

3. Submerge seed in about one and one-half to two times its volume of the 
spore suspension. 

4. Subject to sufficiently high vacuum to withdraw air from under the 
hulls. Two evacuations in succession are preferable. 

5. Pour off the suspension., and dry the seed. 

6. The seed may be stored for several weeks before planting without greatly 
affecting the efficiency of inoculation. 

7. Plant when temperature is moderately high and the soil relatively dry. 

Flax rust (Melampsora lini). 

1. Increase the rust in the greenhouse. 

2. Plant border rows of susceptible varieties around and through the field 
nursery. 

3. Spray a water suspension of spores on border rows of susceptible varieties. 
When rust appears, make spore suspensions, arid spray the rust over the 
entire nursery, or brush the plots with infected plants from the border 
rows. 

4. Save bundles of rusted flax plants in the fall, and scatter the straw on the 
plots in the spring, when the plants are coming up. 

5. Grow the flax in a place where the temperature is relatively low and 
humidity is high, since these conditions are conducive to the develop- 
ment of an epidemic. 

Flax wilt (Fusarium lini). 

1 . In the greenhouse. 

a. Plant susceptible varieties to be tested in sterile soil inoculated 
with the cultures of the causal organism. 

2. In the field. 

a. Collect soil from fields where flax wilt has been prevalent, and mix 
this with the soil in the test plot. 

b. Grow a mixture of races of the causal organism on sterile grain, 
nutrient agar, or in liquid media, and inoculate the soil. 

c. Plant the varieties and strains of flax to be tested in this "wilt 
nursery." 

d. Use the same plot every yealr. 

Fusarial head blight (scab) of wheat and barley. 

1. Increase the different organisms on sterile oats or wheat in jars or 
flasks in the laboratory. 

2. At time of heading, cover the field-test plot with a cloth tent. 



BREEDING FOR DISEASE AND INSECT RESISTANCE 121 

3. After heading, spray the plants every day or two with a spore suspension 
made from the different organisms. Continue the spraying until the 
grain is in the soft-dough stage, or until a satisfactory epidemic has 
been produced. 

4. Spray the plants, soil, and tent with water to maintain high humidity in 
the tent. 




FIG. 15. Flax wilt nursery showing resistant and susceptible strains, the latter 

entirely killed by wilt. 

Corn smut (Ustilago zeae). 

1. Make as many collections of smut as possible in the region in which the 
corn may be grown, 

2. Mix the collections of chlamydospores with manure, and spread between 
the rows when the corn is 6 to 12 in. high. 

3. Dust chlamydospores on the plants, or spray with a spore suspension, 
three or four times during the growing period of the com. 

4. Use the same field as a "smut nursery' 7 every year. 

Loose smut of sorghum (Sphacelotheca cruenta) and covered smut of sorghum 
(S. sorghi). 

1. Make collections the previous year from as many sources as possible, 

2. Dust the spores on the seed before planting. 



122 METHODS OF PLANT BREEDING 

3. Plant the seed when fairly high temperatures are assured. The optimum 
temperature for infection is about 27C., and very little infection will 
result below 15C. 

Head smut of sorghum and corn (Sorosporium reilianum). 

1. Make as many collections of the organism as possible. 

2. Mix chlamydospores with soil, and spread this over the field-test plot, or 
apply with seed at planting time. 

3. Plant in relatively dry soil. 

4. Use the same plot every year. 

Hessian- fly injury of wheat. 

1. Plant replicated Hessian-fly nurseries in short rows, with check rows of 
varieties of known reaction at regular intervals. 

2. Import infested stubble from the localities in which the wheat is to be 
grown ultimately. "Flaxsecd," secured by dissecting plants from pre- 
ceding tests, may be used also. Place these between the rows, and 
sprinkle with water. 

3. Several biologic or physiologic races of the fly are known. The races 
produce a different reaction on different varieties of wheat. 

4. In the greenhouse, grow the plants in pots, and transfer to an enclosure 
in the insectary after the plants are well tillered. Allow adult flies to 
lay eggs, and after emergence of larvae, return the pots to the regular 
greenhouse. After the fly has reached the "flaxseed" stage, the plants 
are dissected and the infestation recorded. 

METHODS OF BREEDING 

It is desirable that the early generations of selections and the 
segregating generations from crosses be grown under controlled 
epidemic conditions, so that the resistant strains can be selected 
and the others eliminated. It is generally considered that a 
mixture of races, or collections, of the pathogen, from the general 
region in which the improved crop will be grown, should be used 
in producing the epidemic. There is, however, some danger in 
carrying inoculum from one locality to another, since a virulent 
form of the disease may be introduced. For this reason, the 
more promising of the selections may be grown in several locali- 
ties and exposed to an epidemic in each locality, created by using 
disease organisms collected in that locality. 

The fact that plant pathogens are composed of physiologic 
races that can be differentiated only by their manner of reaction 
on a series of varieties known as differential hosts is appreciated 
today by students of plant breeding. A knowledge of the number 
and nature of these physiologic races is important, Two 



BREEDING FOR DISEASE AND INSECT RESISTANCE 123 



general methods may be followed. These are not necessarily in 
opposition to each other but may go hand in hand. One consists 
of a study and isolation of as many physiologic races of the 
organism as are available and a determination of the reaction of 
parents and hybrids to individual races. The other method 
consists of using a collection of races in producing the epidemic 
and selecting only those strains that are resistant to all races. 

Knowing the reaction of parental varieties to special races 
makes possible a definite breeding program ir_ relation to these 
races. Thus, with the physiologic races of stem rust of wheat, 
Puccinia graminis tritici, to which Kanred is immune both in the 
seedling and in the mature-plant stage, immunity from a rather 
large group of races is dependent upon a single genetic factor. 
Breeding for resistance to a single one of these races gives an 
accurate idea of the reaction to all races from which Kanred is 
immune. 

An illustration may be given from the studies of Smith (1934) 
with respect to stem rust of oats. 

TABLE 9. REACTION OF VARIETIES OF OATS TO NINE RACES OF STEM RUST 



Variety 


Reaction to races 


1 


2 


3 


4 


5 


6 


7 


V 8 


White Russian 


R* 
R 
R 

S 


R 
R 

S 

S 


st 

R 
R 

S 


S 
S 
R 

S 


72 
R 

S 
S 


S 
S 
S 
S 


S 
R 

S 
S 


R 

S 
S 

S 


Rainbow 


Joanette ... 


Victory ... 





* R resistant, 
t S susceptible. 

Races 1, 2, and 5 are the most common in the central northwest 
section of the United States. It seems probable that reaction to 
races 1, 2, 3, 5, and 7 may be dependent upon an allelic series of 
three factors, one governing resistance to all five races, another 
resistance to races 1, 2, and 5 and susceptibility to 3 and 7, and 
still another susceptibility to all five races. Rainbow, a selection 
from dreen Russian, made at the North Dakota Agricultural 
Experiment Station, is resistant to all five races; White Russian is 
resistant to 1, 2, and 5 but susceptible to 3 and 7. The resistance 
of Rainbow is somewhat greater to races 1, 2, and 5 than that of 



124 METHODS OF PLANT BREEDING 

White Russian, and as it is resistant also to races 3 and 7, its type 
of resistance is more desirable than that of White Russian. 

It is advantageous in some cases to duplicate the nursery, 
making two planting dates. The material that gives the most 
satisfactory disease epidemic may be used for selection and the 
material from the other planting date discarded. 

Breeding for disease resistance can be carried on most advan- 
tageously by carrying on the studies of disease reaction as a part 
of the main breeding project, selecting for disease reaction, for 
quality, and for agronomic characters at the same time, although 
in some cases in special nurseries. In this way, if selection must 
be made for several characters, progenies that excel in all these 
characters may be used as a basis of selection. 

STUDY OF FUNDAMENTAL PROBLEMS 

The importance of a knowledge of the pathogen and the 
environmental conditions favorable for the development of the 
disease will be appreciated by students with training in plant 
pathology. From extensive studies with many organisms, more 
especially species of rusts, smuts, powdery mildews, pasmo, 
Fusarium root rots, Helminthosporiurrij Colletotrichurrij and others, 
it has been learned that many and perhaps most of the organisms 
causing diseases are composed of numerous physiologic races 
that can be differentiated only by the manner of their reaction on 
a series of varieties known as differential hosts. 

The identification of physiologic races of pathogens responsi- 
ble for particular diseases has made possible a more definite 
attack on fundamental problems, such as the effect of environ- 
mental conditions in causing marked changes in disease reaction, 
the ability of different races to develop to epidemic proportions 
as affected by environment, the screening effect of varieties as a 
means of modifying the proportion of particular races present 
during any particular season, and other similar problems. These 
questions belong logically in the subject-matter field of plant 
pathology and cannot be handled adequately here. An illustra- 
tion of the manner of identification of physiologic races based on 
host reaction will be given for loose smut of oats, Ustilago levis, 
after Reed (1940). Differential species and varieties used 
include A vena brevis; A. strigosa; A. sativa, varieties Black Dia- 
mond, Black Mesdag, Black Norway, Danish Island, and 



BREEDING FOR DISEASE AND INSECT RESISTANCE 125 

Monarch; ^4. saliva orientales, variety Green Mountain; A. nuda, 
variety Hull-less; A. byzantina, variety Fulghum. The manner 
of differentiation is given in Table 10, taken from Reed. 

TABLE 10. DIFFERENTIATION OF SPECIALIZED RACES OF Ustilago levis 

(K. & S.) Magn. 

a. Monarch susceptible Race 

b. Black Mesdag susceptible 
c. Fulghum susceptible 

d. Black Norway susceptible 6 

d. Black Norway resistant 

e. Black Diamond susceptible 7 

e. Black Diamond resistant 8 

c. Fulghum resistant 9 

b. Black Mesdag resistant 
c. Black Norway susceptible 

d. Green Mountain susceptible 13 

d. Green Mountain resistant 14 

c. Black Norway resistant 

d. Green Mountain susceptible 
e. Danish Island susceptible 

/. Hull-less suscept^ble 11 

/. Hull-less resistant 12 

e. Danish Island resistant 

/. Avena strigosa susceptible 1 

/. Avena strigosa resistant. . . . , 10 

d. Green Mountain resistant 

e. Black Diamond susceptible 4 

e. Black Diamond resistant 3 

a. Monarch resistant 

b. Avena brevis susceptible 2 

b. Avena brevis resistant 

c. Hull-less susceptible 5 

A summary of the status of physiologic races has been made 
by Reed (1935) and Stakman et al (1935). Studies of physi- 
ologic races and the use of races common to the region where the 
improved resistant varieties, when obtained, will be grown, will 
aid the breeder in producing varieties with the necessary resist- 
ance to races common in the locality. A knowledge of stability 
of pathogenicity and the basis of new races in terms of mutation 
or hybridization is essential. 

The genetics of plant pathogens has been reviewed recently by 
Stakman et al. (1940). A few examples will be cited to illustrate 
principles involved. 



126 METHODS OF PLANT BREEDING 

Selfing of individual physiologic races of black-stem rust on 
the barberry often leads to the isolation of several to many differ- 
ent races. Hybridization between races within the same species 
or between different species of rusts may lead to the production 
of new races. When two races of stem rust, homozygous for 
pathogenicity, are crossed, the Fi resembles one or the other 
parent, and there appears to be Mendelian dominance. If 
heterozygous races are crossed, new races with greater virulence 
than either parent may be obtained. 

A knowledge of the nature and frequency of mutation for 
pathogenicity is fundamental, especially the probability of a 
change from a mild form of the disease to a more virulent form. 
From studies made so far, it would appear that mutations that 
lead to an increase in virulence are relatively infrequent. 

A knowledge of the genetics of the pathogen is very important 
in planning breeding studies in which the breeding for disease 
resistance is one of the major objectives. Close cooperation 
between plant breeders and plant pathologists would appear to be 
essential if maximum progress were to be made. 

A knowledge of the nature and causes of disease resistance in 
terms of physiology, morphology, or functional behavior are basic 
to a real understanding of the problem. 

Walker (1935) discusses the nature of resistance to cabbage 
yellows and describes two categories of inherited resistance that 
have been obtained. In Type A, resistance is dominant to 
susceptibility and controlled by a single dominant gene. All 
collections of the parasite react in the same manner to plants of 
Type A, and the behavior is constant over a wide range of 
temperatures. There is a second type of resistance, known as 
Type B, which is complex in inheritance, and the reaction varies 
with the temperature, all plants being susceptible at a soil 
temperature of from 22 to 24C. Thus, plants of the Type A 
resistant group may be selected by raising the soil temperatures 
to 24C. While the physiological or morphological differences 
that differentiate the two types of resistance are unknown, the 
information regarding genetic differences makes it possible to 
breed for the required resistance. 

From the plant-breeding standpoint, there are two major types 
of resistance to stem rust. Stakman (1914) showed that resist- 
ance to certain physiologic races of Puccinia graminis tritici is 



BREEDING FOR DISEASE AND INSECT RESISTANCE 127 

due to physiological incompatability between the host plant and 
the fungus. The germ tube of the fungus may enter resistant 
varieties, but the fungus is unable to establish itself to the extent 
that it can cause severe injury. Physiological or protoplasmic 
resistance functions throughout the life of the plant. This 
appears to be the type of resistance to stem rust found in oats 
(Smith 1934) and barley (Brookins 1940). 

The second general type of resistance to stem rust in wheat is 
called mature-plant resistance. Some varieties are susceptible to 
one or more races in the seedling stage yet resistant to these and 
other races in the stage from heading to maturity. The exact 
nature of mature-plant resistance is not known. Whatever its 
nature, the mode of inheritance of this type of resistance appears 
to be relatively simple in crosses differentiated by this type of 
resistance and involving crosses with Hope or H44. It appears 
to function against all physiologic races found in the spring- 
wheat region of the United States and Canada. 

A knowledge of the mode of inheritance of reaction to disease 
helps in planning the breeding prograwn. The genetics of reaction 
to disease frequently can be studied during the segregating gen- 
erations of hybrids made during the course of the regular breeding 
program at little additional cost. Such information, analyzed 
and reported, will leave an ever-increasing store of information 
that will be available as a guide to future investigations. 

The extent of correlation between reaction to disease and other 
important character differences should be determined. A 
knowledge of genetic linkage may serve as a guide in planning 
breeding programs or in fundamental inheritance studies. 

Cooperation between breeders in different states and countries 
will be of benefit to all. New facts will become known earlier, 
and free exchange of material and ideas will speed up the solution 
of all breeding problems. Jealousies leading to the withholding 
of information from others working on similar problems will 
impede such progress. The testing of material in many places 
leads to a more rapid determination of its real value. 

Painter et aL (1940) described extensive experiments in Kansas 
in breeding wheat resistant to Hessian fly [Phytophaga destructor 
(Say)]. From crosses of Marquillo, a Hessian-fly resistant spring 
wheat, with desirable varieties of winter wheat susceptible to 
Hessian-fly attacks, these workers have nroduced strains of winter 



128 METHODS OF PLANT BREEDING 

wheat that combined resistance to Hessian fly and tolerance to 
wheat joint worm, with resistance to leaf rust, stem rust, bunt, 
and mildew. The fly resistance of Marquillo is probably derived 
from its lumillo durum parent. In crosses, the resistance of 
Marquillo tends to be recessive and due to more than a single 
genetic lac tor. Resistance appears to be due to the interaction 
of three separate heritable mechanisms: low larval survival, 
ability to withstand infestation, and, under some conditions, low 
oviposition. The best explanation of the differences in varietal 
behavior in different regions lies in the presence of biological 
strains of the fly, which differ in their ability to infest different 
varieties of wheat. 



CHAPTER IX 
INHERITANCE IN WHEAT 

The relationship of Triticum and related genera was given in 
Chap. II by means of genom analysis. In vulgare wheats, for 
example, there are three genoms, called A, B, and C, each con- 
taining a set of seven chromosomes. Thus, for many characters, 
there may be three pairs of factors for the dominant and recessive 
condition. If, as some believe, the basic chromosome number 
of the Gramineae is five instead of seven, a greater number of 
duplicate factors than three could be accounted for, depending 
upon the means by which the basic number five was changed to 
seven. Instances of three duplicate factors are common in 
members of the Spelta group, including Triticum vulgare, T. 
compactum, and T. spelta, and two duplicate factors have been 
found in members of the Eminer group, including T. dicoccunij T. 
durum, T. turgidum, and T. polonicum. It is well to recall the 
fact that T. monococcum carries genom A; T. dicoccum, T. 
durum, T. turgidum, and T. polonicum, genoms A and 5; and 
T. vulgare, T. spelta, and jP. compactum, genoms A, B, and C. 

Studies of glume shape help to illustrate types of inheritance 
that may be expected in amphidiploids. 

Glume Shape. Extensive studies of glume shape and keel 
development have been made by Watkins (1940), who has sum- 
marized the present status of the problem. Wheat species may 
be described as follows: 

Hexaploids. 

vulgare round, loose glumes and tough rachis. 
speltoid keeled, thick glumes and tough rachis. 
speUa keeled, very thick glumes and brittle rachis. 



Tetraploids. 
urum 



looge gimneg and.tough rachis. 

* 



dicoccum keeled, thick glumes and brittle rachis. 

129 



130 METHODS OF PLANT BREEDING 

Watkins concludes that the tetraploids contain two sets of 
factors, perhaps representing completely linked groups of genes 
with the genetic formulas 

dicoccum K d K d K d K d 
turgidum KK KK 

He also suggests the formulas for the hexaploids to be 

vulgare kk KK K d K d 
speltoid KK KK K d K d 
spelta KK* KK K d K d 

In crosses between turgidum and dicoccum, the FI has the 
formula K d K K d K and is somewhat intermediate, resembling 
dicoccum more closely than turgidum, with rather thick glumes 
and intermediate brittle rachis. In the FI meiosis, autosyndesis 
probably occurs as first suggested by Darlington (1927) to explain 
the reason for a lack of complete recovery in the segregating gen- 
erations of parental glume lengths in crosses between poloni- 
cum X durum f called shift by Engledow (1920). In the cross 
of turgidum X dicoccum, the FI gametes presumably are all 
K d K because of pairing in FI in the form of K d K d KK, leading to a 
true breeding form in F% that resembles the FI. 

In crosses of vulgare with dicoccum and turgidum f respec- 
tively, it was concluded that K d remained unpaired when crossed 
to turgidum and K, when crossed to dicoccum^ which is in agree- 
ment with the lack of pairing of K and K d in the turgidum X 
dicoccum cross. 

With this hypothesis, /b, K, K d , and K 8 are allelic groups of 
completely linked genes, and K d and K are similar or identical 
in effect. The glume, keel, and rachis characters that differenti- 
ate the five wheat species are caused by variations in a single 
chromosome complement, present four times in tetraploids and 
six in hexaploids. 

Watkins presents evidence also of a linkage between the factor 
pair for bearded vs. tip awns,/ called Bibi, and for glume condi- 
tion, K d k or. Kk f with a recombination value of approximately 
41 per cent. 

Awnedness. There are three major groups of wheats: awnless, 
awnleted, and bearded. The awnleted groups produce short 
awns, these being longer and more numerous, usually near the 



INHERITANCE IN WHEAT 131 

tip of the spike in one group of wheats, and more evenly dis- 
tributed in another group. Probably as a result of minor modi- 
fying factors or allelic series, there are intermediate classes also 
that in some cases breed true. Homozygous awnleted varieties 
may differ in the extent of development of awns, and definite 
classification of the genotype of homozygous material is difficult 
without a breeding test. 

Watkins and Ellerton (1940) have postulated the following 
factors for different types of awns in hexaploid wheats: 

BI, the gene for tipped 1 belonging to the allelic series BI, 61, and bi a . 

A few awn tips up to 1 to 2 cm. in length are produced, the longest 

tips being found near the top of the spike. 
61, recessive gene for bearded. 
bi a , belonging to a series of allels including BI and 61 ; producing half- 

awned types with short awns, 
J5 2 , the gene for tipped 2 belonging to the allelic series B 2 , bz and perhaps 

containing A. Awns reduced to a few short tips occurring from top to 

bottom of the spike. 
&2j recessive gene for bearded in the presence of the homozygous condition 

for bi. 

A, another gene for the half-awned condition that may be an allele of 
the 62 series and that gives half-awned types in the presence of the 

recessive condition for 61 and 62- 
Hd, a gene that reduces the length of the awns, making them curved and 

twisted near the base. 

Possible combinations of factors include 6161 i> 2 >2 hdhd, bearded; 
BiBi bj)2 hdhd, tipped 1 ; 6161 J? 2 5 2 hdhd, tipped 2; 6161 6 2 &2 HdHd, 
hooded; and B\B\ B^B?, hdhd, beardless; and bibi B^B^ HdHd, 
hooded beardless. 

Bi is linked with genes for pubescent node, square-headedness, 
and keeled glumes. 

The Howards (1915), in India, explained the results of a cross 
between awnless and bearded varieties on the basis of two pairs 
of factors, the homozygous dominant condition of both leading 
to the production of the fully bearded condition. Quisenberry 
and Clark (1933) crossed two awnleted wheats, Quality and 
Sonora, and obtained true breeding awned, awnleted, and awnless 
wheats, respectively, in F 9 in addition to a wide range of segregat- 
ing groups. They used the same hypothesis as given originally 
by the Howards except that they considered awnless to be the 
dominant group rather than bearded. 



METHODS OP PLANT BREEDING 

The student should not be confused by the question of domi- 
nance. It is relatively easy to differentiate the Fi from either the 
awnleted or fully bearded parents when representative varieties 
are crossed that differ in awnedness. Percival (1921) reported 
F% segregations approximating a 1:2:1 ratio, with the intermedi- 
ate or heterozygous condition producing longer tipped awns that 
often extended down the head to a greater extent than in the 
awnleted parent. 





' -' L V!4 

- .,<"$" L.M 



^,i*SP 



FIG. 16. Quality and Sonora, two types of tipped awn wheats, and five 
different types of progeny obtained in Ft. Two new homozygous types were 
selected, awnless and bearded. (After Quisenberry and Clark, 1933.) 

Chaff Characters. Color of glumes is a varietal character 
ranging from deep brownish red color to colorless. Segregation 
in crosses between colored vs. colorless with 3:1 and 15:1 ratios 
has been reported (Biffin 1905, Kezer and Boyack 1918). There 
are inherited differences in color of awns that have been reported 
to segregate in simple ratios (Howards, 1915). 

Hairy chaff is a varietal character used in classification. In 
crosses between members of the Emmer group with varieties of 
Triticum vulgare, some cases of complete association have been 
reported between chaff color and the hairy chaff character 



INHERITANCE IN WHEAT 133 

(Biffin 1905, Engledow 1914, Henkemeyer 1915, Kezer and 
Boyack 1918). The Howards have reported two kinds of hairs 
on the glumes of Rivet wheat. In a cross between two Indian 
varieties that differed in the sorts of hairs produced on the chaff, 
a ratio of 15 pubescent: 1 smooth was obtained in F^ It seems 
probable that the two pairs of factors for pubescent vs. smooth 
chaff are carried in separate genoms and therefore are independ- 
ently inherited. Since there are at least two pairs of factors for 
pubescence, this would explain variations in linkage relations 
between chaff colors and pubescence. 

Seed Characters. Color of seed, resulting from a brownish 
red pigment in the testa, has been commonly used in varietal 
classification and in determining market grades. It is a plant 
character and is not immediately affected by cross-pollination. 
Red is dominant over white, and from one to three pairs of dupli- 
cate factors are involved, as first shown by Nilsson Ehle (191 la) 
and later found by many other workers. Segregating ratios 
3:1, 15:1, and 63:1 have been observed, and crosses between two 
varieties, both breeding true for red seed color, may give plants 
lacking red seed color in F%, provided that the parents differ in the 
genetic factors involved. One parent, for example, may be 
R iRi rtfrz, whereas the other may have the genotype r\r\ RzRz, 
leading to the production of some white-seeded plants of the 
genetic constitution r\r\ ry^. 

Texture of seed is used also in varietal classification and in 
market grades. Biffin (1916) observed the immediate effect of 
cross-pollination in a cross of Rivet, a corneous seeded variety 
belonging to Triticum turgidunij with a soft Polish variety of 
T. polonicum. In crosses of corneous-seeded duruins with the 
soft-seeded variety Sonora, belonging to T. vulgar e, Freeman 
(1918) observed variation in texture of seed in FI with hard, 
intermediate, and soft-seeded kernels on the same plant. Hard 
seeds of the FI tended to give more hard-seeded plants in F z than 
the progeny of soft seeds from FI plants. Freeman carried the 
study through F 4 . He explained his results on the basis of two 
pairs of factors, the heterozygous condition being intermediate 
in soft-starch production. Since the endosperm results from 
the union of two polar nuclei with a male generative cell, there 
could be a range from zero to six factors for soft starch. The 
type of soft starch worked with by Freeman is different from the 



134 METHODS OF PLANT BREEDING 

type called yellow berry, which is conditioned by inheritance but 
is easily modified by environmental conditions. 

Spike Density. Crosses between Triticum compactwn with 
T. vulgare by Spillman (1909) and Gaines (1917) have shown one 
main factor for compactness of head. In similar crosses, Parker 
(1914) concluded that multiple factors were involved. Nilsson- 
Ehle (191 la) studied crosses of Swedish Club (compact) with 
Squarehead, a mid-dense-headed type, obtaining compact heads 
in FI and segregation into compact, mid-dense, and lax in 
FV He explained his results by the hypothesis of (7, a factor for 
compactness epistatic to Li and L^ factors for length of internode 
carried by Swedish Club and the recessive condition carried by 
Squarehead, cc l\l\ hh- Fz plants of the phenotype c LiL% were 
lax-headed. It is common, in crosses of vulgare with durum, to 
obtain Emmer-like wheats with very dense heads. Stewart's 
(1926) results from a cross of Sevicr with Federation, two varieties 
of T. vulgare show that transgressive segregation for head density 
may occur. Scvier is somewhat more dense than Federation. 
The nature of segregation in F% was determined from F 3 progeny 
trials of F% plants selected at random. Homozygous dense, 
heterozygous, arid homozygous lax forms occurred in a 1:2:1 
ratio, although the dense forms were more dense than Sevier and 
the lax forms more lax than Federation. 

Spring vs. Winter Habit. The main character that differenti- 
ates spring from winter habit is heading behavior when wheat is 
sown in the spring. In the spring-wheat areas of the United 
States and Canada, winter wheat, when sown in the spring, 
remains in the rosette stage and fails to head. Spring wheat 
may be sown in the fall, and varieties of spring wheat often are 
fall-sown in those sections where the winters are mild. Spring- 
wheat varieties, as a rule, are less winter hardy than true winter 
wheats. 

In crosses between spring and winter wheat* the spring habit, 
as a general rule, is completely dominant in FI, and segregation 
occurs in F 2 . The type of ^2 ratio obtained without doubt 
depends to a considerable extent upon the environmental con- 
ditions used to differentiate spring from winter habit. Ratios 
reported include simple ratios of spring to winter of 3 :1 by Cooper 
(1923) and 15:1 by Nilsson-Leissner (1925); Vavilov and Kouz- 
netsov (1921) and Aamodt (1923) obtained much more complex 



INHERITANCE IN WHEAT 135 

ratios. In the F% of Kanred X Marquis, Aamodt classified 
plants from spring seeding for date of heading at weekly intervals 
into eight weekly periods and into a winter group consisting of 
types that failed to head. From 5253 F 2 plants, 980 headed as 
early as the spring parent, and 442 were classified as winter. The 
numbers of plants in other weekly periods for heading date were, 
respectively, from early to late, 1503, 883, 568, 417, 313, 128, and 
19. Plants heading in F 2 as early as Marquis bred true for spring 
habit. Intermediates for date of heading bred true also in some 
cases. Studies by Hayes and Aamodt (1927) of cold resistance 
in crosses between Marquis with Minturki and Minhardi winter 
wheats included a study of growth habit also. A late heading 
type, when spring-sown, was selected that, when sown as winter 
wheat, was rather highly winter-hardy. When recrossed with 
Marquis and studied for cold resistance and for date of heading, 
when spring-sown, there appeared to be almost complete correla- 
tion between cold resistance and late heading (unpublished). 
In general, there is a close correlation between winter habit and 
cold resistance, but some wheats of winter habit are lacking in 
high cold resistance. Some varieties of spring wheats have 
considerably more resistance to winter killing when fall-sown 
than other varieties. 

Powers (1934) studied spring vs. winter habit of growth in a 
cross of Hybrid 128 X Velvet Node. Under conditions at 
Pullman, Washington, the parents and hybrids were classified 
for date of ripening into weekly groups. The results were 
explained by the interaction of three main factor pairs, where 
A A, BB, and cc were factors for spring habit of growth and their 
alleles for winter habit. A A was epistatic to bb and CC, BB to 
aa and CC, and cc to aa and bb. 

Stem-rust Reaction. There are 177 physiologic races of 
Puccinia graminis tritici that have been differentiated by their 
mode of reaction on 12 host varieties when inoculated with stem 
rust in the greenhouse in the seedling stages [Stakman et al. 
(1935), Johnson and Newton (1940), and Dickson (1939)]. It 
is generally accepted that a variety of wheat, when resistant in 
the seedling stage to a particular physiologic race of the dis- 
ease organism, usually is resistant under field conditions from 
heading to maturity to the same physiologic race. A variety 
of wheat, however, may be highly resistant to one physiologic 



136 METHODS OF PLANT BREEDING 

race and completely susceptible to another. New physiologic 
races originate (Craigie 1940) from hybridization on the bar- 
berry, the alternate host of black-stem rust, and in the presence 
of barberry bushes there is always the possibility of new physio- 
logic races being developed. 

The literature on the mode of inheritance of seedling reaction 
is very extensive. Illustrations will be given of several types of 
segregation. In a cross of H44-24 X Marquis (Goulden, Neatby, 
and Welsh 1928), where H44 was resistant to physiologic race 
36 and Marquis susceptible, results were explained by supposing 
H44 to carry two duplicate factors for resistance, either alone in 
the homozygous dominant condition leading to semiresistance. 
Thus, the parental genotype of H44 was RiRi R^R^ arid of 
Marquis T\TI r 2 r 2 . F% genotypes were as expected from a dihybrid 
ratio with the genotypes RiRi R^R^ RiRi Rtfi, Rtfi R^R^ and 
showing the resistant type Of phenotypic behavior, 
R\Ri r 2 r 2 , rvi R^r^ and Rir^ r 2 r 2 being phenotypically 
semiresistant, whereas the double recessive nr\ r 2 r 2 was highly 
susceptible. 

Harrington and Aamodt (1923) studied crosses between two 
durum wheats; Pentad, resistant in the seedling stages to 
physiologic race 34 and susceptible to race 1, and Miiidurn, 
which reacts in a reciprocal way to these two races. A single 
main genetic factor difference was responsible for reaction to each, 
and the two factors were independently inherited. 

In a cross of Kanred, immune to over 11 physiologic races, 
with Marquis, which was susceptible to these same races (Aamodt 
1923), immunity was dominant over resistance, and the manner 
of reaction to all races to which Kanred was immune and Marquis 
was susceptible was conditioned by a single genetic factor pair. 

The few studies of seedling resistance that have been reviewed 
briefly are representative of the many extensive studies of the 
manner of inheritance of seedling reactions. The problem of 
obtaining in a single variety resistance in the seedling stages to 
all available races, and those races that may be found after further 
study, has seemed rather difficult, since new physiologic races 
are being found almost constantly, and the total number of 
races is increasing rapidly from year to year. Recently, however, 
the problem has appeared to be somewhat less difficult by the 
discovery of several new wheats, notably wheats from the 



INHERITANCE IN WHEAT 



137 



R.10 



R55 



R.14 



R36 



R.56 



R.15 



R38 



R59 



R.17 



R.19 



R.48 



R.71 



R.Z1 



RHP 



R.79 



R.23 



R.55 



FIG. 17. Reaction in the seedling stages of a selection from the cross, Kenya 
X Gular. Resistance to many physiologic races, both in the seedling and 
mature plant stages, is due to a single dominant factor. (Courtesy of S. L. 
Macindoe.) 



138 METHODS OF PLANT BREEDING 

Kenya Colony in Africa that have been described by Macindoe 
(1931) as resistant to the prevalent races in Australia. Some of 
these wheats have proved resistant in the seedling stages to %0 
representative physiologic races (Peterson, Johnson, and Newton 
1940) and have remained resistant also under field conditions, 
where 30 prevalent Canadian races have been used to produce 
the field epidemic. 

The breeding of stem-rust-resistant vulgare types of wheat 
originally consisted of attempts to transfer stem-rust resistance 
from members of the Emmer wheat group to vulgare wheats by 
crosses between the 14 and 21 chromosome species. Hayes, 
Parker, and Kurtz weil (1920) obtained a vulgare type of wheat 
resistant to stem rust, later named Marquillo, from a cross of 
lurnillo, a durum variety, with Marquis. Marquillo proved less 
resistant than lumillo, although under field conditions it has 
continued to be moderately resistant to*a collection of prevalent 
physiologic races. A sister selection of Marquillo was crossed 
with a spring-wheat selection obtained from Kanred X Marquis 
that carried the Kanred type of immunity to several races. From 
this latter cross, Hayes, Stakman, and Aamodt (1925) concluded 
that resistance in the stages from heading to maturity to a col- 
lection of prevalent races was conditioned by two complementary 
factors and that susceptibility was dominant to resistance. It 
was found also that Marquillo and Thatcher, the latter selected 
from the cross (Marquis X lumillo) X (Marquis X Kanred), 
were highly susceptible in the seedling stages to several of the 
prevalent races used in producing the field epidemic. The 
resistance of the Marquillo type, conditioned by two main 
factors in the field, proved independent in inheritance of the 
Kanred near immunity to certain physiologic races. 

A more satisfactory type of stem-rust resistance was obtained 
by McFadden (1930) from crosses of a variety of Triticum 
dicoccunij Yaraslov Ernmer, with Marquis. Two varieties 
obtained from this cross, Hope and H44, although not entirely 
satisfactory in agronomic characters, have in recent years been 
used by practically all breeders as a source of stem-rust resistance. 
These two wheats, like Thatcher and Marquillo, are susceptible 
in the seedling stages to several physiologic races that occur 
naturally both in United States and Canada, but both Hope and 
H44 have proved highly resistant in the mature-plant stages in 



INHERITANCE IN WHEAT 139 

the field, from heading to maturity, to natural and artificial 
epidemics of black-stem rust. As soon as McFadden obtained 
these new wheats and before they were named, he generously 
supplied seed to all breeders interested. It was soon evident, 
as published by several workers at about the same time (Clark 
and Ausemus 1928, Goulden, Neatby, and Welsh 1928) that the 
type of resistance carried by Hope and H44 was simply inherited 
in crosses with susceptible varieties of vulgare. Resistance is 
dominant in Fi, and segregation in F% and later generations has 
been found to be dependent upon one or two pairs of factors. 
From crosses studied by Pan (1940) it seems probable that 
resistant lines obtained from crosses with H44 carry the same 
factors for resistance as Hope. In studies of ^3 lines from Hope 
and H44 crosses with stem-rust-susceptible varieties of vulgare, 
however, numerous workers have found a rather wide variation 
in types of segregation including ratios of resistant to susceptible 
of 9:7, 3:1, 15:1, 1:3, and 1:15 (Ausemus 1934, Churchward 1931, 
1932). The important fact for the breeder is that resistant lines 
continue to breed true for resistance in later generations. 

Bunt Resistance. Farrar, in Australia, as early as 1901, 
reported studies in the breeding of wheat varieties resistant to 
bunt (Tilletia tritici (Bjerk.) Wint. and T. levis Kuhn). Gaines, 
in Washington, has made extensive studies of inheritance of 
bunt reaction. He classified his material as immune, resistant, 
intermediate, and susceptible. In crosses of resistant and sus- 
ceptible varieties, susceptibility was dominant, but when 
immune varieties were used as one parent, there was a dominance 
of immunity in FI. Although Gaines was unable to place his 
results on a simple factorial basis, he found it possible to select 
homozygous bunt-immune and bunt-resistant lines. 

Briggs, working with nearly immune types of bunt resistance, 
determined the genetic constitution of 10 bunt-resistant varieties. 

The Martin factor is completely dominant, whereas the Turkey 
and Hussar factors, when heterozygous, give an intermediate 
reaction (Briggs 1933). There is some evidence of modifying 
factors and Churchward (1931, 1932) has reported that the bunt 
resistance of Florence is due to a single recessive factor. Recently 
Briggs (1940) has concluded that there is a linkage between the 
Martin and Turkey factors with a recombination value of 34,22 
per cent, 



140 METHODS OF PLANT BREEDING 

TABLE 11. THE GENETIC CONSTITUTION OP 10 BUNT-KESISTANT VARIETIES 

OF WHEAT (AFTER BRIGGS 1934) 
Variety Bunt-resistant Factors 

Martin MM hh it 

White Odessa MMhhtt 

Banner Berkeley .... MM hh it 

Odessa MM hh tt 

Sherman MM hh tt 

Hussar ... MM HH tt 

Selections 1418 and 1403 . . ... mm HH tt 

Turkey 1558 . . mm hh TT 

Turkey 3055 . . .... mm hh TT 

Oro mmhh TT 

Other Problems of Disease-resistance. Considerable infor- 
mation is available regarding inheritance of resistance to other 
diseases and insect pests, including reaction to scab, Hdmintho- 
sporium sp., black chaff, mildew, leaf rust, stripe rust, and 
Hessian fly. Varieties differ widely in their mode of reaction, 
and for most of these pests it seems feasible to breed resistant 
varieties. In many cases, however, sufficient information is not 
available to place results on a genetic-factor basis. 

Quantitative Characters. It seems reasonable to conclude 
that all characters of crop plants are conditioned by genetic 
factors. Yield of grain is a complex character that results from 
the inheritance of genetic factors and their interaction under 
particular conditions of environment. What is inherited is 
manner of reaction under particular conditions and not the 
character itself. Yield of grain is the end result of vigor of 
plant, as expressed in number of heads, number of kernels per 
spike and spikelet, and size of individual kernel. Anything that 
interferes with the normal development of the plant, including 
injury from diseases and unfavorable environmental conditions, 
affects yield. The usual method adopted by the breeder, when 
quantitative characters are concerned, is to select parents of 
good yielding ability with desirable characters, including those 
particular qualities for which the crop is used, select during the 
segregating generations for the characters desired, and test 
hybrids for yielding ability and other characters before deciding 
which is the more desirable, 



CHAPTER X 
INHERITANCE IN OATS 

Cytological studies made by Kihara, Nishiyama, and others 
place A vena species in three groups, based on differences in chro- 
mosome numbers. These have been summarized by Stanton 
(1936): 

Group 1. n = 7 chromosomes. Avena brevis Roth (short oat); A. 
wicstii Steudel (desert oat); A. strigosa Schreb. (sand oat) and A. nudi- 
brevis Vav. (small seeded naked oat). 

Group 2. n = 14 chromosomes. A vena barbata Pott (slender oat) 
and A. abyssinica Hochst. (Abyssinian oat). 

Groups, n 21 chromosomes. Avenafatua"L. (common wild oat); 
A. saliva L., including A. oricntalis Schreb. (common white or northern 
oat); A. nuda L. (hull-less oat); A. sterilis L. including A. ludoviciana 
Dur. (wild red or animated oat); and A. byzantina C. Koch, including 
A. sterilis algcricnsis Trabut (cultivated red oat). 

Kihara and Nishiyama (1932) have reported extensive studies 
of species crosses. Interspecific crosses between species belong- 
ing to the same chromosome group can be made easily. Crosses 
between the 14 X 28 chromosome species are relatively easy but 
produced fertile seeds only when the 28-ehromosome species was 
the female. Crosses between the 14- and 42-chromosome species 
are difficult, and only a few successful crosses have been obtained. 
Viable seeds were produced only when the n = 21 species was the 
female. Reciprocal crosses between the 28- and 42-chromosome 
species gave well-developed kernels that germinated well. 

Chromosome affinities in species crosses have not been com- 
pletely worked out. A table by Nishiyama (1929) summarized 
some relationships by listing the number of bivalent associations 
inclusive of trivalents in hybrids between different species. He 
says, "If two parents differ in chromosome numbers, as many 
bivalents as the lower chromosome number of one parent may 
be expected. A full affinity between two species is, therefore, 
represented as LOGO and no affinity as 0.000," 

141 



142 METHODS OF PLANT BREEDING 

These results indicate that A. barbata is not closely related to 
A. fatua. A. strigosa (n = 7) when crossed with A. barbata 
(n 14) showed more than seven bivalents, due possibly to 
autosyndesis of barbata chromosomes. 



TABLE 12. CHROMOSOME AFFINITIES IN SPECIES CROSSES OF Avena 
Avena strigosa Avena saliva 0.983 Avena byzantina 

i f 

0.998 0.986 



iwjd at/i frj, 

1.041 



Avena barbata 0.456 Avena fatua 0.992 Avena sterilis 

0.675 



As would be expected, crosses between species with different 
chromosome numbers are partly or nearly completely sterile 
because of irregularities of chromosome behavior during meiosis 
in the FI hybrid. 

In the first-division metaphase of crosses between species that 
differ in chromosome numbers, bivalents and trivalents form a 
normal equatorial plate with the univalents scattered throughout 
the cell. Univalents divide equationally and pass to the poles, 
being included in the daughter nuclei, except for a few lagging 
chromosomes. The second division is irregular, since the uni- 
valents that have already divided equationally pass to the poles 
at random. There are many lagging chromosomes. In a cross 
between A. barbata with A. strigosa, 7 bivalents inclusive of 
trivalents are found commonly, and in some cases 8 or 9 bivalents. 
Trivalents are frequent. In crosses between A. barbata with 
A. fatua, the number of bivalents varied from two to eleven, 
with 1 to 4 trivalents; in the FI crosses of A. barbata X A. 
sterilis, 7 to 13 bivalents were found, inclusive of to 4 trivalents. 
These results are not widely different from those in species crosses 
in wheat and give some reason for the belief that desirable charac- 
ters from species with lower chromosome numbers can be trans- 
ferred to the cultivated species with 42 chromosomes. 

Cultivated varieties of oats belong chiefly to the species A. 
saliva j including the side-oat group A, sativa orientalis, commonly 
believed to have been derived from the wild oat (A. fatua L,) 
and the red oat varieties of A. 'byzantina, derived from the wild 
red oat, A. sterilis. Crosses between different species belonging 
to the 42-chromoeome group are highly fertile, although there is 



INHERITANCE IN OATS 143 

some evidence of abnormal chromosome behavior possible 
because of structural changes in one or more chromosomes within 
the various sets. This may cause trivalent, quadrivalent, or 
lagging chromosomes at meiosis. Nishiyama (1929) concludes, 
"All hexaploid hybrids have normal bivalents in the majority of 
P.M.C. at the metaphase of the first division. Sometimes l*-4 
univalents and certain chromosome complexes are found together 
with normal bivalents. These irregularities are probably caused 
by mating between semihomologous chromosomes, not being 
normal partners. 7 ' 

Inheritance of Characters in Crosses between 42-chromosome 
Species. Surface (1916), Philp (1933), and others have studied 
the inheritance of characters in crosses between Avena fatua 
and A. saliva. Characters associated with the fatua b^tse on the 
grain of the lower floret that are completely correlated in inherit- 
ance include (1) heavy awn on the lower grain, (2) awn on the 
upper grain, (3) fatua base on the upper grain, (4) pubescence 
on the rachilla of the lower and upper grain, (5) pubescence on 
all sides of the lower grain and on the base of the upper grain. 
Philp explained these results by a factor C carried by the fatua 
parent that was partially dominant to c carried by A. sativa. 
It was suggested by Philp that the chromosomes carrying C 
in A. fatua and c in A. sativa were not entirely homologous and 
that the factor pair Cc responsible for a group of linked charac- 
ters was inherited as a group complex. A partial lack of chromo- 
some homologies was given as the probable reason for the 
complete linkage of the several character pairs. 

The upper grains of the floret are persistent to their rachillas 
in A. sterilis and A. byzantina, which differentiates them from 
A. fatua and A. sativa , whereas cultivated varieties of A. byzan- 
Una differ from varieties of A, sativa in that there is a well-defined 
deep, oval cavity or "sucker mouth" on the base of the lemma of 
A. byzantina. These differences were illustrated in Chap. II. 

Different investigators, including Fraser (1919), Hayes, Moore, 
and Stakman (1939), and Torrie (1939), have studied linkage 
relations of differential characters in crosses between varieties of 
A. sativa with A. byzantina. Coffman, Parker, and Quisenberry 
(1925) studied variability in Burt oats, belonging to A. byzantina } 
with particular reference to the following characters, using three 
characters in their classification: 



144 , * METHODS OF PLANT BREEDING 

Spikekt disarticulation, or the separation of the lowet floret of 
the oat spikelet from the axis of the spikelet, was divided into 
three groups: (1) abscission, leaving a well-defined cavity in the 
face of the callus on the base of the lemma of the lower grain, 
(2) disarticulation by fracture, resulting in a rough fractured 
surface with little or no cavity in the base of the lemma, charac- 
teristic of A. saliva j (3) disarticulation by semiabscission, more 
or less intermediate between 1 and 2. Groups 1 and 3 charac- 
terize varieties of A. byzantina and homozygous segregates of the 
byzantina type from A. saliva X A. byzantina. 

Floret disjunction, or the separation of the second or upper floret 
from the lower, was also classified in three groups: (1) disjunction 
by basifracture, the rachilla segment breaking near its base and 
remaining firmly attached to the upper floret, (2) disjunction by 
disarticulation at the apex of the rachilla segment, the rachilla 
segment remaining attached to the lower floret, the normal 
method in A. sativa, and (3) disjunction by heterofracture, the 
break occurring more or less intermediate between (1) and (2). 

Basal hairs refer to conspicuous bristles on the base of the lower 
floret. Three classifications are given: (1) abundant long, (2) 
abundant mid-length, and (3) few. 

In a series of crosses between Bond, A. byzantina, and cultivated 
varieties of A. saliva, several workers have found linkages for 
various character pairs. The linkages for the following charac- 
ters were given by Hayes, Moore, and Stakman (1939). 

1. Spikelet disarticulation and basal hair development, recom- 
bination value 2.7 per cent. 

2. Floret disjunction (one of two genes involved) and basal 
hair development, recombination value 24.0 per cent. 

3. Spikelet disarticulation and floret disjunction, recombina- 
tion value 25.7 per cent. 

Torrie (1939) observed linkage relations, in crosses between A. 
sativa, Iowa 444, and A. byzantina, Bond, for character differ- 
ences including spikelet disarticulation, floret disjunction, 
rachilla attachment, basal hair length, awning, and red lemma 
color. The exact linear order of the genes was not accurately 
determined. The results indicated, however, that it was possible 
to obtain new combinations of these characters if desired. 

Differences IE Awn Development. Varieties of oats differ 
widely in awn development, both in the number of awns on the 



INHERITANCE IN OATS 145 

upper and lower florets and in the degree of development of awns. 
The extent of awn development in a pure line varies rather widely 
from plant to plant and from one panicle to another on the same 
plant because of environmental conditions. Under uniform 
conditions, pure lines may be selected that show a range in awn 
development from nearly awnless to lines that have strongly 
developed awns on both the upper and lower florets. In some 
crosses, 3:1 or 1:2:1 ratios have been obtained when the separa- 
tion is made into the larger groups, although, as a rule, minor 
modifying factors that modify the degree of development of the 
main factor pair are also involved. 

Nilsson Ehle (19116) and Love and Craig (19186) found evi- 
dence that the gene for yellow lemma color inhibited the develop- 
ment of awns. Fraser (1919) studied a cross between Sixty-day, 
with yellow grains and no awns, with Burt, A. byzantinaj with 
weak awns on the lower floret and frequently on the upper. 
In F 2 , there was a ratio of fully awned (like Burt) to awnless of 
1:3. The fully awned plants bred true in jP 3 . The degree of 
development of the awns ranged from weak awns like Burt to 
strong awns that were stiff and long, the strong awn being sharply 
twisted at the base, with a sharp bend about three-eighths of the 
way from the base to the tip. In crosses between logold, with 
weak to intermediate development of awns and with less than 
50 per cent of the lower florets bearing an awn, and Bond, with 
100 per cent weak awns in the lower florets, a range in F% from 
strong to weak awns was obtained and also a range from 25 per 
cent awned to fully awned (Hayes et al. 1939). 

Color of Grain. The color of the lemma has been classified as 
black, brownish red, gray, yellow, and white. Intensity of color 
is influenced by environmental conditions, and it is sometimes 
difficult to differentiate yellow and white. With bright sunshine 
during the later stages of development, the intensity of color is 
deeper than when wet, cloudy weather conditions prevail. 

Black is epistatic to gray and yellow (Nilsson-Ehle 1909, 
Surface 1916), (Love and Craig 19186), and gray is epistatic to 
yellow. Black vs. colorless, gray vs. colorless, and yellow vs. 
colorless segregated on a single factor basis in some crosses. In 
other crosses, there may be duplicate factors for black and for 
yellow. In a cross of Sixty-day, which produces yellow grain, 
with Burt, which produces brownish yellow, Fraser (1919) 



146 



METHODS OF PLANT BREEDING 




For descriptive legend see opposite page. 



INHERITANCE IN OATS 147 

obtained a ratio of 48 red: 15 yellow: 1 white4n F*. Apparently 
Burt carries a factor for red, R, and for yellow, F, red being 
epistatic to yellow. The factor for yellow in Sixty-day is inde- 
pendent in inheritance of the factor for yellow carried by Burt. 
In crosses of Bond, reddish yellow X Iowa 444, colorless, Torrie 
(1939) concluded that the Bond parent carried two dominant 
factors, one for reddish color and one for yellow, that were inde- 
pendently inherited. Philp (1933) concluded that black and 
gray were independently inherited. 

Hulled vs. Hull-less. The Avena nuda species has been dif- 
ferentiated on the basis of its hull-less condition, Love and 
McRostie (1919), in crosses of hulled X hull-less, obtained an 
intermediate condition in Fi and a ratio in F% of l:2:.l. Some 
evidence was given of a factor that modified the percentage of 
hulled grains on heterozygous plants. Philp (1933) obtained 
some hull-less F% plants in crosses of A. saliva X A. fatua, 
although they were not completely hull-less. He reports A. 
nuda plants from crosses of the A. sativa varieties made by 
W. Bobb. The results can be explained by supposing that A. 
sativa carries two types of chromosome complexes, called Z and 
Zj with Z epistatic to z. The Z complex carries a factor for hulled 
while z carries a factor for naked. A change of pairing whereby 
Z occasionally pairs with z will lead to the production of hull-less 
plants. 

Spreading vs. Side Panicle. Nilsson-Ehle explained a cross 
between spreading vs. side-panicle varieties on the basis of 
duplicate factors, either factor in the dominant condition pro- 
ducing an open panicle. Gaines (1917) and Garber (1922) found 
it difficult to separate spreading and side-panicle forms in 
segregating generations. Either 3:1 or 15:1 ratios would be 
expected in later generations if duplicate factors were involved 
from crosses of spreading vs. side-panicled varieties. There 

FIG. 18. Panicle arid floral structure of oats, 

1. Branch of oat panicle. 

2. Spikeiet, showing tertiary floret just after blooming: (a) primary floret. 

3. Spikeiet, showing floral parts: (a) outer glume; (b) flowering glume; (c) palea; 
(d) lodicules; (e) anther; (/) stigma; (0) secondary floret; (h) awn. 

4. Outer parts removed, showing sexual organs. 
6. Longitudinal section of ovary. 

6. Anther. 

7. Showing outer and flowering glume of lower spikelet removed: (a) lodicules, 
and sexual organs. 

Size; 1, 2, about X; 3, about 2x; 4, 5, 6 fereatly enlarged; 7, about 2X. 



148 METHODS OF PLANT BREEDING 

probably are modifying factors that make the separation between 
open and side panicle difficult in some crosses. 

Pubescence. Cultivated varieties of sativa oats differ in the 
amount and in the presence of basal hairs on each side of the 
callus of the lower floret. One or two pairs of factors are involved 
in various crosses. Transgressive segregation, therefore, occurs 
in some crosses, forms being obtained in F 2 that are more pubes- 
cent than either parent or that lack pubescence. Pubescence 
on the back of the lower grain, the wild type of A.fatua, is domi- 
nant to the glabrous condition and may be controlled by one or 
two duplicate factors. One of these is closely linked and in some 
crosses completely linked with a factor for black grain color 
(Nilsson-Ehle 1909, Surface 1916, Love and Craig 19186, and 
Philp 1933). 

DISEASE REACTIONS 

Three important diseases of oats are stem rust, Puccinia 
graminis avenae Eriks. & Henn., crown rust, P. coronata Corda, 
and the smuts, Ustilago avenae (Pers.) Jens, and U. levis (K. & S.) 
Magn. 

Physiological specialization occurs for all three diseases. Dick- 
son (1939) listed 9 physiologic races of stem rust and 44 of 
crown rust; Reed (1940) listed 29 of U. avenae and 14 of U. lens. 
In a breeding program, it is essential to use physiologic races 
prevalent in the locality to produce the artificial disease epidemic. 

Stem Rust. Varieties of oats are available that are resistant 
to several of the races common in the sections where stem rust 
frequently causes severe injury to susceptible varieties. logold 
and Rainbow are resistant to races 1, 2, 3, 5, and 7, and White 
Russian and derivatives are resistant to races 1, 2, 5, 8, and 9. 
Resistance to the five races 1, 2, 3, 5, and 7, to the three races 

1, 2, and 5 and probably 8 and 9, and susceptibility to all five 
races form an allelic series (Smith 1934), and in any one cross the 
only homozygous types that can be obtained are the parental 
types. The resistance of logold and Rainbow under both field 
and greenhouse conditions to the races to which logold, Rain- 
bow, and White Russian are resistant is of somewhat higher 
type than that of White Russian. 

Welsh (1931) pointed out that resistance of Hajira to races 1, 

2, 3, 5, and 7 was governed by the same factor pair. Joanette 



INHERITANCE IN OATS 149 

is resistant to race 4, and in crosses with Hajira, segregation for 
rust reaction to race 4 was on the basis of 9 resistant: 7 suscepti- 
ble. From a test of 21 lines breeding true for resistance to race 
4, about half of these were resistant also to races 1, 2, 3, 5, arid 7. 
Welsh (1937) has reported obtaining strains resistant to race 6 
from crosses of Hajira with Joanette and explains the results on 
the basis of transgressive segregation. It is of some interest 




FIQ. 19. Culms of resistant and susceptible varieties of oats. From left 
to right: Victory, susceptible to stem rust; a susceptible Ft plant of Victory X 
White Russian; a resistant Fz plant of Victory X White Russian f resistant 
White Russian. 

that White Russian was semiresistant to race 6 under field con- 
ditions in trials made by Welsh. 

Although resistance to all races is to be desired, resistance of 
Rusota and Rainbow to races 1, 2, 3, 5, and 7 and of White 
Russian, Anthony, and Minrus to races 1, 2, 5, and perhaps 8 
and 9 has protected these varieties from serious injury from stem 
rust under Minnesota conditions for many years when suscepti- 
ble varieties such as Victory are often severely injured. 

Crown Rust. Although some -varieties have been available 
that in some seasons show resistance to crown rust, the intro- 



150 METHODS OF PLANT BREEDING 

ductioii of Victoria from South America and Bond from Australia 
(Stanton & Murphy 1933) has furnished a basis for the breeding 
of resistant varieties, since both Bond and Victoria are resistant 
to many races of crown rust. 

Using Victoria as one parent in crosses with susceptible varie- 
ties, Smith (1934) concluded that resistance was a partial 
dominant in Fi. Variable infection made it impossible to decide 
the number of factors involved. Stanton (1936) indicates a 
single factor pair with resistance dominant. 

In crosses of Bond with susceptible varieties, Hayes et al. 
(1939) concluded that two pairs of factors were involved and 
placed segregation on a 9 : 7 basis, whereas Torrie (1939) explained 
crown-rust inheritance in crosses of Bond with Iowa 444 on the 
basis of two pairs of factors, Ss for resistance vs. susceptibility 
and lij a factor pair that in the dominant condition partly 
inhibited the effect of S. 

Correlated Inheritance of Reaction to Three Diseases. 
Stanton et al. (1934) obtained selections from crosses of Victoria X 
Richland that were resistant to the three diseases, and Murphy, 
Stanton, and Coffman (1936) reported selections from crosses 
where Bond was used as one parent that were resistant also to 
the three diseases. Hayes et al. (1939) and Torrie (1939) in 
crosses of Bond with varieties of A vena saliva found that reaction 
to all three diseases was inherited independently and found no 
evidence of association of reaction to the three diseases and other 
characters differentiating A. byzantina and A. saliva. 

Smuts. Reed (1940) summarized the reaction of a consider- 
able group of varieties and species of oats to all physiologic 
races of both species of smuts. Markton, a well-known variety, 
Navarro (Stanton 1933), and Victoria are resistant to all races 
of both smuts. Black Mesdag has been used extensively in 
crosses and is resistant to all races of Ustilago avenae and resistant 
to 10 of the 14 races of U. levis. So far as tested, A. barbata 
is susceptible to all races of both smuts. A few varieties of oats 
are susceptible to most races. Canadian, for example, is sus- 
ceptible to 28 races of loose smut and 13 of covered, being 
resistant to one race of each. 

In crosses of Monarch selection X Black Mesdag (Stanton, 
Reed, & Coffman 1934), inoculated with races of 7. avenae from 
Missouri, resistance was a dominant, and segregation on a 3:1 



INHERITANCE IN OATS 151 

basis occurred. Cresses of Markton X Black Mesdag inoculated 
with U. avenae, where both parents were resistant, gave some 
susceptible F$ progenies. 

Hayes et al. (1928) studied crosses of Black Mesdag with other 
A. saliva selections, using a mixture of smuts for inoculation, and 
obtained results indicating that the Black Mesdag resistance to 
both smuts was due to the action of two pairs of factors, R for 
high resistance and I for immunity carried by Black Mesdag. A 
selection from this cross that has proved highly resistant to a mix- 
ture of races of smuts at University Farm, St. Paul, Minnesbta, 
was crossed with Bond, resistant also to the races used. Some 
susceptible plants and lines occurred in F% and F 3 , respectively. 
In crosses of Bond with susceptible varieties, resistance was 
dominant and the segregation was on a 3:1 basis. Results of 
this nature are common in polyploids of an amphidiploid nature 
where cases of duplicate or triplicate factors that condition the 
development of a character are of relatively frequent occurrence. 

QUANTITATIVE CHARACTERS 

Many characters of oats of interest to the breeder are undoubt- 
edly due to the interaction of multiple factors. These include 
such characters as data of maturity, height of plant, resistance 
to lodging, number of culms, winter hardiness, drought resist- 
ance, percentage of hull, weight per bushel, and yielding ability. 

It is important for the breeder to analyze the varieties that are 
used as parents for all characters of importance and select during 
the segregating generations, under controlled conditions when 
possible, for the characters desired. 



CHAPTER XI 
INHERITANCE IN BARLEY 

CLASSIFICATION AND GENETICS OF BARLEY SPECIES 

Harlan (1918) classified barley into four species, essentially on 
the basis of fertility of the lateral spikelets. The following key 
is taken from Harlan's paper: 

All spikelets fertile (6-rowed barley) : 

Lemmas of all flowers awn eel or hooded Hordeum vulgar -e L. 

Lemmas of lateral flowers bearing neither awns nor hoods 

//, intermedium Keke. 

Only the central spikelets fertile (2-rowed barley) : 
Lateral spikelets consisting of outer glumes, lemma, palea, raehilla, arid 

usually rudiments of the sexual organs Hordeum distichon L. 

Lateral spikelets reduced, usually to only the outer glumes and raehilla, 
rarely more than one flowering glume present, and never rudiments of 
sexual organs Hordeum defidens Steud. 

The H '. intermedium group would be classified more accurately 
by the statement: Central spikelets fertile, lateral spikelets 
partially fertile. 

A single-factor difference for type of head is found in crosses of 
some varieties of //. vulgare X H. defidens; H. vulgare X H. 
distichon; and //. distichon X H. defidens. Engledow (1924) 
and Hor (1924) concluded that an allelic series of factors differ- 
entiated the type of lateral florets found in these three species. 

In some crosses of varieties of //. vulgare with H. distichon, 
as has been already mentioned, a segregation of two-rowed 
(VV) : intermediate (Vv) : six-rowed (vv) of 1:2:1 is obtained. In 
cases of monohybrid segregation, the lateral florets are usually 
infertile but will always be awn-pointed. In other crosses of 
H. vulgare with H. distichon } seven classes may be differentiated 
by the breeding behavior in F 3 . Harlan and Hayes (1920) gave 
the first complete genetic analysis of the results from such 
crosses, explaining the results on the basis of two factor pairs. 
Robertson (1933) obtained similar results. Both obtained true- 

152 



INHERITANCE IN BARLEY 153 

breeding intermedium types in F 3 . The lateral spikelets in the 
intermedium obtained by Harlan and Hayes (1920) were par- 
tially fertile, varying from 18 to 55 per cent in different F s lines. 
In the intermedium obtained by Robertson (1933), the lateral 
spikelets were infertile, i.e., less than 2 per cent fertile. Leonard 




FIG. 20. Heads of the cultivated species of barley. From left to right, 
Hordeum vulgare, H. intermedium (fertile), H. intermedium (infertile), H, dis- 
tichon, H. deficiens. 

(1940) found that the fertile, infertile, and nonintermedium types 
were differentiated by genes belonging to a multiple-allelic series, 
designated as I h l h , //, and ii, respectively. 

Intermedium barley can be classified on the basis of the 
rounded lemmas of the lateral florets, which are never awn- 
pointed. This condition is expressed only in the presence of VV. 
In the presence of Vv, the lateral florets are always awn-pointed. 



154 



METHODS OF PLANT BREEDING 



These are designated intermediates. Varieties that are geno- 
typically vv are six-rowed, with complete fertility of the lateral 
florets. These may be vv I h l h j vv II, or vv ii. 

The genotype of an unknown six-rowed variety for the inter- 
medium series may be determined by crossing it with a tester 
strain of known genotype, such as Nigrinudum, which is known 
to be VV II. The term infertile intermedium may be used when 
less than 2 per cent of the lateral spikelets are fertile and the term 
fertile intermedium used to designate those types with more than 
2 per cent (usually 10 to 60 per cent) of fertile lateral florets. 
The following scheme will illustrate how the genotypic constitu- 
tion of the six-rowed variety may be determined when crossed 
with a variety that has the genotype VV II. The phenotypes of 
the Fi and Ft generations are given for crosses of VV II with three 
different homozygous six-rowed genotypes. 



Phenotype of: 



Genotype of 

six-rowed 

variety 



Fertile intermediate. 
Fertile intermediate . 



Infertile intermediate 



Infertile intermedium, fertile in- 
termediate, and 6-rowed in 
ratio of 1:2:1 

Infertile intermedium, fertile in- 
termedium, fertile intermediate, 
and 6-rowed in ratio of 3:1:8:4. 
The distinguishing feature is the 
presence of fertile intermediums. 

2-rowed, infertile intermedium, 
infertile intermediate, fertile in- 
termediate, and 6-rowed in a 
ratio of 3:1:6:2:4. The dis- 
tinguishing feature is the pro- 
duction of 2-rowed segregates 
but no fertile intermedium 



mil 



vv I h l h 



VV 



It is sometimes difficult to Determine morphologically whether 
barley varieties are genetically of the distichon type (VV ii) or 
are infertile intermediums (VV II). To discriminate between 
them, they may be crossed to tester strains of the genotype vv II. 
If segregation is on a monohybrid basis, the genotype of the two- 
rowed parent is VV /I, and the variety is an infertile inter- 



INHERITANCE IN BARLEY^ 155 

medium. If a dihybrid segregation occurs, the two-rowed 
parent is a true two-rowed barley with the genotype VV ii. 

The four species of barley described by Harlan (1918) are 
differentiated genetically by only two factor pairs and their allelek 

CHROMOSOME NUMBER IN GENUS HORDEUM 

"), 
In the genus Hordeum, as in Triticum $nd Avena, the basic 

chromosome number is seven pairs. Multiples of this basic 
number are obtained also. Numerous investigators have 
reported the chromosome number of different species, and some 
of these are listed below: 

7 pairs of chromosomes: 

Hordeum bulbosum, H. deficiens, H. distichon, H. gussoneanum, H. hexa- 

stichum, H. intermedium, H. jubatum, H. murinum, H. nodosum, H. 

pusillumj H. spontaneum, H. vulgare 
14 pairs of chromosomes: 

H. bulbosum, H. jubatum, H. murinum, H, secalinum 
21 pairs of chromosomes: 

H. nodosum 

The species bulbosum, jubatum, and murinum have been 
reported by different investigators as having either 7 or 14 pairs 
of chromosomes. H. nodosum has been reported as having 7 or 
21 pairs. The economic species all have 7 pairs of chromosomes. 

LINKAGE GROUPS 

There are numerous characters in barley that are easily dif- 
ferentiated. Since the number of chromosome pairs is seven for 
each of the four cultivated species, barley has been used extensively 
in studies of linkage relations. More than one hundred different 
characters have been investigated. Robertson, Wiebe, and 
Immer (1941) summarized the known* linkage information and 
suggested symbols to be used in designating the various charac- 
ters. In Table 13 are given some of the characters that are 
known to be simply inherited and that have been placed in one 
of the linkage groups. 

It is of some interest to note that to date the only four factor 
pairs known for group 6 involve lethal seedlings. In all other 
chromosomes, easily differentiated, completely viable characters 
are available. 

Internode Length in the Racbis of the Spike. Varieties of 
barley vary greatly in density of the head, as measured by length 



156 METHODS OF PLANT BBEEDIN6 

TABLE 13. SIMPLY INHERITED CHARACTERS IN DIFFERENT LINKAGE GROUPS 

Character Differences Symbol 

Group 1: 

Non-6-rowed vs. 6-rowed Vv 

Red vs. white pericarp Re\re\ 

Purple vs. white lemma Pp 

Purple vs. white straw Prpr 

Toothed vs. untoothed lemma . Gg 

Awnless vs. awned Lklk 

Normal vs. albino seedlings Aa 

Normal vs. albino seedlings At&i 

Normal vs. albino seedlings A 404 

Green vs. chlorina seedlings Ff 

Green vs. virescent seedlings Yy 

Green vs. orange seedlings Oror 

Group 2: 

Black vs. white lemma and pericarp Bb 

Normal vs. "third outer glume" Trd trd 

Normal vs. albino seedlings At i 

Group 3: 

Hulled vs. naked Nn 

Normal vs. albino seedlings A cZ a cz 

Dense vs. lax head LI 

Group 4: 

Hooded vs. awned Kk 

Blue vs. white aieurone Bl bl 

Fertile intermedium, infertile intermedium, and noninter- 

medium /*, /, i 

Group 5: 

Rough vs. smooth-awned Rr 

Long vs. short-haired rachilla , . , Ss 

White vs. orange lemma Oo 

Normal vs. albino seedlings Ab a& 

Red vs. white pericarp Re re 

Group 6: 

Green vs. xantha seedlings * X e x e 

Green vs, xantha seedlings X x 

Green vs. albino seedlings A e a e 

Green vs. albino seedlings A n a n 

Group 7: 

Normal vs. brachytic Br br 

Green vs. chlorina seedlings. . . / F e f e 

Green vs. virescent seedlings Y c y^ 

Resistance vs. susceptibility to Pucdnia graminis , , , Tt 



INHERITANCE IN BARLEY 157 

of the internodes of the spike. The density varies comparatively 
little from year to year. Hayes and Harlan (1920) studied the 
mode of inheritance of internode length in five crosses. In two 
crosses, a single-factor-pair difference explained the results 
satisfactorily. Short internode length was dominant in one of 
these crosses, but the head density in the second cross was inter- 
mediate in FI. In another cross, a broad difference of two factor 
pairs was indicated by the segregation in F 2 and F 3 . 

In the cross of Hanna X Zeocriton (see Table 14), lax and 
dense varieties, respectively, the F 2 ranged from above the modal 




FIG. 21. Average spikes of the Zeocriton (left), Hanna (right), and four 
homozygous lines. Mean densities are as follows: Zeocriton, 1.9 mm.; Hanna X 
Zeocriton, 448-1, 2.3 mm.; 448-5, 2.9 mm.; 448-11-3, 3.7 mm.; 448-16, 4.3 mm.; 
Hanna, 4.6 mm. (After Hayes and Garber, 1927.) 

class of Hanna to the modal class of Zeocriton, even though only 
141 individuals were studied. F 3 families were grown from F% 
plants representing different densities. Progenies from selected 
plants in certain FZ lines were tested further in F 4 . Some F$ 
lines bred comparatively true, the range for density being no 
greater than for the parental varieties. Other F$ lines were as 
variable as the F 2 generation and still others more variable than 
the parents but less variable than the F%. Typical heads of the 
parents and segregates from homozygous lines are illustrated in 
Fig. 21. 

Homozygous lines differing in density were obtained in F% and 
F 4 . The homozygotes appeared to fall in groups. The general 



158 



METHODS OF PLANT BREEDING 





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INHERITANCE IN BARLEY 



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nature of the results is illustrated by Fig. 22. The results could 
be explained on a genetic basis by the hypothesis that the parent 
varieties differed by three independently inherited factors. 
These factors were considered to have a cumulative effect. Other 
factors, having smaller effects, doubtless were present also and 
modified the expression of the main density factors. 

Wexelsen (1934), from studies of six crosses involving five 
different varieties, found that internode length in different crosses 

50 
40 
80 
20 
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Density in MM 

FIG. 22. Diagrams showing the densities of parental forms and of the Fi 
generation in a cross between the Zeocriton and Hanna barleys (upper), of four 
pure lines (middle), and of several heterozygous lines (lower). (After Hayes 
and Harlan, 1920.) 

was differentiated by one to five factor pairs. A total of six 
factor pairs appeared to be involved in these crosses. These 
factors had different effects on internode length when hetero- 
zygous, some heterozygous types being intermediate, one being 
near the short, and another near the long internode parental 
type. One of the internode-length-factor pairs (L^k) was found 
to be linked with rough vs. smooth awns (Rr) and long vs. short- 
haired rachilla (Ss), and another (L 4 ^) was linked with non-six 
rowed vs. six-rowed head type (Vv). 

Reaction to Helminthosporium sativum. The best proof that 
quantitative characters are inherited in the same manner as 
qualitative characters has been obtained from linkage studies. 
Quantitative characters may be correlated with qualitative! 




160 METHODS OF PLANT BREEDING 

characters when the mode of inheritance and linkage relations 
of the qualitative characters are known. By means of such 
studies, it is possible frequently to determine the minimum 
number of genes controlling the quantitative character in crosses 
between known varieties. This mode of attack was used by 
Griff ee (1925) in a rather extensive study of reaction to spot 
blotch Helminthosporium sativum P. K. & B. 

The contrasted characters of the parent varieties were as 
follows : 

Svanhals Lion 

White hull and pericarp Black hull and pericarp 

2-rowed (distichon) 6-rowed (vulgare) 

Rough awn Smooth awn 

Resistant to spot blotch Susceptible to spot blotch 

Each of the character pairs, black vs. white, two-rowed vs. 
six-rowed, and rough vs. smooth awn, are known to be dependent 
upon single-factor differences and to be independently inherited. 
By considering each of these character pairs separately, a definite 
association was found in F% (each Ft plant was tested by growing 
and examining its F 3 progeny), between each character pair and 
reaction to spot blotch. The nature of the results is illustrated 
in Fig. 23, in which the lower Helminthosporium figure indicates 
susceptibility and the higher figure, resistance to the disease. 
More resistant plants were found in the two-rowed group than 
in the six-rowed, in the white than in the black, and in the 
rough- than in the smooth-awned. It seemed fair to conclude that 
at least three factor pairs, or groups of factors, were involved in 
determining reaction to H. sativum, and these were located in 
the same chromosomes as the factors for color, row number, and 
smooth vs. rough awns. Resistance and susceptibility were not 
dependent upon the same factors that conditioned the other 
characters since it was possible to obtain a resistant, white- 
hulled, six-rowed, smooth-awned variety and also a resistant, 
black-hulled variety from the Cross of Svanhals X Lion. 

Reaction to St6m Rust Powers and Hines (1933) studied 
the reaction to stem rust Puccinia graminis tritici in crosses of 
Peatland X Glabron and Peatland X Min. 462. Peatland was 
the resistant parent. Glabron and Minn. 462 are sister selections 
from a cross of Smooth Awn X Manchuria, and both are sus- 



INHERITANCE IN BARLEY 



161 



ceptible. Reaction to stem rust in the mature-plant stage was 
due to a single-factor pair with resistance dominant. Rust 



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FIG. 23. Distribution of Helminthosporiura reaction of F$ lines homozygous 
for other characters in cross of Svanhals X Lion. Lower figure for Hdmintho- 
sporium reaction indicates susceptibility and higher figure resistance to the 
disease, (from Griffee, 1925.) 

reaction was found to be independent of rough vs. smooth awns. 
Reid (1938) corroborated the foregoing conclusions regarding 



162 METHODS OF PLANT BREEDING 

reaction to a large collection of physiologic races of stem rust 
in the mature-plant stage in a cross of Barbless X Peatland. 

Brookins (1940) found the factor pair for resistance vs. sus- 
ceptibility to stem rust (Tt) to be located in the seventh linkage 
group, linked with normal vs. brachytic plant type (Brbr) and 
normal vs, chlorina seedlings (P\f c ). The gene order was 

T 12.6 Br 9.8 F c 



16V7 

Brookins found also that reaction to physiologic races 19, 36, 
and 56 in the seedling stage, in crosses involving Peatland, was 
monohybrid, with resistance dominant. The same factor pair 
that differentiated seedling reaction to these three races also 
controlled reaction to a large collection of races in the mature- 
plant stage in the field. Apparently the type of rust resistance 
found in Peatland is physiological, since the same gene pair 
controlled the same reaction to rust throughout the life of the 
plants. 

Resistance to Mildew. Stanford and Briggs (1940) sum- 
marized the studies on inheritance of resistance to barley mildew 
(Erysiphe graminis hordei) carried out at the California Agri- 
cultural Experiment Station. From studies of the genetics of 
resistance to race 3 in 10 resistant varieties, crossed with one 
another and with susceptible Atlas, the factorial composition of 
the resistant varieties was as follows: 

Variety Factors for Resistance to Mildew 

Hanna Mlh Mlh 

Goldfoil MlgMlg 

Arlington awnless Ml p Ml p Ml y Ml u 

Chinerme Ml p Ml p Ml y Ml u 

Nigrate Ml p Ml p Ml, Ml v 

Algerian Ml a Ml a 

S.P.I. 45492 Ml* Mla 

Kwan V MlkMk 

Psaknon MI P Ml p 

Duplex Ml h Ml h MlpMl P ml A mLd 

Seven different factors for mildew resistance six dominant 
and one recessive were found. The number of resistant factors 
in a single variety varied from one to three. 



INHERITANCE IN BARLEY 163 

The two different factor pairs differentiating Algerian and 
Kwan were found to be linked with 9.81 per cent recombination. 
The other five factors appeared to be independent of these two 
and independent of one another. Thus, seven different factors 
are involved in the control of a single physiologic race of a 
single disease. This appears to be the largest number yet located 
in any species of plants. 



INTERACTION OF FACTORS AFFECTING 
QUANTITATIVE CHARACTERS 

Quantitative characters are extremely important to the plant 
breeder. Studies of the genetics of these characters present seri- 
ous difficulties, since the number of genes involved usually is 
large and the effect of single genes frequently is small. Informa- 
tion on the nature of interaction of factors affecting quantitative 
characters is very meager. 

Powers (1936) studied the nature of the interaction of genes 
affecting the four quantitative characters, yield of seed per plant, 
number of spikes per plant, height of plant, and length of awn 
in a cross between varieties of Hordeum deficiens and H . vulgar e. 
Single plants of the parents F\ and F 2 were classified for black vs. 
white glumes (Bb), deficiens vs. vulgare type of spike (Ft;), and 
normal vs. brachytic type of growth (J3r6r). The yield of seed, 
number of spikes, plant height, and awn length were determined 
for individual plants. The genotype of the F 2 plants for the 
qualitative characters was determined from a progeny test in FS. 

Powers found that the homozygous black (BB) and homozy- 
gous white (66) segregates did not differ significantly in the 
four quantitative characters measured. The heterozygotes (Bb) 
exceeded the two homozygotes in all four quantitative char- 
acters, although not significantly so in some comparisons. This 
increase in the J56 segregates in ^2 over the BB and 66 may be 
explained as being due to favorable and at least partially domin- 
ant genes located in the chromosome pair carrying J56, 

Plants with the vulgare type of spike (vv) yielded more than 
those with the deficiens (FF) or the heterozygotes (Ft;). The Vv 
segregates yielded more than the FF plants. Normal plants of 
the genotypes BrBr or Brbr were higher in yield than the brachy- 
tic plants (6r6r) 



164 METHODS OF PLANT BREEDING 

In making comparisons of the differences in yield of seed 
between plants of the genotypes vv Brbr and VV Brbr with vv 
brbr and VV brbr, the cross difference (w Brbr VV Brbr) 
(w brbr VV brbr) was positive and significant. It is apparent 
that the difference in yield between segregates of the vulgare 
type (vv) was greater in the presence of the nonallelic genes Brbr 
rather than in the presence of the less favorable brbr and of the 
deficiens type (VV). In general, it was found that genes favor- 
able to high plant yield when transferred from a low to a high 
yielding geno-type of a nonallelic factor pair, in comparison with 
their alleles, were still more favorable to the development of grain 
yield than in the presence of the low yielding genotype. 

The foregoing evidence is the reverse of that expected according 
to Rasmusson's (1935) interaction hypothesis, which assumes 
"that the effect of each factor on the genotype is dependent upon 
all the other factors present, the visible effect of a certain factor 
being smaller the greater the number of factors acting in the same 
direction," Rasmusson found support for his theory in a study 
of interaction of factors governing early and late maturity in 
Pisum. Powers (1934) in a study of factors governing habit of 
growth in Triticum obtained results that support this hypothesis 
also. 

It is apparent that differences in interaction between genes 
controlling quantitative characters occur and that no general 
rule can be given at the present time that will describe all condi- 
tions. Powers concluded that at the present time any hypothesis 
regarding the nature of gene interactions is of doubtful value as 
a means of prediction. 



CHAPTER XII 
INHERITANCE IN FLAX 

All cultivated varieties of flax belong to the species Linum 
usilatissimum L. The haploid chromosome number usually 
found is 15, although 16 in the haploid and 32 in the diploid have 
been reported by several investigators (Tammes 1928, Dillman 
1936). Tammes gave the chromosome numbers of other Linum 
species as 8, 9, 10, 12, 14, 15, and 18 in the haploid condition. 
Extensive attempts to cross common varieties of flax with many 
of the wild-flax species have been made, but without success 
except in crosses between L. usitatissimum and L. angustifolium, 
which can be made without difficulty. The hybrids are com- 
pletely fertile as a rule. Because L. angustifolium has the same 
number of chromosomes and crosses readily with the common 
species, it has been considered by Tammes as the probable ances- 
tor of common flax. L. angustifolium differs from common 
cultivated varieties of flax in that the seeds and capsules are 
smaller, the edges of the partition walls of the capsule are hairy, 
and the capsules open or dehisce at maturity. 

Hairy capsules were dominant to glabrous in FI, and segrega- 
tion in F% was on a 3:1 basis. Dehiscence of the capsule at 
maturity was imperfectly dominant over the closed type of 
capsule, and several factors were necessary to explain segregation 
in F%. In a cross of cultivated varieties with a particular form 
of L. angustifolium having a strongly tillered and branched habit 
of growth of more delicate type of plant than cultivated varieties, 
Tammes found no plant among 300 grown in the F% generation 
that belonged strictly to the L. usitatissimum type. The length 
and width of petal and length of seed in L. angustifolium was less 
than that of the cultivated varieties. The inheritance of these 
character differences was dependent upon multiple (polymeric) 
factors. 

There is a similar range of flower colors in L. angustifolium as 
in cultivated varieties, although of the factors involved in flower, 

165 



166 



METHODS OF PLANT BREEDING 




FIG, 24. For descriptive legend see opposite page, 



INHERITANCE IN FLAX 



167 



seed, and plant colors, only two were exactly the same in L. 
angustifolium as in L. usitatissimum. 

Factors for Flower and Seed Color in Common Flax. Dillman 
(1936) has summarized the major effects of the interaction of 
eight genes for seed and flower colors as determined by Tammes. 
The pure lines that he obtained from Tammes, their petal, 
anther, and seed colors and genetic composition are summarized 
in Table 15. 

TABLE 15, GENETIC COMPOSITION AND CHAKACTEKS OF PURE LINES 
OF FLAX (AFTER DILLMAN) 







Description 


C.I. 

No. 


Factor composition* 














Petals 


Anthers 


Seeds 


765 


AA BiBi BtBz C'C' DD EE FF HH 


Blue 


Blue 


Brown 


766 


hh 


Blue 


Yellow 


Brown 


768 


aa 


Light blue 


Blue 


Brown 


769 


ee hh 


Pale blue 


Yellow 


Brown 


770 


ff 


Lilac 


Blue 


Brown 


771 


aa ff 


Light lilac 


Blue 


Brown 


772 


dd 


Pink 


Yellow 


Brown 


773 


dd ff 


Deep pink 


Yellow 


Light brown 


774 


c'c' 


White, flat 


Blue 


Brown 


775 


bibi 


White, 


Yellow 


Greenish yellow 






crimped 






776 


6*62 


White, 


Yellow 


Brown 






crimped 






777 


bibi c'c' 


White, flat 


Yellow 


Greenish yellow 


778 


c'c' dd 


White, flat 


Yellow 


Grayish brown 



* All dominant factors are present in common blue flax, C. I. 765, the recessive factors 
given, being those actually determining the character differences from common blue. 

These eight factors are believed by Tammes to be carried in 
different chromosomes. From the table it may be noted that 
BI, B%, and C f are basic color factors, all in the dominant condition 
being necessary for the production of color in the petals. The 

FIG. 24. Structure of the flowers of flax. 

1. Single flower: (a) calyx; (5) corolla 

2. Branch showing: (a) seed boll; (6) calyx; (c) flowers just after blooming; (d) bud. 

3. Calyx and corolla removed to show sexual organs in position: (a) anther; (6) 
filament; (c) stigma; (d) one of 5 divisions of style; (c) ovary. 

4. 6. Cross and longitudinal section of ovary. 

5. Ovary, stigma, and 5-lobed style. 

7. Cross section of anther. 

8. Anther. 

Size: 1, about 5 X ; 2, about X ; 3, nearly 4 X ; 4-8, greatly enlarged. 



168 METHODS OF PLANT BREEDING 

factors D and F determine the tint of the petals. When D is 
recessive, in the presence of the basic factors, the petal color is 
pink; F in a recessive condition causes lilac; and when both D 
and F are recessive, deep pink results. Factors A and E are 
intensifies. When a or e are homozygous, recessive, the color 
is of a lighter shade. 

J5i, -82, C" and D influence the shape of the petals, all four 
factors being in a dominant condition in most common flax 
varieties with broad, flat petals. If either 61 or 62 are recessive ; 
in the presence of both C" and D, the petals are narrow antJ 
"crimped," i.e., inrolled at the outer margins. If either C' or D 
is recessive, the petals are flat, regardless of the dominant or 
recessive condition for BI and J5 2 . The dominant condition of 
four factors BI, B 2 , D, and // leads to the production of blue 
anthers. When any one of the four factors BI, B^ D, and H is 
in a homozygous recessive condition, the color is yellow. 

The interaction of two of the genes that influence petal color, 
BI and D and a basic factor G for seed color conditions the 
development of color in the seed. When G is recessive, the color 
of the seed is yellow, because the yellow cotyledons are visible 
through the colorless seed coat. There are other factors that 
influence the intensity of seed color, and if G is present the seed 
may still be yellow. If B i is recessive, in the presence of G and 
D, there is a greenish color to the seed. When D or both BI and 
D are recessive, the color of the seed is modified from the normal 
brown color. Shaw et al. (1931) have postulated the interaction 
of at least seven factors that influence the inheritance of petal 
color in Indian varieties of flax. Their results are similar to those 
of Tammes. Their explanations of the inheritance of seed colors 
and crimping of the petals differed materially from those of 
Tammes. The genetic factors involved in these Indian varieties 
have not been studied in relation to those postulated by Tammes. 

Dehiscence of the Bolls. Three types of flax bolls may be 
distinguished: dehiscent, semidehiscent, and indehiscent. Most 
cultivated varieties of flax in the United States have the semi- 
dehiscent type of boll, where the boll opens at the apex and the 
five segments separate slightly along the margins. In the inde- 
hiscent type is found most of the Indian and Argentine varieties. 
The character is of economic importance, since the semidehiscent 
types thresh more easily than the indehiscent. Dillman sum- 



INHERITANCE IN FLAX 169 

marizes crosses made by J. C. Brinsmade, Jr., between the 
two types. Semidehiscent was dominant, and ratios in F* 
approached 15 semidehiscent:! indehiscent. 

Smooth vs. Ciliate Septa. Dillman points out that in most 
cultivated varieties of flax the septa are ciliate, although a few 
varieties have smooth septa. In most American systematic 
botanical statements, the bolls are described as having nonciliate 
septa. He credits Brinsmade and A, C. Arny with having 
obtained a ratio in F 2 of 3 ciliated:! smooth. 

Weight of Seed and Oil Content. Dillman has given the 
weight of 1000 seeds in grams for L. angustifoUum and varieties 
of common flax grown in 1930 under irrigation at Bozeman, 
Montana. The lowest weight was that of the wild species L. 
angustifoUum , at 1.5 g. per 1000 seeds, with the heaviest weight 
being obtained for the Lino Grande variety of 11.55 g. per 1000 
seeds. 

Myers (1936) studied seed weight in a cross between Redwing 
with a 1000-seed weight of 4.33 g., and Ottawa 770B with a mean 
of 5.35 g. There was a partial dominance of large seeds in FI. 
One hundred F* lines were grown, and studies of seed weight 
were made in comparison with Redwing and Ottawa 770B. One 
Fs line had a seed weight nearly as low as Redwing, with a rela- 
tively low variance. Two F 3 lines had as great or greater seed 
weight than Ottawa 770J3, although the variance for both lines 
was significantly greater than that of the parents. In this cross 
it is apparent that weight of seed cannot be placed on a simple or 
definite factor basis. 

Dillman found that the oil content may vary from 33 to 44 per 
cent or more, depending upon the interaction of heredity and 
environment. Johnson (1932) studied the oil content of 46 
varieties of flax grown in replicated rod-row trials at University 
Farm, St. Paul, Minnesota, in 1929 and 1930. The material 
included both Argentine and domestic varieties and selections 
from varietal crosses. The correlations for weight of 1000 seeds 
and oil content were +0.72 and +0.78 for the 2 years, respec- 
tively. Dillman studied 124 varieties and strains grown at 
San Antonio, Texas, in 1926, that ranged in weight of 1000 seeds 
from 3.5 to 7.5 g. and in oil content from 36 to 44 per cent. He 
obtained a correlation between seed size and oil content of 
+0.70, 



170 



METHODS OF PLANT BREEDING 



Dillman placed varieties in four groups on the basis of seed size, 
small, midsize, large, and very large. In general, the varieties 
with larger seed tend to have higher oil content and selection for 
seed size in a cross between parents that differ in seed-size aids 
in obtaining varieties with higher oil content. 

Inheritance of Quality of Oil. The drying quality of oil is 
dependent upon the quantity of oxygen absorbed in the process 
of drying to form the characteristic paint film. The chemist 
determines the relative drying quality of oils by the absorption 
of iodine per unit quantity of oil, the drying quality being 
expressed as the iodine number. Values may range from 150 to 
200 in extreme samples. Johnson obtained a negative correlat- 
tion coefficient of 0.31 for drying quality and weight of 1000 
seeds, using 46 varieties grown in rod-row trials in 1930. 

Arny (1936) has studied the inheritance of iodine number in 
several crosses between common varieties. The character is 
influenced rather strongly by environmental factors, individual 
plant determinations in the same pure line giving rather wide 
ranges in iodine index. Iodine index of parent plants of Bison 
and Ottawa 770B and of the Fi and Fa generations are given in 
Table 16. 

TABLE 16. IODINE NUMBER OF OIL FROM INDIVIDUAL PLANTS OF BISON 

AND OTTAWA 770B AND FROM THE Fi AND F z GENERATIONS OF CROSSES 

BETWEEN THESE Two VARIETIES 

University Farm, 1933* 





CO 
IQ 


05 

*Q 


S 


S 


$ 


r I 
t^. 


s 


i> 
j> 


8 


s 




Culture 


* 





8 


4 


ci 

CD 


A 

CO 


& 


JL 

> 


i 


JH 

00 


Total 


























Bison 


3 


3 


7 


14 


6 


4 










37 


770B 














fl 


14 


7 




23 


Bison X 770BFi 








4 


3 


5 










12 


Bison X 770BF 2 


?, 


10 


?4 


?4 


38 


37 


20 


13 


6 


?, 


176 



























* Unpublished data kindly furnished by A. C. Arny. 

In this cross, the FI resembled the low-iodine-index parent, 
although dominance was not complete. Segregation occurred 
in F%. In backcrosses of the F\ to the parent with higher iodine 
index, Arny obtained a 1 : 1 ratio when plants that fell within the 
range of the higher iodine-index parent were considered homo- 
zygous and those with a lower iodine index were classified as 



INHERITANCE IN FLAX 



171 



heterozygous. These and other data led to the conclusion that a 
single factor pair was responsible for the main differences in 
quality of oil in most of the crosses studied. 

Arny (1936) found rather close linkage between iodine index 
and seed color. The following results (cited by Dillman 1936) 
are from backcrosses in the coupling phase. 





Year 


Yellow 


v seed 


Browi 


i seed 


Cross 


crown 


High 


Low 


High 


Low 


(Bison: brown, low X C. I. 355; 
yellow, medium) X C. I. 355 
(C. I. 355 X C. I. 423; yellow, 
high) X C. I. 355 


1933 
1934 


64 
25 


3 

7 


12 
6 


56 
21 


(Bison X C. I. 391; yellow, high) X 
C. I. 391 


1934 


75 


4 


13 


87 














Total 




164 


14 


31 


164 















The calculated recombination percentage of 12.0 1.7 was 
obtained. 

DISEASE RESISTANCE 

Bolley, about 1900, in North Dakota, discovered the organism 
that causes wilt in flax and named it Fusarium lini Boll. He was 
one of the first to produce an artificial epidemic of a plant disease 
as an aid in selecting for resistance. His early work of selection 
for wilt resistance in flax and for disease resistance in other crop 
plants emphasized the importance and desirability of breeding 
for disease resistance. 

Wilt Resistance. The severity of infection with wilt is greatly 
influenced by environmental conditions, particularly soil tem- 
peratures, heritable differences in the degree of resistance of 
different varieties, and physiologic races (Broadfoot 1926) of 
the pathogen that causes the disease. Tisdale (1916, 1917) made 
important contributions to the nature and inheritance of wilt 
resistance. High temperature was a favorable agent in overcom- 
ing resistance. The fungus penetrates the flax plant through the 
stomata of seedlings, the root hairs, or through the young epi- 
dermal cells. In a resistant plant, the fungus on entering stimu- 
lates cork-wall formation of cells adjacent to those attacked. 



172 



METHODS OF PLANT BREEDING 



Tisdale studied the inheritance of wilt reaction in crosses between 
resistant and susceptible strains. Some Fi crosses were much 
more resistant than others, and in some crosses there appeared 




FIG. 25. Two varieties of flax grown at St. Paul, Minnesota, showing range 
in height. Left: Redwing, a typical seed-flax variety. Right: Cirrus, a typical 
fiber flax. Varieties of fiber flax are taller and less branched than varieties of 
seed flax and produce lower yields of seed, 

to be a dominance of resistance, 8 whereas other crosses indicated 
a dominance of susceptibility. Although segregation occurred 
in JP 2 , the results could be explained only on a multiple-factor 
basis. 

Bolley (1912) was unable to explain adequately the gradual 
accumulation of resistance when the crop was grown on wilt-sick 



INHERITANCE IN FLAX 173 

soil and the loss of resistance that was often observed after a wilt- 
resistant variety had been introduced. He favored the idea that 
disease resistance developed by a gradual accumulation of 
resistance under infection conditions. He was an early leader 
in developing wilt-resistant varieties, and the variety Bison 
selected by Bolley is the most widely grown wilt-resistant variety 
in the flaxseed area of Minnesota, North Dakota, and adjacent 
states. Barker (1923) made a careful study of these problems 
and found that some varieties contained no resistant genotypes 
and that in these cases resistance was not developed from a 
constant association with the pathogen. He found also that 
wilt-resistant pure lines did not lose their resistance when grown 
on wilt-free soil. 

In a study of reaction to wilt, parental lines were self-pol- 
linated by Burnham (1932) for at least three generations to ensure 
homozygosity. Studies were carried on under field conditions 
in wilt-infested soil, and the flax was planted late to ensure 
optimum infection. Certain strains of flax used as parents were 
completely susceptible; others, highly resistant; but occasional 
wilted plants were found in resistant lines used as parents. 
These were not believed to be genotypic variations. The extent 
of wilting obtained in progeny tests of different inbred parents 
ranged from highly resistant through partially susceptible to 
highly susceptible. Because of the nature of the disease, plants 
for producing F 2 and F 8 progenies were grown on wilt-free soil 
and random F 3 lines used to study the genetics of wilt reaction. 
From several crosses between resistant and susceptible parents, 
the mean for wilting of the F% was generally intermediate between 
that of the parents, and F 3 lines were obtained with mean per- 
centages of wilting that ranged from high resistance to complete 
susceptibility. Approximately 1 out of 10 F 3 lines were as resist- 
ant as the resistant parent. In several crosses between resistant 
parents, there was a high percentage of susceptibility in F^ 
indicating that the parents may have differed in factors for resist- 
ance. The difficulty of making a genetic analysis is due partially 
to the variability in wilt reaction from season to season and to 
variations in wilt reaction of the same pure line in different parts 
of the wilt nursery. The number and nature of genes responsible 
for wilt resistance could not be determined. Even though more 
than a single factor pair for wilt reaction was necessary to expla ;i a 



174 METHODS OF PLANT BREEDING 

the results, it appeared relatively easy, in crosses between resist- 
ant and susceptible strains, to recover lines as resistant as the 
resistant parent. 

Resistance to Rust. The importance of rust resistance in the 
seed-growing areas in North America is generally recognized. 
In a recent report, Flor (1940) has listed 24 physiologic races 
of Melampsora lini (Pers.) Lev. that have been differentiated on 
the basis of the reaction of 11 varieties of flax. No varieties of 
flax were found that were resistant to all races. Ottawa 770B, 
which has been used extensively in studies of the inheritance of 
rust reaction, and flaxes of the Argentine type have remained 
immune from all races collected in North America. The Argen- 
tine selection was susceptible to three physiologic races 19, 20, 
and 22 collected in South America, whereas Ottawa 770B 
proved susceptible only to race 22. Varieties of flax are available 
that are resistant to the South American races of rust but sus- 
ceptible to North American races. 

Henry (1930) used Ottawa 770B as one of several immune 
parents in crosses of immune X susceptible. Immunity was 
dominant in Fi. Only a single factor pair was necessary to 
explain the crosses between immune vs. susceptible when Ottawa 
770B was used as the immune parent. When Argentine selection 
was used as the immune parent, segregation was on a 15 : 1 basis. 

Myers (1937) grouped parental varieties used in studies of 
inheritance of rust reaction into five groups; immune, near 
immune, resistant, semiresistant, and susceptible, with the use 
of a collection of rust for the source of infection. He explained 
results obtained by two allelic series where L and M are duplicate 
factors conditioning immunity from the collection, l n and m n 
condition near immunity, l r and m r are duplicate factors for 
resistance, and I and m are the recessive alleles conditioning sus- 
ceptibility. The two series of alleles then would be L, Z n , J r , I, 
and At, m n , m r , m. The genotype of Ottawa 770B was considered 
to be LL mm. 



CHAPTER XIII 
METHODS OF SELECTION FOR SPECIAL CHARACTERS 

It has been emphasized in preceding chapters that the breeding 
of improved varieties almost invariably involves selection for 
many characters. Some characters ca& be classified easily, and 
visual inspection will determine the desirable ones. Other 
characters are difficult to evaluate, and special methods must be 
developed to make controlled selection possible. To make the 
most rapid progress possible in plant breeding, it is essential that 
the breeder cooperate with other plant-science specialists in order 
that efficient methods of selection be developed. The methods 
used may vary with the nature of the material, the training 
of the investigator, and the facilities available. The plant 
breeder of today can well afford to make a greater use of plant 
physiological technics already available and to take an active 
leadership in the development of new technics. Illustrations 
will be given of certain technics that have been developed to 
aid in character differentiation. 

QUALITY TESTS IN WHEAT 

A determination of the desirability of a particular variety of 
wheat, for human consumption, will depend on the use to be 
made of it. The more important uses include bread, macaroni, 
pastry, crackers, and breakfast foods. Wheat especially adapted 
to one use may be very inferior for some other. The science of 
milling and baking is highly specialized, and the satisfactory 
evaluation of wheat quality can be made only by the cereal 
technologist. This emphasizes again the need of close coopera- 
tion between the plant breeder and technologists in other fields. 

Among the necessary characteristics of satisfactory bread 
wheats is suitable baking strength. This may be defined as the 
inherent capabilities of a wheat or flour to produce a loaf of good 
volume and satisfactory crumb grain and texture, provided it is 
baked under conditions that preclude yeast starvation. Some 

175 



176 METHODS OF PLANT BREEDING 

wheats require special treatment in milling or baking to bring 
out optimum results, making it necessary to vary fermentation 
time, mixing treatment, and use of " improvers" in order to 
obtain a complete evaluation of breadmaking characteristics. 
Crumb color in the bread and pigment concentration in the 
flour are sometimes important, and so are the dough-handling 
properties. 

For a discussion of milling and baking methods and tests for 
different properties of the flour, the student may be referred to a 
book published by the American Association of Cereal Chemists, 
"Cereal Laboratory Methods" (1941). 

A complete study of the milling and baking properties of a 
series of wheats is relatively expensive, and larger quantities of 
wheat are required than can be made available during the early 
generations in the breeding program. A number of simple, 
rapid methods for evaluating certain properties of flour have 
been developed. To be of greatest use to the plant breeder, in 
selection, such methods must be rapid and inexpensive and must 
require relatively small amounts of wheat. None of these 
methods alone can replace actual baking trials under commercial 
conditions. One such rapid test of baking strength will be 
mentioned. 

Wheat-meal Fermentation-time Test. The wheat-meal-fer- 
mentation-time test originated by Saunders and Humphries 
(1928) and developed by Pelshenke (1930, 1933) in Germany and 
Cutler and Wor^ella (1931, 1933) in America has aroused a great 
deal of interest as a possible means of evaluating baking strength 
from small amounts of seed. The method is rapid, inexpensive, 
and only 15 g, of wheat is needed. It is of interest to the plant 
breeder as a means of selection during the early generations in a 
breeding program when large numbers of strains need to be tested 
for baking quality. The test is based on the resistance of fer- 
menting dough (made from medium finely ground whole-wheat 
meal) to disintegration in water. The test consists of making a 
ball of dough from the wheat meal, to which a standard amount 
of yeast has been added, placing Ihe dough ball in distilled water 
in a temperature-controlled incubation chamber, and recording 
the time it takes for the dough ball to disintegrate. The time 
required for the dough balls to break will furnish a measure of 
baking strength, the stronger wheats requiring a longer time. 



METHODS OF SELECTION FOR SPECIAL CHARACTERS 177 

In general, it may be said that the results of the wheat-meal- 
fermentation-time test have been in fair agreement with baking 
behavior when wheats differing materially in baking strength are 
studied. The test has been used to good advantage, particularly 
with soft winter wheats, where soft wheats with a short period of 
dough-ball disintegration have been selected. For wheat 
varieties that do not differ greatly in baking strength, the meal- 
fermentation-time test can not be relied on to differentiate the 
varieties according to their reaction in standard baking trials. 
This appears to be true particularly with the hard wheats and in 
breeding experiments in which both parents have good baking 
strength. 

COLD-RESISTANCE TESTS WITH WHEAT 

Cold resistance of winter-wheat varieties is best measured in 
field tests in the region in which the wheat is to be grown. Dif- 
ferential killing is obtained only in certain years, and slight 
depressions in the field often lead to killing in " patches" with 
little relation to varieties. The development of a satisfactory 
laboratory test would be of great aid in selecting for cold resistance. 

Numerous investigators in the hard-red-winter- and soft-red- 
winter-wheat regions of the United States have shown that 
artificially produced low temperatures could be used as an index 
of the ability of strains of winter wheat to survive in the field. 
The methods used and results obtained in a recent study by 
Weibel and Quisenberry (1941) will be given briefly. 

Thirty varieties of winter wheat grown in the cooperative Great 
Plains Uniform Winterhardiness Nursery were used for the study 
because of the great amount of information available as to their 
relative winter hardiness in the field. 

For the test of cold resistance, seed of the varieties was sown 
in flats outside during the first week in October (at Lincoln, 
Nebraska). Good growing conditions were maintained and the 
plants reached the tillering stage before going into a dormant 
condition for the winter. Freezing tests were made November 
15, December 5, December 15, and January 15 by exposing the 
plants to temperature of 17 to 26C. for 24 hr., in a mechani- 
cally controlled freezing chamber. After this freezing period,, 
the flats were transferred to a greenhouse maintained at 21C 
and kept watered to allow live* plants to .recover. Survival 



178 METHODS OF PLANT BREEDING 

counts were made 10 days after freezing. Twelve replications 
were used in each of 2 years. 

The interannual correlation between the survival of these 30 
varieties in artificial freezing tests in each of 2 years was +.930. 
When the average survival, for 2 years, in controlled freezing 
tests was correlated with the survival of the same varieties in 
the field a coefficient of +.866 was obtained, a highly significant 
value. 

These wheat varieties differed markedly in cold resistance. 
Extensive studies in Minnesota with strains of wheat not differ- 
ing greatly in winter survival have shown very little association 
between winterkilling under field conditions with reaction in 
controlled freezing tests. Winter hardiness involves more than 
cold resistance. Alternate freezing and thawing, " heaving " of 
the soil, and other factors are of importance also. 

SHATTERING IN WHEAT 

Most American varieties are relatively resistant to shattering, 
probably because of selection for nonshattering during the breed- 
ing programs, although marked differences in this character 
may be observed. Shattering probably is of greater importance 
in the Pacific northwest than in other regions, since wheats in 
that region frequently are allowed to stand in the field after 
ripening for longer periods of time before being harvested. Wheat 
breeders in China have noted that one of the most undesirable 
characters of Chinese varieties is their extreme susceptibility to 
shattering, as contrasted with introduced varieties (Chang 1940). 

Vogel (1938) studied the relation of the amount of mechanical 
tissue in the basal portion of the glumes to shattering in wheat. 
In general, a direct relationship was found between relative 
resistance to shattering and the extent of mechanical tissue at 
the breaking point of the glumes. Chang (1940) found a direct 
relationship between shattering and the amount of strengthening 
tissue in the inner basal portion of the empty glume and the 
peripheral region of the basal portion of the lemma. 

A simple machine was constructed by Chang to determine 
resistance to shattering. This instrument was constructed in 
such a manner that turning a crank would cause a rubber paddle 
to beat the wheat heads, held on a shattering board, and thresh 
a portion of the grain. Three heads were tested in each trial 



METHODS OF SELECTION FOR SPECIAL CHARACTERS 179 

and 20 trials used for each plot. The mean percentage of shatter- 
ing, in different varieties, obtained by the use of this instrument, 
varied from 1.3 to 29.6. There was good agreement between 
shattering under field conditions and in the controlled studies 
with the shattering machine. 

DORMANCY IN RELATION TO BREEDING 

Afterharvest sprouting may be a problem in the grain fields 
of many parts of the world. Varieties are known to vary greatly 
in length of the dormancy period after grain is ripe. In certain 
regions, the plant breeder wishes to select strains or varieties 
that are not susceptible to early germination in order to escape 
the losses in yield and in quality from germination of the grain 
in the shock as a result of rains after harvest. 

Larson et al, (1936) studied the length of the rest period of 
common varieties of wheat, oats, barley, and rye by germination 
tests at three stages of ripeness: soft dough, hard dough, and ripe. 
The rest period was longest in immature seeds. The length of 
the rest period varied greatly with the variety. In general, 
winter wheats had a shorter rest period than spring wheats. 
The spring-wheat varieties Mindum, Marquillo, Kubanka, and 
Thatcher were found to have a long rest period. 

Harrington and Knowles (1940a) presented the results of tests 
of the length of the dormancy period of varieties of wheat and 
barley. Head samples were collected from the varieties to be 
studied at the stage of maturity when the lower kernels on the 
spikes could be indented with difficulty with the thumbnail. 
Germination tests were made at intervals of 4, 8, 12, 16, 21, 26, 
and 36 days after maturity. 

The varieties of spring wheat varied from the inability of 
Reliance to remain dormant more than 2 days after maturity 
to the ability of Renown to hold a high degree of dormancy for 
2 weeks. 

In another paper, Harrington and Knowles (19406) concluded 
that the failure of the seeds of some varieties to germinate after 
exposure to moist weather for several days after harvest is due 
to the dormancy period of the varieties and not due to slow 
germination. Apex, Thatcher, and Renown were high in resist- 
ance to sprouting, whereas Garnet was very low. Chang (1940) 
also found afterharvest sprouting to be related definitely to 



180 METHODS OF PLANT BREEDING 

length of dormancy in hard red spring wheat, barley, and oat 
varieties. 

Harrington and Knowles found that the variation in amount of 
sprouting of strains from crosses was related directly to the 
sprouting characteristics of the parents. Transgressive segrega- 
tion occurred in some crosses, strains more resistant to sprouting 
than either parent being obtained. Tests of the amount of 
sprouting immediately after harvest can be used in selecting 
strains that are not deficient in this character. 

LODGING IN SMALL GRAINS AND CORN 

Lodging frequently results in serious losses in yield and quality. 
It is a difficult character to evaluate, since it is affected by 
numerous characters of the plant and conditions of the environ- 
ment. In some seasons little or no lodging is obtained. In other 
seasons storms may cause most or all varieties to lodge. This 
situation naturally has led investigators to study differences in 
plant characters that might be associated with lodging. 

Holbert (1924), Hall (1934), and others have found lodging 
in corn to be significantly correlated with the force necessary to 
pull the plant from .the soil. This has led to determinations of 
the pulling resistance of inbred strains and hybrids of corn as a 
measure of their ability to withstand lodging. 

Salmon (1931) devised an instrument for measuring the 
strength of straw of small grains. Strength of straw was meas- 
ured in terms of the force necessary to break a given number of 
straws. Salmon showed that breaking strength of the straw 
was correlated with lodging behavior in the field. These results 
have been substantiated by several other investigators. 

Atkins (1938) made an extensive study of strength of straw 
and other characters in relation to lodging in winter wheat. 
Straw strength was based on the force required to break five 
straws taken at the first upright internode above the crown of the 
plant. Twenty determinations were made per variety. 

Relative breaking strength pf straw was fairly constant from 
year to year, whereas lodging was not. Average lodging for 
several years was correlated significantly with average straw 
strength. In a single season, the correlation was not significant. 
In view of the variability in lodging from year to year, Atkins 
concluded that breaking strength for a single season was a more 



METHODS OF SELECTION FOR SPECIAL CHARACTERS 181 

reliable index of lodging than was a record of lodging for a single 
season. 

Clark and Wilson (1933) correlated the average breaking 
strength of 30 culms per variety in spring wheat, for a single 
test, with the average lodging index determined from rod-row 
trials at four stations in Minnesota for 3 years. The correlation 
coefficient was nonsignificant. Breaking strength and diameter 
of the culms were correlated to the extent of + .537 .148, 

DROUGHT STUDIES WITH CORN 

Corn yields in the Great Plains region of the United States are 
frequently reduced greatly by periods of very high temperature, 
low humidity, and deficient soil moisture in midsummer. Under 
these conditions, it has been noted that inbred lines and hybrids 
vary in their ability to withstand such periods of high tempera- 
ture. Seasonal conditions vary greatly, and high temperatures 
do not occur every year, making selection for drought resistance 
difficult. Consequently a laboratory test would be highly 
desirable. 

Hunter et al. (1936) and Heyne and Laude (1940), in Kansas, 
described a method for testing corn seedlings for resistance to 
high temperatures. The corn was planted in 4-in. unglazed 
pots, with enough seed to ensure a uniform stand of seven 
plants per pot. When the seedlings were from eighteen to 
twenty days old, they were placed in a heated room at a tem- 
perature of 130F. and a relative humidity of from 25 to 27 per 
cent for 5 hr. The plants were supplied with enough water prior 
to the test to keep the soil moist throughout the 5-hr. test. The 
amount of injury, expressed as a percentage of exposed leaf and 
sheath tissue that had been killed, was estimated 3 days after 
treatment, and the number of plants killed and degree of recovery 
were determined 10 days after treatment. 

The reaction of 90 per cent of the inbred lines of corn subjected 
to controlled high temperature in the seedling stage was in 
accord with the known behavior in the field under extreme 
temperatures in midsummer. All lines that were low in resistance 
to heat in the field reacted in a similar manner in the seedling 
test. The high-temperature test in the seedling stage was con- 
sidered a valuable supplement to. studies of drought resistance 
in the field. 



182 METHODS OF PLANT BREEDING 

INDUCING BIENNIAL SWEET CLOVER TO FLOWER THE 
FIRST YEAR 

Planting sweet clover in the field results in flowering plants 
being obtained only in the second year. This makes for slow 
progress in breeding. 

It has been found that extending the length of day to from 18 
to 24 hr. by means of supplementary light stimulates flowering of 
seedlings of biennial sweet clover from 6 to 8 weeks after emer- 
gence of the seedlings. This makes it possible to grow a genera- 
tion in the greenhouse during the winter months. The plants 
would be small, however, and selection for type would be 
relatively ineffective. 

A seed crop the first year on relatively normal plants may be 
obtained by planting the seed in pots or flats in the greenhouse 
in February and subjecting the seedlings to enforced dormancy 
when they are from 2 to 3 in. tall by keeping them at 0C. for 
about 20 days. After the cold treatment, the seedlings are 
allowed to grow under normal temperatures in the greenhouse 
until ready to transplant in the field. Seedlings so treated will 
produce fairly large plants the same season and flower profusely. 

DETERMINATION OF COUMARIN CONTENT IN SWEET CLOVER 

Strains and species of sweet clover, Melilotus, vary greatly in 
amount of coumarin, the compound that gives sweet clover its 
bitter taste and that has recently been shown by Campbell 
et al. (1940) to form the hemorrhagic substance in spoiled sweet- 
clover hay. Development of strains of sweet clover low in cou- 
marin would improve the palatability of the crop greatly and 
reduce danger in its use as hay. 

Several methods for the determination of coumarin content in 
sweet clover have been developed. The method developed by 
Clayton and Larmour (1935) and Stevenson and Clayton (1936) 
has been modified slightly in Minnesota and is described for 
leaf-tissue analysis here in detail. 

Approximately 40 leaves are collected from each plant, in 
duplicate, well distributed among several branches. The leaves 
are taken from the region 4 to 12 in. from the tips of the main 
stem or side branches and with as short petioles as possible. It 
is known that the amount of coumarin varies considerably in 



METHODS OF SELECTION FOR SPECIAL CHARACTERS 183 

different parts of the plants. Consequently, care should be used 
in collecting the sample of leaves from the same relative portions 
of the plants. 

The leaves collected from each plant are mixed, and a 1-g. 
sample for extraction and a 1-g. sample for dry-matter deter- 
mination are weighed. The dry-matter sample is dried in an 
oven kept at 105C. for 20 hr. and the dry weight determined. 

The 1-g. sample for coumarin determination is placed in a small 
glass vial closed with a cork stopper, frozen as soon as possible, 
and kept frozen until ready for analysis. The advantage of 
storing the frozen samples is that many plants may be rapidly 
sampled, and any plants that may be discarded later on the 
basis of disease or plant characters have not been needlessly 
analyzed. 

In making the analyses, the sample is ground in a mortar with 
1 cc. of fine, washed sand. The ground sample is transferred to 
a 70-cc. test tube. The mortar and pestle are cleaned during 
transfer with 50 per cent methyl alcohol and the sample brought 
up to 51-cc. volume with 50 per cent alcohol. The sample is 
shaken thoroughly (in a shaking machine) for 30 min. to extract 
the coumarin from the ground-leaf tissue. A portion (about 
25 cc.) of the extract is filtered, and 5 cc. is placed in a tightly 
stoppered vial. This is allowed to stand in light for 12 hr. to 
break down the chlorophyll. 

The 5-cc. sample of the filtrate is transferred to a test tube 
graduated for 50 cc., and 5 cc. of 1.1 per cent Na2COs and 20 cc. 
of distilled water are added. The mixture is now placed in a 
water bath at 80C. for 15 min., removed, cooled to room tem- 
perature; 5 cc. of ice-cold diazonium solution is added, and the 
volume made to 50 cc. with distilled water and mixed. The 
sample is then allowed to stand for 2 hr., after which the amount 
of coumarin is determined through comparison with standard 
solutions with known amounts of coumarin. 

Twelve standards containing 0.0 to 1.2 mg. of pure coumarin 
per 50 cc. are made up. To do so, the requisite amount of 
standard coumarin solution is placed in a test tube graduated for 
50 cc., about 20 cc. of distilled water, 5 cc. of alfalfa extract, 1 and 
5 cc. of 1.1 per cent Na2C(>3 are added. The test tubes are placed 

1 The alfalfa extract is prepared by adding 500 cc, of 50 per cent methyl 
alcohol to 10 g. of finely sliced alfalfa, shaking for 2 hr., and filtering. 



184 



METHODS OF PLANT BREEDING 



in a water bath at 80C. for 15 min., cooled, 5 cc. of the cold 
diazonium solution is added, the resultant solution made up to 
50-cc. volume, mixed, and allowed to stand for 2 hr. Readings 
on these standards are obtained in a photoelectric colorimeter and 
a curve drawn. 

The diazonium solution is prepared from two solutions, A and 
B, as follows: 

Solution A. Dissolve 3.5 g. of p-nitraniline ill 45 cc. of 37 per 
cent hydrochloric acid, dilute to 500 cc. with distilled water, and 
filter. This solution keeps indefinitely if stoppered. 

Solution B. Dissolve 5 g. of sodium nitrite in 100 cc. of dis- 
tilled water. Keep this solution in a dark bottle away from light. 
This solution should be renewed frequently, since it does not 
keep well. 

Diazonium Solution. Thoroughly chill a 100-cc. flask, solution 
A and solution B, on chipped ice. Pipette 3 cc. of solution A and 
3 cc. of solution B into the 100-cc. flask, chill for 5 min., add 
12 cc. of solution J5, shake, chill for another 5 min., fill to the 
100-cc. mark with ice-cold distilled water, mix, and place on 
chipped ice for 15 min. befol-e using. If kept on ice, this solution 
will remain stable for at least 24 hr. 



TABLE 17. FREQUENCIES OP COUMAKIN PERCENTAGES IN PARENT CHECKS 

AND IN F 2 OF CROSSES BETWEEN HlGH AND LOW CoUMARIN SELECTIONS 

AND THEIR PARENTS 



Parent or F% 


Number of plants with coumarin percentage of 


0.00 


0.01 


0.02 


0.03 


0.04 


0.05 


0.10 


0.20 


0.30 


0.40 


0.50 


0.60 


Low parent. . . 
High parent . . 
F z 


11 
17 


25 

7 


2 

12 


1 
8 


1 

7 


2 

4 


1 


1 
19 


4 
21 


10 
43 


12 
35 


1 
35 





The field samples are tested in the colorimeter, the reading 
being compared with the curve for the standards. Since a 5-cc. 
aliquot of the unknown sample represents 0.1 g. of the original, it 
follows that the colorimeter reading for a given standard solution 
in milligrams represents the percentage of coumarin in the sample 
for analysis. The amount of coumarin is calculated to a mois- 
ture-free basis, For coumarin analysis of seed, an incubation 



METHODS OF SELECTION FOR SPECIAL CHARACTERS 185 

period'is necessary. An alternative micromethod of analysis has 
been described by Roberts and Link (1937). 

Stevenson and White (1940) reported that through continuous 
selection in inbred lines a strain of sweet clover has been devel- 
oped with only about one-tenth the amount of coumarin found in 
ordinary sweet clover. Stevenson and White crossed low- with 
high-coumarin selections and studied segregation in JFV The 
results are given in Table 17. 

The F% distribution appears to be definitely bimodal. There 
were 55 F 2 plants with 0.00 to 0.05 per cent coumarin and 153 
with 0.10 to 0.60 per cent. The results indicate that low 
coumarin is inherited as a recessive in an apparently simple 
manner. 

METHOD FOR DETERMINING HYDROCYANIC ACID CONTENT OF 
SINGLE PLANTS OF SUDAN GRASS 

Individual plants of sudan grass vary greatly in hydrocyanic 
acid content. Since HCN is extremely toxic, it is highly desirable 
to breed strains of sudan grass free from or very low in HCN 
content. If single plants are to be the unit of selection, a test 
for HCN must be rapid and relatively inexpensive. 

Hogg and Ahlgren, at Wisconsin (unpublished), have used a 
procedure based on a method developed by Nowogad and Mac- 
Vicar (1940). A description of this method, by Henry L. 
Ahlgreif (unpublished communication) is given here. 

The method consists of placing .15 grams of green plant material, cut 
into short pieces with a scissors or macerated, in a test tube, adding 
three or four drops of chloroform, and suspending a strip of moist filter 
paper saturated with sodium picrate solution above the mixture. The 
saturated filter paper is held in place with a cork stopper which is used 
to seal the test tube. The mixture is incubated at room temperature 
(20C.) for 12 to 24 hours. The sodium picrate present on the filter 
paper is reduced in the presence of hydrocyanic acid. The color is 
dissolved out of the paper by placing the paper in a clean test tube 
containing 10 cc. of distilled water and is matched with color standards. 
The test is sufficiently accurate quantitatively for the selection of plants 
low in hydrocyanic acid. The results may be expressed in relative 
terms such as "high," "medium" or "low" or in approximate P.PJV1. 
based on the percentage of dry matter in the sample. 

Tillers from 5 to 7 inches in height can be used regardless of the height 
of growth of the remaining portions of the plant. The samples for 



186 METHODS OF PLANT BREEDING 

analysis for hydrocyanic acid are taken from that portion of the tiller 
immediately below the uppermost leaf collar. 

The^ reagents and standards are prepared as fdllbws: 

The alkaline picrate solution is prepared by dissolving 25 g. of NazCOs 
and 5 g. of picric acid in 1000 cc. of distilled water. 

Chloroform of Merck's U.S.P, grade is used. 

The color standards are prepared by dissolving 0.241 g. KCN in 
1000 cc. of water. This gives a stock solution containing 0.1 mg HCN 
per cc. Place 5 cc. of the alkaline picrate solution and fSoc, of the KCN 
solution in a test tube. Add the following amounts of the KCN-alkaline 
picrate solution to eight test tubes 

Tube Number Cc. Solution 

1 0.00 

2 0,10 

3 0.20 

4 0.40 

5 -0.60 

6 0.80 
. 7 1,00 

8 1.60 

Bring the volume of each test tube up to 10 cc. by adding distilled 
water and heat to boiling in a beaker of water. Permit test tubes to 
stand in boiling water for five minutes. Stopper tubes and keep in a 
cool place. The number of milligrams of HCN present in each test 
tube is as follows: tube 1, 0.00; tube 2, 0.005; tube 3, 0.01; tube 4, 0.02; 
tube 5, 0.03; tube 6, 0.04; tube 7, 0.05; and tube 8, 0.08. These stand- 
ards can be used for two weeks. 

The test paper is prepared by cutting sheets of filter paper into strips 
10 to 12 cm. long and 0.5 cm. wide and saturating them with alkaline 
picrate solution. 



CHAPTER XIV 

DEVELOPMENT OF METHODS OF CORN BREEDING 
SELECTION WITHOUT CONTROLLED POLLINATION 

* * '", 

Methods of corn breeding have been studied Extensively since 
the introduction of the ear-to-roi? method of breeding by Hopkins 
(1899) in 1896. This consisted of growing and studying the 
progeny of each ear selected in a single rx>w and continuing selec- 
tion from the better yielding rows. Later the method was 
improved by replication of rows from each ear and detasseling a 
part of the rows from which seed was selected to prevent too close 
inbreeding. Williams (1905, 1907) first suggested a remnant 
method by which a part of each ear was saved to use for increase 
after the better yielding rows had been determined. By this 
plan three plots were needed each year, the ear-to-row trial plot, 
an increase plot, where the better lines as determined from the 
ear-to-row trial were increased, and a multiplication plot from 
seed produced the previous year in the increase plot. He also 
suggested cooperation and exchange of material among several 
breeders as a means of avoiding too close inbreeding. Mont- 
gomery (1909) suggested that the ear-to-row plot be used only 
once in several years. In intervening years, a seed plot was 
planted, and selection of seed was made from vigorous plants in 
perfect stand hills. 

The usual result from this type of selection is well illustrated by 
studies made by Kiesselbach (1922), in which the yields given 
represent averages from 1911 to 1917, 

Data obtained gave an opportunity to compare the yields of 
foiir different methods of seed selection and were as follows: 

Average Yield, 
Type of Selection Bu. 

1. Original Hogue's (without selection.) 53,6 

2. Continuous ear-to-row since 1903 53 . 3 

3. Increase from single high-yielding strain selected in 

1906 , 47,7 

4. Increase from composite of four high-yielding strains 

selected in 1906 5,0 

187 



188 METHODS Of PLANT BREEDING 

In method 2, the better ears from the highest yielding strains 
were selected, whereas in method 3, the remnants of the high- 
yielding strain were planted in an isolated plot, and in subsequent 
years the better developed ears were selected. Method 4 was an 
increase from ear-to-row trials made in 1906 and 1907, where the 
four high-yielding ears gave an average yield of 79.4 bu., com- 
pared with 64.4 bu. for the original. Subsequent selection was 
made in the same manner as in method 3. 

It is generally agreed that the ear-to-row method is valuable as 
a means of selection with an unadapted variety but, in general, of 
little use with an adapted variety. Several studies may be 
summarized to emphasize these conclusions. 

Hayes and Alexander (1924) compared various methods of selec- 
tion in isolated plots, using Rustler White Dent, which had been 
grown previously in central Minnesota for many years without 
close selection to type. The methods of selection were as follows : 

1. Selection of good ears at husking. 

2. Selection during seed-corn week in the first half of Septem- 
ber, from perfect stand hills and vigorous plants, without close 
selection to ear type. 

3. Selection as in method 2 and then reselection for ear type, 
i.e., good buts, medium dent, straight rows, cylindrical ears, 
14 to 16 rows, good ear length. 

4. Montgomery's method from 100 ear-to-row plots, where 
remnants from the 25 higher yielding ears were bulked and sub- 
sequent selection was carried on by method 3. 

5. Williams' method, Fi cross of remnants of three better 
yielding ears. 

6. Multiplication of seed produced by method 5. 

The following data are an average of 4 years' results, except as 
noted. 

Method of Selection Yield, Bu. 

1 54.5 0.8 

2 54. 3 0.8 

3 53. 2 0.7 

4 ' 55.2 0.8 

5 55.5 0.8 

6 96 per cent of method 1.3 years 

Comparing methods 2 and 3, by pairing the differences for each 
of ttye 4 years, the chances were 37 : 1 that the difference in yield- 



DEVELOPMENT OF METHODS OF CORN BREEDING 1?9 

ing ability was significant. These data indicate a harmful result 
from close selection to ear type. 

Smith and Brunson (1925) compared ear-to-row breeding with 
simple mass selection in an isolated field of several acres, making 
comparative trials over a 10-year period. They started originally 
with 990 ears in an ear-to-row trial, selecting the 40 high-yielding 
and 40 low-yielding, respectively. The remnants of ears used to 
plant the high-yielding rows were mixed to make a high-yielding 
group, and the remnants of the low-yielding ears were mixed to 
make a low-yielding group. They continued breeding plots 
separately for high yield and low yield, selecting 40 ears for each 
type of selection, respectively, in subsequent years, and detasseled 
alternate halves of rows, saving the seed from the detasseled half 
for planting next year. Four ears were selected from each of the 
10 highest yielding rows in the high-yielding selections and, 
similarly, 4 ears from each of the 10 lowest yielding in the low- 
yielding selections. Each of the three methods of selection 
simple mass, high, and low yield were carried in isolated plots. 
Yield trials were made in another plot with the use of composite 
samples of seed. The chances were very great that the high 
selection yielded more than the low, but the odds were only 
approximately 3 : 1 that the high selection yielded more than the 
nonpedigree. Smith and Brunson concluded that continuous 
ear-to-row breeding was of little value. 

It seems unnecessary here to summarize the extensive experi- 
ments that have been made to determine the relationship between 
ear characters and yielding ability. In general, the well-known 
experiments of Williams and WeltOn (1915) and many others 
show no close relationship between ear characters and yielding 
ability. The probable reason for these results can be appreciated 
by referring to a study reported by Garrison and Richey (1925) 
on 'the effects of continuous selection with Boone County White 
(C. I. 119). They selected continuously for 6 different ear types 
for an 8-year period and compared the yielding ability with 
unselected seed of Boone County White. Each type of selection 
was made in an isolated seed plot, and mixed seed from at least 
50 ears was used to plant each plot. The following types of 
selection were made: 

1. Strain 1. Rough ears, 8 in. or more in length, with 20 or 
more rows of crease- to pinch~dent#d kernels, 



190 METHODS OF PLANT BREEDING 

2. Strain 2. Rough ears, 8 in. or more in length, with 16 rows 
of crease- to pinch-dented kernels. 

3. Strain 3. Smooth ears, 10 in. or more in length, with 20 or 
more rows of dimple to slightly crease-dented kernels. 

4. Strain 4. Smooth ears, 10 in. or more in length, with 14 
rows of dimple-dented kernels. 

5. Strain 5. Smooth ears, 10 in. or more in length, with 12 
rows of dimple-dented kernels. 

6. Strain 6. Smooth ears, any length, with eight rows of 
dimple-dented kernels. This strain originated from a few eight- 
rowed ears found among those in strains 4 and 5 in 1918. 

Selection was effective, since row numbers were rather rapidly 
modified. The following quotation taken from Garrison and 
Richey (1925) gives a good idea of the more important results and 
conclusions. 

Without regard to the reason, it is evident that close selection to any 
type, as practiced in these experiments, resulted in decreased productive- 
ness. The most productive strain, No. 4, the 14-rowed smooth selec- 
tion, yielded 8.4 0.20 per cent less than C. I. No. 119, and the least 
productive, No. 3, the 20-rowed smooth selection, 14.3 0.19 per cent 
less. The 14-rowed smooth and the 16-rowed rough selections, Nos. 4 
and 2, were more productive and also departed less from the character- 
istic condition of the parent variety than the others. 

In their practical application the experiments indicate that a decrease 
in vigor and productiveness similar to that followiiig inbreeding may 
result from too close selection for a particular kind of ear. Careful 
experiments have failed to demonstrate a marked consistent superiority 
for any specific kind of ear. Other experiments have shown that the 
yields of crosses between varieties of corn frequently are more productive 
than the average of the parents, thus indicating that the parent varieties 
are too homozygous to permit maximum yields. Just what constitutes 
too close selection is not known. In view of the lack of evidence in 
favor of any particular kind of ear and the abundant evidence of the 
decreased yields that follow close breeding, however, it seems best to 
stay on the safe side by avoiding such close selection. 

In view of the lack of evidence of marked consistent superiority for 
any particular kind of ear, it is finfortunate to teach that uniformity 
among the ears of a variety of corn is desirable by attaching importance 
to uniformity of sample, as is done in corn shows. 

These and many other similar studies show that mass- or 
individual-plant methods of selection with an adapted variety 



DEVELOPMENT OF METHODS OF CORN BREEDING 101 

cannot be expected greatly to increase the potential yielding 
ability of the variety, and for this reasdfi plant breeders have 
rather generally adopted controlled pollination methods of 
breeding during the last 15 years. The student who may wish to 
make a more extensive study of earlier methods of corn breeding 
is referred to a paper written by Richey (1922) that reviews the 
studies in considerable detail and contains, also, citations of the 
more important literature, 

The conclusions to be reached from these studies is that simple 
mass selection for vigor of plant, time ctf, maturity, etc*, is all that 
is worth while and that close selection for ear type is not desirable. 
These conclusions have aided in a rather rapid acceptance of 
modern methods. 

EARLY STUDIES OF SELF- AND CROSS-FERTILIZATION 
WITH CORN 

Although Beal, in 1876, at Michigan, suggested the use of Fi 
crosses between strains of corn for a commercial crop and 
Morrow and Gardner, in 1892, in Illinois, gave an outline of a 
method for producing FI seed and presented further data regard- 
ing its value, the utilization of hybrid vigor in corn has been 
developed only after extensive experiments on the effects of 
cross- and self-fertilization. Studies by East, at the Connecticut 
Experiment Station, and of Shull, at Cold Spring Harbor, have 
been discussed under the heading of Heterosis. Both started 
studies of the effects of self-pollination in corn in 1905. One of 
the present writers worked under East's direction in 1909 and had 
charge of the corn-breeding program at the Connecticut station 
from 1910 to 1914. Part of the self-pollinated lines started by 
East, in 1905, have been continued at the Connecticut Agricul- 
tural Experiment Station until the present time, being carried on 
by D. F. Jones since 1915. Because of the relation of principles 
learned with corn to the breeding of other cross-pollinated crops, 
it may be desirable to mention other early investigators who have 
studied self- and cross-fertilization with corn. G. N. Collins, of 
the U.S. Department of Agriculture, who was interested chiefly 
in fundamental principles, published his first paper on corn 
breeding in 1909. Vice-president Henry A. Wallace started 
studies of self-pollination and selection in 1913 as a private enter- 
prise, This led eventually to the formation of the Pioneer 



192 METHODS OF PLANT BREEDING 

Hi-Bred Corn Company of Iowa. Self-pollination and selection 
with corn was begun *at the Minnesota station in 1914. F. D. 
Richey, who began self*pollination of corn in 1916, was placed in 
charge of corn improvement for the U.S. Department of Agricul- 
ture in 1922, and his leadership was responsible to a considerable 
extent for the rapid development of hybrids adapted to the corn 
. belt. Studies of selection in self-pollinated lines were started also 
in 1916 by C. H. Kyle and J. R. Holbert as a part of the program 
of the Bureau of Plant Industry. Corn improvement was placed 
on a cooDerative basis by corn-belt experiment stations and the 
U.S. Department of Agriculture under the Purnell Act in 1925. 
A committee was appointed to formulate a program. Annual 
meetings in the field and laboratory furnished a medium for the 
exchange of ideas and materials and without doubt were responsi- 
ble to a considerable extent for the rapid development in recent 
years of adapted hybrids for all sections of the corn belt. 

A summary of conclusions drawn by Shull (1910) from his 
studies of self- and cross-fertilization show the detailed knowledge 
that was available many years ago. The following summary is 
quoted from Shull. 

1. The progeny of every self-fertilized corn plant is of inferior size, 
vigor, and productiveness, as compared with the progeny of a normally 
cross-bred plant derived from the same source. This is true when the 
chosen- parent is above the average conditions as well as when below it. 

2. The decrease in size and vigor which accompanies self-fertilization 
is greatest in the first generation, and becomes less and less in each 
succeeding generation until a condition is reached in which there is 
(presumably) no more loss of vigor. 

3. Self-fertilized families from a common origin differ from one 
another in definite hereditary morphological characters. 

4. Regression of fluctuating characters has been observed to take 
place away from the common mean or average of the several families 
instead of toward it. 

5. A cross between sibs within a self -fertilized family shows little 
or no improvement over self-fertilization in the same family. 

6. A cross between plants belonging to two self-fertilized families 
results in a progeny of as great vigor, size, and productiveness, as are 
possessed by families which had never been self-fertilized. 

7. The reciprocal crosses between two distinct self-fertilized families 
are equal, and possess the characters of the original corn with which 
the experiments were started. 



DEVELOPMENT OF METHODS OF CORN BREEDING 193 

8. The FI from a combination of plants belonging to certain self- 
fertilized families produces a yield superior to that of the original 
cross-bred stock* 

9. The yield and the quality of the crop produced are functions of 
the particular combination of self-fertilized parental types, and these 
qualities remain the same whenever the cross is repeated. 

10. The FI hybrids are no more variable than the pure strains which 
enter into them. 

11. The Fa shows much greater variation than the FI. 

12. The yield per acre of the Fife less than that of the FI. 

Effects of self-fertilization were discussed in somewhat greater 
detail by East and Hayes (1912). The following statements 
summarize the more important results of inbreeding and selection. 

1. Loss of vegetative vigor has followed continued self-pollina- 
tion in all inbred lines of corn. 

2. Inbred lines exhibit differences in many normal characters; 
for example, some inbred lines have long ears; others, short ears. 

3. Some inbred lines are much more vigorous than others, even 
though they do not differ in degree of homozygosity. 

4. Some pure strains are so lacking in vegetative vigor that 
they cannot be propagated. 

5. Continued inbreeding leads to purity of type. 

Shull (1909) outlined a pure-line method of corn breeding based 
on the isolation of self-pollinated lines and the use of FI crosses 
between them for the commercial crop. The difficulty of this 
method was the cost of seed from single crosses. 

The work of Jones, at the Connecticut Experiment Station, 
since 1915 was continued with some of the inbred lines available 
from the early work of East and Hayes. The Mendelian eiplana- 
tion of hybrid vigor, given by Jones (1917) was of great value in 
a.n understanding of corn-breeding principles. The double-cross 
plan of corn breeding, developed by Jones about 1917, has helped 
materially to make hybrid seed production economically feasible. 

CONTROLLED POLLINATION METHODS 

Many workers have taken part in the extensive studies that 
have Jed to a partial standardization of modern methods of corn 
breeding. Some of the investigations will be briefly summarized. 
Although individual research has been the basis of a standardiza- 
tion of technic, the rather rapid acceptance of methods has been 



194 



METHODS OF PLANT BREEDING 



brought about by cooperation and free exchange of ideas and 
material among investigators. 

The following brief summaries of investigations are given to 
furnish a background for an understanding of the development of 
methods of corn breeding. 

Two major problems are faced by the corn breeder. There are 
(1) the isolation of the most desirable inbred lines and (2) the use 
of these lines to produce hybrids with high yielding ability that 
excel also in other characters. 

One of the problems not entirely solved yet and one that per- 
haps never will be solved is the extent of homozygosity necessary 
in inbred lines. Richey and Mayer (1925) made a comparison 
of crosses between inbred lines after 3 and 5 years of self-fertiliza- 
tion and concluded that there was no general advantage in yield- 
ing ability from crosses between lines inbred for 5 years over 
crosses between lines inbred for 3 years. They found little or no 
relationship between the productiveness of self ed lines and that of 
their crosses. Richey (1924) and Richey and Mayer (1925) 
found that certain lines behaved rather uniformly in different 
crosses and that, on the average, certain strains gave high-yielding 
crosses when combined with a random series of other inbred lines ; 
i.e., certain lines were good combiners. 

At Minnesota, Nilsson-Leissner (1927) and Jorgenson and 
Brewbaker (1927) compared the yielding ability of inbred lines 
and of possible F\ crosses between them by means of the correla- 
tion coefficient. The number of lines, source of material, place of 
study, and the correlation coefficients are given in the following 
summary : 



Source of 
material 


Number of 
inbred lines 


Place 


Correlation 
coefficient 


Flints 


9 


University Farm, St. Paul, 


+ .74 .04 


Dents 


13 


Minn, 
University Farm, St. Paul, 


+ .19 06 


Silver King 


10 


Minn. 
Waseca, Minn. 


+ .50 .08 



Multiple correlation coefficients were calculated also between 
five characters of the inbred lines and the yield of their Fi crosses 



DEVELOPMENT OF METHODS OF CORN BREEDING 195 

as follows: University Farm, Dents, R = .67; Flints, R = ,82; 
Waseca, Silver King, R = .61. 

In these studies, some lines tended to give good yields in 
crosses, and others generally were low combiners. Although 
some high-yielding inbred lines did not combine well in general, 
the more vigorous inbred lines, on an average, were better 
combiners than the less vigorous inbred lines. 

Jenkins (1929) made a more detailed and extensive study of a 
similar nature. In a study of the relationship of the yielding 
ability of inbred lines and their F\ crosses, he found, on an 
average, less association than in the Minnesota studies. Coeffi- 
cients of correlation in 1926 and 1927 for the mean yield of inbred 
lines and their P\ crosses were +.20 .03 in both years. When 
the mean of several crosses was used as a criterion of the combin- 
ing ability of the inbred lines and correlated with the yield of the 
inbred lines, coefficients of +.32 .07 and +.12 .09 were 
obtained in 1926 and 1927, respectively. When the mean yield 
of the cross-bred progeny was correlated with four characters of 
the inbred lines, indicating plant vigor and size, a multiple 
correlation coefficient of +.42 .05 was obtained. 

Kiesselbach (1930) has shown that advanced-generation 
crosses produced, on an average, as high yields in double crosses as 
when Fi crosses are used as parents for the double cross. An 
advanced generation is the product of normal uncontrolled 
pollination in the progeny of an F\ or later generation cross grown 
in an isolated plot. One difficulty of using advanced-generation 
crosses for producing double-crossed seed, as pointed out by 
Kies^elbach, is the reduction in seed production of Ft and F$ in 
comparison with F\. His F% and F 3 generations averaged about 
67 per cent as much grain yield as the FI. Richey et al. (1934) 
found that the F% of 10 double crosses yielded 5 to 24 per cent less 
(average 15.2) than the FI. Neal (1935) obtained an average 
yield in F 2 and F 3 for advanced-generation single crosses of 70,5 
and 75.7 per cent of the F\, respectively. Various investigators 
have suggested that advanced-generation seed be used as the male 
parent in the commercial crossing plot. 

After obtaining as desirable inbred lines as possible, the prob- 
lem remains of how to use these inbred lines in hybrid seed 
production. Several methods haye been put in practical use. 
These include : 



METHODS OF PLANT BREEDING 



1. Single crosses. 

2. Inbred-variety crosses, sometimes called top-crosses. 

3. Three-way crosses. 

4. Double crosses. 

5. Multiple crosses. _ 

Single crosses can be used only when the inbred lines yield 
sufficiently well to make seed production economical. The 
higher yielding inbred line should be used as the female parent. 




.. . 

FIG 26 At left, Cl, an inbred line of Japanese hull-less popcorn; at right, C6, 
another inbred iu ceAter, the f i cross, Minhybrid 250. The mbreds yield 
sufficient ywcU so that the use of F l crossed seed for commercial planting ; 
feasible The F. cross yields approximately 16 per cent more than Japanese 
hull-less and has approximately 29 per cent greater popping expansion. 

Single crosses are being used in producing sweet corn for canning, 
where uniformity of maturity and for ear characters are of major 
importance. If the inbred lines are reduced only to practical 
homozygosity by 3 or 4 years of inbreeding, single crosses in 
sweet corn are economically feasible. An illustration of inbred 
lines and the commercial Fj cross of Japanese hull-less popcorn is 

given in Fig. 26. 

Top-crosses, or inbred-variety crosses, may be expected to 
yield somewhat less than single, three-way, or double crosses, on 
an average. They have been used 'extensively in sweet-corn 
breeding because of their practical features. Before the best 
single, three-way, or double crosses have been determined, it 
frequently may be of value to use inbred-variety crosses, since 
such crosses, when carefully selected, may have a higher yield and 
greater uniformity than standard varieties. 



DEVELOPMENT OF METHODS OF CORN BREEDING 197 

In a three-way cross, a good pollen-producing inbred line is 
used as the male parent, and a single cross is used as the female 
parent. Both the inbreds used in the single cross should combine 
well with the pollen parent. An illustration of the parent inbred 
lines, FI cross and three-way cross, Minhybrid 301 is given in 
Fig. 27. 




FIG. 27. The three-way cross at the right, Minhybrid 301, produced by 
crossing the Fi cross, upper center, of two inbred lines of Minn. 13 with an 
inbred line of Reid's Yellow Dent, lower center. At the left are representative 
ears of inbred lines 14 and 11 of Minn. 13. 

In a double cross, two single crosses are used as the parents. 
Advanced-generation single crosses can be used to advantage as 
the male parents. This is valuable as a means of extending the 
pollen-sheddjng period of the male parent. 

One of the major problems of the corn breeder is to devise some 
method of selecting the better crosses. Richey and coworkers 
advocated a series of inbred testers as a means of selecting inbred 
lines that were good combiners, determining the combining 
ability of each inbred line by crossing it with each of the testers 
separately. Jenkins and Brunson (1932) have compared differ- 
ent methods of testing the combining ability of inbred lines. In 
one case they compared two methods, using 37 inbred lines. The 
combining ability was tested in a series of crosses of each of the 
37 lines with 9 tester inbred lines in 1927 and in an inbred-variety 
cross in 1929. The combining ability of the 3.7 lines determined 
by yields obtained by these two methods was correlated, obtain- 
ing a correlation coefficient of +-53, where .32 represented a 
significant relationship based on odds of 19:1. 



198 



METHODS OF PLANT BREEDING 



In a second study, they used 12 early inbreds in a series of 
crosses with 9 comparable inbred lines and 17 late inbreds in a 
series of crosses with 10 comparable inbred lines, correlating the 
average combining ability of each line with its combining ability 
in top- or inbred-variety crosses. The results were as follows: 





Lines 


used 


Correlation coefficient 


12 early 


17 late 


Calculated r, , ... 


+ .80 


+ .65 


Significant r 


.58 


.48 



In a third group, the combining ability in top-crosses and in a 
series of 10 comparable single crosses was determined with the 
following results : 



Lines used 



Correlation coefficient 


10 early 
white 


17 early 
yellow 


10 late 
yellow 


10 Lancaster 


Calculated r 
Significant r. . . 


+ 90 
.60 


+ .86 
.48 


+ .63 
.63 


+ .90 
.63 



In a fourth group, GO inbred lines of Pride of Saline were placed 
in 6 groups of 10 lines each, and all possible crosses were made 
between each line in the odd group with each 10 in the next 
higher even group. They determined the combining ability of 
each line also by the top-cross method and compared the results 
of the two trials, i.e., combining ability in top-crosses with the 
combining ability obtained from an average of single crosses, for 
each of the 60 lines, obtaining an r of +.56 where a significant r 
was .26. 

To determine whether crosses with a series of inbred lines used 
as testers are more satisfactory as a measure of combining ability, 
they studied the combining ability of inbred lines in two different 
series of inbred crosses. They used the following groups: (1) 9 
early white endosperm inbreds, (2) 9 early yellow, and (3) 10 late 
yellow lines. In test A, the combining ability of each line was 



DEVELOPMENT OF METHODS OF CORN BREEDING 199 

determined from crosses with every other line in the same sub- 
group. In test B, the following studies were made of combining 
ability. The 9 early white lines were crossed with 13 other inbred 
lines of white endosperm; the 9 early lines of yellow were each 
crossed with 12 other inbred lines of yellow endosperm, and each 
of the 10 late lines were crossed with 17 other late inbreds. 
Correlating the combining ability in tests A and B gave the 
following : 



Correlation coefficient 


Groups 


9 early 
white 


9 early 
yellow 


10 late 


Calculated r . .... 
Significant r . ... 


+ .82 
.67 


+ .69 
.67 


+ .65 
.63 



These coefficients are about the same magnitude as those 
obtained by correlating the yielding ability in top-crosses with 
that of a series of inbreds used as testers. 

The results justify the use of inbred-variety crosses to deter- 
mine the combining ability of inbred lines. 

Johnson and Hayes (1936) studied the combining ability of 
1 1 inbred lines of Golden Bantam in all possible single crosses arid 
in top-crosses. The correlation between the average yield of the, 
1 1 lines in all possible single crosses and the average yield in top- 
crosses with Golden Bantam and Del Maiz was +.78 .12. 
The combining ability of 39 lines in two series of top-crosses was 
studied also. Johnson and Hayes suggested the need for many 
replications and of making yield trials at several locations, prefer- 
ably, to determine accurately in a single year the combining 
ability of inbred lines by the top-cross method. This plan has 
been adopted as a standard practice in the Minnesota corn- 
breeding program. 

After selecting the more desirable inbred lines by the top-cross 
method, it is necessary to determine the best combination of lines 
for single, three-way, and double crosses. An actual field trial 
must be used to determine the value of a particular combination, 
but methods of prediction based on a previous knowledge of 
combining ability may be of value. 



200 



METHODS OF PLANT BREEDING 



For a three-way cross between lines, a good pollen producer 
must be used as the male parent. If inbred lines 1, 2, and 3 are 
used in a three-way cross and inbred line 3 seems most satisfactory 
as a pollen parent, it is then necessary that single crosses 1X3 
by 2X3 both be good producers in order that the three-way 
cross (1 X 2) X 3 be desirable. Thus, a three-way cross may be 




-^^^^^^^^^^^^^^^MMaMMBMmaffiaBaBllllilliiiimiliHiliiii \\mmm\mw\m?* 

FIG. 28. Representative ears of inbred lines used in double crosses adapted to 
south central Minnesota, J^J normal. 

selected on the basis of single crosses and a knowledge of the 
desirability of the lines as pollen parents. 

In a double cross of four lines, i.e., (1 X 2) X (3 X 4), where 
single crosses 1X2 and 3 X 4 are planted alternately in. a plot 
for hybrid seed production, it would seein desirable to use the 
most satisfactory cross 1 X 2 or 3 X 4 as the female parent, 
giving consideration to yielding ability and size and uniformity 
of the seed of the two FI crosses. Inbred lines used in double 
crosses adapted to south central Minnesota, the two FI crosses 
used as parents, and the double cro&, Minhybrid 502, are given in 
Figs. 28 and 29. 

Some studies have been made that furnish a logical basis for the 
prediction of the performance of double crosses and that aid in 
selecting the more promising combinations for yield trials. 



DEVELOPMENT OF METHODS OF CORN BREEDING 201 

Jenkins (1934) has presented a study in which 11 inbred lines 
were used. From these 11 inbred lines, all but 2 of the possible 
single-cross combinations were obtained, and the combining 
ability of each of the lines was also tested in an inbred-variety 
cross. Forty-two of the possible double crosses of these inbred 
lines were studied also, and four methods of predicting the 




FIG. 29. Representative ears of single crosses and of the double cross, Minhybrid 
502, adapted to south central Minnesota, % normal. 

probable value of these 42 double crosses were compared. These 
methods are as follows : 

1. The yield of all six single crosses from the four lines used in 
each double cross was used as a basis for prediction of the prob- 
able value of the double cross. If the lines are 1, 2, 3, and 4, these 
single crosses are 1 X 2, 1 X 3, 1 X 4, 2 X 3, 2 X 4, and 3X4. 

2. ' The yield of four single crosses, excluding the two used as 
parents, was used to estimate the probable performance of the 
double cross. If the double cross was (1 X 2) (3 X 4), the four 
single crosses selected to predict yielding ability would be 1 X 3, 
1 X 4, 2-X 3, and 2X4. 

3. The mean yielding ability of each line in all possible single 
crosses was first determined, and from these means the combining 
ability in a particular double cross was estimated. In double 
cross (1 X 2) (3 X 4), the probable value of the double cross was 



202 



METHODS OF PLANT BREEDING 



estimated by averaging the combining ability of lines 1 , 2, 3, and 4 
in all possible combinations with the other inbred lines. By this 
method ; the prediction value for four lines in a double cross 
would be the same for (1 X 2) (3 X 4) as for (1 X 3) (2 X 4) or 
other combinations of single crosses of these four lines. 

4. The combining ability was determined of the four lines in 
each double cross by an average of their yields in inbred-variety 
crosses. 

The value of these four methods of prediction was determined 
by correlating yields obtained from each of the prediction 
methods with the yield of 42 double crosses, with the following 
result : 



Predicted yield with 
actual yield of 


Correlation coefficients by methods 


A 


B 


C 


D 


Significant 


42 double crosses .... 


+ 75 


+ .76 


+ 73 


+ .61 


39 



Although prediction of the value of the double cross by method 
D, the inbred-variety cross plan, gave a lower value of r than 
methods A , 5, and C, it is possible that this may have been due to 
insufficient replication in D or to a chance deviation rather than 
to the fact that this method is the least desirable or reliable of any 
of the four methods tested. 

In discussing method B, Jenkins stated, "In any double cross 
the genes of each of the four parental lines are united only with 
allelomorphs of the two lines which entered the double cross from 
the opposite parent." Extensive studies at Minnesota have 
shown that this method can be used to predict the yield of a 
double cross about as accurately as by testing the actual double 
cross. Doxtator and Johnson (1936) compared the yielding 
value of inbred lines in double crosses on the basis of the way that 
they are combined and have proved clearly that it is of extreme 
importance how these lines are combined, i.e., which combinations 
of single crosses are used as parents for the double cross. In 
general, other things being equal, the two lower yielding single 
crosses of the possible six should be selected as parents of the 
double cross. 



DEVELOPMENT OF METHODS OF CORN BREEDING 203 

The results of these studies are summarized in Table 18. 

The predicted yields were obtained by averaging the actual 
yields from single crosses. Thus, the predicted yield of (62 X 
67) X (66 X 68) was obtained by averaging the yields of the 
single crosses (62 X 66), (62 X 68), (67 X 66), and (67 X 68), 
which were 58.8, 17.1, 58.9, and 38.8, respectively. This gave a 
predicted average yield of 43.4 bu. In general, the agreement 
between predicted yields and actual yields obtained was very 
close in these studies. 

TABLE 18. ACTUAL AND PREDICTED YIELDS OF DOUBLE AND THREE-WAY 

CROSSES 





Yield, bu. per acre 


Hybrid 










Obtained 


Predicted 


Wascca branch station: 






(11 X 14) X (374 X 375).. . . 


78.70 


85.55 


(11 X374) X (14 X 375) .. .. 


66 33 


70.79 


(11 X 375) X (14 X 374). . 


70.58 


69.31 


(11 X 14) X374 


81 67 


86 92 


(11 X 14) X375.. 


82.63 


84.17 


University Farm: 






(62 X 67) X (66 X 68) . . 


48 4 


43.4 


(62 X 66) X (67 X 68) . . 


41.8 


41.7 


(64 X 66) X (62 X 68) 


54.1 


47.5 


(64 X 68) X (62 X 66) 


44 5 


39.8 



Data from Anderson (1938) are presented to give further 
information regarding actual and predicted yields. The results 
in Table 19 give yields of single crosses in bushels per acre and 
show the method of predicting the yield of an actual double cross. 

A comparison of actual and predicted yields of double crosses 
by Anderson (1938) is given in Table 20 to show the value of the 
method. 

During recent years extensive unpublished data at Minnesota 
show the accuracy of predicting the yielding ability of double 
crosses and lead to the conclusion that such predicted yields can 
be used as actual measures of the yielding ability of new double 
crosses. By comparing the single crosses used in the predictions 
with standard double crosses of known yielding ability, one can, 
with a high degree of accuracy, accept the predicted yield and use 



204 



METHODS OF PLANT BREEDING 



TABLE 19. METHOD OF PREDICTING YIELDS OF THE THREE DIFFERENT 

DOUBLE CROSSES THAT CAN BE MADE FROM FOUR INBRED LINES WITH 

THE USE OF THE YlELDS IN BUSHELS PER ACRE OF ALL SlX POSSIBLE 

SINGLE CROSSES 



(23 X 24) X (26 


X 27) 


(23 X 26) X (24 


X 27) 


(23 X 27) X (24 


X 26) 


Single cross 


Yield, 
bu. 


Single cross 


Yield, 
bu. 


Single cross 


Yield, 
bu. 


(23 X 26) 
(23 X 27) .... 
(24 X 26) ... 
(24 X 27) 


62.6 
70.8 
65.6 
72 1 


(23 X 24) . . . 
(23 X 27) . 

(26 X 24) .... 
(26 X 27) 


41 7 
70 8 
65 6 
64.2 


(23 X 24) 
(23 X26) 
(27 X 24) 
(27 X 26) 


41.7 
62.6 
72.1 
64 2 














Average .... 


67 8 


Average 


60 6 


Average 


60 2 















TABLE 20. A COMPARISON OF ACTUAL YIELDS OF Six DOUBLE CROSSES 

WITH PREDICTED YIELDS OBTAINED BY AVERAGING THE YIELDS OF THE 

FOUR SINGLE CROSSES NOT USED IN MAKING THE DOUBLE CROSS 



iJilieo UUIIILHIIUU. UI1U Ul/UUiU L'iUWM 


Actual 


Predicted 


23, 24, 26, 27: 

(23 X 24) X (26 X 27) .... 


68 8 


67 8 


(23 X 26) X (24 X 27) 
(23 X 27) X (24 X 26) 
23, 24, 26, 28: 

(23 X 24) X (26 X 28) 


62 4 
62.0 

65 


60.6 
60.2 

65 5 


(23 X 26) X (24 X 28) 


59.8 


58.0 


(23 X 28) X (24 X 26) 


56 


58 5 


23, 24, 27, 28: 

(23 X 24) X (27 X 28) 


71 1 


69 2 


(23 X 27) X (24 X 28) 


58 1 


59 4 


(23 X 28) X (24 X 27) 


58 


60 4 


Difference for significance ui 5 per cent 
level 


5.3 


3.4 



Bu. per acre 



it in the same manner to determine the value of a double cross as 
if the actual yield of the double cross had been obtained. The 
value of the method is emphasized by giving formulas that show 
how many single and double crosses can be produced from n 
inbred lines, 



DEVELOPMENT OF METHODS OF CORN BREEDING 205 

The number of single, double, and other crosses that can be 
made from n inbreds may be calculated from the number of 
combinations of n inbreds taken r at a time, where r is the number 

n\ 
of inbreds in the cross. This is given by -77 : r-.- 

J r\(n r)! 

AND THEIR FiRST CROSSES ; 



AU6 



A 14ft 




AW) 



FIG. 30. Above, representative ears of four inbred lines; center, the two 
single crosses used as parents to produce the double cross; below, representative 
ears of four single crosses used to predict double-cross yields. The double cross, 
produced by crossing the single crosses given in the center of the picture, matures 
satisfactorily in the corn-growing regions of the Minnesota Red River Valley 
and has good agronomic characteristics for this region. 

For single crosses, r = 2, and the number of possible single 

-11 i n (n ~ 1) 
crosses will be ^ - 



For double crosses, r = 4, and the formula becomes three 

nl 
times 777 ,.,> since three double- crosses can be made from 

4![n 4)! 



206 METHODS OF PLANT BREEDING 

any four inbreds. This formula may be expressed as 

3n(n - \)(n - 2)(n - 3) 
24 

Thus, for 20 inbred lines, 1 90 different single crosses can be made, 
and from the yield trials with these one can predict the actual 
yielding ability of 14,535 double crosses. 

BREEDING IMPROVED INBRED LINES 

A problem of great importance to the breeder is the develop- 
ment of improved inbred lines. The following methods are 
available at present: 

1. Inbreeding and selection from commercial varieties. 

2. Inbreeding and selection from high-yielding crosses. 

3. Breeding improved lines by a definite plan of crosses and selection. 

a. Pedigree methods, as with small grains. 

b. Backcrossing. 

c. Convergent improvement, 

It seems unnecessary to describe these methods in great detail. 
Inbreeding and selection from commercial varieties has been the 
common practice and is necessary as the first step. As with 
other plant-breeding studies, it is important to use as large num- 
bers as possible and to determine the breeding value of a line by 
progeny trials. A plan in common use is to grow a short row of 
30 or more plants from each desirable inbred ear from the previous 
generation and to continue inbreeding and selection until practi- 
cal homozygosity has been reached. Jones and Singleton (1935) 
have suggested growing only a few plants from each inbred ear, 
thus making it possible to grow several thousand inbred lines per 
acre, with the view that the more important differences will be 
those between lines rather than selection within lines. Jenkins 
(1935) studied the combining ability in top-crosses with Krug of 
14 inbred lines of lodent and 14 of Lancaster for 8 inbred genera- 
tions. It was shown that the inbred lines established their 
individuality as combiners early and maintained it during succes- 
sive generations of selfing. It was suggested that the selection of 
desirable combining lines should be determined by crosses made 
during early generations of selfing. 

As with other methods of plant breeding, it is important to 
know the characters desired and carrv on breeding studies with a 



DEVELOPMENT OF METHODS OF CORN BREEDING 207 

definite plan. If these characters are present in the inbred lines 
used in various types of crosses, then these crosses may be a 
promising basis as material for developing a new series of inbred 
lines. In some cases, this will lead to the pedigree method of 
breeding that has been outlined already for self-fertilized crops. 

THE PEDIGREE METHOD OF SELECTION IN THE SEGREGATING 
GENERATIONS AFTER CROSSING INBREDS 

Such a method has been used extensively at Minnesota, and its 
value has been discussed by Hayes and Johnson (1939). Most 
inbreds obtained from varieties adapted to Minnesota lacked 
ability to withstand lodging, and at least one inbred parent of the 
single crosses used as a basis for selection of inbred lines was 
outstanding in ability to withstand lodging. Selection was made 
during the segregating generations from selfed progenies for 
ability to withstand lodging, for smut resistance, and for other 
desirable characters. Many inbred lines were isolated that 
excelled in standing ability and in other characters. The inbred 
lines obtained in this way, together with the inbred parents used 
in single crosses, were tested for combining ability by crossing 
with Minn. 13 and making the necessary yield trials. When 
both inbred parents of a single cross were high in combining 
ability, as determined from yield trials of inbred-variety crosses, 
then practically all inbreds isolated from this particular cross also 
showed high combining ability. Conversely, inbreds selected 
from a single cross between two lines of low combining ability 
were mostly of low combining ability when tested in inbred- 
variety crosses, whereas inbreds selected from a cross of a low 
combiner inbred with a high combiner gave a range in combining 
ability from low to high. These data show that combining 
ability is an inherited character. Twelve characters that for the 
most part represent vigor of growth, such as leaf area, height of 
plant, volume of root clump, pulling resistance, etc., of 110 inbred 
lines were correlated with each other and with the yield of inbred- 
variety crosses. The multiple correlation between inbred- 
variety yields in bushels per acre and these 12 characters of the 
inbreds was .67, indicating that approximately 45 per cent of the 
variability in yield of the inbred-variety crosses was dependent 
upon the characters of tfye inbreds, leaving 55 per cent unac- 
counted for. 



208 METHODS OF PLANT BREEDING 

These results show the desirability of selecting vigorous inbreds, 
not only because of their value in seed production but also in 
relation to the yielding ability of double crosses. It is evident 
that by selecting inbred lines that have high combining ability 
and making crosses between inbreds that have complementary 
characters, followed by selection in self -pollinated lines, improved 
inbreds can be obtained that excel both in their inherent charac- 
ters and as parents of double crosses. 

GENETIC DIVERSITY 

Studies by Wu (1939) and Hayes and Johnson (1939) and 
Johnson and Hayes (1940) of the FI crosses between these same 
inbred lines have shown the value, in relation to yield of grain, of 
genetic diversity of inbred lines used in double crosses. Three 
groups of lines based on relationship were studied, and the yields 
of single crosses were compared on the basis of origin. The three 
groups may be illustrated as follows: 

Inbred Cultures after Selection in Self- 
Original Cross pollinated Lines 

A48 X H* A94, A96 

A9 X A26 A102, Alll, A116, A122, A124 

A9 X A39 A99 

A39 X A26 A136, A143, A145 

* A48 was ail inbred from Northwestern Dent, H from Reid's, A26 from Osterland's Dent, 
A39 from Rustler Dent, and A9 from Minn. 13. 

Group I, no parents in common; i.e. y A94 X A102, etc. 
Group II, one parent in common; i.e., A 102 X A99, etc. 
Group III, both parents in common; i.e., A102 X Alll, etc. 

As would be expected, group III of single crosses yielded much 
less, on the average, than group I or group II, and group I of 
single crosses were considerably higher yielding, on the average, 
than group II. 

Genetic diversity may be of as great value or of greater value 
than combining ability. This is indicated by studies of Johnson 
and Hayes (1940), who used inbred lines produced by the 
pedigree method and made crosses only between inbred lines of 
different genetic origin. These inbreds were classified into four 
groups on the basis of their yields in top-crosses, in percentage of a 
standard group of hybrids and Minn. 13 that was used as the 
variety parent of the inbred-variety crosses. Four yield clasps 



DEVELOPMENT OF METHODS OF CORN BREEDING 209 



in percentage values were 80 to 89, 90 to 99, 100 to 109, and 110 
or above. In the final classification, hybrids in 80 to 99 per cent 
classes were considered as low combiners and 100 or above as high 
combiners. The inbred lines were then studied in single crosses 
in three groups of crosses: high X high, low X high, and low X 
low. The single crosses were then placed in frequency distribu- 
tions in comparison with recommended double crosses of like 
maturity. Results are given in Table 21. 

TABLE 21. SUMMARY OF FREQUENCY DISTEIBUTION OF SINGLE-CROSS 

YIELDS AT THREE LOCATIONS WITH THREE REPLICATIONS AT EACH 

LOCATION, WHEN COMPARED WITH RECOMMENDED DOUBLE 

CROSSES OF SIMILAR MATURITY IN RELATION TO THE 

COMBINING ABILITY OF THEIR INBRED PARENTS 



Type of cross 


Class centers of plus and minus 
1 to 8 times the standard error 
of a difference 


Total 


Mean class 


-7 
to 
-8 


-5 

to 
-6 


-3 

to 
-4 


-1 
to 
-2 





+ 1 
to 

+2 


+3 
to 

+4 


+5 
to 
+6 


+7 
to 
+8 


Low X low 




1 
3 

1 


1 

5 


2 

11 
12 


4 
6 

8 


4 
16 
33 


9 
20 


5 

4 


1 


12 
52 
83 


-0.50 0.66 
+1.06 0.42 
+1.10 0.24 


Low X high 


1 


High X high 







Low X low combiners yielded distinctly less in single crosses 
than low X high or high X high combiners. However, low X 
high and high X high yielded about the same, on the average, 
when the inbred lines used in the study were genetically of rather 
diverse origin. These results emphasize the value of genetic 
diversity of inbred lines used in hybrid combination. 

Eckhardt and Bryan (1940), at Iowa, have given data from a 
series of double crosses that also emphasize the value of genetic 
diversity from the standpoint of origin in relation to the yielding 
ability of double crosses. If inbreds from one variety were 
designated as A and B and from the other as X and F, they 
compared the yields of the double cross (A X B)(X X F) with 
(A X X)(B X F) or (A X F)(5 X X). The double crosses 
illustrated by (A X B)(X X F) were decidedly superior to the 
combination from the same inbreds (A X X)(B X F). These 
facts show that crosses between inbreds that originated from 



210 METHODS OF PLANT BREEDING 

different varieties may be expected to be superior, on the average, 
to comparable crosses from inbreds originating from the same 
variety. 

THE BACKCROSS 

Backcross methods may be desirable in some cases to add one or 
two characters to an available inbred line. 

An undesirable character of the three-way cross Minhybrid 301 
is smut susceptibility, dependent to a large extent on the extreme 
susceptibility of inbred B164, which is used as the male parent. 
The pedigree of the three-way cross is as follows: 

Inbreds 11 14 

\/ 

Fi (11 X 14) Inbred B164 




3-way cross (11 X 14) X 1*164 



B164 has been improved in its smut susceptibility by backcross- 
ing, as illustrated in the following outline: 

B164, Smut Susceptible Early Inbred 037, Smut Resistant 

Method: 

1. (B164 X C37) X B164. 

2. [(B164 X C37) X B164] X B164. 

Selection in 1 and 2 for smut-resistant plants to backcross to B164. 

3. Self-pollination and selection for smut resistance for 3 years. 

In field trials in 1938 and 1939 at the Waseca branch station, 
several inbred lines were obtained after self-pollination and 
selection had been practiced for 2 and 3 years, that during both 
years had less than 10 per cent of their progeny smutted, whereas 
B164 in near-by rows ranged from 85 to 90 per cent of its plants 
smutted. 

CONVERGENT IMPROVEMENT 

This method of breeding suggested by Rickey (1927) and dis- 
cussed by Richey and Sprague (1931) has been used rather exten- 
sively in recent years. 

The value of the method, which is equivalent to double back- 
crossing, is that it furnishes a plan for the improvement of each of 
two inbred lines that combine well in a single cross without 



DEVELOPMENT OF METHODS OF CORN BREEDING 211 

modifying the yielding ability of the single cross. Richey and 
Sprague have stated that the theoretical basis for convergent 
improvement assumes that: 

1. Selfed lines that give a high yield in F\ carry together impor- 
tant dominant genes necessary for yield and are alike in necessary 
recessive genes. 

2. Excess yield of the FI cross over one parent is attributable to 
favorable dominant genes received from the other parent. 

3. Back-pollinating a cross as N X R to R y in several successive 
generations, without selection and in the absence of linkage, will 
recover the genotype of the recurrent parent Rj according to the 
series J^, %, %, etc. 

4. Selection of the more vigorous heterozygous crosses during 
the period of back-pollination will retain some of the dominant 
favorable characters of N in a heterozygous condition. 

5. Selection within selfed lines after back-pollination will 
produce a line homozygous for R and for some dominant favorable 
N genes. 

6. Recovered lines N(R f ) and R(N') will differ in fewer 
dominant favorable genes than N and R. Repetition of back- 
crosses would gradually produce better and better lines with 
more and more favorable genes in a single strain. 

The more important steps in the convergent improvement 
program consist of the following: 

1. Selection of a high-yielding desirable FI cross. 

2. Backcrossing the FI to both parents and then further back- 
crossing in successive generations in two series to the respective 
parents. 

3. During the period of backcrossing, selection of vigorous 
plants that have other desirable characters and use of these in 
making the backcrosses. 

4. Selection within selfed lines after several generations of 
backcrossing. 

5. Repetition of the four steps with the better recovered inbred 
lines in order to obtain further improvement. 

The practical possibilities from backcrosses have been studied 
experimentally by Richey and Sprague (1931) and compared 
with the theoretical as a means of learning whether heterosis is 
dependent upon the interaction of dominant factors, a part of 
which are contributed by each parent. In this summary, JBi, R Zj 



212 



METHODS OF PLANT BREEDING 



Ra, etc., refer to the first, second, and third backcross progeny, 
respectively. The results are summarized for six crosses. The 
theoretical expectation is calculated by subtracting the yield 
of the inbred R parent from the FI and assuming that one-half of 
this difference will be retained in the first backcross generation, 
one-fourth in the second backcross, etc., if selection is not prac- 
ticed. The amount of vigor retained if selection is practiced will 
represent the value of this selection. The following results were 
obtained : 



Cross or selfed line 


Actual yields 


Theoretical 


(R X N)Fi 


19.7 07 




(R X N)Ri 


11 7 + 5 


11 7 


(R X N)Rt 


82 + 04 


7 6 


(R X N)R* 


7.2 + 3 


5.6 


(R X N)R* 


5.8 +03 


4 6 


(R X N)R 6 (only 2 crosses) 
(R X N)R& (only 1 cross) 


4.5 0.2 
4 6 3 


4.1 


R selfed 


3.6 + 0.2 











The results give some evidence for a belief that the method 
may be used to produce better inbred lines. Richey and Sprague 
also studied the yields of FI crosses between the nonrecurrent 
parent and the lines recovered after successive generations of 
back-pollination. Except as noted, each yield given is an average 
of six crosses. 



Cross 
(AT X R)Ft 

N X (N XR 2 )* 

N X (N X R,) 

N X(N X R<) 

N X (N X #5) (only 3 crosses) 

N X (N X Rs) (only 1 cross) 
(N X R)F l 

*(N X R)R is written N X Rt. 



Yield 

9.4 0.6 

13.5 0.3 

15.7 0.4 
17.5 0.4 

18.3 0.4 

17.4 0.2 

17.8 0.5 



Just as the yields under continuous back-pollinating methods 
should approach the yield of the recurrent parent, so the yields of 
crosses, between unselected back-pollinated lines in different 
backcross generations and the nonrecurrent parent, should 
approach the yields of FI crosses as a limit according to the series 
of > etc. 



DEVELOPMENT OF METHODS OF CORN BREEDING 213 



It has been a common experience that backcrosses between 
inbred lines of corn approach the recurrent parent in appearance 
rather rapidly, and consequently it seems probable that two or 
three generations of backcrossing are all that can be used and still 
stand much chance of greatly changing the inbred line by the 
convergent-improvement plan. 

Rather extensive studies of convergent improvement have been 
carried on by Hayes and Johnson (unpublished) at the Minnesota 
Station. Murphy (1941) has completed one of these studies 
with four inbred lines of Rustler White Dent known as C15, C16, 
C19, and C20. These lines were used in two single cross com- 
binations, (C15 X C19) and (C16 X C20). Within each of these 
two crosses, a rather extensive convergent-improvement program 
was started in 1931. In 1937, after 2 years of self-pollination and 
selection, the recovered lines were crossed with the nonrecurrent 
parent and the yields of these crosses compared in replicated 
trials with the FI yields of (C15 X C19) or (C16 X C20). The 
yields were placed in classes of plus and minus one to five times 
the standard error of a difference when compared with (C15 X 
C19) or (C16 X C20). The results of all crosses are summarized 
in Table 22. 

TABLE 22. FREQUENCY DISTRIBUTION OF YIELDS OF CROSSES FOR THE 

RECOVERED LINES TESTED IN SINGLE CROSSES TO THE NONRECURRENT 

PARENT. YIELDS OF RECOVERED C16 X STANDARD C20 AND 

RECOVERED C/20 X STANDARD C16 ARE COMPARED WITH 

STANDARD (C16 X C20). YIELDS OF RECOVERED C19 X 

STANDARD C15 AND RECOVERED C15 X STANDARD 

C19 ARE COMPARED WITH STANDARD 

(C15 X C19) 







Class centers of minus 5 to plus 2 times the 


Number of 


Years -back- 


standard error of a difference 


lines 


crossed 
























-5 


-4 


-3 


-2 


-1 





+1 


+2 


30 


2 


1 


2 


1 


4 


13 


5 


3 


1 


14 


3 




2 




1 


6 


4 


1 




7 


4 










1 


5 


1 





Of the 51 crosses tested, 1 was placed in the yield class of +2 
times the standard error of a difference more than the original FI, 
and 1 1 crosses were in classes of 2 to 5 of the standard error 



214 METHODS OF PLANT BREEDING 

of a difference and were therefore probably significantly lower in 
yield than the original FI cross. 

Seventeen FI crosses between recovered lines were studied in 
1940. Of these 17 crosses, where both parents were recovered 
lines, there were 2 crosses that were placed in the +2 class and 
2 in the +4 class in comparison with the original FI crosses. 
These results give sonic reason to believe that the yield of F\ 
crosses in themselves can be improved by the method of conver- 
gent improvement. They indicate the necessity of testing the 
yielding ability of recovered lines, and the results show that the 
first test of a recovered line may be made by crossing with the non- 
recurrent parent. All lines that do riot yield as well in crosses 
to the nonrecurrent parent as the original F\ cross may be 
discarded. 

The improvement of an inbred line by convergent improvement 
seems relatively easy for those characters in which it is seriously 
lacking, and the other inbred carries these characters. In two 
cases in which one of the inbred parents in a convergent-improve- 
ment program was oustanding in smut resistance and lodging 
resistance and gave a good yield for an inbred and in which the 
other parent was deficient in these characters and gave a low 
yield, it was relatively easy to improve the more undesirable 
parent through convergent improvement and rather difficult to 
obtain recovered lines that were superior or even equal to the 
more desirable parent in yielding ability and in other important 
characters. 



CHAPTER XV 
INHERITANCE IN MAIZE 

More is known regarding the genetics of maize than of any 
other organism except Drosophila. Some of the reasons why 
maize has been used extensively by students of genetics may be of 
interest. The plant is adapted to a wide range of environmental 
conditions and shows many differential characters. It is rela- 
tively easy to control pollination, and a large number of seeds can 
be produced on a single ear with a single pollination. There are 
many endosperm and seedling characters that can be studied in 
the laboratory and greenhouse. Technics have been developed 
that have made maize an especially favorable organism for cyto- 
genetic studies. 

Studies of the effects of self- and cross-fertilization with maize, 
which started early in the present century, have furnished the 
basis for the Mendelian explanation of heterosis. Later studies, 
with particular attention to economic characters, including the 
combining ability of inbred lines, have helped to give a genetic- 
understanding of such complex characters as vigor of growth and 
yielding ability and have made possible the development of 
efficient breeding technics. In the short review given here, all 
that will be attempted is a brief summary of those phases of 
genetic studies that seem of greatest value to the student of corn 
breeding. 

ORIGIN AND CLASSIFICATION 

A rather complete review of early theories on the origin of corn 
and intensive recent studies have been made by Mangelsdorf and 
Reeves (1939). A major criterion of the probable center of 
origin of crop plants is the one given by Vavilov that the region of 
greatest diversity of type is usually the region of origin. They 
conclude that the wild ancestor of Zea mays probably occurred 
somewhere in the lowlands of Paraguay, northeastern Bolivia, or 
southwestern Brazil. Secondary centers of domestication include 

215 



216 METHODS OF PLANT BREEDING 

the Andean region, Central America, and Mexico, where great 
diversity of types has been observed. Mangelsdorf and Reeves 
visualize maize "as a wild pod corn originating from a remote 
Andropogonaceous ancestor which gave rise on the South 
American continent to a single species Zea mays, on the North 
American continent to a more variable genus, Tripsacum." 

Maize belongs to the tribe Tripsaceae, Hitchcock (1935), and 
contains three genera that are of American origin, Tripsacum, 
Euchlaena, and Zea. Z. mays L. contains normally 10 pairs of 
chromosomes and comprises a rather diverse group of varieties of 
Indian corn. Euchlaena, called teosinte, contains two species, 
E. mexicana Schrad., the annual form with 10 pairs of chromo- 
somes, and E. perennis Hitchc., a perennial form of autotetraploid 
type with twice the chromosome number of the annual form. 
Extensive cytogenetic studies reviewed by Mangelsdorf and 
Reeves lead to the conclusion that Zea and Euchlaena do not differ 
widely in their chromosome make-up. In crosses between maize 
and teosinte, crossing-over values, with a few exceptions, which 
Mangelsdorf explains by differences in chromosome structure, are 
very similar in the hybrid to values obtained in maize. It is 
believed by Mangelsdorf and Reeves that teosinte was produced 
by hybridization between Zea and Tripsacum. They found that 
the major differences are a result primarily of four segments of 
chromatin, all bearing genes with Tripsacum effects. The third 
American genus Tripsacum, with n = 18 chromosomes, and Zea. 
are believed by them to have descended from a remote common 
ancestor. It has been found possible to hybridize Zea and 
Tripsacum, and evidence indicates that they have certain genes 
in common, Tripsacum differing in its evolutionary history from 
Zea by a tendency to polyploidy accompanied by a perennial 
habit of growth. The wild pod maize (tunicata) believed to be 
the ancestor of Indian corn, presumably had its origin in South 
America; Tripsacum originated in Central and North America. 
It is believed that Tripsacum and Zea by hybridization and 
chromosomal interchange of some sort led t6 the development of 
varieties of maize that were contaminated with small additions of 
chromatin from Tripsacum. Thus, maize varieties of North 
America are supposed to comprise two groups: (1) pure maize, 
which traces its descent to wild pod corn, and (2) Tripsacum con- 
taminated maize, The evidence regarding origin of many crop 



INHERITANCE IN MAIZE 217 

plants is not very definite. The monograph by Mangelsdorf and 
Reeves summarizes the present status of knowledge and reviews 
the literature in this field. The relationships between Zea, 
Euchlaena, and Tripsacum are emphasized. 

Although Sturtevant (1899) divided Z. mays into several groups 
and considered each to be of specific rank, several of the major 
character differences are dependent upon a single factor pair. A 
description of the more important groups is given here. 

The Pod Corns. Each kernel is enclosed in a pod or husks; the 
ear is enclosed in husks as in the other groups. The ordinary 
type of pod corn is heterozygous, the homozygous type being 
usually highly self-sterile. Mangelsdorf and Reeves have 
described a true-breeding pod corn bearing no ears, resulting from 
a combination of the homozygous condition of Tu, the pod-corn 
factor, and of Ts^ the dominant factor for tassel seed. The 
rachis of the ear of pod corn is definitely more brittle than in 
normal maize, and there is an indication that the rachises of the 
tassel are more brittle also. In the true breeding form, this 
brittleness would aid in seed dissemination. 

The Flint Corns. The flint corns comprise varieties with a 
starchy endosperm in which the soft starch is surrounded by 
corneous starch on the outside. The relative amounts of soft 
and corneous starch differ widely in different varieties. Mangels- 
dorf and Reeves state that the original flint corn from South 
America was probably a small-seeded tropical form with large 
cobs and irregular rows. Crossing with Euchlaena was believed 
to produce the pointed popcorns, and backcrosses with tropical 
forms led to the development of new types of flints with straight 
rows. 

The Popcorns. The endosperm contains only a small propor- 
tion of soft starch, by far the major part of the starch-bearing 
cells carrying corneous starch. There is generally some soft 
starch surrounding the germ. The small size of its seeds and 
cobs characterizes this group. Small, hard, pointed seeds occur 
from crosses of maize with Euchlaena, and such crosses are 
believed to be the original source of popcorns. Several writers 
have shown that teosinte may be popped much like popcorn. 

The Dent Corns. The corneous starch is located at the sides 
of the seed, and the soft starch extends to the summit. The soft 
starch dries more rapidly than the corneous, which causes the 



218 METHODS OF PLANT BREEDING 

characteristic indentation of the seed. Dent corns probably 
originated in Mexico, and this is considered to be the center of 
diversity of this type. Jones (1924) obtained dent types .from 
hybridization of Rice popcorn and Cuzco flour corn. Wallace 
and Bressman (1928) state that the dent corns of the corn belt 
probably arose from a cross between a large flint type with a late 
maturing type of dent that produced ears with 22 to 36 rows of 
rough, very soft, shoe-peg kernels. 

The Flour Corns. There is an almost complete lack of corne- 
ous starch, the group being characterized by the large amount of 
soft starch in the endosperm. Small amounts of corneous starch 
are produced by many flour corns. The location of the small 
amount of corneous starch determines whether the seed has an 
indentation. 

The Sweet Corns. This group is characterized by a trans- 
lucent, horny appearance of the kernel and a wrinkled condition 
when dry. East (1909) concluded that sweet-corn varieties are 
dent, flint, or popcorns that have lost their ability to produce 
starch. The few starch grains produced are small and angular. 

The Waxy Corns. This group is characterized by an endo- 
sperm of waxy nature resulting from a carbohydrate of different 
form than in starchy varieties. The original source was China, 
although waxy varieties have resulted from mutation in experi- 
mental cultures. 

ENDOSPERM CHARACTERS 

Endosperm characters are used to differentiate several of the 
major corn groups. Xenia is a result of double fertilization, the 
following statement being quoted from Hayes and Garber: 

Xenia may result from crossing varieties which differ in a single visible 
endosperm character. When a character difference is dependent upon 
a single dominant factor, xenia occurs when the factor is carried by the 
male parent, or, when dominance is incomplete, xenia results when 
either variety is the male. When a character difference is dependent 
upon more than one factor, all located in one parent, and dominance 
appears complete, xenia occurs only when these differential factors are 
located in the male; when dominance is incomplete, xenia occurs if the 
factors are located in either parent. When two varieties have a similar 
character or a different character expression but contain between them 
endosperm factors necessary for the production of a new character, 
xenia occurs when either variety is the male. 



INHERITANCE IN MAIZE 



219 



A summary of the mode of inheritance of the principal normal 
endosperm characters is given in Table 23. 

TABLE 23. INHERITANCE OF ENDOSPEKM CHARACTERS* 



Parental type 


Fi 


Segregation in F* 


Yellow vs. colorless 


Yellow or intermediate 


3 yellow:! colorless 


Dominant white vs. yel- 


Ivory, somewhat vari- 


3 ivory:! yellow 


low. 


able in shade 




Brown aleurone vs. 


Pale yellow, partially 


3 colored:! colorless 


colorless. 


dominant 


when a single factor 






pair is involved 


Colored aleurone (pur- 


Purple or red 


Ratios 3:1, 9:7, 27:37, 


ple or red) vs. color- 




etc., depending on 


less. 




whether 1-5 factor 






pairs are involved 


Purple vs. red aleurone 


Purple 


3 purple : 1 red 


Colored (purple or red) 


Colorless, because of 


Segregation, ratios de- 


vs. colorless. 


dominant inhibitory 


pending on number of 




factor 


factor pairs involved 


Starchy vs. sweet 


Starchy 


3 starchy : 1 sweet 


Starchy vs. waxy 


Starchy 


3 starchy : 1 waxy 


Waxy vs. sweet 


Starchy 


9 starchy : 3 waxy : 4 






sweet 


Floury vs. corneous. 


No immediate effect 


1 floury : 1 corneous 


Normal vs. defective 


Normal 


Segregation 3 normal : 1 


(various types of 




defective when single 


shrunken and shriv- 




factor par is involved 


eled). 







* For references to literature, see Kmerson et al. (1935). 

Emerson et al. (1935) have listed the genes responsible for many 
of the inherited characters of maize, particularly those used in 
linkage studies. Their monograph has been used freely in this 
review. There are two pairs of factors for yellow endosperm 
color. When both are segregating, ratios of 9 yellow: 7 white are 
obtained ; when either is segregating in the presence of the homo- 
zygous dominant condition of the other, ratios of 3 : 1 are obtained. 
There is some evidence that genes for yellow belong to an allelic 
series of various shades of yellow, although it is difficult to make 
clear-cut classifications. 

Hauge and Trost (1930) found a close physiological association 
in dent corn between vitamin A and the yellow endosperm. 
Mangelsdorf and Fraps (1931) demonstrated a direct relation 



220- 



METHODS OF PLANT BREEDING 



between the vitamin content of corn and the number of genes for 
yellow pigment in the endosperm. The average results for 2 
years were as follows: 



Number of genes 


Factorial composition 


Units of vitamin 


for yellow 


of endosperm 


A per gram 





yyy 


0.05 


1 


yyY 


2.25 


2 


yYY 


5.00 


3 


YYY 


7.50 



- 





FIG. 31. Inheritance of starchy and sweet endosperm in maize. Upper left, 
ear of sweet corn with wrinkled seeds; lower left, ear of flint corn with starchy 
seeds; left center, immediate result of pollinating an ear of the starchy parent with 
pollen from the sweet parent; center, an Fi ear self -pollinated that segregated in a 
ratio of 3 starchy: 1 sweet; upper right, a self -pollinated ear with wrinkled seeds 
obtained by planting sweet seeds of the Fi. The three remaining ears at the 
right were produced by self-pollinating ears produced by planting starchy seeds 
of Fi plants. Note that, on the average, one out of every three ears is homozy- 
gous for the starchy character. (Photograph by East.) 

Brown aleurone, appearing as pale yellow, is dominant over 
colorless in the absence of purple or red aleurone. There are two 
factor pairs for brown aleurone, either in a dominant condition 
producing color in the aleurone. 

There are a series of basic pigment genes designated as 4i, 4 2 , 
A s, C, and JB, all of which are necessary for production of red 



INHERITANCE IN MAIZE 221 

aleurone color. When Pr also is present the color is purple. 
Red or purple is epistatic to brown. When a dominant inhibitor 
is present, called 7, in the presence of the basic dominant aleurone 
factors for red or purple, the aleurone is colorless. In addition, 
there are several intensifying or diluting factors that modify 
aleurone color. There is a series of allelic factors for the R locus 
and also for the / locus that cause modifications of alexirone color. 

In crosses of either dent or flint corn with floury, there is no 
immediate effect of double fertilization on the endosperm condi- 
tion. Segregation on the ears of FI plants occurs in a 1 : 1 ratio. 
Hayes and East (1915) explained these results by the hypothesis 
that two genes of the floury factor are dominant over one gene for 
corneous and vice versa. In crosses between dent and floury, the 
floury segregate may show an indentation when there is a small 
amount of corneous starch on the sides of the kernel. Classifica- 
tion of floury vs. corneous is relatively easy by the use of trans- 
mitted light on a ground-glass background illuminated from 
below. 

There are a considerable number of characters with incomplete 
development of the endosperm. Most of these are lethal when 
homozygous recessive and normal development of endosperm is 
dominant over defective. Mangelsdorf (1926) collected 14 defec- 
tives at random and made the necessary crosses to show that 13 
of the 14 were due to different genetic factors. Sixteen different 
defectives have now been reported. There are also at least 15 
different factor pairs that are responsible for premature germina- 
tion of kernels. Certain of these give 3:1 ratios when hetero- 
zygous. There is one group of four duplicate factors that may 
give ratios of 3:1, 15:1, 63:1, or 255:1, depending on whether 
one to four pairs of factors are segregating. There are also 
several pairs of factors for germless seeds. Thus, it would seem 
that the development of normal endosperm is the result of the 
interaction of many factor pairs. 

CHLOROPHYLL VARIATIONS 

There are many recessive heritable chlorophyll abnormalities in 
maize. Many factors have been located in the genetic linkage 
map, and it is evident that there are several factors in each 
chromosome that in their interaction are responsible for the 
development of chlorophyll, These rQC^ssives are pf two types, 



222 METHODS OF PLANT BREEDING 

those that appear in seedling progenies and those that appear in 
mature plants. In a few cases, the same factor modifies chloro- 
phyll development in both seedlings and mature plants. 

The seedling types are frequently lethal. They include eight 
or more white-seedling types, each the result of a single gene in 
the homozygous recessive condition and two cases in which 
duplicate genes are involved. White seedlings are devoid of 
chlorophyll and generally of chloroplasts; therefore the seedlings 
die when the food reserve in the seed is exhausted. 

There are at least seven recessive genes for luteus seedlings. 
One of these acts only in the presence of white-seedling genes; 
others produce yellow seedlings in the presence of the dominant 
condition of a factor for white seedlings. Most luteus types are 
lethal; others give yellow seedlings and plants and therefore 
produce some chlorophyll. 

Twenty virescent seedling types have been described. The 
seedlings are yellowish and sometimes nearly white. There is 
considerable variability, ranging from types that are lethal to 
those with normal development. The rapidity of turning to 
green depends upon the genes involved and on temperature and 
light. 

There are at least 10 different genetic types of pale-green 
seedlings that produce a yellowish green color in the seedling. 
Some are lethal; others develop to maturity. In addition, about 
37 other genes affect seedling chlorophyll color alone or both 
seedlings and mature-plant color. Thus, there are at least 86 
genes that affect normal chlorophyll development in the seedling. 
In addition, at least 17 different genes have been described that 
affect chlorophyll development in the mature plant but not in the 
seedlings. The interaction of more than 100 genes is necessary, 
therefore, for normal chlorophyll development. 

PLANT COLOR 

There are several different plant colors that are of interest to 
the corn breeder. The plant and anther color resulting from the 
interaction o*f several of the genes for aleurone color with genes 
B and PI for plant color (Emerson et al. 1935) are given in 
Table 24. 

There is a series of alleles of a\ that, with other factors, affect the 
development of plant, pericarp, and silk color that were given in 



INHERITANCE IN MAIZE 223 

TABLE 24. INTERACTIONS OP THE PLANT-COLOR GENES ai, a*, B, PI, AND R 



Gene inter- 
actions 


With r rr 


With Roff 


Plant color 


Anther color 


Plant color 


Anther color 


PI 
B 
pi 


Purple 
Sun red 


Purple 
Pink 


Purple 
Sun red 


Green 
Green 


PI 
b 

pi 


Dilute purple 
Dilute sun red 


Purple 
Pink 


Green 
Green 


Green 
Green 


ai PI 
a* B 
or pi 


Brown 
Green 


Green 
Green 


Brown 
Green 


Green 
Green 


a\az PI 
b 
pi 


Green 
Green 


Green 
Green 


Green 
Green 


Green 
Green 



considerable detail by Emerson and others. These cannot be 
summarized in this short review. 

A series of al eles for pericarp and cob colors is of interest, P rr 
is the factor for red pericarp and red cob, P for red pericarp and 
white cob, P wr for white pericarp and red cob, and P ww for white 
pericarp white cob. The series varies from self- or solid red 
through various shades of variegation, designated as P vv . 

GLOSSY SEEDLINGS 

There are a number of different glossy seedlings that, in general, 
have a similar phenotypic appearance that are recessive to nor- 
mal. The leaves have a glossy appearance in the early seedling 
stages. One of these shows the glossy character only on the third 
and fourth seedling leaves, whereas the usual condition is for the 
glossy appearance to show on the first seedling leaves. Classifica- 
tion is made easy by sprinkling with water from a sprinkling can, 
the water on glossy seedlings adhering to the leaves in large 
droplets. The vigor of glossies is not greatly different from 
normals, and the characters may be used to detect outcrosses in 
an inbred line. 



224 METHODS OF PLANT BREEDING 

LINKAGE STUDIES WITH MAIZE 

The genes determining the characters in maize that have been 
studied fall into 10 linkage groups, corresponding to the 10 differ- 
ent chromosomes. Cytological study has demonstrated that 
these 10 chromosomes are morphologically distinguishable, espe- 
cially at prophase in meiosis. The chromosomes are character- 
ized by differences in total length, in the ratio of short to long arm 
lengths, and in the position and size of terminal or subterminal 
dark-staining regions. The chromosomes are numbered mainly 
in order of decreasing length from 1 to 10, the number 1 being the 
longest and the number 10 the shortest. 

The independence of the 10 linkage groups has been established 
by both cytologic and genetic studies. In addition, the linkage 
groups have been identified with the particular morphological 
chromosomes. Thus, the longest chromosome, 1, carries linkage 
group 1, and the shortest, 10, carries linkage group 10. In all 
cases, the orientation of the linkage group within the chromosome 
is known, and in most cases the spindle-fiber region can be at least 
approximately located in the linkage map. 

In the linkage map in Fig. 32, only those genes are included 
whose order is well established. The locus of the spindle fiber, 
designated S.F., must be considered to be only approximate 
except for group 5, genes in the part of the map above this point 
being located in the shorter arm of the chromosome. The 
terminal knob in chromosome 9 is shown. This map was drawn 
by C. R. Burnham from information published by Emerson, 
Beadle, and Fraser (1935) and from unpublished information 
generously supplied by several investigators. 1 The description 
of the characters was obtained from the same sources. 

The location of the genes on the linkage map for each of the 10 
chromosomes, with a description of the character produced, will 
be given separately for each chromosome (linkage group). In all 
cases, a gene symbol without subscript indicates the first or only 
gene with that literal symbol. 

1 Permission to use certain unpublished data in the preparation of these 
linkage maps of maize was given to C. R. Burnham by L, F. Randolph, 
A. C. Fraser, R. A. Emerson, M. T. Jenkins, E. W, Lindstrom, R. A. Brink, 
and H. S. Perry. 



INHERITANCE IN MAIZE 225 


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Is 




118 


g! 3 




* 


\O "\ 


<=4 




124 


Ch ^ 


Cl 


130 


Kn 


139 


gs 



166 bm 2 

FIG. 32. Linkage map of the ten chromosomes of Zea mays, showing the 
locus of the genes where the position has been determined with reasonable 
certainty. The locus of the spindle fiber, designated S.F., is only approximate 
in each group except group 5. 



226 



METHODS OF PLANT BREEDING 



Chromosome 1. This is the longest chromosome, physically, 
of the 10. The allelic series of P, which produces pericarp and 
cob colors, is located in this chromosome. The gene order and 
locus of 15 genes have been determined. These are listed below: 

0-sr Striate. Leaves with fine longitudinal striations throughout the 

life of the plant. 

25-wsn Male sterile- 17. Anthers usually not exserted. Some pollen 
occasionally shed. 

27-/S2 Tassel seed-2. Terminal inflorescence usually completely pis- 
tillate; no pollen produced. Ear develops if terminal inflores- 
cence is removed soon after emergence. Secondary florets in 
ear development, giving irregular arrangement of kernels. 
Tassel seed-2 is similar to ts (chromosome 2) except that the 
plants are usually stronger, and terminal inflorescence is less 
compact. 

28-P Pericarp and cob color. A large series of allelic genes for pericarp 
and cob color. 

30-zZ Zygotic lethal. Lethal that kills the very young sporophyte and 

endosperm. 

86-264 Zebra striped-4. Seedlings with irregular chlorotic crossbands on 
leaves in early stages. Bands may disappear as plants get 
older. 

55-as Asynaptic. Partially sterile type characterized by lack of associ- 
ation of homologous chromosomes during the first meiotic 
division. Produces a few kernels when pollinated by normal 
plants. Usually sheds no pollen. 

86-frr Brachytic. Culm notably shortened as a result of shortening of 
internodes. Plants one-fourth to one-half normal height. 
Leaves stiff and straight. 

90-F(7 Vestigial glume. Glumes of tassel and flowering glumes of cobs 
greatly reduced. Anthers of tassel exposed, pollen shed only 
occasionally. 

91-/ Fine stripe. Seedling virescent. Plant shows fine stripes of 

white tissue in the leaf blades, only rarely in the auricles. 

108-an Anther ear. Leaves broad. Plant variable in size, often almost 
normal in stature. Stamens develop throughout pistillate 
inflorescence. Ear usually ends in an unbranched spike con- 
sisting of staminatS flowers only. 

120-7^3 Tassel seed-3. Similar to is and ts z except that the terminal 
inflorescence usually is mixed pistillate and staminate. Usually 
pollen can be obtained. Secondary florets develop in ears. 

130- Kn Knotted leaf. Overgrowth of areas of midrib and other vascular 
tissue resulting in kinking or knotting of the veins. 

139-0S Green striped. Leaves in three- or four-leaf stage, and later, 
show light green stripes between main vascular bundles. 
Plant weak. 



INHERITANCE IN MAIZE 227 

166-&W2 Brown midrib-2. Brown color develops in midrib and over 
vascular bundles of leaf blade and sheath. Similar to bm but 
less intense. 

Chromosome 2. The factor pair for flinty vs. floury endosperm 
(Ff) is located in this chromosome. The location of 10 genes in 
this chromosome are: 



White sheath-3. Partial absence of chlorophyll in culms and 

sheaths of seedling and older plants. 
ll-lg Liguleless leaf. Leaf usually lacks ligule and auricles and stands 

upright at base. 
Glossy seedling-2. Seedling character. Younger leaves have 

glossy appearance, visible in bright sunlight. 
Green striped-2. Mature plant with green stripes. 
49-B Booster. Plant-color intensifier. In appropriate genotypes, gives 

intense sun-red, purple, or brown plant color. 
56-sfc Silkless. Pistils abort. No silks. Plants female sterile. Cobs 

grow normally and contain many anthers. 
68-// Floury endosperm. Endosperm floury (noncorneous). Female 

contribution to endosperm determines character; fl fl Fl gives 

floury endosperm, and Fl Flfl gives normal (flinty) endosperm. 
74-ts Tassel seed. Terminal inflorescence usually completely pistillate, 

no pollen produced. Ears develop if terminal inflorescence is 

removed soon after emergence. 
82-i>4 Virescent seedling-4. Seedlings yellowish green. Plants turn 

green slowly and may be distinguished from normal plants later 

than can most virescent seedlings. 
124-CVi Chocolate pericarp. Pericarp dark brown or chocolate in color. 

Chromosome 3. The allelic series A, A b , a p , a is in this 
chromosome. These genes are essential to the development of 
plant, aleurone, and pericarp colors. The 11 genes in this 
chromosome are: 

0-cr Crinkly leaf. Plants somewhat shorter than normal. Leaves 

broad, with characteristic crinkling at base. * 
18-d Dwarf plant. Plant of very low stature, with broad thick leaves. 

Starninate inflorescence compacted. Stamens produced in ears. 
26-m 2 Ramose ear-2. Much less extreme than ra in tassel and ear. 
46-L0s Liguleless leaf-3. Only a portion of the ligule present. 
4&-Rg Ragged leaf. Chlorotic areas in leaves of older plants, leaves 

becoming much split and torn. Character shows when plants are 

about half-grown. 
55-fe* Tassel seed-4. Terminal inflorescence produces staminate and 

pistillate flowers. Usually few kernels produced in the tassel. 

Secondary florets develop in ears. Pollen usually shed. 



228 METHODS OF PLANT BREEDING 

72-6a Barren stalk. Plant characterized by absence of pistillate inflores- 
cence. Stem circular in cross section, lacking the characteristic 
groove. 

83-na Nana. Plants dwarfed, from one-fourth to one-third normal height. 
- Leaves characteristically stiff and twisted. 

111-a Anthocyanin. Plant, aleurone, and pericarp color. Inappropriate 
genotypes, gives green or brown plants, colorless aleurone and 
brown pericarp. 

123-etf Etched endosperm. Endosperm scarred, seedling virescent. 

Chromosome 4. The factor pair for starchy vs. sugary endo- 
sperm (Su su) is located in this chromosome. The factor produc- 
ing tunicate plants (Tu) (pod corn) is also in this chromosome. 
The order of 11 genes has been determined. The exact location 
of the spindle fiber has not been determined. It is near silkless 
(sk) and is indicated on Fig. 32 by dotted lines. 

Q-de Defective endosperm. Incomplete development of the endosperm. 
Viability poor. 

35-Oa Gametophyte factor. Ga pollen, in competition with ga pollen on 
Ga silks, functions in the production of 95 to 99 per cent of the 
kernels. 

Tassel seed-5. Tassel contains both silks and anthers and is not 
compacted. Usually few kernels develop in tassel. Secondary 
florets develop in ears. 

Small pollen. Pollen grains small but filled with starch. Trans- 
mitted usually through the ovules only. 

71-su Sugary endosperm. Endosperm translucent and wrinkled. 

73-/o Lethal ovule. Ovules abort. Gene transmitted almost wholly by 
pollen. 

75-cfeie Defective endosperm- 16. Incomplete development of endosperm. 
Lethal. 

84-Z&0 Zebra striped-6. Chlorotic crossbands in leaves of nearly mature 
plants. 

107- Tu Tunicate ear. Glumes in both staminate and pistillate inflores- 
cence long, enclosing individual kernels in 'ear more or less 
completely. 

112-ja Japonica-2. Variegated striping. Expressed in seedlings as well 
as mature plants, some seedlings nearly white. 

118-gZs Glossy seedling-3. Glossy surface on younger leaves. 

Chromosome 5. The factor pair for purple vs. red aleurone 
(Pr pr) is in this chromosome. The location of eight genes and 
the characters produced by them is as follows: 

0-a2 Anthocyanin-2. Dominant allele complementary to the Aa pair in 
the production of plant and aleurone colors. Has no effect upon 
pericarp color. 



INHERITANCE 1$ MAIZE 

Brown midrib. Brown color develops in midrib and over vascular 
bundles of leaf blade and sheath. Character appears in three- to 
four-leaf stage but shows better at later stages. 

S.F. Spindle fiber. Known to be between bm and bt. 

8-bt Brittle endosperm. Endosperm translucent, usually shrunken and 
wrinkled. 

10-Vs Virescent seedling-3. Seedling light yellow but turns green quickly. 

12-bv Brevis. Plants usually about one-half normal height, owing to 
shortening of internodes in region of pistillate inflorescence. 

Bl-pr Red alcurone. In presence of other genes necessary for aleurone 
and scutellum color, gives red aleurone and scutellum as con- 
trasted with purple in presence of Pr. 

40-?/s Yellow stripe. Leaves show yellow stripes between main vascular 
bundles. 

72-Vz Virescent seedling-2. Seedlings very light yellow. Plants turn 
green rather slowly. 

Chromosome 6. This chromosome carries the factor pair for 
yellow vs. white endosperm (Yy) and the plant-color factor pair 
(PI pi). Five genes have been definitely located as follows: 

0-pc Polymitotic. Plants partially sterile. Young microsphore cells 
undergo several mitotic-like divisions in rapid succession without 
division of the chromosomes. No pollen shed; few seeds pro- 
duced in crosses with normal. 

13-F Yellow endosperm. 

4:l-Pl Purple plant color. In appropriate genotypes gives dilute purple, 
intense purple, or brown plants. 

51-sm Salmon silk. In presence of red pericarp (P rr , etc.) silks are salmon 
in color. In absence of pericarp color, silks are brown. 

61-p?/ Pygmy. Plant short, with short, thick, striated leaves. 

Chromosome 7. The gene for brown aleurone (Bri) is located 
in this chromosome. Nine genes have been located in this 
chromosome. These are: 

Q-Hs Hairy sheath. Leaf sheaths hairy throughout development. 
20-in Intensifier of aleurone color. Intensifies purple and red aleurone. 
24~z>6 Virescent seedling-5. Seedlings greenish yellow, turn green very 

quickly. 
32-ra Ramose ear. Ear much branched throughout, conical. Tassel 

much branched, conical in shape. 

36-grZ Glossy seedling. Leaves have glossy appearance. 
46- Tp Teopod. Plant strongly tillered, with narrow leaves. Number of 

nodes greater than in normal plants. Many small podded ears. 

Staminate inflorescence with long bracts, many plants not 

shedding pollen. 
52-tj lojap striping. Variegated stripe tnat shows throughout life of 

the plant. Varies from albino to variegated. 



230 MJSTtiuDS OF PLANT BREEDING 

71-Bn Brown aleurone. Pale yellowish aleurone color. Shows only in 

absence of purple and red aleurone. Often confused with light 

yellow endosperm. 
109-&d Branched silkless. Ears branched at base, often without silks. 

Tassel has characteristic branches, the spikelets occurring in 

groups of more than two. 

Chromosome 8. Fewer genes have been located in this 
chromosome than in any other. Of the three genes known to be 
in this chromosome, all are in the long arm. Consequently, the 
spindle fiber is not shown in Fig. 32. The order of the known 
genes is as follows: 

O-^ie Virescent seedling-16. Seedlings yellowish green. 

I4-mss Male sterile-8. No anthers exserted. Microsporocytes usually 

disintegrate. 
28-j Japonica. Variegated striping in leaves and sheath. Does not 

show in seedling stage. 

Chromosome 9. One of the basic aleurone color factors (C) is 
located in this chromosome. So is the gene for waxy endosperm 
(wx) . This chromosome, in certain stocks, has a terminal knob at 
the end of the short arm. Six genes have been placed in order on 
this chromosome, five being in the short arm. These are as 
follows : 

0-knob Terminal knob on the chromosome. 

2-ygz Yellow green-2. Seedling and plant yellowish. 

"21-C Aleurone color. In appropriate genotypes, gives purple or red 
aleurone. 

24-sft Shrunken endosperm. Endosperm shrinks during drying stage at 
maturity, giving a smooth indentation at the crown or a collapse 
at the sides of the kernel. 

39-6p Brown pericarp. In presence of P, gives brown pericarp. 

54-wx Waxy endosperm. Waxy starch in endosperm; embryo sac and 
pollen grains stain reddish brown with iodine solution, as con- 
trasted with normal starch, which stains blue. 

66-u Virescent seedling- 1. Seedlings yellowish, become green relatively 
early in development. 

Chromosome 10. This is the shortest chromosome, in terms of 
physical length, of the 10. It has a genetic map length of 99 
units. One of the basic aleurone and plant-color factor pairs (Rr) 
is located in this chromosome. The locations of 8 genes have 
been mapped. 



INHERITANCE IN MAIZE 231 

Resistance to leaf rust. Resistance to physiologic race 3 of 

Puccinia sorghi. 
16-00 Old gold. Dominant chlorophyll striping. Light-green or yellow 

striping begins after 5- 6-leaf stage. 
24-nZ Narrow leaf. Plants weaker than normal, with narrow leaf blades. 

Leaves tend to be longitudinally striated, like lineate (li). 
38-Z 8 Luteus-8. 

43-0 Golden. Full-grown plants of a yellowish green color. 
57-JK Colored aleurone and plant. In appropriate genotypes, gives purple 

or red aleurone. Exists in a series of alleles affecting aleurone, 

plant, and anther color. 

73-w 2 White seedling-2. Seedling albino, devoid of chlorophyll. 
84-dr Dwarf-7. Plant of low stature. 
99- 2 Luteus-2. Yellow seedling. 

In addition to the 86 genes whose location on the chromosome 
map has been determined with reasonable certainty, there are 
about 108 other genes that have been placed in particular 
chromosomes, although the location on the map, in relation to the 
genes whose locus is known, has not been determined. Some 102 
chromosome translocations have been found in which the chromo- 
somes involved have been determined. 

INHERITANCE OF QUANTITATIVE CHARACTERS 

Studies on the inheritance of quantitative characters in maize 
were started by East, in 1906, in Connecticut, and a little later by 
Emerson, in Nebraska. These and other experiments created a 
wide interest in the multiple-factor explanation of the inheritance 
of size characters. It is rather generally accepted that many 
normal characters are the result of the interaction of many genetic 
factors. A method commonly used with size characters is to 
cross parents that differ rather widely in a character, such as 
length of ear in maize, and study the Fi, F^ and F 3 generations in 
comparison with the parents. 

For quantitative characters, dominance is often incomplete or 
lacking. When dominance is complete, the expected ratios may 
be obtained by the expansion of the binomial (3 + l) n , where n 
is the number of allelic pairs of factors. When the hetero- 
zygous condition of a factor pair gives half the effect of the 
dominant homozygous condition and there is a cumulative effect 
of one factor on another and all factor pairs are of equal value in 
their effect on the character, the expected ratios in F^ may be 
obtained by the expansion of the binomial (1 + l) 2n . Where n 



232 



METHODS OF PLANT BREEDING 



is 3, for example, or three factor pairs are involved, the expected 
ratio will be 1:6:15:20:15:6:1. 

Such a ratio approaches the normal curve, and when suffi- 
cient Fz individuals are studied the parental combination of 
characters should be recovered. If each of the parents contains 
different factors that have an effect on the character, illustrated 
by the cross of aaBB X AAbbj types will be obtained in F% and 
later generations that exceed the limit of the parents. In actual 
practice, there is no reason to expect that all factors have like 
value in their effect on the character. This will affect the form 
of the curve but not its regularity in the absence of dominance. 
With partial to complete dominance, the curve will be of the skew 
types but cannot easily be distinguished from normal when a large 
number of factor pairs are segregating. 

An illustration of the usual type of data that are obtained, 
where dominance is incomplete, may be observed from a cross 
between Tom Thumb pop with Black Mexican sweet, as given by 
Emerson and East (1913). 

TABLE 25. FREQUENCY DISTRIBUTION FOR LENGTH OF EARS IN THE 

PARENTS Fi, F 2l AND F B GENERATIONS OF A CROSS BETWEEN TOM 

THUMB POP AND BLACK MEXICAN SWEET CORN 









Ear classes, cm 




Gen- 






Parent or 




Parent 




cross 




class 












































5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


20 


21 


Mean 


Tom Thumb 


p 




/\ 


1 


94 


s 




























6 6 07 


Black Mexi- 


P 




















3 


11 


12 


15 


26 


15 


10 


7 


2 


16.8 .12 


can 


Fi 












1 


\?. 


1? 


14 


17 


q 


4 














12.1 -1- .12 




F 2 








4 


5 


22 


56 


80 


145 


129 


91 


63 


27 


17 


6 


1 






12.7 .06 




Ft 


11 










1 


5 


8 


9 


25 


20 


2 














12.7 .11 




F 8 


18 
















9 


7 


13 


18 


25 


20 


6 


4 






15.8 .13 




Fa 


10 




1 




8 


22 


25 


15 


22 


7 


2 
















10.5 .10 




F s 


9 




5 


13 


20 


28 


28 


30 


10 


7 


6 


3 


2 


1 










10.0 .12 




Ft 


10 




3 


10 


33 


47 


40 


18 


3 




















9.2 .07 



From these results, it will be noted that the Fi was intermediate 
in ear length but no more variable than the parents and that the 
Fz was more variable than the parents. The few F% lines illus- 
trated give wide differences; the shortest eared line had a mean 
of 9.2 .07 and the longest, 15.8 .13. If sufficient lines had 
been tested, it is reasonable to expect that the parental forms 



INHERITANCE IN MAIZE 



233 



would have been recovered, the frequency of such recovery 
depending upon the number of factor pairs involved and the 
nature of their interaction. 

Similar data were given by Emerson and East for diameter of 
ears, weight of seeds, breadth of seeds, height of plants, number of 
nodes per stalk, internode length, number of stalks per plant, 
total length of stalks per plant, and duration of growth. For 
these quantitative characters, it should be emphasized that when 
several pairs of factors are involved it may be difficult to recover 
the parental types in JFV The usual method used by the breeder 
is to grow as large a population in F 2 as can be studied and select 
for the character desired. Recovery of the parental types may 
be obtained, as a rule, by continuing selection in F 3 and in the 
later segregating generations. 

LINKAGE OF FACTORS FOR ROW NUMBER WITH GENES AT 

KNOWN LOCI 

Further proof of the multiple-factor explanation of the inherit- 
ance of quantitative characters has been obtained by studies of 

TABLE 26. COB COLOR AND Row NUMBER IN THE F 2 OF THE CROSS OF 
IODENT X GOLDEN BANTAM AND IN THE BACKCROSS 



Rows 


Fi generation 


FI X Golden Bantam 


per ear 


R* 


r 


72 


r 


8 






24 


62 


10 


3 


4 


94 


109 


12 


40 


17 


116 


101 


14 


46 


6 


19 


10 


16 


17 


3 


3 





18 


2 









Total 


108 


30 


256 


282 


P 


0.03 


0.0001 



* In this table, R stands for red cob arid r for white. 

linkage between quantitative characters with genes that are 
known to be located in particular loci of the chromosome map. 
Studies have been made by Lindstrom (1931) of the linkage 
relations of row number with the gene P for pericarp and cob 
color, the R factor for aleurone color, Su for starchy endosperm. 



234 METHODS OF PLANT BREEDING 

and Y for yellow endosperm color. An illustration of the type of 
results obtained will be given for a cross of lodent with a modal 
value of 16 rows per ear and red cob X Golden Bantam, an 
8-rowed, white-cobbed variety. The extent of association was 
determined by the calculation of X 2 and P for independence. 

In both F% and the backcross, it is evident that the white- 
cobbed (r) ears average lower in row number than the red-cobbed 
ears. The data given illustrate one of a rather extensive series of 
crosses where there appeared to be an association between row 
number and cob color. This linkage relation seems best explained 
by the hypothesis that one of the factor pairs for row number is 
located on chromosome 1 and shows genetic linkage with one of 
the allelic pairs of factors for pericarp and cob color. 

In studies of linkage relations between row number and the 
factor pair Su su for starchy-sugary endosperm, crosses were 
made in both phases, i.e., high row, sugary X low row, starchy 
and low row, sugary X high row, starchy. In certain crosses of 
both types, there was definite evidence of genetic linkage; other 
crosses did not show association. 

With the Yy factor pair, there was some evidence of a loose 
linkage. The greater part of the data also showed evidence of 
linkage between the factor pair for aleurorie color Rr and row 
number. 

INHERITANCE OF SMUT REACTION 

Studies of linkages for smut reaction have been made by vari- 
ous workers. Immer (1927) and Hoover (1932) made crosses 
between resistant inbreds and genetic testers that were suscepti- 
ble. Most of the cases of association were between characters 
such as tassel seed, brachytic and liguleless, and susceptibility. 
These are of such a nature that the association may be explained 
on the basis that the morphological character tends to make the 
plant more susceptible. Immer observed an association between 
the pericarp factor pair Pp and smut reaction; Hoover obtained 
evidence in certain crosses, but not in others, of linkages between 
smut reaction and su } v%, and sh wx located in chromosomes 4, 5, 
and 9, respectively. 

More recently, studies of linkage of smut reaction have been 
made by the use of chromosome interchanges. In these experi- 
ments, smut-resistant inbred lines were crossed with particular 



INHERITANCE IN MAIZE 



235 



interchanges that were smut-susceptible. In the studies of 
Burnham and Cartledge (1939), the FI was rather highly resistant, 
and this was outcrossed to a normal susceptible inbred. Inter- 
change plants can be differentiated from normal, since they 
produce approximately 50 per cent aborted pollen grains. In the 
experiments of Saboe and Hayes (1941), the Fi cross between a 
resistant inbred and a susceptible interchange was intermediate in 
susceptibility. The Fi was backcrossed to the resistant inbred 
parent. 

In both experiments, the plants in the segregating families were 
first classed as normal or interchange on the basis of pollen 
sterility, and data were taken on smut reaction. A portion of 
Burnham and Cartledge's results will be summarized to show how 
linkages were determined. 

TABLE 27. REACTION TO SMUT IN THE PROGENY OF BACKCBOSSES OF 
THE Fi (RESISTANT INBEED X SUSCEPTIBLE INTERCHANGE) X SUS- 
CEPTIBLE NORMAL 





Normal 


Semisterile 




^1 






P 


cross 














Smutted 


Not smutted 


Smutted 


Not smutted 




l-2a X resistant 


57 


215 


55 


198 


0.80 


l-2c X resistant. . 


53 


261 


91 


257 


<0.01 


3-8a X resistant 


210 


602 


250 


488 


<0.01 


l-9c X resistant. 


10 


38 


17 


34 


0.20 



Highly significant deviations from random expectation were 
obtained with interchanges involving l-2c and 3-8a, as shown in 
the table, and also with l-6a, l-9t>, 2-6a, and 6~8a. In the case 
of the interchange l-2c, where definite linkage is noted, and the 
point of interchange is close to l-Qc in chromosome 1, where there 
was no evidence of linkage, it seems probable that the linkage 
relation is with chromosome 2. Break l~2c occurred near the 
location v in the longer arm of chromosome 2. 

In the studies by Saboe and Hayes, significant associations 
were observed with interchanges 3-76, 5-7dI, 6-9a, and 8-10a in 
the crosses of interchanges with the resistant inbred line of Minn. 
13 and with interchanges l~4a, 3-5c> and 5-8a in crosses with the 
resistant inbred from Rustler. 



236 METHODS OF PLANT BREEDING 

From these results, it is evident that there are many loci for 
reaction to smut. Various investigators, including Jones (1920), 
Hayes et al. (1924), and Garber and Quisenberry (1925), have 
found it relatively easy to isolate resistant inbred lines by selec- 
tion in self-fertilized lines. It is possible that the number of 
factor pairs for smut resistance is not necessarily very great from 
any one source of origin. 

INHERITANCE OF COMBINING ABILITY 

There is a great deal of information that leads to the conclusion 
that some inbred lines combine well in top-crosses or with most 
unrelated lines, whereas other inbreds rather generally have 
lower combining ability. This entire problem has received some 
consideration in the chapter on Breeding Methods, but some of 
the more salient facts in relation to inheritance of combining 
ability will be reviewed briefly. Experiments at Minnesota and 
Iowa, already reviewed, show that there is a direct correlation 
between the vigor of inbred lines and their yielding ability in top- 
crosses. It is equally evident that the relationship is not easily 
measured by the eye, since it is impossible to determine by inspec- 
tion whether a particular inbred will give high or low yields, on 
the average, in crosses. 

There is general acceptance that the yielding ability of inbreds, 
as determined by their crosses, is dependent upon the number and 
nature of dominant growth factors of each inbred in relation to 
the dominant factors carried by the other parent. This has led 
to the test of inbred lines for their combining ability and the 
selection of genetically diverse lines to use in any particular 
hybrid. Davis (1929) first suggested the use of top-crosses to 
test combining ability, although the general wide use of the 
method should be credited to the work of Jenkins and Brunson 
(1932). Wu (1939), Hayes and Johnson (1939), and Johnson 
and Hayes (1940) have summarized extensive studies that show 
that yielding ability in single crosses is greater, on the average, in 
lines that are unrelated on the basis of origin than in lines of a 
somewhat similar origin. Using inbreds of diverse origin that 
had been classified on the basis of combining ability in top-crosses 
into two groups for yielding ability, low and high, Johnson and 
Hayes (1940) found that, on the average, crosses between low X 
low yielded less than low X high or high X high, although F\ 



INHERITANCE IN MAIZE 



237 



crosses between low X high yielded as well, on the average, as F\ 
crosses between high X high* 

Eckhardt and Bryan (1940) selected inbreds from two different 
varieties and called those from one variety A and B and from the 
other, X and Y. From any double cross, where two inbreds were 
selected from one variety and two from the other, the yield of 
(A X B) X (X X F) was significantly greater than (A X X) X 
(B X F) or (A X F) X (B X X). 

Several studies on the inheritance of combining ability have 
been made. Jenkins (1935) concluded that inbred lines showed 
their individuality as parents in top-crosses in the early segregat- 
ing generations and remained relatively stable in later inbred 
generations. This has led to a consideration of the value of test- 
ing combining ability in the early generations of selfing and 
continuing selection in self-pollinated lines from lines of high 
combining ability. Jenkins explained these results on the basis 
that combining ability was controlled * by a large number 
of dominant genes and that the effect of different genes was of 
approximately the same value. He thought equal numbers of 
favorable dominant genes would be preserved by chance through 
the successive generations of selfing. 

In a recent study, Jenkins (1940) selected seven inbred lines of 
the variety Krug that had been tested in top-crosses for each of 4 
successive years, the tests having been begun after the lines had 
been selfed for 3 years. The results of these trials are as follows: 



Inbred 


Acre yield in top-crosses 


1930 


1931 


1932 


1933 


Mean 


K679 


39.7 
37.3 
51.9 
22.4 
37.9 
31.1 
36.2 
37.5 


75.8 
74.6 
81.1 
70.4 
79.8 
79.5 
76.4 
76.5 


71.3 
81.8 
77.6 
74.7 
79.5 
66.1 
71.7 
75.1 


80.9 
92.3 
84.3 
79 2 
86.3 
73.6 
82.0 
79.6 


66.9 
71.5 
73.7 
61.7 
70.9 
62.6 
66.6 
67.3 


K682. 


K683 


K685 


K686 


K687 


K689 


Krug variety 





Remnant seed of the first-year selfs Si was used for each line, 
and within each line pollen of each of 16 plants was applied to the 



238 



METHODS OF PLANT BREEDING 



silks of 25 plants of the Krug variety. Seed for each top-cross 
was obtained by mixing the seed of 25 ears, and the 112 top- 
crosses so made were tested in replicated yield trials. The 
analysis of variance is as follows : 

TABLF- 28 ANALYSIS OF VARIANCE OF YIELDS OF TOP-CROSSES OF INDI- 
VIDUAL PLANTS IN ONE-GENERATION KRUG SELFS 



Source of variation 


Degrees of 
freedom 


Mean 
squares 


F 


Lines 


6 


680 32 


34 07* 


Sibling plants within lines 


105 


77 21 


3.87* 


Replications within lines 


63 


403 45 


20.20* 


Error 


945 


19 97 












Total 


1119 















* Highly significant. 

On the basis that heterozygosity, and therefore variance, will be 
reduced among siblings within lines in the various succeeding 
generations of selfing according to the series %, ^ %, etc., 
Jenkins determined the probable significance of segregation for 
combining ability. The variance for sibling plants within lines 
in the first selfed generation was 77.21. This is composed of error 
mean square 19.97 and variance due to genetic differences or 
57.24. The calculated mean squares for sibling plants in the 
various generations of selfing from Si to $ 8 were Si 77.21, $ 2 
48.59, S s 34.28, S 4 27.13, S, 23.55, S 6 21.76, S 7 20.86, and S 8 20.42, 
respectively. Although all generations except $ 8 showed highly 
significant calculated variations, it is apparent that the chances 
for segregation were much the greatest in the early generations of 
selfing and on the average became progressively less as selection 
progressed. 

Sprague and Bryan (1941) studied segregation for yield, lodging, 
and damaged kernels in top-crosses of 73 F% lines selected from a 
single cross between inbreds. Twelve F 3 lines were selected that 
represented low, medium, and high yielders in top-crosses and 
that differed in damaged kernels and lodging resistance. Five F& 
plants were chosen from each F* line and top-crossed to the 
synthetic hybrid 8037 and tested in yield trials for 1938 and 1939. 
Highly significant variances between F 4 lines within F 3 families 



INHERITANCE IN MAIZE 239 

were obtained for yield and lodging, and a significant variance 
on the basis of odds of 20 : 1 was obtained for damaged kernels. 

Hayes and Johnson (1939) studied 110 inbreds obtained from 
selection through F G in the progeny of single crosses between 
inbred lines. These crosses comprised three general types of 
crosses between inbreds that were classified as low and high 
combiners in top-crosses. From crosses between low X low, 
most of the inbreds selected proved low in combining ability. 
Crosses of low X high combiners and subsequent selection 
through FG gave both low and high combining lines, whereas from 
crosses of high X high and subsequent selection in selfed lines 
through F& only high combining lines were isolated. 

INHERITANCE OF OTHER IMPORTANT CHARACTERS 

A complete review of important studies of inheritance in maize 
cannot be made in the space available. Inheritance of protein 
content has been studied by Hayes and Garber (1919), East and 
Jones (1921), and Hayes (1922). Crosses between low and high 
protein lines have low protein content in F\. It seems probable 
that many genes are responsible for the inheritance of protein. 
East and Jones concluded that the apparent dominance of low 
protein over high protein was a result of heterosis, which is a 
further indication of the multiple-factor theory of protein 
inheritance. 

Jenkins (1932) has shown that inbred lines and crosses in corn 
have differential resistance to heat and drought. Haber (1938) 
obtained similar results with inbred strains of sweet corn. Heyne 
and Brunson (1940) have found also that selfed lines of corn can 
be isolated that differ in reaction to heat and drought. Heat 
tolerance was definitely inherited and usually intermediate to 
dominant in FI. A case of linkage of reaction to heat with the 
Pr pr factor pair was noted. The su gene was directly responsible 
for susceptibility to heat while certain of the glossy seedling genes 
gl and gl% apparently protected the seedlings from heat. 

Holbert and Burlison (1928) noted marked differences in reac- 
tion to cold between inbred lines and within commercial varieties. 

Most maize plants are proterandrous, the pollen being shed 3 
to 5 days before the silks appeal*. A variety of popcorn from 
Spain was found to have proterogynous habit, the pollen being 
shed 2 or 3 days after the silks emerge, which is the normal condi- 



240 METHODS OF PLANT BREEDING 

tion in Tripsacum and Euchlaena. The inheritance of this 
character has been studied by Kempton (1924). The proter- 
ogynous strain used in crosses averaged 2.96 0.18 days from 
silking to pollen shedding; the proterandrous strain shed pollen 
2.3 0.11 days before the silks appeared. No proterandrous 
plants were found in the proterogynous strain. The proter- 
ogynous strain produced an occasional plant that showed a 
tendency to be proterandrous. The proterogynous strain also 
produced several plants that failed to extrude anthers and never 
shed pollen. In crosses between the two strains, the F\ was 
proterandrous. Segregation occurred in Fz, the number of 
proterogynous plants obtained being too few for a simple 
Mendelian ratio. Male sterile plants appeared also, and the 
conclusion was reached that proterogyny was a result of a variable 
expression of the male sterile condition brought about by modify- 
ing factors. 

Pericarp tenderness has been found by Johnson and Hayes 
(1938) to be an inherited character. Different inbred lines give 
wide deviations for the mean expression of tenderness. The 
number of factor pairs involved was not determined, but the 
results proved that it was relatively easy to modify the tenderness 
of an inbred line of sweet corn by a process of crossing, backcross- 
ing, and .selection. 

Harvey (1939) has reviewed previous studies of differential 
responses of corn to various levels of fertility. The various 
studies show clearly that inbred lines and their FI hybrids fre- 
quently show differential response to various nutrients, including 
phosphorus and nitrogen, and in water economy. Harvey dealt 
with the absorption and utilization of nitrogen ionic forms by 
corn inbreds and hybrids. The inbred strains and their F\ 
hybrids were grown in aqueous mineral solutions. Differential 
response to ammonium and nitrate nitrogen was statistically 
significant. Some strains made relatively more growth than 
other strains on ammonium nitrogen compared with their growth 
on nitrate nitrogen. The response of FI crosses indicated that 
there was a partial dominance of the genetic complex for efficient 
utilization of ammonium nitrogen. 

There are wide differences among varieties, inbred lines, and 
hybrids in reaction to important diseases and insect pests. Mains 
(1931) studied reaction to leaf rust, Puccinia sorghi, using physi- 



INHERITANCE IN MAIZE 241 

ologic races 1 and 3. Resistance to both races was due to the 
same genetic factor. In crosses of resistant X susceptible, 
resistance was dominant, and segregation in F 2 was on the basis 
of 3 resistant: 1 susceptible. Ivanoff and Riker (1936) and 
Wellhausen (1937) have shown that resistance to bacterial wilt 
was an inherited character. In general, in crosses of resistant 
with susceptible inbreds, resistance behaves as a dominant. 
Wellhausen concluded that there were at least three pairs of 
factors, independently inherited, that condition resistance. The 
presence of all three dominant factors in either a heterozygous or 
a homozygous condition resulted in a high degree of resistance. 
Differences in reaction to ear, stalk, and root rots have been 
observed by many investigators. The mode of inheritance has 
not been worked out in detail. 

Resistance to insect pests has been studied by several workers. 
The leaf aphid, Aphis maidis Fitch, attacks the strains of suscepti- 
ble plants and prevents pollen shedding. Snelling et al. (1940) 
reviewed the literature on resistance to aphis attack and presented 
data on inbreds and crosses between them to show that resistance 
to aphis injury is a heritable character. There have been 
numerous studies of resistance to the European corn borer. 
Marston (1930) studied crosses of Maize Amargo, a resistant 
variety, with Michigan varieties and concluded that reaction to 
the borer segregated in a ratio of 3 susceptible: 1 resistant. 
Meyers et al. (1937) found resistance to be an inherited character 
but conclude " no thing suggestive of immunity nor of a genetically 
simple resistance was found." Inherited resistance to the corn- 
ear worm was reported many years ago by Collins and Kempton 
(1917), and considerable progress has been made in the develop- 
ment of resistant varieties. Blanchard et al. (1941) found that 
some inbiled lines were resistant to the corn-ear worm, whereas 
others were susceptible. Some resistant inbreds transmit a high 
degree of resistance to their FI crosses with either resistant or 
susceptible inbreds. Other FI crosses of resistant X susceptible 
did not show a dominance of resistance. FI crosses of susceptible 
inbreds were generally susceptible, although one case of a 
resistant FI was obtained from a cross of susceptible inbreds. 
Marked differences in reaction to the chinch bug have been noted 
by Snelling and Dahms (1937). 



CHAPTER XVI 

CONTROLLED POLLINATION METHODS OF BREEDING 
CROSS-POLLINATED PLANTS 

Darwin (1876) made the first carefully controlled extensive 
experiments of the effects of self-fertilization. He noted the 
great uniformity of inbred lines and in general a marked reductior 
in vigor in self -pollinated lines, although he recorded exceptions 
In several cases he found little harmful effect of continued self- 
fertilization after the first generation. He observed that con- 
tinued brother-sister mating had the same effect as continued 
self-fertilization. He believed, however, that this similarity wag 
the result of growing the inbred cultures under the same environ- 
mental conditions, for he found that crosses between his inbred 
stocks and those from another locality were very vigorous. 

In spite of these results, Darwin agreed with Knight that self- 
fertilization was not a natural process. They were the chiei 
exponents of the so-called Knight-Darwin law that " nature 
abhors perpetual self-fertilization.^ The vigor of FI crosses wa& 
explained by Darwin on the basis of germinal differences con- 
tributed by the parents. 

EFFECTS OF SELF-FERTILIZATION 

East and Jones (1919) summarized many of the experiments on 
the effects of inbreeding and on hybrid vigor and gave what seems 
to be a sound biological explanation of the results. This mono- 
graph furnishes a wealth of information for the student of plant 
breeding. 

In its application to plant and animal improvement, inbreeding 
gives an opportunity for controlled selection and in this way aids 
in the rapid isolation of strains homozygous for the desired char- 
acters. In many cases, the vigor of growth of a plant or animal 
is dependent upon the interaction of a large number of growth 
factors. Most of these factors are dominant or partially domi- 

242 



CONTROLLED POLLINATION METHODS 243 

nant in hybrids, and, because of their number, linkage is involved. 
Inbreeding tends to reduce the number of heterozygous pairs of 
growth factors present in the inbred line of the organism. 

In self -pollinated crops, natural and artificial selection has led 
to the development of vigorous inbred lines. It would seem that 
artificial inbreeding and selection with cross-pollinated crops 
might be expected to accomplish similar results. Continued 
studies of the effects of inbreeding and selection with cross- 
pollinated crops plants show the value of the methods, although 
there are many instances where the reduction in vigor is so great 
that inbreeding cannot be continued for many generations with 
the hope of obtaining inbred lines that are vigorous. 

Studies of self-fertilization with corn and other organisms, since 
the rediscovery of Mendel's laws, have furnished the basis for the 
Mendelian explanation of hybrid vigor and the partial standard- 
ization of breeding technic with cross-pollinated plants. The 
extent to which controlled inbreeding can be used, the desirability 
of breeding by adding the factor for self-fertility to many lines 
when it is available in the organism and where extensive self- 
sterility is involved, as well as many other similar problems, can 
be solved only by extensive study with each particular crop 
plant. A brief review of the effects of self-fertilization with 
several different crop plants will serve to show the wide diversity 
of results when selfing is practiced and indicate the difficulty of a 
close standardization of breeding methods. It seems probable 
that such standardization will depend, in a large measure, on the 
effects of self- and cross-fertilization with the crop plant in 
question. 

As has been emphasized in Chaps. Ill and XIV, it is probable 
that more information is available on the effects of self-fertiliza- 
tion in corn than for any other cross-pollinated plant. In 
general, all inbred lines of corn obtained so far are less vigorous 
than normal corn, although some inbred lines are relatively 
vigorous and normal in habit of growth. Inbred lines differ 
widely in resistance to diseases, such as bacterial wilt in sweet 
corn and reaction to smut, as well as ability to withstand environ- 
mental conditions generally considered unfavorable. The most 
noticeable effect of inbreeding in corn, in addition to reduction of 
vigor and the isolation of lines that are .relatively homozygous, is 
the appearance of many recessive abnormalities. 



244 METHODS OF PLANT BREEDING 

Studies of inbreeding with alfalfa have been made by Kirk 
(1927, 1932, 1933). In general, the loss in vigor is rather great 
when alfalfa is self-fertilized for several generations. Kirk says, 
*'The results of selfed line breeding have not been impressive as a 
practical method of improvement." H. M. Tysdal, of the U.S. 
Department of Agriculture, cooperating with the Nebraska 
Agricultural Experiment Station, has continued self-fertilization 
with alfalfa for a greater number of generations than has been 
reported by any other investigator. The results are given here in 
considerable detail and may be compared with those for corn that 
have been discussed in Chap. III. From three trials under 
Nebraska conditions using, in two of the three studies, lines of 
alfalfa with known genetic characters, Tysdal concluded, "As an 
average of the three tests under open-pollinated conditions, 89.1 
percent natural crossing was found." This is somewhat lower 
than in corn but higher than has usually been reported for 
alfalfa. 

The following statement from Tysdal (1941) describes the 
results of a study of the effects of selfing on forage and seed yields : 

From the amount of natural crossing found in alfalfa, it would be 
expected that self-fertilization would lead to a reduction of vegetative 
[,7owth and seed yield. The selfing program has been included for a 
number of years as a part of the alfalfa improvement and breeding 
program at Nebraska. While most of the lines have been selfed for 
only one or two generations, a few have been carried into the seventh 
and eighth generations of inbreeding. A number of these lines were 
planted in space-planted nurseries with the rows spaced 27 inches apart 
and the plants separated by 18 inches in the row. The self -fertilized 
lines were planted in comparison with hybrids between these lines, their 
open-pollinated progeny, and the standard varieties, Grimm, Ladak 
and Hardistan, the latter belonging to the Turkestan group, which 
represented the varieties from which practically all of the inbred lines 
originated. 

Yields of seed and of forage were obtained in terms of the 
average yield of the three varieties. The forage yields were 
obtained by taking green-weight yields on a 2-year basis and the 
seed yields for a single season. Results given in Table 29 are an 
average for the number of lines tested, all lines containing at least 
10 plants. Us7m])y 30 V> 60 pla,nte formed the basis for taking 
yields- 



CONTROLLED POLLINATION METHODS 



245 



TABLE 29. YIELDS OF SELF-FERTILIZED LINES OF ALFALFA IN PERCENTAGE 
OF THE PARENTAL OPEN-POLLINATED VARIETIES GRIMM, HARDISTAN, 

AND LADAK* 



Number 
of selfed 


Number 
of lines 


Actual yield in per cent 
of original parents 


Theoretical yield 


generations 


tested 


Forage 


Seed 


Forage 


Seed 


1 


54 


68 


62 


68 


62 


2 


17 


48 


39 


52 


43 


3 


9 


59 


38 


44 


33 5 


4 


13 


51 


36 


40 


28.75 


5 


1 


41 


29 


38 


26 37 


6 








37 


25.18 


7 


1 


26 


15 


36 5 


24 58 


8 


4 


28 


* 8 


36 25 


24 28 



of H. M. Tywdal. 



IUU 

90 

to 
o 

ieo 

6 

I 

fD 
g. 6 

IBQ 

2-40 

c 

0> 



8ZO 
t- 

0> 
CL 

EIO 

T3 
0> 


I 
















\ 


x = Actual forage productivity 
Upper curve - Theoretical tbrage productivity 
- Actual seed productivity 
Lower curve = Theoretical seed productivity 


N 


\ 
















\\ 




) 


( 










( 


\ v 














\ 


x 


^ - 





J 










^^^n 




. 


) 

~- 


X 














< 


















4 



I 



6 



23456 
Number of selfed generations 

FIG. 33. Point diagram showing average forage and seed yields of self-fertilized 
lines of alfalfa after one to eight generations of inbreeding, and curves showing 
theoretical decrease in yield of self-fertilized lines. (Courtesy of H. M. Tysdal.} 



246 METHODS OF PLANT BREEDING 

The theoretical yields given in the table were calculated by 
comparing the average yields of the open-pollinated varieties 
Grimm, Hardistan, and Ladak as 100 per cent with the yields of 
54 first-year selfed lines at 68 per cent, giving a reduction of 32 
per cent and the expectation that yields would be reduced one- 
half in each succeeding generation. For example, subtracting 
one-half of 32, or 16, from 68 gives an expected yield for second- 
generation selfed lines of 52 per cent. These results are given in 
the diagram in Fig. 33. Although selection seemed to lead to a 
slowing up in the reduction in yields in the first five selfed genera- 
tions, further years of selfing caused a greater reduction in yields 
of both seed and forage than the theoretical expectation. 

In discussing these results, Tysdal says, in part : 

It would be difficult if not impossible to give an exact curve of reduc- 
tion in yield caused by inbreeding in alfalfa because it would be necessary 
to consider the origin of the material as well as to very carefully refrain 
from any type of selection whatever. Obviously, selection is practiced 
among the inbred lines in a breeding and improvement program and, 
therefore, the results presented above are subject to whatever bias 
may result from such selection. In some cases, lines were carried for 
the purpose of determining the principle rather than for selective pur- 
poses, but on the other hand, some were eliminated in the selection 
program while still others reduced so rapidly in seed yield that they 
could not be carried at all. To indicate the wide range in forage yield 
of selfed lines, for example, it is only necessary to point out that the S\ 
lines varied from 26 per cent to 105 per cent. Seed yield is even more 
variable in selfed lines than forage yield. Some lines in advanced 
generations showed increased productivity over the original parent, 
while others decreased very rapidly. This divergence might be attrib- 
uted, at least to some extent, to the variability in seed setting in alfalfa 
in general, and also perhaps, to the peculiarities of the conditions under 
which the test is made. Those lines which might be selected for high 
self-fertility, as autogamous lines, for example, might produce unusually 
well under conditions of limited cross pollinating insect activity. The 
origin of the selfed lines no doubt also plays an important part. Selfed 
lines from Turkestan origin apparently do not reduce as rapidly as 
those from Grimm or Ladak origin. In general the Turkestan group 
appears to be more homozygous than alfalfas of hybrid origin such as 
Ladak and Grimm, and it may be that the diversity of origin of the 
latter would produce a greater range and possibly a different type of 
curve in yields of inbred progenies. Further, when a given plant is 



CONTROLLED POLLINATION METHODS 247 

chosen for selfing from a mass population, there is no way of knowing 
whether it, itself, was the result of cross- or self-fertilization. 

The results obtained with alfalfa "are remarkably similar to 
those obtained in corn and this together with the fact that hybrid 
vigor has been demonstrated in alfalfa similar to that in corn 
(unpublished data) leads to the conclusion that the principles of 
breeding in this crop are essentially the same as those which have 
been established for com." 

With rye, Heribert-Nilsson (1916, 1919, 1921) found 1 or 2 
plants out of 100 that were highly self-fertile, although self-steril- 
ity was the usual condition. Some inbred strains approached in 
yielding ability the normal variety from which they were 
obtained. The number of recessive abnormalities is somewhat 
less in rye than in corn. Brewbaker (1926) believed self-fertiliza- 
tion and selection a desirable method of breeding rye, although 
from studies that have been continued at Minnesota no inbred 
lines have been obtained as vigorous as normal. Peterson (1934) 
studied crosses between self -fertile and self-sterile inbred lines and 
found that the factor for fertility bred out the sterility allelcs in 
later generations of selfing from a cross between fertile and sterile 
lines. Whether self-fertility is desirable or undesirable in rye is 
an unanswered question. 

With sunflowers, Hamilton (1926) found a reduction in vigor, 
after selfing in most lines. He says, " Unlike the inbred strains of 
corn, however, a number of the sunflower strains, while becoming 
extremely uniform, did not lose any of their former vigor. In fact 
some of the tallest, leafiest and highest yielding rows under test 
during the past five years were strains that had been inbred for 
five consecutive generations." 

In timothy breeding, as developed at Cornell, selfing was 
practiced for a year and the better types then used for breeding 
stocks. Clarke (1927), at Minnesota, concluded that vigorous 
lines of timothy could be obtained without great difficulty and 
believed that self-fertilization and selection in self-fertilized lines 
was a practical means of breeding. Valle (1931), in a breeding 
study in Finland, states that the percentage of self-fertile and 
self -vital lines was too low to make self-fertilization and selection 
a valuable method of breeding timothy. 

Jenkin (19316), at Aberystwyth, placed timothy in two main 
groups, the hay type, with 42 chromosomes, and the pasture tyt)e, 



248 



METHODS OF PLANT BREEDING 



with 14. Self-fertility was variable, the pasture type being much 
less self-fertile than the hay type. Self-sterile plants are frequent 
in commercial varieties of American timothy, although self- 
fertility is common also. Two strains of timothy have been 




FIG. 34. Individual timothy plants grown under like conditions. The upper 
plants are undesirable, one having weak stems and the other lacking vigor. The 
lower plants are more desirable. They differ in density of plant and number of 
culms. (Courtesy of Myers.) 

selected at the Minnesota station that were self -pollinated for a 
3-year period. One of these strains is from a single self-pollinated 
line and the other from a combination of several self-pollinated 
lines. In preliminary comparisons with normal commercial 
timothy, both strains appear somewhat superior to the commer- 
cial variety. These and other results of a similar nature prove 
that in some cases improved varieties can be obtained directly by 
the utilization of self-pollinated lines from crops that presumably 
belong to the cross-pollinated group. In brome grass, Bromus 



CONTROLLED POLLINATION METHODS 249 

inermtSj Kirk (1932) obtained a vigorous nonstooling line after 
four generations of selfing. 

Most perennial grasses show considerable self-sterility, and the 
question of the desirability of selection in self -fertilized lines as a 
method of breeding grasses is undecided at the present time. 
Beddows (1931) has summarized many previous studies on seed 
setting in the grasses and presented further data comparing seed 
setting from enclosed inflorescences in relation to seed setting 
under normal open-pollinated conditions in terms of a ratio of 
heavy seeds per 100 spikelcts in free inflorescences (open-polli- 
nated conditions) over enclosed (self -pollinated conditions). 
Most annual species of grasses were rather highly self-fertile, 
whereas many of the perennial species set much less seed on 
enclosed inflorescences than under normal open pollination. In 
perennial species of grasses, the ratio of seed setting of free over 
enclosed, F/E, ranged from 0.95 in Agropyron tenerum to 152.95 
in B. inermis. In Lolium perennc, Jenkin (193 la) studied several 
different plants and clonal progeny extensively. Plant 43 
produced only an average of 0.8 seeds per 100 spikelets when self- 
pollinated, whereas plant 48 produced 117.6 seeds. Wholly self- 
fertile lines were easy to obtain. With orchard grass, Dactylis 
glomerata, Stapledon (1931) obtained some self-fertile and self- 
vigorous plants, several inbred lines remaining vigorous after 5 
years of selfing. On the average, however, the plants resulting 
from selfing are much less vigorous than those derived from 
crossing. 

With red clover, Trifolium pratcnsc, Williams (1931a) found 3 
plants out of 262 original plants to be truly self -fertile; he 
explained self- and cross-incompatibility on the basis of an 
extensive series of self -sterility alleles. White clover, T. repens, 
was highly self-sterile according to Williams (19316), although 
less so than red clover. Atwood (1940, 1941) has studied self- 
and cross-incompatibility in T. repens and explains his results on 
the basis of a multiple-allelic series of factors. One plant out of 
615, when self -pollinated, set seed freely and may have carried a 
factor for self-fertility, 

A highly self-fertile line of red clover has been bred at the 
Minnesota station, and in crosses between this line and normal 
self-sterile plants fertility continues to be the dominant type 
under self-pollination conditions. Groses between the self- 



250 METHODS OF PLANT BREEDING 

fertile line and normal plants were used as a basis for selection 
under isolated normal open-pollinated conditions. The origin 
consisted of 50 plants from commercial red clover crossed with the 
self -fertile line. The plan of selection consisted of growing about 
1000 plants each generation in a nursery individually spaced, 
the selection of 100 vigorous, desirable plants, and the discarding 
before flowering of other plants in the nursery, allowing cross- 
pollination of the selected plants. Similar selection was made 
in another isolated plot using normal commercial northern-grown 
seed. After three generations of selection, the two types of origin 
were compared by growing their progeny in rows, with the result 
that the cross of the self -fertile with normal appeared less vigorous 
than the selection from normal commercial red clover. 

It is generally believed that the cucurbits, comprising cucum- 
bers, muskmclons, watermelons, pumpkins, and squashes, belong 
to the cross-pollinated group of plants. Rosa (1927) stated that 
the amount of cross-pollination in melons varied with the variety 
and ranged from 5 to 73 per cent. Whitaker and Jagger (1937) 
state that cucumbers, squashes, and pumpkins are normally 
strictly monoecious, whereas muskmelons and watermelons are 
andromonoecious. Andromonoecious species bear bisexual or 
complete flowers instead of strictly pistillate ones, in addition to 
staminate flowers. When one considers the way that these 
plants are grown and the necessity of insect pollination, it is 
apparent that frequent cross-pollination must occur. 

The cucurbits, as a group, show less reduction in vigor due to 
inbreeding than most members of the cross-pollinated group of 
plants. Bushnell (1922), Haber (1929), and Cummings and 
Jenkins (1928) found no great loss in vigor as a result of ( con- 
tinued self-pollination with squashes. Cummings and Jenkins 
studied the effects of continued self-pollination for 10 generations. 
Similar results were obtained by Porter (1933), Rosa (1927), and 
Scott (1932) with watermelons. C. F. Poole reports (unpub- 
lished) that lines of the Northern Sweet watermelon that have 
been selfed for seven generations, show no reduction in size of 
melon when compared with the commercial lines of the same 
variety. Whitaker and Jagger concluded that hybrid vigor 
probably did not occur in any of the cucurbits. There are, how- 
ever, two recent reports by Hutchins (1938) with the cucumber 
and by Curtis (1939) with summer squash that show marked 



CONTROLLED POLLINATION METHODS 251 

hybrid vigor. Hutchins suggested that it would be feasible to 
utilize the hybrid vigor of F\ crosses in commercial production. 
Curtis outlined a method for the production of hybrid seed 
with summer squash, Cucurbita pepo, by growing the two 
varieties to be crossed in alternate rows and the removal of all 
male flowers from the seed variety before the male flowers have 
opened. 

INHERITANCE OF SELF-INCOMPATIBILITY 

Crane and Lawrence (1934) draw a distinction between incom- 
patibility and sterility. Incompatibility is due to some physio- 
logical hindrance to fertilization. The pollen and ovules or at 
least a good proportion of them are functional, the failure to 
obtain seed being due to slow pollen-tube growth. Sterility is 
classified by Crane and Lawrence into: " (1) generational sterility, 
due to the failure of any of the processevS concerned with the 
normal alternation of generations, namely, development of pollen, 
embryo-sac, embryo and endosperm, and the relation of these to 
one another and their parents regardless of the cross made and 
(2) morphological sterility due to suppression or abortion of the 
sex organs." 

Many species of plants are often self-sterile, and among thes^ 
there are many plants of economic importance. These include 
fruits, perennial grasses, rye, sorrie clovers, alfalfa, sugar beets, 
some Brassica species, and some plants grown for ornamental 
purposes. East (1929) and Brieger (1930) have given extensive 
reviews of much of the literature. 

Crane and Lawrence (1934) credit Prell (1921) with first 
suggesting a genetic explanation of self-sterility on the basis of a, 
series of self-sterility alleles and East and coworkers for the firsl 
proof of such a series in Nicotiana. Self -incompatibility appear; , 
to be a somewhat more desirable term than self-sterility for those 
cases where self-fertilization is prevented, although the pollen 
grains and egg cells are functional. 

There has been a rapid a* 'cumulation of information regarding 
self -incompatibility in recent years, and in many species rather 
clear demarcation between self-compatibility and self-incom- 
patibility. In other cases, the differences are not so clear- 
cut, and there may be a gradual graduation from self -fertility to 
self-sterility through a series of causes. Crane and Lawrence 



252 METHODS OF PLANT BREEDING 

have given evidence for the conclusion that in some cases this 
may be the result of polyploidy and the duplication of several 
series of sterility alleles. 

Two types of inheritance seem of general interest. The oppo- 
sitional-factor hypothesis furnished a satisfactory explanation of 
self- and cross-incompatibility in tobacco by East and coworkers. 
The genes responsible belong to a series designated by S, and like 
other alleles, two factors may be carried by a single diploid plant, 
a series of 15 such allelic factors having been found in tobacco. 
A pollen tube carrying any one of these alleles, Si to $15, 
shows slow pollen-tube growth in the stylar tissue carrying the 
same factor but normal pollen-tube growth in stylar tissue carry- 
ing a different genetic factor for self-incompatibility. A factor 
for self-fertility S/ was found, also, that was functional with any 
of the 81 to $15 alleles, and self-fertility was dominant to sterility 
"in crosses. Self-fertility of this nature would breed out incom- 
patibility in the selfed progeny of crosses, which would make it 
possible to add the factor for fertility if desired. 

Types of results that may be expected will be illustrated 
briefly. Parental genotypes FI, F% and backcross progeny in a 
diploid organism make clear the types of breeding behavior. 
Two self-sterile plants are used as parents in the hypothetical 
illustrations, their genotypes being 8183 and 8^8*. When SiS$ 
is self-pollinated, seed production does not commonly result, 
since pollen tubes carrying either of the alleles Si or 83 grow too 
slowly in stylar tissue of the same genotype. Exceptions to this 
rule have occurred in many species of self-sterile plants leading 
to homozygous individuals of the genotype SiSi and 8383, but 
seed is too infrequent to make this method of seed production 
efficient as a means of controlled selection in self-pollinated lines 
of self-sterile species. With some species such as cabbage, 
Brassica oleraceae, controlled bud pollination of a self-sterile 
plant gives good seed production, and selection in self-sterile 
lines may be practiced, leading to the isolation of homozygous 
lines. A cross of 8183 X $2$4 produces four types of FI offspring 
SiS%j SiS^j 8283, Ss$4. Each of the types is self-sterile but fertile 
with their parents in backcrosses and with each other. A cross 
of 8182, X SiSi, for example, will produce plants that are SiSt 
and 8284. The reciprocal cross of 8184 X 8183 will produce 
8183 and S s St. 



CONTROLLED POLLINATION METHODS 



253 



When the self-fertility allele S/ is present, continued self- 
pollination leads to the rapid isolation of self-fertile genotypes. 
For example, S/S f X SiS* -* S f Si and S/S 8 . If S f Si is self- 
pollinated, only two genotypes result, one like the parent SfSi, 



$183x8254 







A B C D 

FIG. t35. Diagrammatic representation of pollen-tube growth in compatible 
and incompatible crosses, (a) and (b) Incompatible, slow pollen-tube growth; 
(c) compatible, all pollen able to effect fertilization; (d) only $2 pollen functional. 

the other homozygous for S/S/. The pollen tube developing 
from a pollen grain carrying Si makes slow growth in stylar tissue 
OS/Si) carrying the self -sterility allele Si. 

Riley (1934, 1936) has explained self-sterility in Capsella 
grandiflora, a diploid species with eight haploid chromosomes, on 
the basis of the sporophytic nature of the parent plants and on the 
interaction of two pairs of genes. Before giving the genetic 
explanation, a brief summary of the results of the crosses will be 
given. 

Three intrasterile, interfertile classes have been found in 
C. grandiflora. These have been designated classes A, C, and B. 
Class A X class C will produce classes A and C, or A, jB, and C, 
but never A and B only. Class A X class B will produce classes 
A and B, or classes A, B, and C or classes A and C. Class 
B X class C will produce classes B and (7, or class C only, but 
never class A. Reciprocal crosses give the same result. 

When a plant of C. grandiflora was crossed with any one of the 
three self-fertile species of Capsella, the FI was fully fertile and 
completely self-compatible. Segregation for self-fertility and 
self-incompatibility occurred in the F%. 



254 



METHODS OF PLANT BREEDING 



The following table (Riley 1936) gives the genetic explanation 
of results from crosses within and between the three self-incom- 
patible groups. 

TABLE 30. STERILITY AND FERTILITY IN CROSSES WITHIN AND BETWEEN 
THE THREE SELF-INCOMPATIBLE GROUPS OF C. grandiflora 





Cltu 


38 A 




Class C 




Class B 


Genotype 


TtS c S c 


Tt&s 


Ttss 


US C S C 


ttS*s 


ttss 


Tt$ c S c 


S 


S 


S 


F 


F 


F 


TtS c s 


s 


S 


S 


F 


F 


F 


Ttss 


8 


S 


s 


F 


F 


F 


ttS e S 


F 


F 


F 


S 


S 


F 


ttS c s 


F 


F 


F 


S 


S 


F 


ttss 


F 


F 


F 


F 


F 


S 

















S sterile, F = feitile. 

These results were explained on the basis of the sporophytic 
nature of the parent plants. Members of class A were incom- 
patible in crosses together, because they possess the dominant 
gene T, which is epistatic to S c . Any plant that is homozygous 
for the recessive condition, or tt, is fertile in reciprocal crosses with 
members of class A. Factor T is never in the homozygous 
condition, since plants bearing it can be crossed only with the 
homozygous recessive tt. 

A second pair of genes S c s is responsible for the differentiation 
of classes C and B. Class C carries this pair of genes either in the 
homozygous condition S C S C or the heterozygous condition S c s, 
and class J5 is homozygous for the recessive condition ss. 

A self-compatible factor S* is a member of the $ series and 
dominant to S c or s and epistatic to T 9 and S c and s are hypostatic 
to T. 

East (1934) suggested that substances in the stylar tissue of 
Nicotiana react with substances in the pollen tube to slow up the 
rate of the pollen tube growth in self -incompatible combinations. 
The further suggestion was made that, in most plants, these sub- 
stances are not present in the young bud but appear during the 
24 hr. preceding the opening of the flower. In self-sterile geno- 
types that are self-fertile when pollinated 24 to 48 hr. before the 
flowers open it was presumed that these substances were not 



CONTROLLED POLLINATION METHODS 255 

produced during the 24 hr. preceding flower opening. In another 
type in which self-sterile plants are self-fertile at the end of the 
flowering period it was presumed that these plants were unable 
to produce an adequate amount of the inhibiting substance late 
in the flowering period. The inhibitory effect appears to be 
localized in a certain region of the style, since the growth rate 
of the pollen tube is slowed up markedly as the pollen tubes 
reach this place, but after this region is passed the growth rate 
again approaches normal. In Capsella, the pollen grains in self- 
incompatible matings do not germinate, or produce tiny abortive 
tubes only. This has led Riley to suggest that these inhibitory 
substances are located at the very end of the stigma in the 
stigmatic hairs. Yasuda (1934) believes these inhibitory 
substances originate in the ovule in petunia, from which they 
may ascend the stigma, depending on genetic differences in the 
plants and the environmental conditions under which they are 
grown. If they reach the stigma, they may inhibit germination 
of the pollen grains. If they only reach the style, they may 
inhibit pollen-tube growth in the stylar region, and in some cases 
these substances stay in the ovary and inhibit pollen-tube growth 
in the ovary. The suggestion is made also that weak self- 
fertility may be the result of a low production of these inhibitory 
substances. 

Studies in Wisconsin by Brink and Cooper (1939) and Cooper 
and Brink (1940) with alfalfa deal with partial self-incom- 
patibility, the type of self-sterility that probably occurs very 
commonly in many crop plants. Cross-pollination produced a 
much higher average number of seeds per flower than self- 
pollination. In a comparison of seven plants selfed, with crosses 
between them, 14.6 per cent of self-pollinated ovules were 
fertile, whereas 66.2 per cent of cross-pollinations led to fertiliza- 
tion. A low degree of fertilization under conditions of self- 
pollination was believed to be explained primarily on the basis 
of the oppositional-factor hypothesis. 

Of the ovules that became fertile, 34.4 per cent containing 
inbred embryos and endosperms collapsed within 6 days after 
fertilization; in the cross-pollinated plants, only 7.1 per cent, 
containing hybrid endosperms and embryos, collapsed. These 
differences are highly significant and seem to be dependent upon 
the relative rate of growth of the endosperm tissue and embryo. 



256 METHODS OF PLANT BREEDING 

The collapse of ovules during the early-development stages after 
fertilization has been called somatoplastic sterility by Brink and 
Cooper. They say: 

The embryo sac in the mature ovule of alfalfa is surrounded by two 
integuments. The inner integument, which is composed of two layers 
of cells, lies in direct contact with the embryo sac except at the chalazal 
end where a few disintegrating cells, remnants of the nucellus, are found. 
Shortly after fertilization active cell division is initiated in the integu- 
ments as well as in the endosperm mother cell and the zygote. 

The critical factor for survival seems to be the manner in which the 
translocated food is shared between the endosperm, on the one hand, 
and the inner integument, on the other. The partition of nutrients 
appears to depend upon the rate of growth inside and outside the 
embryo sac. 

The endosperm is considered to be the dominant tissue within 
the embryo sac. When the endosperm keeps pace in its growth 
with the surrounding material, tissue development of the seed 
continues in a normal mariner. The rate of growth of the embryo 
is much slower than that of the endosperm and not very different 
in hybrid than in inbred embryos. The writers say, "The initial 
conditions iri the ovule outside the embryo sac being alike in the 
two cases, it seems clear that the higher survival following 
crossing is the result of the more active growth of the hybrid 
endosperm. Conversely, following self-fertilization, the rate of 
growth of the endosperm is frequently so low that the balance 
soon shifts in favor of the integuments." 

Other cases were noted by Brink and Cooper from species 
crosses, where fertilization had taken place but early collapse after 
fertilization followed because of slow growth of the endosperm 
and the lack of nutrients for the growing embryo. Although 
these results have not been placed directly on a genetic basis, 
it seems probable that they result from causes similar to those 
responsible for the reduction of vigor in selfed lines of cross- 
pollinated plants. If one accepts the Mendelian explanation of 
heterosis, then it seerns probable that the early collapse of ovules 
after fertilization is due primarily to genetic causes. 

Other cases of self-sterility are known. Heterostylism, i.e., 
differences in relative length of the styles and stamens, may cause 
a lack of seed production under conditions of self-pollination. 



CONTROLLED POLLINATION METHODS 257 

Proterandry or proterogyny also may be causes of cross-pollina- 
tion and make self-fertilization difficult. 

Although much is known regarding problems of self-sterility, 
different investigators have reached widely different conclusions 
regarding the possibilities of using controlled self-pollination 
as an aid in breeding. These differences in opinion are doubtless 
dependent upon species and varietal differences in response to 
self-pollination, or the effects of differences in environmental 
conditions. The extent to which controlled self-pollination can 
be used in breeding remains an unanswered question in many 
cases. 

METHODS OF BREEDING 

Certain principles rather generally accepted as of importance 
in relation to the controlled method of breeding in corn appear 
to be applicable to other cross-pollinated crops. Certain of 
these may be restated. 

1. Yield and many other characters of economic importance are 
the end result of the interaction of multiple factors. 

2. Inbred lines show wide genetic differences and, as a rule, are 
less vigorous than the normally pollinated varieties from which 
they originated. 

3. Inbred lines differ in combining ability in crosses. Although 
there is considerable evidence that combining ability in crosses is 
positively and significantly correlated with those characters that 
are expressions of vigor in the inbred, it is equally evident that, 
of two inbred lines that in themselves seem equally desirable, one 
may give much greater vigor than the other, on the average, in 
crosses with unrelated inbreds. 

4. Combining ability of an inbred may be tested by crossing 
it with a commercial variety, i.e., the top-cross is a relatively 
satisfactory method of learning relative combining ability. 
Crosses with a series of inbreds used as testers is another method 
now in use by the corn breeder for testing combining ability. 
Some investigators have advocated the use of testers that in 
themselves are undesirable for important characters. 

5. Combining ability is inherited in much the same manner as 
other quantitative characters. If two low combining lines are 
crossed and selection practiced during the segregating generation 
under controlled self-pollination until relative homozygosis is 



258 METHODS OF PLANT BREEDING 

obtained, most of the resulting inbreds will be low in combining 
ability. Conversely, inbreds selected from a cross of high- 
combining inbreds are mostly high in combining ability. 

6. Genetic diversity is of importance in relation to heterosis. 
Crosses between inbreds from a different origin show greater 
heterosis, on the average, than from a related origin. 

7. Combining ability may be determined during the early 
generations of selfing by means of the crossing test. 

When controlled cross-pollination can be carried out on an 
extensive scale at a reasonable cost, it seems that the method 
of breeding by controlled pollination that has been developed 
for corn can be applied directly to other plants of the cross- 
pollinated group. In some cases, it seems feasible to introduce 
a factor for male sterility in one of two inbred lines that are to 
be used to produce F\ crossed seed for commercial seed produc- 
tion. The two lines to be crossed would be intcrplanted, and all 
male fertile plants would be removed before pollination. With 
perennial plants, the same field could be used for several years. 
Further increases for seed production could be made by vegeta- 
tive propagation. 

A method suggested by Pearson (1932) for breeding cabbage is 
of interest where self-incompatibility is of common occurrence 
and controlled bud pollination leads to the production of a con- 
siderable amount of selfed seed. In cabbages, both self-fertile 
and self-incompatible lines may be obtained. Pearson suggests 
the selection and isolation of self-incompatible lines by pollinating 
in the bud stage. These self-incompatible lines can be differ- 
entiated from the self-fertile by pollinating at anthesis also and 
discarding the lines that are self-fertile, i.e., lines that set seed 
when pollinated at anthesis. After a considerable number of 
self-incompatible lines have been selected, these then may be 
tested for combining ability. Although not suggested by 
Pearson, it seems that the inbred- variety cross method would 
be desirable to use in the first elimination of lines, with the use 
in the crossing study of only those lines that proved to be good 
combiners. After selecting the best inbred lines by this means, 
artificial crosses between lines should be made, making the 
crosses at anthesis. Those crosses that set seed would then 
be tested for producing ability. After obtaining a desirable 
cross, it could be maintained by bud pollination of the parent 



CONTROLLED POLLINATION METHODS 259 

lines and the continued production of controlled cross-pollin- 
ated seed by interplanting members of the two lines for seed 
production. 

A plan of breeding grasses originally adopted at Aberystwyth, 
Wales, and in New Zealand (Levy 1933) is of general interest. 
It consists of collecting material from its natural habitat, from 
foreign sources, and from other breeders, and of making a study 
of several thousand individual plants, perhaps with the final 
selection of not more than 100 or 200 out of 5000. The progeny 
of these selected plants may be increased and given further study, 
with the use of one of several methods of breeding, depending on 
the nature of the material, the possibility of self-fertilization, 
and the extent to which it is possible to isolate vigorous self- 
fertile lines. In many cases, a rapid increase of material from 
the selected plants may be desirable. A simple method consists 
of interplanting the clonal progeny of these selected plants, 
allowing them to cross by natural means. When facilities are 
available for an intensive breeding program with a particular 
species, desirable-appearing clonal lines or closely bred lines that 
may or may not have been previously bred by controlled self- 
pollinatiori may be used as a basis for breeding of improved 
varieties. By means of brother-sister mating or diallel crossing 
and the test of crosses in F\ and in F 2 , the more desirable progenies 
may be isolated and combined to produce improved synthetic 
varieties. 

Some investigators are using the so-called Macauley (1928) 
method as a means of isolating relatively homozygous lines, where 
controlled self-pollination, because of self -sterility, or where 
reduction in yield as a result of continued selfing is so great that 
the isolation of selfed lines does not seem desirable. Macauley 
suggested a method of close breeding for corn that may be 
adapted for this purpose. As applied to corn, it consists of grow- 
ing the progeny of selected ears each in an individual plant plot 
of approximately 200 plants, preventing cross-pollination between 
plots by means of natural barriers such as the use of border rows 
of a much later maturing corn and thus forcing pollination within 
each plot. The more desirable plots are selected each generation 
and several ears again selected to plant the isolated plots for 
the next generation. It was concluded on theoretical bases that 
four or five generations of this sort of selection would be equiva- 



260 METHODS OF PLANT BREEDING 

lent, in an approach to homozygosity, to a single generation of 
selfing. The inbred lines obtained by this method of breeding, 
where sufficient vigor is retained, could be used directly as an 
improved variety, or several lines could be combined to produce a 
synthetic variety. 

When intensive studies of improvement have not been made 
previously, the recognition arid propagation of improved ecotypes 
that have developed through natural selection may prove of 
value. By these methods, a considerable scries of new strains 
of great value have been developed in New Zealand. These 
include Hawks Bay and Poverty Bay perennial rye grass, Akaroa 
cocksfoot (orchard grass), New Zealand white and New Zealand 
extra-late red clover, Marlborough lucern, and New Zealand 
brown top. 

In spite of some of the difficulties, it seems advantageous to 
outline methods of breeding. These are based to a considerable 
extent on methods found applicable to corn. 

OUTLINE FOR IMPROVEMENT OF CROSS-POLLINATED PLANTS BY CONTROLLED 
POLLINATION METHODS 

I. Selection in self-pollinated lines. 

A. In general, use adapted varieties, arid artificially self-pollinate as 
many plants as can be handled with the available facilities; 
unadapted varieties may be used if any desirable character is 
wanted. 

B. Grow the progeny of each self-pollinated plant from self-fertilized 
seed. The number of plants in each selfed line of the first and suc- 
ceeding generations should be sufficient to give an adequate sample 
of the progeny. This number ordinarily should not be less than 20, 
arid a minimum of 30 to 40 plants is desirable. In many crops it 
will be advantageous to start the seedlings in the greenhouse and 
transplant into the fields. The plants should be spaced far enough 
apart to permit individual study. 

C. Self-pollinate one or more desirable-appearing plants from each 
desirable first-generation selfed line. In general, plants of at least 
average vigor should be selected for selfing. 

D. Following the procedure in (7, grow successive generations of selfed 
lines until relative uniformity is secured. As the process of selec- 
tion proceeds from first to later generations, greater weight should 
be given to vigor of growth and more emphasis placed on high 
fertility. As elimination of weak and undesirable lines is effected, 
their place in the nursery may be filled with additional selections 
from the strong desirable lines, with new first-generation selfed lines, 
or by selections from crosses between selfed lines. 



CONTROLLED POLLINATION METHODS 261 

E. Any selfed lines of promise may be tested for reaction to disease in 
a special disease garden, or a disease epiphytotic may be induced 
in the self-fertilization plots. 
II. Improvement of selfed Unas. 

A. Backcrossing. A desirable method when one wishes to retain all 
or nearly all the characteristics of one line and add some char- 
acters to it. Easy of accomplishment when the character to be 
added is inherited in a relatively simple manner. 

Examples from corn: 

1. To add yellow endosperm to a selfed line that is desirable 

in other characteristics and is breeding true for white endo- 
sperm. 

2. To add tender pericarp to a sweet-corn variety or selfed line 

that has tough pericarp. 

B. Convergent improvement. A desirable method of increasing the 
vigor of each of two desirable selfed lines that combine well in an FI 
hybrid without modifying their combining ability. 

C. The pedigree method. Select selfed lines as parents that have 
complementary characters, i.e., lines that excel in different desirable 

characters. After making the cross, selection during several 
generations of selfing is practiced until practical homozygosity is 
reached. Example: One parent with strong stalk, i.e., ability to 
withstand lodging, the other with good general vigor but weak 
stalk. Make the cross, and self-pollinate, and select during the 
segregating generations. 
III. Use of selfed lines as breeding material. 

A. 1. Top-crosses or inbred sire crosses, an inbred line crossed with a 
variety. 

a. Of value in some cases as a commercial hybrid, or as a basis 

for the selection of an improved clon in such crops as potatoes. 

6. A desirable method of testing the combining ability of selfed 

lines. By this means, the more promising lines are selected 

to test in single, three-way, double crosses or in the production 

of a synthetic variety. 

2. Selfed lines, if sufficiently vigorous, may be increased for use as a 

new variety. 

3. Single crosses between two selfed lines may be made and the 
cross grown as the commercial crop, providing the selfed lines 
are sufficiently good seed producers. 

4. Double crosses between two single-crossed hybrids may be made 
and the cross grown as the commercial crop. Advanced- 
generation single crosses may be used, particularly as the male 
parent. 

5. Three-way crosses may be used as the commercial crop. An FI 
cross of two selfed lines may be used as the female and a selfed 
line as the male parent. 

6. New varieties may be synthesized by composite crossing of 
several inbred lines or in special cases from two lines. 



262 METHODS OF PLANT BREEDING 

B. Compare new varieties and Fi hybrids with standard varieties by 
means of replicated field-plot trials for a sufficient length of time to 
establish their value. 

C. Production of seed of F\. hybrids and new varieties by increasing 
seed of improved varieties and inbred lines in isolated plots. 

IV. Crop plants in which self-sterility is a factor. 

A. Selection of self-fertile lines and the addition of the factor for 
fertility to many lines of the crop plant, i.e., the breeding of self- 
fertile lines and their use later as Fi hybrids or their combination 
into synthetic varieties. 

B. Self-pollination for a generation or two until some desirable char- 
acter is hornozygous, followed by the combination of several lines. 

(7. Selection in self-sterile lines, pseudofertile, by pollination in the 
bud stage or other means such as the self-pollination of many 
flowers and the use of the few seeds obtained as a means of selection 
in normally self-sterile lines. 

I). Cross-mating of plants selected on the basis of outstanding char- 
acteristics. Progeny of crosses selected and better types isolated. 

1. Strain building on the basis of selection of several plants as 
parents and their bulk crossing by natural means. A broad 
system of mass selection is practiced. This method is 
applicable to the rapid increase of ecotypes that have devel- 
oped by natural selection under a particular set of environ- 
mental conditions. 

2. Strain building by brother-sister mating. 

3. Diallel crossing by hand. New strain developed from several 
of the better crosses. 

In diallel crossing, the breeder will have available inbred, 
closely bred, or clonal lines that have outstanding characters. 
After the crosses have been made, it may be desirable to test 
their progeny in F\ and F z . In some cases grazing trials or other 
tests of F% crosses will be helpful. Crosses will be combined in a 
synthetic variety from parent plants or lines that combine well 
with other lines to be used in the synthetic variety. It will be 
possible, in many cases, to use Fi crosses to make the first combi- 
nation of selected lines for use in the improved variety. 



CHAPTER XVII 
SEED PRODUCTION 

The breeding of improved varieties of crop plants is carried on, 
as a rule, by specialists who are trained in plant-breeding methods 
and who have a knowledge of the needs of the grower and con- 
sumer. Although a seed producer may undertake the problem 
of breeding in some cases, the primary task of the seedsman 
will be to produce high-quality seed of varieties and strains of 
known value. 

Good seed of any farm crop must be produced from a variety 
or strain that is superior, insofar as that is possible, in the 
following respects: 

1. Adaptability to the locality and soil. 

2. Purity of type. 

3. Yielding ability. 

4. Desirable agronomic characters. 

5. Disease and insect resistance. 

6. Quality for particular characters. 

The seed of this adapted variety must be superior in the follow- 
ing characters: 

1. Germinating ability. 

2. Color of seed and seed weight. 

3. Uniformity. 

4. Freedom from seed-borne diseases. 

5. Freedom from noxious and other weeds. 

6. Freedom from other damage. 

7. Freedom from mixtures with other varieties. 

These characteristics of good seed are, in general, appreciated 
by seed growers. The first step in the production of good seed 
is the selection of the variety or varieties to be grown. 

SELECTING THE VARIETY 

Improved varieties of farm crops bred by investigators at 
federal or state agricultural experiment stations, including 
varieties of wheat, oats, barley, and cotton, are registered through 

263 



264 METHODS OF PLANT BREEDING 

a cooperative agreement by the Bureau of Plant Industry of the 
U.S. Department of Agriculture and the American Society of 
Agronomy. Registration is under the direction of a committee 
of the agronomy society and is based on information from yield 
trials, carried on for at least 3 years, in comparison with standard 
varieties at federal or state agricultural experiment stations. 
To be eligible for registration, a variety must be significantly 
superior to the standard in some important character or charac- 
ters and equal in other important characters. Registration < 
consists of giving the new variety a register number and publish- 
ing a description of its origin and characteristics in the Journal 
of the American Society of Agronomy. Plant and seed samples 
are furnished by the person or institution submitting the request 
for registration. 

Many of the state agricultural experiment stations list recom- 
mended varieties and describe the conditions under which the 
varieties usually give the most satisfactory performance. These 
lists are based on actual field trials conducted on experiment- 
station or farmers 7 fields in comparison with standard varieties. 
The University of Minnesota Agricultural Extension Folder 22, 
1941, revised whenever it seems necessary, gives the general 
principles used in Minnesota in drawing up the recommendations. 
Somewhat similar methods are used in other states. A variety 
is added or removed from the recommended list of the Minnesota 
Agricultural Experiment Station by vote at an agronomy con- 
ference held each year. The following statement is quoted from 
the folder. 

The list of recommended varieties for Minnesota has the joint 
approval of agronomists, plant breeders, arid plant pathologists of the 
central experiment station at St. Paul and of the superintendents and 
agronomists of the various branch stations at Waseca, Morris, Crooks- 
ton, Grand Rapids, and Duluth. A variety must have been tested in 
experimental plots for at least three years to be eligible for recommenda- 
tion. The basis of recommendation is satisfactory performance in 
competitive trials when compared with standard varieties. These 
tests are conducted at the central and branch stations, in cooperative 
trials on farms, and, in addition, comparative trials of reaction to 
disease are conducted in specially prepared disease nurseries at the 
central station. Varieties introduced from outside the state are given 
the same careful trial as those developed in Minnesota. 



SEED PRODUCTION 205 

The list is followed by a statement of the important characters of 
each recommended variety and its origin and regional adaptation. A 
brief statement of varieties that are riot recommended is also given. 

In Canada, the Canadian Seed Growers' Association has 
accepted responsibility for deciding which varieties shall be 
eligible for the production of certified or registered seed. In 
general, varieties are accepted on the basis of their performance 
in adequately conducted field trials in comparison with standard 
varieties. The list of varieties eligible for use in the production 
of registered seed is an important means in Canada of selecting 
varieties for particular conditions. 

Many of the states in the United States have crop-improve- 
ment societies composed of growers interested in problems of seed 
production. In some cases, the state association may select 
varieties eligible for seed certification. These varieties are 
chiefly those recommended by the state experiment stations, 
although in some cases a few varieties in addition are selected by 
the varietal committee of the crop-improvement society. 

Large and small seed companies may in some cases breed or 
select an improved variety. Improved varieties are described 
in seed catalogues, which helps to make the characters of varieties 
known to the general public. Many of the corn hybrids used in 
the corn belt are produced and introduced by seed companies. 
These companies use inbred lines of their own breeding together; 
with those released by federal or state workers and introduce and 
sell seed of hybrids for commercial growing under their own 
pedigree, which in many cases is kept secret, although the 
pedigree must be filed with a state official to comply with certain 
state laws. In other states, all that is required, in addition to 
the usual information required by seed laws, is a statement of 
the type of hybrid and average days required to mature the 
hybrid in various sections of the state. 

Extensive yield trials of commercial seed-company hybrids, 
in comparison with federal and state-experiment-station hybrids, 
are made annually by most of the corn-belt experiment stations. 
These trials are under the supervision of the Agricultural Exten- 
sion Division and the State Agricultural Experiment Station* 
An entrance fee is charged for each commercial hybrid grown in 
the trials. Reports of the results of these trials are used by 



266 METHODS OF PLANT BREEDING 

growers as a means of selecting the hybrid that is best adapted 
to their conditions. 

The value of new varieties and their characteristics are brought 
to the attention of growers by holding field days at the various 
experiment-station fields at or just prior to harvest time, when 
yield trials are discussed and the characters of particular varieties 
may be observed by the grower. 

In spite of the various methods used to inform the grower of the 
relative merits of different varieties a large amount of seed of 
overexploited and unadapted varieties is sold annually by 
seedsmen. The loss could be done away with by a greater effort 
to inform the producer of varietal characteristics and by a wider 
use by the farmer of the information now available in the hands 
of the state agricultural colleges, the experiment stations, and the 
agricultural extension service, 

FIRST INCREASE OF SEED OF A NEW VARIETY 

A large proportion of new varieties of farm crops in the United 
States are bred by state or federal investigators at agricultural 
experiment stations. After deciding to recommend a new 
variety, the problem of increase of seed and introduction of the 
variety becomes of major importance. Many of the state experi- 
ment stations keep on hand a small amount of pure seed of all 
recommended varieties that serves as an initial source of pure 
seed supply. First increases of new varieties of crop plants 
often are made on experiment-station fields. Subsequent 
increase is usually in the hands of seed growers who are members 
of the state crop-improvement association. 

After making the initial increase of seed of a new variety at 
the state experiment station, further increase is made in Minne- 
sota by the so-called " approved grower plan." A committee 
of agricultural experiment-station workers decides how much 
of the available seed supply will be distributed in each county. 
Growers are selected by a county committee consisting of the 
extension agronomist, county agent, and three farmers appointed 
by the president of the Minnesota Crop Improvement Associa- 
tion. The "approved grower" of registered seed is one who has 
the following qualifications: 

1. Willingness to cooperate to the fullest extent with the experi- 
ment station, extension service, and other agencies interested in 
pure seed production. 



SEED PRODUCTION 267 

2. Available clean land for seed production. 

3. Facilities for storing seed so that mixtures may be avoided. 

4. Previous satisfactory record in crop-improvement work 
and in the community of which he is a member. 

These approved growers purchase seed from the experiment 
station and agree to place at the disposal of the experiment 
station, if requested, at a price agreed upon by the seed-distribu- 
tion committee, all seed over arid above that agreed upon for 
use on his own farm. After this initial increase in the hands of 
approved growers, subsequent seed increase is made by other 
seed producers of the Minnesota Crop Improvement Association 
or by others interested in seed production. 

It was emphasized in the chapter on Corn Breeding that three- 
way and double crosses in field corn were used chiefly by the 
commercial corn grower. The propagation of inbred lines, 
single crosses, and the production of three-way or double crosses 
by the seed grower are essential phases of seed-corn production. 
The larger seed companies take care of the initial increase and 
maintenance of purity of the inbred lines used in their own 
pedigrees. 

There are two rather distinct plans that are followed for 
hybrids released by state or federal workers. One method 
consists of sales of small quantities of pure seed of inbred lines to 
seed producers who make the subsequent increase of the inbreds 
and single crosses necessary for three-way or double-cross seed 
production. Some private breeders specialize in producing 
seed of single crosses. All state experiment stations in the corn 
belt have adopted a plan of initial seed increase of inbreds and 
single crosses for newly released hybrids. Most of the experi- 
ment stations release the inbreds after 2 or 3 years have elapsed 
since the new hybrid was first released. Minnesota and Wis- 
consin have developed methods for the increase of inbreds and 
first crosses in sufficient quantity for the needs of all corn- 
seed producers in their respective states. Similar work is 
carried out in Ohio by a cooperative organization of seed 
growers. Inbreds are not released for the hybrids that have been 
bred and recommended by station workers in Wisconsin and 
Minnesota. 

The Minnesota studies have led to the conclusion that con- 
siderable care must be taken to maintain the purity of inbred 
lines. The methods used and some of the conclusions reached 



268 METHODS OF PLANT BREEDING 

have been summarized by Borgeson and Hayes (1941). The plan 
now used is outlined as given by these writers. 

Hand-crossed and selfed seed of all inbred lines needed in the corn 
"program is planted each year in foundation plots at both the Southeast 
and Central stations. JThe crop risk is distributed as much as possible 
by planting at two stations with several dates of planting at each loca- 
tion. Sufficient sclfed ears are produced to provide the necessary seed 
that is needed the following year in the crossing plots where single 
crosses are produced. The soiled ears are inspected both before and 
after drying. 

The seed is harvested and dried in fine-meshed bags in tray driers. 
Twenty to 30 individual representative selfed ears of each culture are 
saved and the balance of the sol fed seed bulked to use for producing 
single crosses. Short "ear-to-row" cultures from 20 to 30 selfed ears 
of each inbred are planted also in the foundation plot. Hand crosses 
are made between the individual ear cultures obtaining several crossed 
ears from each combination of "ear-to-row" cultures as follows: 1X2, 
2X3, 3X4, etc., where 1 to 4, etc., represent the "ear-to-row" 
cultures of each of the inbred lines, respectively. The hand-crossed 
ears in each culture are examined and desirable crosses are bulked using 
representative cultures. The crossed bulked seed is used the following 
year as the parental source for the rather extensive hand sclfing program 
that furnishes the major source of selfed seed for single cross increases. 
In some seasons it is necessary to use hand controlled sib-pollination 
when self pollination for any reason in some lines does not prove feasible. 
The plan then consists of alternately producing selfed and crossed seed 
for each inbred line. 

The major features of the plan may be summarized briefly as follows: 
When an inbred line seems relatively homozygous, sufficient selfed seed 
of each inbred is produced each year to plant the necessary single cross 
plots the following year. The seed planted for the selling plot is 
obtained the preceding year from hand-pollinated crosses made by 
crossing the progeny of "ear-to-row" cultures within the inbred lines 
produced from selfed ears. 

The rapid increase in demand for hybrid parent stocks made it neces- 
sary to produce the larger part of the single crosses with individual 
farmers. Two types of contracts have been used, one calling for an 
acre rental fee and the other on the basis of production usually by 
pound units. On the acre basis it did not appear that growers were 
sufficiently interested in all cases to place the work on a desirable basis. 
There was no great incentive to produce a high yield. On the other 
hand, the yields of the single crosses were unpredictable, and it waa 
difficult to arrive at a satisfactory price on the pound basis, 



SEED PRODUCTION 269 

This year a new form of contract has been used with the majority of 
the growers. The grower is permitted to retain a share of the seed 
stocks produced for his part in the contract. The balance of the seed 
is then turned over to the experiment station for sale to other growers. 
Small plots used for the increase of advanced generation seed are con- 
tracted on the acre rental or unit payment plan. 

During the past season it was possible to examine the first results of 
the new methods of seed increase. All the single crossing plots were 
planted with hand-pollinated seed. The purity of the parent lines 
was highly satisfactory. Actual counts showed the percentage of off- 
type plants to run on an average of about 0.25%, or 1 to 400. Any 
rogues present were removed prior to tasseling. 

From previous experience it is believed that it will be necessary to 
provide hand-pollinated seed every year for the single cross plots. From 
indications to date, the methods of increase outlined in this article 
should provide both the purity and quantity of inbred seed desired. 

SEED CERTIFICATION AND REGISTRATION 

The Canadian Seed Growers' Association. The Canadian 
Seed Growers' Association, first organized early in the present 
century, was modeled after the Swedish Seed Association that 
was first established in 1886. The objects of the Canadian associ- 
ation, which was incorporated in 1920, may be made clear by 
quoting from its Letters Patent, as given by Wiener (1937). 

(a) Advancing the interest of Canadian agriculture by encouraging 
seed growers and farmer members to maintain a high standard of 
excellence. 

(b) Developing the standards of quality for varieties and strains that 
shall be eligible for registration. 

(c) Establishing and maintaining a record of these varieties and 
strains that are approved for registration. 

(d) Fixing standards for the different classes of propagating stock of 
varieties and strains that may be eligible for registration. 

(e) Making provision for the necessary inspection of field crops and 
propagating stock. 

(/) Maintaining records of registered propagating stocks produced by 
members. 

({/) Encouraging the development and introduction of superior 
varieties and strains. 

(h) Providing for the multiplication and dissemination of propagating 
stock of new varieties approved for registration, 



270 METHODS OF PLANT BREEDING 

(i) Co-ordinating the endeavors of plant breeders and seed grower 
members of the association with the endeavors of crop producers in 
general. 

(f) Utilizing propaganda, advertisement and any other legitimate 
means to increase the use of registered propagating stock. 

(k) Developing a home market and if necessary an export market 
for the disposal of surplus stocks. 

(I) Such other means as may be found expedient from time to time. 

The functions include the selection of varieties that are eligible 
for the production of registered seed, the production of foundation 
or elite stock seed of these varieties, the production by individual 
members of registered seed for sale to commercial growers, such 
seed having been sealed as registered seed after field and bin 
inspection. 

The work of the association is made possible by an appropria- 
tion of the Dominion government, donations from companies 
interested in high-quality productions, and through the help of 
Dominion and Provincial organizations interested and engaged 
in various phases of the crop-improvment projects. 

The methods developed in Canada have been used rather 
extensively as a basis for seed certification in various states in the 
United States. This work has been carried out through the vari- 
ous state organizations. Uniformity in methods has been devel- 
oped through the International Crop Improvement Association. 

The International Crop Improvement Association. This 
association was organized in 1919 at a meeting in Chicago of 
representatives of the Canadian Seed Growers' Association and 
of state crop-improvement associations in the United States. 

The object of the association can be adequately understood by 
quoting from the constitution, where the purpose is stated to be 

... to promote the agricultural interests of the various states and 
provinces of America, emphasizing especially the improvement of field 
crops in general and seed improvement in particular by: 

(a) Encouraging the breeding and improvement of field crops and 
seeds. 

(h) Husbanding, propagating, and disseminating Elite, Registered, 
Certified and Improved seeds. 

(c) Creating a more active interest in better seeds through circulars, 
reports, and otl er publicity, as Avell as encouraging local, state and 
international shows. 

(d) Assisting in the standardization of the seed improvement work 
being done by member organizations. 



SEED PRODUCTION 271 

The active membership may consist of any national, state, or 
provincial organization carrying on activities in the interest of 
improvement of field crops and seeds. At present, between 30 
and 35 state crop-improvement associations in the United States 
and two Canadian associations belong to the international asso- 
ciation. This association has held annual meetings since 1919. 
Through the work of its various committees, standards for seed 
certification and registration have been developed and applied 
in the same general manner by the various certification agencies. 
The annual meetings of workers interested primarily in seed 
certification and registration have aided in the development of 
uniform terminology and in the improvement of methods of seed 
certification. 

Description of Seed Classes. There arc three general classes 
of seed that are recognized by state associations and by the 
Canadian Seed Growers' Association, although the terminology, 
as used, varies some from one association to another. The 
development of more uniform terminology is desirable. The 
following definitions serve to point out three types of seed. 

1. Foundation stock seed is seed that has descended from a 
selection of recorded origin, under the direct control of the original 
breeder or of a delegated representative of the state crop improve- 
ment association or that is under the control of a state or federal 
agricultural experiment station. In many states, such seed is 
registered by the seed-certification official of the state crop- 
improvement association as "foundation-stock seed." 

2. Registered seed is seed of a variety or strain that is the 
multiplied progeny of foundation-stock seed and that traces 
directly to it. Both registered and foundation-stock seed must 
comply with standards of purity and quality laid down by 
the state crop-improvement association or other certifying 
agency. 

3. Certified seed is seed of a variety or strain recommended by 
the state agricultural experiment station that has certain required 
standards of purity and quality. In certain cases, certified seed 
may not meet all the standards required for registered seed. 

At least two inspections are necessary in the production of 
registered seed, a field inspection during the growing season to 
check up on purity of type, admixtures qf other varieties or other 
crops, freedom from noxious weeds, etc. If the crop passes this 
inspection, a laboratory analysis of a representative sample of 



272 METHODS OF PLANT BREEDING 

seed is made after harvest and after the seed has been processed. 
This inspection often is carried out through the help of the official 
state seed laboratory. 

The Minnesota Plan for Certain Crops. As an example of 
methods, a brief description is given for seed registration of farm 
crops in Minnesota. Two classes of registered seed are produced 
by members of the Minnesota Crop Improvement Association 
called Registered No. 1 and Registered No. 2. A grower pro- 
duces registered seed by the plan outlined as follows: 

1. Plant registered seed. Obtain seed that has passed the 
association requirements and that com.es labeled with the blue 
or red tag. Only varieties recommended by the Minnesota 
Experiment Station or the board of directors of the Minnesota 
Crop Improvement Association are eligible. 

2. Plant this seed on clean, well-prepared ground. In the 
case of cross-pollinated crops, the field should be 40 rods removed 
from any other crops of the same kind. 

3. Apply for field inspection before June 15 on crops other than 
open-pollinated corn and alfalfa. For these crops, apply before 
August 1. 

4. Return the application blank, completely filled out, that was 
sent you from the office, along with the dues. Where seed was 
purchased, also send labels that came with the seed. 

After the field and laboratory inspection has been completed, 
the certifying official issues blue or red tags for Registered No. 1 
or No. 2 seed or rejects the seed when the quality is not up to the 
standards. 

The requirements in order to pass the field inspection are 
summarized in the following statements : 

1. Fields will be rejected if plants of field bindweed, leafy 
spurge, or other noxious weeds, the seeds of which are extremely 
difficult of separation, are found in the field. If the noxious- 
weed seeds can be easily separated from the seed crop, the presence 
of plants of these noxious weeds will not be sufficient cause for 
rejection of the field. 

2. More than a mere trace of other crop plants or plants of 
other varieties will be cause for rejection of the field. Mixtures 
that may cause rejection include (a) sweet clover in alfalfa, 
(6) durum wheat in spring wheat, (c) winter wheat in winter rye, 
or vice versa, and (d) timothy in alsike clover. 



SEED PRODUCTION 



273 



3. Instructions are given at the time of inspection regarding 
roguing, harvesting, and other matters pertaining to the handling 
of the seed crop. 

For hybrid corn, certain isolation requirements are necessary. 
As a general practice, the seed plot should be 40 rods from other 
corn. This isolation may be provided by natural barriers, actual 
distance, male border rows, or a combination of these methods. 
If natural barriers are used, permission must be obtained in writ- 
ing from the registration official before planting, in addition to 
the regular field inspection. Border rows of the male parent may 
be used to reduce the actual distance required if the corn inter- 
fering with the isolation of the hybrid plot is of the same color 
as the female parent. 

The following applies only to detasseling plots of 5 acres or 
less: 

Number of Border Rows Actual Distance Female Parent Must Be 
of Male Parent Removed from Other Corn, Rods 





1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 



40 



35 



30 



25 



20 



15 



10 



This minimum distance of 10 rods may be reduced on larger 
fields according to the following plan, provided corn of another 
color is' not involved : 



Male border rows 
needed 


Actual distance female parent 
is removed from other corn, rods 


Size of field, 
acres 


13 


9 


10 


13 


8 


15 


14 


7 


20 


14 


6 


25 


15 


5 


30 


15 


4 


35 


16 


3 


40 



274 



METHODS OF PLANT BREEDING 



The plot shall be detasseled according to instructions furnished 
for the production of the hybrid. Three inspections during the 
detasseling period will be made to determine if the work is satis- 
factorily carried out. 

Laboratory requirements for Registered No. 1 and Registered 
No. 2, the two grades of seed recognized by the Minnesota Crop 
Improvement Association, are given in Table 31 for small grains, 
alfalfa, and hybrid com. 

TABLE 31. REQUIREMENTS FOR REGISTERED No. 1 AND REGISTERED No. 2 
SEED FOR SMALL GRAINS, ALFALFA, AND HYBRID CORN 









Maximum allowance, 














weed seeds 
















Maxi- 










Labora- 




Sec- 




m u 111 
allow- 


Inert 
mat- 


Ger- 
mina- 


Grade 


Tug 


tory 




ond- 




ance, 


ter, 


tion, 






purity, 
per cent 


Noxi- 


ary 
noxi- 


Other, 
per 


01 op 

seeds, 


per 
cent 


per 
cent 








ous* 






per 














ous, t 


cent 




















cent 














pei- 


















cent 










Small Grams: 


















Registered No. 1 


Bluo 


99-100 


None 


01 


10 


0.10 


1.00 


90-100 


Registered No. 2 . 


Red 


98-99 


Noue 


05 


0.15 


0.30 


2.00 


70-89 


Alfalfa: 


















Registeied No. 1 . . 


Blue 


99 3 100 


None 


01 


0.10 


20 


70 


90-100 


Registered No. 2 


Red 


98.5-99 3 


None 


05 


15 


0.50 


1 50 


70-89 






Germina- 


Grad- 


Mois- 


Dam- 










ture, 


age, 






tion 


ing 














per cent 


per cent 


Hybrid Corn: 












Registered No. 1 


Blue 


93-100 


90-100 


14 


0.5 


Registered No. 2. , .... 


Red 


75-92 


75-89 


15 


1 5 





* Primary noxious weeds: Canada thistle, perennial sow thistle, quack grass, dodder, 
buckthorn, oxeye daisy, field bindweed, horse nettle, leafy spurge, Austrian field cress, false 
flax (in flax), and perennial pepper grass. 

t Secondary noxious weeds: Wild mustard, French weed, wild oats, wild vetch, sheep 
sorrel, hedge bindweed, night-flowering catchfly, white cockle, and dragonhead mint. 



No primary noxious-weed seeds are allowed in either class of 
registered seed. The requirements for Registered No. 1 are 
considerably higher than for Registered No. 2. 



SEED PRODUCTION 



275 



The blue tag given for Registered No. 1 may be illustrated as 
follows : 



REGISTERED No. 1 SEED 





THIS SHIPMENT CONTAINS.. 



VARIETY NAME 


<*> PURITY 


% GERM. 


TESTED 








MONTH 


YEAR 







WEED SEEDS 



5 IS SAFE SEED GROW 

5 No Primary Noxiou* Weeds p o _ 




REGISTERED No. 1 SEED 

GROWERS CERTIFICATE 

I hereby certify that the seed contained 

in this sack was produced by me in 19 

in accordance with the rules of the Minn- 
esota Crop Improvement Association. That 
it is of the kind, variety, amount and germ- 
ination as stated on the reverse side of this 
tag. 

That it conforms to the standard of pur- 
ity, grade and cleanliness for Registered 
No. 1 Seed. 



THE REGISTRATION NO IS_ 
MINOR IMPURITIES ARE 



276 



METHODS OF PLANT BREEDING 



Tags used in registering hybrid corn seed are similar to those 
used for small grains. The material carried on the tag is different. 



No. 1 REGISTERED 
HYBRID SEED CORN 



From_ 





Ship to_ 



IS SAFE SEED 

Of Known Inheritance 




REGISTERED HYBRID SEED 

CORN GROWERS CERTIFICATE 

I hereby certify that the seed contained 
in this sack was produced in 19.. in ac- 
cordance with the rules of the Minnesota 
Crop Improvement Association and that it 
conforms to the standards stated below: 



Minhybrid 



Type of Crosa_ 



Approx. Days Maturity. 

Registration No 

Grade 



Germination 
Purity % 
Moisture % 



County Grown_ 
Year Grown 



Date of Test_ 



(Void unless completely filled out) 



SEED PRODUCTION 277 

In addition to the blue- and red-tag grades of hybrid corn seed, 
the Minnesota Crop Improvement Association certifies hybrid 
corn seed for seed companies if they comply with requirements. 
A green tag is furnished bearing the same information as required 
for hybrids produced by growers of experiment-station hybrids. 
The tag carries the following statement: 

The seed in this container is certified on the affidavit of the producer 
filed with the Minnesota Crop Improvement Association that the 
parent lines used in the commercial crossing plot are of the same breeding 
and purity as those parental lines used in the hybrid tested in the official 
yield test. Regular inspections were made of the commercial crossing 
plot for isolation, detasseling and purity. Representative samples of 
the seed, as prepared for market, were inspected in the laboratory for 
moisture, germination, grading and physical appearance as required 
in the rules for certification. 

Hybrids produced by seed companies that have been in 
official yield trials and that have given satisfactory performance 
are eligible for certification. 

Seed (Tuber) Certification for Potatoes. At the present time, 
there are 22 states actively engaged in the production of certified 
seed. In 10 states, certification is under the direction of the 
college of agriculture. These are Colorado, Idaho, Louisiana, 
Maryland, Michigan, Montana, New York, Oregon, Wisconsin, 
and Wyoming. In 9 states, the work is under the supervision 
of the state department of agriculture. These are California, 
Maine, Minnesota, New Jersey, North Dakota, Pennsylvania, 
Tennessee, Vermont, and Washington. In Nebraska, Utah, and 
South Dakota, growers' organizations have charge of certifica- 
tion; in Canada, the work is under the supervision of the Domin- 
ion Department of Agriculture, at Ottawa. 

The objects of seed certification of potatoes include: 

1. The production of high-grade seed potatoes that are rela- 
tively free from diseases and varietal mixtures and that are 
well graded. 

2. Increased yield and better quality that follow the use of good 
seed stock, relatively free from disease. 

3. More satisfactory prices of seed stock to careful growers of 
certified seed. 

4. Better methods of production of tubers used for seed. 



278 



METHODS OF PLANT BREEDING 



Sufficient fees are charged for inspection so that the cost of the 
work is paid for largely by the producer of certified seed. 

The principal steps in potato-seed certification, as carried out 
in Maine, are briefly summarized. 

Potatoes eligible for certification should be grown on land that 
was not in potatoes the previous year and on fields isolated by 
250 ft. from other potatoes. It is recommended that certified 
seed be used to plant the field and that such seed be disinfected 
with corrosive sublimate. It is required that the crop be well 
cared for and be kept reasonably free from weeds and from 
injury by insects. It is required also that the field be sprayed 
with Bordeaux mixture to control late blight. 

Two field inspections of the crop are made; the tolerances 
allowed for various diseases and varietal mixtures are given in 
the summary. 



Tolerances allowed for 
diseases and varietal mixtures 


First 
inspection, 
per cent 


Second 
inspection, 
per cent 


Leaf roll 
Mosaic 


2 
3 


1 
2 


Spindle tuber 


2 


2 


Yellow dwarf 
Total virus diseases 
Blackleg 


5 
5 

2 


0.5 
3 
1 


Wilt 


2 


1 








Total of all diseases 


6 


4 


Giant hills .... 




1 


Varietal mixtures 


1 


25 









It is expected that the grower will remove diseased hills or 
varietal mixtures after each inspection. 

At shipping time, a third inspection must be made. Maine- 
certified seed potatoes shall be equal or exceed II. S. Grade No. 1 
to be eligible for certification. 



SEED PRODUCTION 279 

The blue tag used to designate certified seed is illustrated here. 



MAINE 
CERTIFIED SEED POTATOES 

CROP OF 1941 
Crop inspected twice in field and tuber inspection at time of 

shipping. CARL R. SMITH, Commissioner of Agriculture 



Date 




Maine Department of Agriculture 

DIVISION OF PLANT INDUSTRY 



Variety 



Tha MMd in thu packagr i from held* inpec'd and patted by 
the Maine Department of Agriculture -. 



CROP OF 1941 



Grower^ 



600002- 



Final inspection 
made by 



Address 




CHAPTER XVIII 

SOME COMMONLY USED MEASURES OF TYPE AND 

VARIABILITY 

"~-N 

Statistics are being used extensively in the reduction of data 
and interpretation of results from plant-breeding experiments. 
Whenever a large number of observations are obtained, it will 
be difficult to grasp the full importance of these observations 
because of their number. Consequently, the individual observa- 
tions are replaced by a few statistics that convey all or most of 
the information available from the experiment in a form readily 
comprehended. 

One of the commonest uses of statistics for the plant breeder 
is in their application to field trials where a considerable number 
of varieties are grown under comparable test. In such trials, 
it is necessary to determine the averages of yield and other 
characters and to estimate the significance of differences As 
usually carried out, the first test is to determine whether there 
is a significant difference in the performance of any of the varie- 
ties. If the statistical method used indicates that all varieties 
have the same performance, within the limits of the accuracy 
of the study, no further comparisons are worth while. If there 
is a significant difference in performance, i.e., if the odds are 
rather great that the difference in performance would not occur 
by chance alone, the next step is to compare individual varieties. 
For the plant breeder, this often will consist of a comparison 
between new selections that have been placed under test recently 
and a standard variety that has been shown previously to be the 
most desirable variety available. 

Before the investigator can make these and other comparisons 
of a similar nature, it is necessary to learn the meaning of certain 
statistical terms and the method of their calculation. 

DEFINITION OF STATISTICAL CONSTANTS 

The commonest statistics are the mean and mode as measures 
of type and standard error, standard deviation, and variance ac 
measures of variability. 



SOME COMMONLY USED STATISTICS 281 

The mean, or arithmetic average, is the sum of the measures or 
observations divided by their number. 

The mode is the class of greatest frequency in a series. 

The standard error is a measure of variability in terms of the 
units of measurement. The reliability of a particular statistic 
is determined by its standard error. The smaller the standard 
error in relation to the magnitude of the statistic the greater the 
confidence that may be placed in the significance of that statistic. 

The standard deviation is similar to standard error except that 
it frequently refers to the infinite population rather than to any 
sample drawn from that population. 

The variance is the square of the standard deviation or stand- 
ard error. 

The coefficient of variability is a measure of variability 
expressed in percentage of the moan, making it possible to com- 
pare the relative variability of two populations with widely 
different means. 

CALCULATION OF MEAN, STANDARD ERROR, VARIANCE, AND 
COEFFICIENT OF VARIABILITY 

The calculation of these statistics will be illustrated by using 
data given by Mercer and Hall (1911) on yield of 500 small plots 
of the same variety of wheat harvested from one field. In Table 
32 is given the frequency of occurrence of plots where the yields 
have been grouped into classes of 0.2 Ib. per plot. 

In the calculations that will be illustrated, S means summation, 
/ is the frequency or number of plots having a certain yield, x is 
the class-center value, and N is the total number of plots. 

The formula for the calculation of the mean is as follows: 
Mean yield = x = S(fx)/N. 

In the problem: S(fx) = S[(4 X 2.8) + (15 X 3.0) - 
+ (4 X 5.2)] = 1974.6. To obtain the mean yield, this value is 
divided by N, where N is the total number of plots. Numeri- 
cally, this would be 1974.6 -*- 500 = 3.9492 Ib. per plot. 

The mode is the class with greatest frequency. In this 
problem, the modal class is 4.0 Ib. Plus and minus deviations 
from the modal class often are similar in their frequencies; i.e., 
the distribution is frequently symmetrical about the modal class. 
In pure-line material, these deviations are the result of the inter- 
action of favorable and unfavorable environmental influences, 



282 



METHODS OF PLANT BREEDING 



the number of individuals or plots where all conditions are favor- 
able, or all unfavorable, being much smaller than those with part 
favorable and part unfavorable. In segregating lines, there may 
be also variation due to heritable causes, and in some cases a 
frequency distribution may show a bimodal curve. 

TABLE 32. FREQUENCY OF PLOTS WITH YIELDS GROUPED INTO 0.2-LB. 

INTERVALS 



Class center of 
yield, x 


Number of plots, 
/ 


/* 


fx* 


2 8 


4 


11.2 


31.36 


3 


15 


45 


135 00 


3 2 


20 


64 


204 80 


3.4 


47 


159 8 


543 32 


3 6 


63 


226.8 


816 48 


3.8 


78 


296 4 


1126 32 


4 


88 


352 


1408.00 


4.2 


69 


289 8 


1217.16 


4 4 


59 


259 6 


1142.24 


4.6 


34 


156.4 


719.44 


4.8 


11 


52.8 


253 44 


5 


8 


40.0 


200 00 


5 2 


4 


20.8 


108.16 


Total 


500 


1974^6 


7905.72 











The common measures of variation are the standard error and 
variance, the latter being the square of the standard error. 



The standard error is given by 5 



fry / > 
&(} 

=v~ 



- S(fx)x 



where 



N - 1 
S, /, x, and N have the same designations as above. From the 

- . . U1 .,. ,,, /7905.72 - (1974.6) (3.9492) 
foregoing table, this would be * ^ = 

0.464 Ib. The foregoing formula also may be expressed as 
r _i This is the standard error of a single determina- 
tion. In practice, the value of the mean x used in the correction 
factor S(fx)x must be calculated with sufficient accuracy so that, 
when multiplied by the total, the product is accurate to the 
place desired, Usually it is more convenient to calculate the 
correction factor in the form [S(fx)]*/N, 



SOME COMMONLY USED STATISTICS 



283 



In Fig. 36 is given a histogram of the frequency of plots with 
different yields. In the same figure is superimposed the normal 
frequency distribution. This smooth curve is an estimate of 
the distribution of the infinite population from which these 500 
plots are considered a sample. 



90 


" 










/I 


T*S 


\ 








/i> 










/ 






\ 


y 
















/ 








\ 






w go 










/ 








\ 






"a. 
^ .. 










/ 








\ 


V 




45 

Q> 
J3 




















\ 


S. 


330 






/ 
















\ 


|C 






/ 
















v 






y 


















\_ 





J=^ 


^ 


















T^^ 



~4a -3cr ~2cr -Id M -Her +Zcr +3cr +4or 

FIG. 36. Yield in pounds per plot with ordinates drawn at 1, 2, 3, and 4 times 
the standard deviation. 

In the illustration given, and by the use of tables such as 
Sheppard's (Pearson 1924), it is possible to determine the per- 
centage of the area under the normal curve cut off by erecting 
perpendiculars from the base line to the curve at distances of 
1, 2, or 3 standard deviations (l<r, 2<r, or 3cr, as illustrated in Fig. 
36) from the mean, or M, of the curve, where <r is the standard 
deviation. From such tables, we find that the area between the 
two lines erected at plus and minus 1 times the standard devia- 
tion will be 68.27 per cent of the total area. It can be said, then, 
that the probability of an observation falling within Icr will 
be given by P = .6827. The probability of an observation fall- 
ing outside Iff will be 1.0000 - .6827 = .3173. In like manner, 
the probability of an observation falling within 2cr will be 
.9545, and within 3<r it rises to .9973. In the problem con- 
sidered in Table 32, the mean was 3.95, and the standard error 
was 0.464. One can say, therefore, that the probability of an 
observation falling within the limits set up by the mean 2(r, or 
3.95 + 2(0.464) = 4.88 and 3.95 - 2(0.464) = 3.02, or between a 
yield of 3.02 and 4.88 Ib, is 0.9545. The probability of 



284 METHODS OF PLANT BREEDING 

the yield of a plot, selected at random, falling outside the limits 
4.88 and 3.02 would be .0455. Stated in another way, it may be 
said that the chances of an observation falling within these two 
limits will be .9545:. 0455, or approximately 21:1. There is 
1 chance in 22 of a plot, selected at random, falling outside the 
limits 4.88 and 3.02. The chances of an observation exceeding 
4.88 would be 43: 1. Stated in terms of probability, it would be 
.0455 2 = .02275, or in a little over 2 per cent of the cases by 
chance alone would a plot selected at random yield over 4.881b. 

The standard error of a mean is given by s/\/N where s = 
standard error of a single determination and N = the number 
of observations from which the mean is determined. It is 
obvious that the standard error of a mean must be smaller than 
the standard error of a single determination, since there will 
be less variation among means than among single observations. 

The coefficient of variability (C.V.) is a relative measure 
of variability in percentage. C.V. = (s X 100)/.x, where s and x 
are the standard error and mean for the sample. It is of value 
in comparing the variability of populations with different means 
or differing in units of measurement. 

In many cases, the investigator will be interested in a com- 
parison between the means of two varieties or treatments or in a 
comparison of a selection with the standard. It is essential to 
place these comparisons on the basis of probabilities. The usual 
procedure is to compare the difference with its error and deter- 
mine the probability that a difference as great as or greater than 
that observed could be due to chance alone. 

The standard error of a difference (S^H ) is given by the formula 
~ 



+ si ~ 2r a bS a Sb, where a arid b represent the two treat- 
ments being compared and r is the correlation between sepa- 
rate measurements of the quantities. When r = 0, the formula 
becomes \A + s f. When s a = s b and r = 0, s d if f . becomes 
s \/2. In this and in other similar problems, the significance 
of a difference is determined by comparing it with the standard 
error of the difference. These problems will be taken up in 
detail in later chapters. 

CORRELATION COEFFICIENT 

The coefficient of correlation r is used as a measure of the degree 
of association between two characters worked with at the same 



SOME COMMONLY USED STATISTICS 285 

time. Perfect positive correlation is +1, and perfect negative 
correlation is 1; no correlation is given by r = 0; intermediate 
values denote association of an intermediate degree. A con- 
venient working formula is 

_ S(xy) - S(x)S(y)/N 



VS(x) - [S(x)]*/N VW) - [S(y)]*/N 

where x represents the measures of one variable or character and 
y the other and all other letters have the same meaning as before. 
The caleulaton of simple, partial, and multiple correlation coeffi- 
cients will be given in a subsequent chapter. 

COMPARISON OF DIFFERENCES BY THE t TEST 

The t test provides the usual method for testing the signifi- 
cance of the difference between two means. Such problems 
are common in plant breeding. The statistic t is defined as a 
difference expressed in terms of the standard error of the differ- 
ence. If we have two varieties, or treatments, from which the 
means are different, we shall wish to know in what proportion 
of the cases a difference as great as or greater than that observed 
can be expected to occur as a result of deviations due to random 
sampling. 

Tests of this type fall into two classes: (1) when the samples are 
paired and (2) when the samples from one of the two varieties or 
treatments are not paired with those of the other. Both tests 
will be illustrated with data obtained in Minnesota from strip 
plantings of two varieties of wheat. Seed of the varieties 
Thatcher and Marquillo was sown in adjacent single strips of 
one drill width in each of many fields in the state. The purpose 
of the test was partly demonstration al and was partly to obtain 
comparative yields on many different farms. The yield was 
determined from comparable samples from each variety in each 
strip. In Table 33 are given the yields of these two varieties 
for 12 of the many farms on which tests were made and the sums 
and differences of the two varieties. 

Since the two varieties were grown in paired plots, this fact 
will be utilized in the statistical analysis of the differences. 

In this problem, differences in yield between Thatcher and 
Marquillo were determined for ea^ch of the 12 comparisons, and 



286 



METHODS OF PLANT BREEDING 



the mean difference, called x, divided by the standard error of 
this difference to obtain the value of t. 

TABLE 33. YIELDS OF THATCHER AND MARQUILLO WHEAT TESTED 
IN COUNTY DEMONSTRATION TRIALS IN MINNESOTA IN 1935 



Farm number 


Yield, bu 


. per acre 


QIITYI 




and county 


Thatcher 


Marquillo 






1 . Roseau 
2. Mahnornen 


24.4 
27 9 


17.5 
15 1 


41 9 
43 


6.9 
12.8 


3. Traverse 


28,2 


21.6 


49 8 


6.6 


4. Bigstone 
5 Stevens 


19 8 
23 1 


18.2 
21 6 


38 

44 7 


1.6 
1 5 


6. Stevens 


22 9 


13.7 


36 6 


9.2 


7. Pope 


25.6 


24.8 


50.4 


.8 


8. Kandiyohi 


28.7 


27.8 


56.5 


.9 


9 Kandiyohi 


26 2 


25 2 


51 4 


1 


10. Kandiyohi 


25 7 


19.2 


44 9 


6.5 


11. Renville 


37.0 


34 


71 


3.0 


12. Yellow Medicine 


31 .5 


25 2 


56 7 


6 3 












Sum 


321.0 


263 9 


584.9 


57.1 













The calculated mean difference was obtained by dividing 
S(x) by N, or 57.1 by 12, which gives a mean value of 4.76 bu. 
In other words, Thatcher yielded, as an average of the 12 trials, 
4.76 bu. per acre more than Marquillo. 

The standard error of a difference was obtained by the same 
formula as that presented previously, except that / = I , where 



= j. 



'S(x*) - [S(x)]*/N 



N - I 

From Table 33, S(x*) was computed by squaring each of 
the 12 differences to give 437.85, and the value of s becomes 



'437.85 - 



~ 



Qn , , , . ., 

= 3.89. The standard error of the 



mean difference is 3.89/\/12 or 1.12. 

The statistic t (the mean difference divided by its standard 

\ i_ x 4.76 , OF 

error) is given by t = r- r~ = 4.25. 
l.lz 

In a determination of the significance of this difference, it is 
necessary to introduce the concept of degrees of freedom. That 



SOME COMMONLY USED STATISTICS 287 

term is used in the sense of independent comparisons. In 
calculating the standard error of a difference for the 12 compari- 
sons, or differences in yield between Thatcher and Marquillo, 
only N 1 deviations can vary, one being fixed by the sample 
mean. The degrees of freedom are 1 less than the number of 
comparisons, or 11 in this case. 

Referring to Appendix Table I for 11 degrees of freedom, we 
find the values of t for the 5 and 1 per cent points to be 2.20 and 
3.11, respectively. Values of t as great as these give odds of 
19:1 and 99:1, respectively, against a difference as great as this 
occurring by chance alone. In this problem, with a value of 
t = 4.25, the chances are much greater than 99:1 that the 
difference is not due to chance. 

In some cases, it may be desirable to compare the yields of 
two varieties when they are not grown in paired comparisons. 
Fisher (1938) has given a method where the value of t is calculated 
by comparing the mean difference in yield of the two varieties 
with its standard error, where x\ and x% are the mean yields, 
s = the standard error, and Ni and N% are the number of plots 
of each variety. Then 



where s 2 



(JVl - i) + (N* - 

For such comparisons of means, the number of plots of each 
variety need not be equal. Calculating the sums of squares of the 
12 yields of Thatcher and Marquillo, we obtain 219.55 and 365.31, 
respectively. Then 

/219.55 + 365.31 __ K 1A 
o.lo 




5.16 \ 24 " 2.11 



The degrees of freedom for comparing these two varieties in 
unpaired comparisons are 2 less than the sum of the number of 
trials of the two varieties, or 22 in this case. Entering the i 
table for t ~ 2.26 and 22 degrees of freedom, it is seen that the 
observed value of t lies between P = .05 and P = .01. The 



288 METHODS OF PLANT BREEDING 

chances that a difference as large as the observed would occur 
through random sampling would be less than 5 in 100 and more 
than 1 in 100. 

It sometimes happens that in comparing two means based on 
the same number of observations, the data may be analyzed 
according to cither method illustrated above. If either method 
gives a significant value of f, its testimony should not be ignored. 
With the paired relationship, the degrees of freedom will be one- 
half as large as when the data are not paired. This will result 
in a larger difference being required to reach the minimum level 
of significance because of the reduced number of degrees of 
freedom. If the correlation between paired plots is sufficiently 
high, the standard error of the difference will be reduced suffi- 
ciently so that the minimum level of significance is smaller in 
spite of the reduced degrees of freedom. 



CHAPTER XIX 
FIELD-PLOT TECHNIC 

After making the initial selections from promising material, 
the final test in plant-breeding studies will consist of comparable 
trials in which the selected material will be compared with 
standard varieties. Although special technics may be adopted 
for studying such characters as winter hardiness and drought 
resistance, disease resistance, and other special qualities, it will 
be necessary in most cases to make comparable yield trials under 
actual field conditions. In these cases, the field becomes the 
experimental laboratory. The usual method consists of the use 
of small plots, adequately replicated and dealt with in such a 
manner as will give a reliable index of comparable yielding 
ability under actual farm conditions. In order to obtain the 
desired results, it has been found necessary to handle the experi- 
mental field, insofar as possible, in a manner that will approach 
the practices in use by the better farmers, i.e., to follow estab- 
lished principles of farm management. Some of the important 
considerations may be summarized: 

1. As far as possible, the soil and climatic conditions of the 
experimental field should be similar to those under which the 
crop will be grown by farmers. 

2. A system of crop rotation should be followed that ap- 
proaches, as closely as feasible, that used by the better farmers. 

3. A bulk crop sown after the experimental trial aids in keeping 
the soil in a uniform state of fertility. 

4. Competition between varieties and strains in the experi- 
mental trial must be eliminated or its effects controlled by 
randomization or by grouping varieties of like nature. 

5. Satisfactory methods must be devised for handling the 
experimental plots, including weighing or counting the seed for 
planting, sowing, cultivating, harvesting, and threshing the crop. 

6. Replication and the calculation of a standard error of the 
experiment aid in furnishing a basis for reliable conclusions, and 

289 



290 METHODS OF PLANT BREEDING 

a well-designed experiment helps in controlling the effect of soil 
heterogeneity. 

Some of these points seem self-evident; others need to be 
explained in greater detail. Each experiment must be planned on 
the basis of the information desired. All that will be attempted 
is the formulation of principles of wide application. 

In order to determine the adaptation of varieties to actual farm 
conditions, it is necessary to make the field trials in various 
regions. For this purpose, it has become a standard practice 
to develop branch stations or test on selected farms in representa- 
tive regions in order to test the new strains under those conditions 
to which they will be exposed after introduction to the farmer. 

These experimental fields should be operated according to 
approved farm-management practices. Among these practices, 
the importance of an adequate system of conserving soil fertility 
will be generally appreciated. Crop rotation will be desirable 
in many cases. 

CROP ROTATION FOR EXPERIMENTAL FIELDS 

The system of rotation used should be similar to that recom- 
mended as a desirable farm practice. Several such rotations 
may be illustrated, although they are representative only of 
desirable practices for certain specific types of farming. 

For the corn-yield trials at Minnesota, a 3-year rotation is 
practiced. In this case, one-third of the land is used in the yield 
trials. The rotation is as follows : 

1. Corn-yield trials. Farm manure is applied, and super- 
phosphate is added at the rate of 100 Ib. per acre. 

2. Small grain follows corn, this field being used to increase 
seed of a recommended variety. 

3. Sweet clover is sown with the small grain and used for 
pasture or hay the third year. 

Rotations have been developed for the final trials of spring and 
winter wheat made in )^o~&cre plots that have proved satis- 
factory and that are similar to systems in use by Minnesota 
farmers. These need not be given in great detail. 

Spring Wheat Winter Wheat 

1. Yield trial 1. Yield trial 

2. Clover hay 2. Bulk corn for silage 

3. Bulk corn for silage 3. Oats and peas for hay 



FIELD-PLOT TECH NIC 291 

Manure is added to the silage corn, which aids in maintaining 
soil fertility. Clover is planted with the spring wheat, and the 
first crop of clover is used for hay the following year, the second 
crop being turned under. The oats and peas for hay are har- 
vested sufficiently early to permit adequate preparation of the 
land for the winter wheat. A part of this winter-wheat series 
is used for the winter- wheat breeding nursery. 

At Cornell, the following general rotation for the experimental 
trial of cultivated crops has been used. The plan is as follows: 

1. Soybeans as green manure, turned under. 

2. Silage-corn-yield trials, manured, with addition of super- 
phosphate, or yield trials of cabbage. 

3. Yield trials of soybeans, field beans, sunflowers, or corn. 
Such a rotation results in high fertility, and the yields are high 
if the seasonal conditions are satisfactory. This plan is followed 
because high yields are expected by New York farmers who grow 
silage corn and the other cultivated crops worked with. 

In the rotations for these cultivated crops, as well as in the 
small grain trials at Cornell, variety trials may be made on the 
same fields for 2 consecutive years, and then a legume is turned 
under the third season. The small-grain trials are in a 3-year 
rotation, consisting of the following: (1) rod-row trials of oats, 
(2) rod-row trials of wheat, (3) clover cut off once and then 
plowed under. 

These rotations will serve to illustrate methods that have 
proved fairly satisfactory. Although it is better to have a sepa- 
rate rotation for each yield trial, where the yield comparison of a 
crop occupies the position taken by that crop in a desirable crop 
sequence for the locality, it is not always possible to follow this 
plan because of insufficient cropland. 

SOIL HETEROGENEITY 

One of the difficulties encountered in field experiments is due 
to the fact that uniform soil conditions seldom exist, if ever, even 
over small portions of a field. Soil heterogeneity, as measured 
by yield of crops grown on a field and harvested as small plots, 
may be due to topography of the field, soil moisture, variation 
in fertility, or previous cropping practice. 

In 1915, J. Arthur Harris proposed a criterion for measuring 
soil variation that he called a coefficient of soil heterogeneity. 



292 METHODS OF PLANT BREEDING 

Five years later Harris (1920) reported the results of tests made 
on published data involving a wide variety of crops and charac- 
ters from experiments conducted over the entire world and 
demonstrated clearly that soil heterogeneity is practically 
universal. In concluding his paper, Harris stated, "The demon- 
stration that the fields upon which the plot tests have been carried 
out in the past arc practically without exception so heterogene- 
ous as to influence profoundly the yields of the plots emphasizes 
the necessity for greater care in agronomic technic and more 
extensive use of the statistical method in the analysis of the data 
of plot trials if they are to ho of value in the solution of agri- 
cultural problems. " The many studies conducted since that 
time have amply substantiated these conclusions. 

Uniformity trials, or blank tests, have been used extensively 
in studying the nature and extent of soil heterogeneity. In 
such uniformity trials, the field is planted to a single variety 
and harvested as small plots. The entire field is planted at 
the 'same rate of seeding, and cultural practice is the same 
bver the entire area. The unit plots harvested can then be 
grouped to form plots of varying size and shape, the only vari- 
able being size or shape of the plots, Cochran (1937) published 
a catalogue of uniformity-trial data, listing 191 uniformity 
trials with field experiments, the data from 135 having been 
published. 

The nature of soil heterogeneity may be demonstrated in 
graphical form by means of contour maps drawn from data 
obtained in uniformity trials. An example of such a contour 
map, drawn from data on yield of sugar beets in a uniformity 
trial, was given by Immer and Raleigh (1933) and is reproduced 
in Fig. 37. 

In this study, the yields of six-row plots, each 2 rods long, were 
used. Points deviating by 15, 10, 5, 0, +5, and +10 per 
cent from the mean yield were interpolated between the centers 
of the plots and the contour map drawn by connecting these 
points. Figure 37 shows in a graphic way that fields that may 
appear to be very uniform are rather heterogeneous from the 
standpoint of productivity, as measured by yield on small areas. 
Such contour maps demonstrate graphically that soil variability 
is, to a certain extent, regular over small areas. There is a sort 
of "regular irregularity 77 to the fertility contours. The use of 



FIELD-PLOT TECHNIC 



298 



different sizes or shapes of plots would change the contour map, 
but the general characteristics would remain the same. 

The extent of soil heterogeneity may be measured by determin- 
ing the degree of correlation of yields of near-by plots. Hayes 
and Garber (1927) presented data giving the correlation coeffi- 




456 
Block no. 



10 



-20 -15 -10 -5 45 410 415 

Scoile of shades 

FIG. 37. Contour map of weight of sugar-beet roots in a uniformity trial from 
100 six-row plots each 2 rods long; contour lines drawn through the points 
deviating by 15, 10, 5, 0, +5, and +10 per cent from the mean weight. 

cient between adjacent rod rows within tests with oats, spring 
wheat, and winter wheat and between rod rows separated by one 
or more plots. These data are reproduced in Table 34. 

It is evident that the correlation is greatest between adjacent 
plots and decreases as the distance between the plots is increased. 
However, there was a sensible correlation between the yield of 
rod-row plots separated by as much as 10 rows. 

Harris (1920), using the intraclass correlation coefficient, made 
an extensive study of soil heterogeneity, using data from uni- 
formity trials obtained- by numerous investigators. The extent 
to which contiguous plots resemble each other was measured in 
terms of intraclass correlation, the larger the coefficient the 
greater the degree of soil heterogeneity. The results are given 
in Table 35. 

The data given in Table 35 are only a small part of those avail- 
able but are presented to emphasize the usual extent of soil 
heterogeneity in plot studies. 

The method of calculating simple correlation coefficients will 
be taken up in Chap. XX. The method of intraclass correlation 
will be illustrated here. Harris calculated the intraclass cor- 



294 



METHODS OF PLANT BREEDING 



TABLE 34. CORRELATION OF PERCENTAGE YIELDING ABILITY IN NEAR-BY 
PLOTS OF OATS, SPRING WHEAT, AND WINTER WHEAT, 1924 



Crop 


Correlation of 


Correlation 
coefficient 


I 
Oat-rod rows 


Adjacent plots 
Separated by 1 
Separated by 2 


.572 .025 
.490 029 
.407 .034 


Spring- wheat rod rows 


Separated by 3 
Separated by 4 
Separated by 10 

Adjacent plots 
Separated by 1 
Separated by 2 


.412 .035 
.264 .041 
.275 .057 

.618 .023 
.518 .028 
.454 .030 


Winter-wheat rod rows < 


Separated by 3 
Separated by 4 
Separated by 10 

Adjacent rows 
Separated by 1 


.383 .034 
.449 .034 
.429 + .060 

.552 .068 
.293 + .028 




Separated by 4 


- .114 .118 



TABLE 35. CORRELATION COEFFICIENTS PRESENTED BY HARRIS THAT 

EXPRESS THE EXTENT OF SOIL HETEROGENEITY IN DIFFERENT 

LOCALITIES AND WITH DIFFERENT CROPS 



Crop 


Character 


Size of plot 


Investigator 


Correlation 
coefficient 


Wheat 


Yield, grain 


5.5 by 5.5 ft. 


Montgomery, Nebr. 


.603 .029 


Wheat .... 


Nitrogen content 


5 . 5 by 5 . 5 ft. 


Ivloiitgomery Nebr. 


.115 .044 


Oats 


Yield, grain 


i/ n acre 


Kiesselbach Nebr, 


.495 .035 


Mangels. . . . 


Yield, roots 


To wvi c 

}-2oo acre 


Mercer and Hall, England 


.346 .042 








(Rothamsted) 




Mangels .... 


Yield, leaves 


^oo acre 


Mercer and Hall, England 


.466 .037 








(Rothamsted) 




Potatoes 


Yield 


Rows, 72 ft., 7 


Lyon 


.311 .043 






in. long 






Cora . , 


Yield, grain 


\4 rt acre 


Smith, 111 (1895) 


.830 .019 


Alfalfa 


Yield, hay 


710 **v*c 








1913, first cutting 


0.085 acre 


Scofield, Huntley Experi- 


.407 .059 








ment Farm, Montana 






1913, second cut- 


0.085 acre 




.343 .062 




ting 










1914, first cutting 


. 085 acre 




.602 .045 




1914, second cut- 


. 085 acre 




.657 .040 




ting 









FIELD-PLOT TECHNIC 



295 



relation coefficient (which he designated a coefficient of soil 
heterogeneity) from the formula appropriate for analysis of a 
symmetrical correlation table. The manner of calculating the 
intraclass correlation as given by Fisher (1938) is illustrated 
from the simple illustration given below, assuming data from 16 
plots in a field divided into four blocks of four each. 



4 


5 


4 


3 


5 


6 


5 


4 


6 


6 


5 


5 


5 


7 


6 


4 



The sum of the 16 plot yields is 80 and the mean is 80 -f- 16 = 5. 
The total sum of squares is calculated from S(x*) S(x)x J where 
x = individual plot yields, x = mean yield, and S = summation, 
or 416 - (80) (5) = 16. The sums of the yields of the four blocks 
of four plots each are 20, 16, 24, and 20. Squaring these four 
sums, dividing by the number of plots in each sum, and subtract- 
ing the correction factor S(x)x gives the sum of squares between 
blocks. Numerically, this is 163 % 400 = 8. The sum of 
squares within blocks is obtained by subtraction. The degrees 
of freedom for total and block variation will be 1 less than the 
number of total plots or blocks. An analysis of variance is 
given in Table 36, 

TABLE 36. ANALYSIS OF VARIANCE 



Variation 


Degrees of 
freedom 


Sum of 
squares 


Mean 
square 


F 


Between blocks 


3 


8 


2.667 


4.00 


Within blocks 


12 


8 


667 














Total 


15 


16 

















The mean square is obtained by dividing the sums of squares 
by the respective degrees of freedom. F is the mean square for 
blocks divided by the mean square for variation within blocks 



296 METHODS OF PLANT BREEDING 

If the mean square within blocks is set equal to B and the mean 
square between blocks equal to (kA + -B), where k is the number 
of plots per block, the intraclass correlation coefficient will be 
given by 

A 
A + B 

In this illustration, B = 0.667, k = 4, and kA + B = 2.667. 
Therefore kA = 2.000, and A = 0.500. The intraclass correla- 
tion will be % 

0.500 



0.500 + 0.667 



= +.428 



The significance of the intraclass correlation coefficient may bo 
determined from a comparison of mean squares between and 
within blocks. In this case, the mean square between blocks 
divided by the mean square within blocks gives a value for F of 
4.00. Themeaning of F will be discussed in greater detail in Chap. 
XX. An F of 4.00 is in excess of the 5 per cent point (Appendix 
Table II) for n\ = 3, and n 2 = 12 degrees of freedom, n\ and n 2 
being the degrees of freedom for the larger and smaller mean 
squares, respectively. The intraclass correlation therefore may 
be judged significant. This coefficient presents in correlation 
form the ratio of the variance between and within blocks. It 
expresses the average correlation of plots within each group of 
adjacent plots that are studied. 

It is important to know whether there is a tendency for plots 
that produce low yields in one season to produce low yields in 
succeeding seasons, etc. The results given by Harris and 
Scofield (1920, 1928) indicate a tendency for plots to yield in a 
similar manner from year to year, although there were some 
exceptions. Garber, Mclllvaine, and Hoover (1926) found the 
interarmual correlation between the yields of oat hay on 270 plots 
in 1923 and the yield of wheat grain on the same plots in 1924 
was +.364. Garber and Hoover (1930) found that the inter- 
annual correlation between yields of plots in uniformity trials 
and yields of crops in a rotation test on the same field in succeed- 
ing years was positive in each test made. The differences in 
natural productivity of the plots persisted over a period of several 
years, 



FIELD-PLOT TECHNIC 



297 



Summerby (1934) presented the most extensive data on a study 
of permanence of difference in yields of crops over a period of 
years. The interannual correlation coefficients were mostly 
positive, but 13 out of 143 were negative, and 3 of these exceeded 
the 5 per cent point. As a result of his study, Summerby con 
eluded, "Under the conditions of this experiment the use of 
preliminary uniformity trials for the purpose of adjusting yields 
of subsequent experiments by regression is only rarely as effective 
in increasing precision as is the use of the same amount of land 
and labor in replicating the experiment in the year of the 
trial." 

COMPETITION 

Plants growing along the sides and ends of plots frequently are 
larger than those in the middle of the plot because of greater 
available fertility or water supply. This is true particularly when 
the plots are adjacent to uncultivated areas or are surrounded 
by alleys. The extent and nature of this border effect is impor- 
tant in comparative crop tests. 

, Amy and Hayes (1918) and Amy (1921, 1922) studied the 
extent of border effect in multiple-row plots. In Table 37 are 
presented data obtained by Amy and Hayes from plots seeded 
with a grain drill in rows 6 in. apart. Eighteen-in. alleys sur- 
rounded the plots with a roadway at each end. The plots were 
17 drill rows wide and were trimmed to 132 ft. in length. Each 
of the outside border rows was harvested separately, and the 
yields compared with those of the 13 central rows. The plants 
on the end, to a depth of 1 ft., were cut off. 

TABLE 37. COMPARISON OF AVERAGE YIELD OF OATS, WHEAT, AND BARLEY 
HARVESTED FROM BORDER Rows AND CENTRAL Rows OF PLOTS 132 X 8,5 FT. 





Oats 


Wheat 


Barley 


Source 


Num- 


Yield 


Num- 


Yield 


Num- 


Yield 




ber of 


per acre, 


ber of 


per acre, 


ber of 


per acre, 




plots 


bu. 


platH 


bu. 


plots 


bu. 


Outside border rows 


44 


132.0 


20 


55.0 


16 


97.7 


Inside border rows 


44 


88.0 


20 


41.0 


16 


64 5 


Central 13 rows . . 


44 


71.4 


20 


27.5 


16 


42.9 





298 METHODS OF PLANT BREEDING 

It is clear that border effect may profoundly influence yield. 
Not all varieties were affected alike by surrounding alleys. The 
rank order in yield frequently may not be the same with and with- 
out border rows removed. Arny (1922) found that sowing winter 
grains in the spring in the alleys between spring-grain plots 
reduced border effect somewhat but did not prevent it completely. 
Removing the outside two rows, 6 in. apart, before harvesting 
for yield removes the larger part of the border effect and gives a 
more accurate idea of the expected yields under good farm 
conditions. 

In variety trials in small plots, usually no alley is left between 
plots. Varieties with different habit of growth consequently 
grow adjacent to one another. Hayes and Arny (1917) demon- 
strated that the border rows of tall varieties in three-row plots 
replicated three times that grew adjacent to short varieties 
yielded more than the central row. Often the intervarietal 
competition was sufficient to cause differences of 4 or 5 bu. per 
acre in yield of the border rows as compared with the central 
row of the same variety. 

Kiesselbach (1918) gave some illuminating information of the 
effect of intervarietal competition in small grains. He compared 
the differences in yield of adjacent single-row plots of different 
varieties with the differencevS in yield of the same varieties grown 
in alternate blocks, each consisting of three to five rows. The 
yield of border rows was in some instances included in the yield 
of the blocks. His results are summarized in Table 38. 

The data illustrate clearly that competition between adjacent 
varieties in one-row plots may seriously disturb the yields of 
these varieties. In general, the varieties grown in alternate 
rows show greater differences than when grown in alternate 
blocks of multiple-row plots. The higher yielding varieties 
usually benefit by planting in adjacent single rows, but this is 
not always the case. 

Intervarietal competition can be overcome by planting 
multiple-row plots and discarding the bprder rows before harvest- 
ing. Three- to five-row plots with one border discarded on each 
side are commonly used. At Minnesota, the three-row plot 
has become the standard for rod-row trials. Grouping the 
material so that only strains of similar habit of growth and 
maturity are grown adjacent to one another will tend to reduce 



FIELD-PLOT TECHNIC 



299 



the effect of competition and permit harvest of the entire plot. 
Such procedure implies, however, that the experimenter can 
determine in advance whether competition will or will not be a 
disturbing factor, an assumption for which there is no evidence, 
usually, prior to the time the experiment is conducted. 

TABLE 38. SUMMARY OF RELATIVE GRAIN YIELDS OF VARIETIES TESTED 
IN SINGLE-ROW PLOTS AND ALSO IN BLOCKS CONTAINING SEVERAL Rows 



Varieties compared in alternating 
rows and in alternating blocks 


Year 
of 

test 


Ratio of variety 1 to variety 2 


Alter- 
nating 
rows 


Alter- 
nating 
blocks 


Com- 
peting in 
same hill 


Turkey Red (1) and Big Frame (2) 
winter wheat 


1913 
1914 
1913 

1914 
1913 
1914 

1913 
1914 
1912 
1914 
1914 
1916 


100:107 
100:85 
100:107 

100:63 
100:130 
100:139 

100:82 
100:89 
100:66 
100:38 
100:90 
100:31 


100:97 
100:97 
100:107 

100:85 
100:112 
100:101 

100:77 
100:93 
100:85 
100:53 
100:98 
100:37 


100:47 
100:26 
100:99 
100:21 


Turkey Red (1) and Big Frame (2) 
winter wheat 


Turkey Red (1) and Nebraska No. 28 
(2) winter wheat 


Turkey Red (1) and Nebraska No. 28 
(2) winter wheat 


Kherson (1) and Burt (2) oats 
Kherson (1) and Burt (2) oats 
Kherson (1) arid Swedish Select (2) 
oats 


Kherson (1) and Swedish Select (2) 
(2) oats , , 


Hogue's (1) and Pride of the North 
(2) corn . . 


Hogue's (1) and Pride of the North 
(2) corn 


Hogue's (1) and University No. 3 
(2) corn 


Crossbred Hogue's (1) and inbred 
Hogue's (2) corn 





Tysdal and Kiesselbach (1939)" found that plots of alfalfa, of 
the varieties Hardistan and Ladak, drilled in rows 7 in. apart, 
were definitely subject to serious interplot varietal competition. 
This could be overcome by removal of border rows. They found 
little or no differential interplot competition in rows 12 in. apart. 

Immer (1934) reported the results of tests with two varieties 
of sugar beets, Old Type and Extreme Pioneer. These two 



300 



METHODS OF PLANT BREEDING 



varieties were grown in alternate single-row plots and alternate 
four-row plots, with the central two rows harvested. The rows 
were 22 in. apart in 1930 and 1931 and 20 in. apart in 1932. As 
an average of 10 replications in each of 3 years, Old Type yielded 
3.78 0.44 tons more than Extreme Pioneer in single-row plots 
but only 1.78 0.31 tons more in four-row plots. The difference 
between these two differences was 2.00 0.54 tons. The higher 
yielding variety profited at the expense of the lower in single-row 
plots as compared with a multiple-row plot from which the border 
rows were discarded. 

The effect of competition within and between hills of corn is 
frequently very striking. Kiesselbach (1923) has furnished some 
pertinent information on the relative yields of one- , two- , and 
three-plant hills adjacent to or surrounded by hills of variable 
stand. These data are given in Table 39. 

TABLE 39. RELATIVE YIELDS OF ONE-, Two-, AND THREE-PLANT HILLS 
ADJACENT TO OB SURROUNDED BY HILLS OF VARIABLE STAND 





Total 


I\ T umber 




Type of comparison 


number 
of hills 


of ears 
per 100 


yield, 




averaged 


plants 


per cen 


3-plant hills surrounded by 3-plant hills . . . 


598 


89 


100 


2-plant hills surrounded by 3-plant hills . . . 


120 


99 


82 


1 -plant hills surrounded by 3-plant hills . . 


80 


141 


61 


3-plant hills adjacent to 1 hill with 2 plants 


360 


91 


102 


3-plant hills adjacent to 1 hill with 1 plant. 


302 


94 


107 


3-plant hills adjacent to 1 blank hilll 


366 


94 


114 



The four hills adjacent to a blank hill increased by 4 X 14 = 56 
per cent. Therefore, only 44 per cent of the potential yield of 
the missing hill was lost. This recovery is without consideration 
of the slight increase that would be expected from hills on the 
corners of the blank hill. A one-stalk hill surrounded by three- 
stalk hills yielded but 61 per cent as much as three-stalk hills 
surrounded by three-stalk hills, resulting in a loss in yield of 
39 per cent. The four three-plant hills adjacent to a one-plant 
hill increased in yield by 4 X 7 = 28 per cent of normal and 
resulted in a net loss of 39 28 = 11 per cent because of the 
inclusion of a one-stalk hill and the four adjacent three-stalk 



FIELD-PLOT TECHNIC 



301 



hills in the yield determination. In the case of two-stalk hills, 
the loss in yield was 18 per cent, but 8 per cent of this was 
recovered in the four adjacent three-stalk hills. 

Brewbaker and Immer, in Minnesota (1931), studied the effect 
of missing hills, or hills with reduced stands, in inbred lines of 
corn and F\ crosses. The data for an average of 2 years for the 
FI crosses are given in Table 40. The average yield of the check 
hills was 76.3 bu. per acre in 1928 and 78.4 bu. in 1929. The yield 
of three-stalk hills surrounded on the four sides as well as four 
corners was used as a check for the other yield comparisons. 

TABLE 40. EFFECT OF COMPETITION WITHIN AND BETWEEN HILLS OF FI 

('ROSSES OF CORN 







Yield in 




Number 




Type of comparison 


of hills 


percentage 






of check 


3-phint hills between 2 blank hills 


117 


108 9 


3-plant bills opposite 1 blank hill 


78 


105 6 


3-plaut hills blank hills on 2 comers 


69 


100 2 


3-plant hills between two 1-stalk hills 


94 


104 5 


3-plant hills opposite one 1-stalk hill 


72 


103 7 


3-plant hills between two 2-stalk hills 


76 


102 5 


3-plant hills opposite one 2-stalk hill 


77 


101.5 


2-plant hills surrounded by 3-plant hills 


87 


75 4 


1-plant hills surrounded by 3-plant hills . 


90 


41 



Each of four three-stalk hills adjacent to a blank hill increased 
in yield by 5.6 per cent. The increase in yield of each of the four 
adjacent three-stalk hills due to one- or two-stalk hills on one 
side was 3.7 and 1.5 per cent, respectively. One-stalk hills and 
two-stalk hills yielded but 41 .0 and 75.4 per cent, respectively, 
as much as three-stalk hills. It follows, therefore, that the 
inclusion of one- or two-stalk hills introduces *a greater error 
than to ignore their effect on the yield of the surrounding three- 
plant hills. Harvesting only hills with a perfect stand and 
surrounded by perfect-stand hills sometimes reduces the number 
of hills available for harvest materially, resulting in an increase 
in the intraplot error. A part of the variation (frequently the 
major portion) in stand between F\ crosses is due to random 
causes and will tend to equalize over an average of the several 



302 METHODS OF PLANT BREEDING 

replications. In view of these considerations, a working rule has 
been adopted at Minnesota of harvesting only three-plant hills 
surrounded by one- , two- ; or three-plant hills in yield tests with 
FI crosses. A further reason for this procedure is that frequently 
one wishes to obtain the potential yield of the crosses without the 
influence of differential stand resulting from differences dependent 
upon the ability to produce a stand as influenced by different 
inbred lines. 

In yield tests with three-way or double crosses that are to be 
grown commercially, a frequent practice is to determine the 
percentage stand of each hybrid in the yield tests, but the yields 
are based on the actual production of the plots without correction 
for stand. 

Kiesselbach and Weihing (1933) studied the effect on yield 
of variable number of plants per hill in plots all having the same 
total number of plants, under Nebraska conditions, to determine 
the effect of variable stand on yield. The corn was planted with 
an average of three plants per hill in the plots. The treatments 
consisted of uniform three-plant hills and variable stands of 
2-4, 1-3-5, and 1-2-3-4-5 plants per hill. The average yields of 
these four treatments, for a 14-year period, was 49.9, 50.6, 49.3, 
and 50.0 bu. per acre. It appears from these data that the yield 
per plot is essentially the same provided that the total stand is 
the same. 

SIZE AND SHAPE OF PLOTS 

In general, there are two kinds of experimental plots. Nursery 
plots usually are small and are planted by hand or with special 
nursery equipment and are cared for by hand cultivation. Field 
plots generally are larger and are adapted to the use of standard 
farm machinery. The distinction between these two types of 
plots may, in some instances, be more or less arbitrary. 

For cereal gra&ns, the rod-row plot is relatively standard in this 
country. Such plots usually are 18 ft. long, and the plants to a 
distance of 1 ft. at both ends of the plots are removed before 
harvest. In the case of wheat, the yield in grams of a single row 
16 ft. long with 1 ft. between rows multiplied by 0.1 converts the 
yield to bushels per acre. Rod-row plots vary, in different types 
of experiments and in different stations, from single to five-row 
plots. In the case of multiple-row plots, one border row from 



FIELD-PLOT TECHNIC 303 

each side of the plot frequently is discarded to correct for possible 
differential intervarietal competition. Rod-row plots frequently 
are sown at the same rate of seeding recommended for com- 
mercial farm planting in that area, although a lighter rate of 
seeding is practiced by some workers. The distance between 
rows usually is greater than that used by commercial farm drills, 
since hand cultivation between the rows is needed to control 
weeds satisfactorily. 

Field plots vary from about ^{oo to J'lo acre in size. They 
offer somewhat greater opportunity than single or three-row 
plots to observe crop behavior under conditions comparable with 
those found on farms. In general, experience has shown that 
rod-row tests and large field plots compare very favorably in 
testing for varietal differences, provided that adequate precau- 
tions are taken to guard against competition and other errors. 

Increasing plot size will, in general, decrease the error of a 
single-plot yield. On the other hand, increasing plot size will 
increase the land area in the blocks and, consequently, soil 
heterogeneity in the blocks. The variability among sets of plots 
of varying size will depend on the balance between these two 
opposing tendencies. 

Studies of the variability among plots varying in size and shape 
are numerous. It is found generally that increasing replication 
will decrease the standard error more rapidly than increasing 
size of plots. Plots relatively small, adapted to the type of 
nursery equipment available, should be used. The size used will 
vary with the crop and conditions of the test. Field trials under 
irrigation, for example, frequently require some modification in 
procedure not necessary in tests without irrigation. 

In general, it appears that long and narrow plots lead to a lower 
error than square ones. Christidis (1931), from theoretical 
considerations, suggested that long, narrow plots would control 
soil heterogeneity better than plots more nearly square, occupying 
the same area of land. He examined data from six uniformity 
trials and found support for this hypothesis. Others have found 
essentially the same thing. The relative efficiency of plots of 
varying shape will depend on the direction of the fertility contour 
lines across the field. If the predominant direction of these 
contours is known, long narrow plots planted at right angles to 
the direction of the fertility contours would lead to the low- 



304 METHODS OF PLANT BREEDING 

est error, since variability within blocks is then reduced to a 
minimum. 

In tests involving varieties of naturally cross-pollinated crops ? 
the size of plot needed to obtain a given precision will depend 
somewhat on the nature of the material. Bryan (1933) found 
that about one-half as many plants or hills of corn were needed 
to obtain the same level of precision in tests of the yielding ability 
of crosses between inbred lines as compared with open-pollinated 
varieties. Since the plants from crosses between inbred lines 
are less variable than plants from open-pollinated varieties, the 
variability within plots of hybrids will be reduced, and this, in 
turn, will decrease the calculated variability between plots. 

REPLICATION 

Replication serves two purposes. (1) Replication increases 
the precision of the experiment, since the mean of several replica- 
tions provides a more accurate measure of varietal performance 
than does a single plot. (2) From replicated trials, it is possible 
to calculate an estimate of error of the experiment. 

The number of replications used will depend on the variability 
of the soil, the variability of the material to be tested, the degree 
of precision desired, and the amount of seed available. 

In experiments in which randomized blocks are used, the 
standard error of the mean will be s/\/N, where 8 is the standard 
error of a single determination and N is the number of plots of 
each variety or treatment. The standard error of the mean may 
be reduced, therefore, to whatever level is desired through 
sufficient replication. After the standard error of a single 
determination for plots of the desired size and shape is learned, 
the number of replications needed to reduce the standard error 
to a certain degree of accuracy may be obtained by the formula 

/Standard error of a single determination^ 2 
\ Standard error desired / 

METHODS OF MAKING YIELD TRIALS USED IN MINNESOTA 

If careful notes are taken on all characters such as lodging, 
winter hardiness, and reaction to diseases and if varieties or 
strains that are inferior to the standard variety in any important 



FIELD-PLOT TEC UN 1C 305 

respect are freely discarded before making extensive yield trials, 
this, in many cases, will reduce the number of strains that must 
be studied for yielding ability. 

Where only a limited number of varieties or strains are included, 
randomized blocks have considerable advantage over other 
methods. The number of varieties included in each block should 
be sufficiently small so that all varieties in each block are under 
similar conditions. At Minnesota, 25 or fewer varieties in each 
block have given relatively satisfactory results. One or two 
standard varieties are grown in each block where more than a 
single group of 25 varieties are under trial, and the standard 
error is computed separately for each group of randomized 
blocks. The methods of making yield trials may be illustrated 
as they are carried on at Minnesota for spring wheat. 

First Year. Rod-row trials are made at University Farm, St. 
Paul, in single-row plots with two to four replications, depending 
upon the amount of seed available. In these studies, check plots 
of standard varieties are grown in each randomized block and in 
each of the three disease nurseries: (1) for studies of reaction to 
stem and leaf rust, (2) for studies of reaction to bunt, root rot, 
and black chaff, and (3) for studies of reaction to scab. For the 
scab trials, the rows are grown under a tent, which increases 
humidity and makes infection relatively heavy. Notes are taken 
on agronomic characters in the yield trials, and all varieties 
or strains inferior to the check in any important respect are 
eliminated. 

Second Year. Rod-row trials are made at University Farm 
in randomized blocks with not more than 25 varieties per block 
and the inclusion of two or three standard varieties in each block. 
Three-row plots replicated four times are used, the central row 
of each plot being harvested for the yield trial and the border 
rows for milling and baking tests. The data are analyzed by 
means of the analysis of variance to determine if there are signifi- 
cant differences in yield. A calculated standard error is obtained 
by dividing the standard error of a single determination by the 
square root of the number of replicates, i.e., randomized blocks. 
Significant differences are considered to be twice the standard 
error of a mean difference. In these and in subsequent trials, 
all varieties are grown also in the disease nurseries and are 
eliminated when found inferior to the standard varieties in any 



306 METHODS OF PLANT BREEDING 

important respect. The more promising varieties are tested also 
in milling and baking trials. 

If the number of strains available for testing is not too great 
and there is sufficient seed, they may be tested the first or second 
year at several stations. 

Third to Fifth Year. Three-row plots are used as in the second 
year, and trials are made in randomized blocks with three repli- 
cations at each of four stations, University Farm, St. Paul, and 
the branch stations at Morris, Crookston, and Waseca, making 
12 replications in all. The data taken are similar to that out- 
lined for the second year at University Farm. A mixture of seed 
from the four stations is used for the milling and baking tests. 

Sixth to Eighth Year. The more promising varieties in the 
rod-row trials are increased and placed in )4(r acre plt trials in 
randomized blocks, with three replications at each station, tests 
being conducted at the same four stations and, in addition, at 
Grand Rapids and Duluth. Very promising varieties in the 
rod-row trials may be advanced to the ^o-acre plot trials before 
the sixth year. Fewer than 20 varieties are in these yield tests, as 
a rule, even though several thousand plant selections are grown 
yearly. This means that varieties are discarded freely. 

The standard errors for each trial are averaged for a series of 
years and stations, considering that each trial may be a test of 
the desirability of the new variety for use in some region in 
Minnesota. The formula for the standard error of an average 
that is used is 1/N -\/ sf + si s, where s\, si, etc., are errors 
for each season and station and N is the number of trials made. 
This generalized average error is used as a standard error for the 
average yield of the varieties at several stations and for several 
years. 

Varieties grown in similar trials are then compared on the 
basis of a standard error of a difference. The error is calculated 
by multiplying the generalized average error by \/2. The differ- 
ence in yield between any two varieties is obtained and the 
significance of this difference determined by the t test, as 
explained previously. 



CHAPTER XX 
RANDOMIZED BLOCKS, LATIN SQUARES, AND x 2 TESTS 

Experimental designs and statistical methods that are in most 
common use by the plant breeder will be illustrated for the 
beginning student who has not had extensive mathematical 
training or previous experience in the application of biometrical 
methods to plant-breeding problems. 

TESTS IN RANDOMIZED BLOCKS 

One of the simplest experimental designs for testing the yield- 
ing capacity of a group of varieties, particularly if the number is 
not unduly large, say less than 25, is that of randomized blocks 
In such designs, the varieties are grown in random order in each 
of several complete replication series or blocks, the number of 
replications used depending on the degree of precision desired 
for the comparisons of the variety means. 

R. A. Fisher stated that randomization of the order of varieties 
in a block must be followed if an unbiased estimate of error is to 
be obtained. Tedin (1931) tested the validity of this assumption 
and confirmed Fisher's conclusion. Before describing studies in 
randomized blocks, a method of obtaining a randomized order for 
planting will be given where 20 varieties are being compared. 

The following plan is one suggested by Fisher (1937) in "The 
Design of Experiments." Use a pack of cards numbered from 
1 to 100, and arrange them in random order by repeated shuffling. 
If 20 varieties are to be tested, they are then numbered from 1 to 
20 and cards drawn from the pack. Divide the number of the 
card drawn by 20, and the remainder will give the variety to be 
planted in the first plot. Suppose that the first card drawn is 
33. Dividing by 20 leaves 13 as a remainder, and variety 13 
is taken first. Suppose that the second card is 40, giving zero 
as a remainder. Numbers divisible by 20 correspond to variety 
20. Cards are drawn in this manner until the order of all varie- 
ties has been obtained. The remainder corresponding to any 

307 



308 



METHODS OF PLANT BREEDING 



variety is disregarded after its first occurrence in the block. 
After one block arrangement has been completed, the cards are 
reshuffled before drawings are made for the second block. 

Since 100 is divisible by 20, each variety will be represented in 
the pack five times. If 19 varieties were to be placed in random- 
ized order, the same pack of cards could be used but cards with 
numbers above 95 discarded, since 95 is directly divisible by 19, 
leaving no remainder. 

Tables of random numbers, when available, such as those 
given by Tippett (1927) and Fisher and Yates (1938) can be used 
instead of a pack of cards in order to save labor. In such tables, 
one may start at any point and proceed in any direction, taking 
each pair of digits to represent the numbers of a card in a pack of 
100. In these tables, 00 will be used in place of 100. 

The analysis of variance is used to determine the significance 
of results obtained in raiidomized-block designs. By this pro- 
cedure, developed by Fisher (1938), the total variation is sepa- 
rated into a number of components attributable to known or 
controlled sources of variation and leaving a residual portion 
due to uncontrolled causes and called the error. 

Data from a randomiaed-block trial with 10 varieties of barley, 
reported by Immer, Hayes, and Powers (1934), will be used to 
illustrate the computation. The data are given in Table 41. 

TABLE 41. YIELDS IN BUSHELS PER ACRE OF 10 VARIETIES OF BARLEY 
GROWN AT UNIVERSITY FARM, ST. PAUL 



Variety 


Block number 


Sum 


Average 


1 


II 


III 


Manchuria 


29 2 

44 6 
33 9 
36 7 
41 2 
45.8 
35 S 
38 5 
15.5 
44.3 


25 
39 1 

39 4 
41 
31 9 
38.8 
36.0 
29 6 
32.8 
37.4 


26 8 
45 5 
32.1 
42 
36 6 
45 2 
38 
30 2 
25 7 
36.2 


81 
129.2 
105 4 
119 7 
109 7 
129.8 
109 8 
98 3 
74.0 
117.9 


27.0 
43.1 
35.1 
39 9 
36 6 
43.3 
36 6 
32.8 
24 7 
39.3 


Glabron 
Svansota 


Velvet 


Trebi 


Minn. 457 
Minn. 462 
Peatland 


Minn. 475 


Barbless 


Sum 


365.5 


351.0 


3&8 3 


1074.8 / 







RANDOMIZED BLOCKS, LATIN SQUARES, AND x 2 TESTS 309 

First it will be necessary to calculate the sum of squares of 
deviations for the total variation and for blocks and varieties. 
The sum of squares for error is obtained by subtracting the sum 
of squares for blocks and varieties from the total. 

The total sum of squares will be given by S(x 2 } S(x)x. 
Squaring the 30 individual-plot yields and summing gives 
S(x 2 ) = 39,949.06. The total, or S(x), = 1074.8. The mean 
x = 1074.8 -T- 30 = 35.826,667. Then, the correction term 
S(x)x will be 1074.8 X 35.826,667 = 38,506.50. Care must be 
used to calculate the mean to sufficient accuracy. This difficulty 
is overcome by squaring the total and dividing by the total 

number of plots. Thus, ^^ = ^^ = 38,506.50. The 

total sum of squares will be 8(x' 2 ) S(x)x = 39,949.06 - 
38,506.50 = 1442.56. 

The sum of squares for blocks is obtained by adding the squares 
of the block totals, dividing by the number of plots in each 
total, and subtracting the correction term. Expressed as a 

S(x 2 ) 
formula, this will be TT?- ~ S(x)x, where x b refers to the block 

totals. Numerically, this is 386,170.14 _ 38j506 50 = 10 51 

The sum of squares for varieties is calculated in a manner 
similar to that for blocks. If x v represents the variety totals, 

118,668.36 



^ * -111 , ._ ,. . 

the sum of squares will be Q &(x)x. I his is -$ - 

o o 

- 38,506.50 = 1049.62. 

In these and other calculations where totals are used, it is 
necessary to calculate the sums of squares on a unit basis. This 
is accomplished by dividing the squares of the totals by the 
number of unit plots in each before subtracting the correction 
term. 

The complete analysis of variance is given in Table 42. 

The degrees of freedom for blocks, varieties, and total are 1 less 
than the number of blocks, varieties, and total plots, respectively. 
The degrees of freedom for error will be the remainder after sub- 
traction of the degrees of freedom for blocks and varieties from 
the total. In randomized-block trials, the error degrees of free- 
dom will be the product, also, of the degrees of freedom for 
blocks multiplied by the degrees of freedom for varieties. 



310 



METHODS OF PLANT BREEDING 



The column of mean squares in Table 42 is obtained by dividing 
the sums of squares by the appropriate degree of freedom. 
These values are the estimated variances expressed on a single- 
plot basis. The standard error of a single plot is the square root 
of the error mean square, i.e., -\X21.25 = 4.61. 

TABLE 42. ANALYSIS OF VARIANCE OF YIELDS OF 10 VARIETIES OF BARLEY 
IN A RANDOMIZED BLOCK TRIAL 



Variation due to 


Degrees of 
freedom 


Sum of 
squares 


Mean 
square 


F 


s 


Blocks 


2 


10.51 


5.26 


25 




Varieties 


9 


1049 62 


116 62 


5 49* 




Krror 


18 


382 43 


21 25 




4 61 














Total 


29 


1442 56 





















* Exceeds the 1 per cent point. 

To determine whether block or varietal differences are signifi- 
cant, the variance ratios, or values of F, are calculated. These 
are the mean squares for blocks and varieties each divided by the 
error mean square. For comparing variety and error mean 
squares, use is made of the table of F published by Snedecor 
(1940) and reproduced as Appendix Table II. The expected 
value of F for n\ = degrees of freedom for the larger mean 
square and n^ = degrees of freedom for the smaller mean square, 
or in this case for n\ = 9 and n 2 = 18, is found to be 2.46 and 
3.60 at the 5 and 1 per cent points, respectively. The observed 
value of F) for comparing variety arid error mean square, 
exceeded the 1 per cent point. Therefore, we may conclude that 
less than once in 100 trials could varietal differences as great as 
those observed be obtained by chance. We may say, therefore, 
that some of the varietal differences are highly significant, using 
the term highly significant when the observed value of F exceeds 
the 1 per cent point. 

The mean square due to blocks was less than that for error. 
This shows that the variation between block totals was less than 
expected through random sampling alone. Whenever the mean 
square for blocks or varieties is less than error mean square, there 
is no point in calculating and testing the significance of F, The 
removal of variability due to blocks removes differences due to 



RANDOMIZED BLOCKS, LATIN SQUARES, AND x 2 TESTS 311 

the placing of one block on land of different productivity from 
another. This makes it possible to place each block on a sepa- 
rate field if one so desires. 

Standard malting barley varieties in Minnesota are Manchuria, 
Velvet, and Barbless. The question may be asked, what are the 
chances that these three varieties were significantly different in 
yield in this test? The mean yields of Manchuria, Velvet, and 
Barbless were 27.0, 39.9, and 39.3 bu. per acre, respectively. The 
standard error of a mean of three plots is obtained by dividing 
the standard error of a single determination (s) by \/N, where 
N is the number of replications. The standard error of the 
difference between two means of three plots is obtained by multi- 
plying the standard error of the mean by \/2. This is on the 
basis that the error in bushels, as calculated, will be the same for 
all varieties regardless of their mean yield. The standard error 
of the difference between two means may be calculated from 



'2 X 21 25 

- = 3.76 bu., where N is the number of plots 



@_ /! 

\ N V 3 
in each mean. To determine the minimum difference required 
for odds of 19.1 or 99 : 1, we must multiply the standard error of 
the difference by the value of t for the degrees of freedom for error 
in the analysis of variance at the 5 and 1 per cent points, respec- 
tively. It is seen in Appendix Table I that for 18 degrees of 
freedom t = 2.10 at the 5 per cent point and 2.88 at the 1 per cent 
point. Multiplying 3.76 by 2.10 and 2.88 gives 7.90 and 10.83, 
respectively. Yields of Velvet and Barbless were 39.9 and 39.3 
bu. respectively, whereas Manchuria yielded only 27.0 bu. Since 
Velvet and Barbless differed in yield from Manchuria by 12.9 
and 12.3 bu., respectively, we may state that the chances are 
less than 1 in 100 that these differences in yield are due to 
chance. 

If, instead of comparing the differences between these 
varieties, irrespective of the direction of the difference, we want 
to determine the probability that Velvet and Barbless exceeded 
Manchuria in yield, we should need to use one tail only of the 
probability curve. In that case, we should use t for P = .10 
and .02 instead of .05 and .01 to obtain the probability of a devi- 
ation in one direction only occurring in 5 and 1 per cent of the 
time through random sampling. 



312 METHODS OF PLANT BREEDING 

The plant breeder usually compares the performance of new 
strains with standard varieties whose performance has been well 
established. If the odds were 19.1, for example, that the differ- 
ence in yield between Barblcss and Manchuria, plus or minus, 
are not due to chance, the odds would be 39 : 1 [(2 X 19 + 1) : 1] 
that Barbless exceeded Manchuria. The odds that the increased 
yield of Barbless over Manchuria is not due to chance would 
be two times, plus one, that found from the t table. 

Some practices essential to satisfactory randomized-block tests 
can be summarized at this point. Size of plot used may be 
decided on two general bases. Sufficient plants to give a measure 
of the characters of the strain or variety and a plot of convenient 
size from the standpoint of handling and cost are the bases for 
selection of a plot of proper size. In general, the number of 
varieties in a block should not be much greater than 25, or the 
area of the block will be so great that soil heterogeneity may 
lead to too large a standard error. In simple plant-breeding 
experiments, when large numbers of strains are available for 
testing, the trials may be made by using randomized blocks with 
not more than 25 varieties in a block and the growing of one or 
more standard varieties in each block., New strains are com- 
pared with the standard by this method before comparing those 
that survive this test with each other. 

LATIN SQUARES 

The Latin square has been shown to be a desirable method of 
making precise comparisons when the number of treatments 
or varieties to be compared is small, i.e., from about 4 to 10. 
Although of less general value for the plant breeder than random- 
ized blocks, it is a desirable method for special experiments. 

In a Latin-square design, there are as many replications as 
treatments. The treatments are arranged in a random order 
in a square or rectangle, with the restriction that each treatment 
can occur but once in each row and each column. For randomiz- 
ing the order of the varieties, use may be made of a pack of cards, 
as described for randomized blocks, or by reference to the pub- 
lished sets of Latin squares [from 4 X 4 to 9 X 9, given by Fisher 
and Yates (1938)]. A Latin-square arrangement for five treat- 
ments, A, J? ? C ? D ? E, is illustrated below; 



RANDOMIZED BLOCKS, LATIN SQUARES, AND % 2 TESTS 313 

E B D C A 

A C E B D 

B E A DC 

C D B A E 

D A C E B 

The degrees of freedom for an analysis of variance would be 
keyed out as follows: 

Degrees of 
Variation Due to Freedom 

Rows 4 

Columns 4 

Treatments 4 

Error 12 

Total 24 

The calculation of the sums of squares proceeds as outlined 
for randomized blocks. If x = the yield of each plot, x r) x c , and 
Xt the total yield of each row, column, or treatment, and p = the 
number of rows, columns, and treatments, the sum of squares 
for rows, columns, and treatments and the sum of squares for the 
total may be calculated as follows : 

Sum of squares for rows - S(x)x 

P 

Sum of squares for columns _JL _ fi( x ) 

P 

Sum of squares for treatments 8(x)$ 

P 

Sum of squares for total S(x 2 ) - S(x)x 

The sum of squares for error is obtained by subtracting the sum 
of squares for rows, columns, and treatments from the total. 

The shape of plots in a Latin square need not be square. They 
may be rectangular in shape. If very long and narrow, however, 
the variation in soil fertility in the narrow direction will be small, 
and little will be gained by removing the variation in this direc- 
tion. With plots for which the ratio of length to width is not 
extreme, removing variability in two directions usually will 
result in reduction in the error as compared with randomized 
blocks, 



314 METHODS OF PLANT BREEDING 

ESTIMATING THE YIELD OF A MISSING PLOT 

It sometimes happens that the yield of some plot, or plots, is 
lost or is known to be unreliable. When that happens, it may be 
desirable to interpolate yields for the missing plots before the 
analysis of variance can be completed. 

Yates (1933) has given a formula for estimating the yield of a 
missing plot. The interpolated yield is so calculated that the 
error variance is made a minimum. The formula appropriate 
for randomized-block trials is as follows: 

pP + qQ-T 
(p- l)(q - 1) 

where X = yield of missing plot. 

p = number of treatments. 

q = number of blocks. 

P sum of known yields of treatment with a missing plot. 

Q = sum of known yields of block with a missing plot. 

T = total yield of known plots. 

As an example, assume that the yield of Minn. 462 in block II 
of Table 41 were missing. Then 

p = 10 

g = 3 
P = 73.8 
Q = 315.0 

T = 1038.8 

v - (10 X 73.8) + (3 X 315.0) - 1038.8 _ 

-- - 



which is the estimated yield of the missing plot. 

If two or more plots are missing, a method of approximation 
may be used based on the foregoing formula. With, say, two 
plots missing, a yield is assumed for one of the missing plots and 
the formula used to estimate the second. The assumed yield 
of the first missing plot is then erased and the formula used to 
estimate that. The yield estimated first is then recalculated and 
the same procedure applied in rotation to obtain the accuracy 
desired. 

After obtaining the estimated yield of the missing plot, the 
analysis of variance is carried through in the usual manner except 
that 1 degree of freedom is subtracted from the error and 1 from 



RANDOMIZED BLOCKS, LATIN SQUARES, AND x 2 TESTS 315 

the total for each missing plot interpolated. In plant-breeding 
trials in randomized blocks, the data for the variety in which one 
or more plots are missing may be disregarded in computing the 
analysis of variance, providing that the degrees of freedom used 
are for the varieties actually used in the analysis. 

In Latin squares, the formula for estimating the yield of a 
missing plot is 

P (P r + P c + P t ) ~ 2T 

(p- l)(p - 2) 

where X = missing plot yield. 

p = number of rows, columns, or treatments. 
P r , P c , P t = sum of the known yields of the row, column, or 
treatment with a missing plot. 

T = total yield of known plots. 

SPLIT-PLOT EXPERIMENTS 

In designing experiments involving two or more factors, the 
split-plot arrangement is often useful. The arrangement of the 
plots and the mariner of calculation of the data will be illustrated, 
with the use of data obtained by A. C. Arny. 

This experiment was one designed to determine the effect of 
varying the width between rows and spacing of seed within rows 
on the yield of soybeans. Four-row plots 132 ft. long were 
planted in rows 16, 20, 24, 28, 32, or 40 in. between rows. These 
long plots were then divided into four subplots of 33 ft. each and 
the soybeans spaced J^, 1, 2, or 3 in. apart within the subplots. 
The entire experiment was replicated four times, and only the 
central two rows of each four row plots were harvested. The 
field arrangement of the plots in block III is given below: 



16 





1 


3 


2 


32 


1 


3 


2 


M 


28 


3 


1 A 


1 


2 


40 


2 


1 


M 


3 


24 


1 


3 


2 


M 


20 


3 


1 





2 



316 



METHODS OF PLANT BREEDING 



The order of the plot widths within each block was random, 
and the four spacings were randomized within each main or 
width plot. The dimensions of each block were 53}i by 
132 ft. 

In Table 43 are given the yields in bushels per acre for each 
plot, arranged in a convenient form for computation. 

TABLE 43. YIELD OP SOYBEANS IN BUSHELS PER ACKE 



Block 


Width 
of rows, 


Spacing within rows, in. 


Block 


























total 




in. 


M 


1 


2 


3 


Sum 




I 


16" 


25 1 


21.3 


22.3 


22.1 


90 8 






20" 


21.8 


22.7 


22.2 


22.8 


89.5 






24" 


21.9 


21.8 


21 2 


20.6 


85.5 






28" 


21.2 


20.4 


20.4 


17.9 


79.9 






32" 


20.7 


20.0 


18.3 


20.0 


79 






40" 


19.5 


18.3 


17.5 


16.3 


71 6 


496.3 


11 


16" 


25.2 


19.9 


22.1 


22 7 


89 9 






20" 


21.9 


21 3 


22.1 


22 9 


88.2 






24" 


19 7 


19 8 


20 1 


19.8 


79 4 






28" 


20 8 


21 2 


18.8 


20.6 


81 4 






32" 


18.5 


20.7 


17 5 


16.4 


73 1 






40" 


18.5 


18.2 


19 8 


15 9 


72.4 


484.4 


111 


16" 


15 7 


21.6 


22.9 


20.3 


80 5 






20" 


22 


20 4 


22 4 


20.7 


85.5 






24" 


25 5 


20.7 


20 7 


20 5 


87.4 






28" 


21.5 


19.9 


20 5 


20.9 


82.8 






32" 


22.0 


19.3 


18.1 


17.8 


77.2 






40" 


20.5 


16.4 


17.5 


18 5 


72.9 


486.3 


IV 


16" 


23.8 


29.0 


12.3 


23 5 


88 6 






20" 


27.0 


21.2 


20.5 


20.7 


89 4 






24" 


23.5 


20 


22.3 


19.8 


85.6 






28" 


22 5 


21.5 


22 7 


18 9 


85.6 






32" 


23.9 


18.4 


20 7 


18.7 


81.7 






40" 


19 9 


17 8 


16.9 


18.5 


73.1 


504 


Sum 




522.6 


491.8 


479 8 


476.8 


1971 


1971.0 





Squaring the 9G individual plot yields gives S(x 2 ) = 41,045.92. 
The correction term will be S(x)x = (1971.0) 2 /96 = 40,467.09. 
The total sum of squares is then 41,045.92 - 40,467.09 = 578.83. 



RANDOMIZED BLOCKS, LATIN SQUARES, AND % 2 TESTS 317 



The block sum of squares will be 

S(xl) c , , 971,460.74 
' S(x)x = - ^ - 



1AAA 
= 10.44 



where x$ represents the squares of the block totals. 

The sum of squares for the main or width plots is calculated 
from the column of sums on the right-hand side of Table 43. 
Thus, 

90.8 2 + 89.5 2 + +73.1 2 a/ .. 



162,768.54 



- 40,467.09 = 225.05 



The data in Table 43 are next assembled in the form given in 
Table 44 in order to obtain the sums of the four replications for 
each width of row and spacing within the rows. 

TABLE 44. TOTAL YIELD FOR EACH WIDTH OF Row AND SPACING FOK 
THE FOUR REPLICATIONS 



Width of 


Spacing within rows, in. 


Sum 


Average 










rows, m. 
















>'2 


1 


2 


3 






16 


89 8 


91.8 


79.6 


88.6 


349.8 


21 9 


20 


92.7 


85.6 


87 2 


87 1 


352 6 


22.0 


24 


90.6 


82 3 


84 3 


80 7 


337 9 


21 1 


28 


86.0 


83 


82.4 


78 3 


329 7 


20 6 


32 


85 1 


78 4 


74 6 


72 9 


311 


19 4 


40 


78 4 


70.7 


71 7 


69 2 


290 


18 1 


Sum . . . 


522 6 


491 8 


479 8 


476 8 


1971 




Average. . . 


21.8 


20.5 


20.0 


19 9 







The sum of squares for widths of row will be ~~ S(x)x = 



650,386.30 
16 



16 
- 40,467.09 = 182.05, where xl is the square of the 



totals of 16 plots for each width. 

The sum of squares for spacings will be ^-^ S(x)x = 
972,524.28 



24 



- 40,467.09 = 54.75, where xl is the square of the 



totals of 24 plots for each spacing. 



318 



METHODS OF PLANT BREEDING 



Next, the 24 sums within Table 44 are squared and added. 



Thus 



89.8 2 + 92.7 2 



+ 69.2 2 



- 40,467.09 = 267.23 for 



these 23 degrees of freedom. From this sum of squares is sub- 
tracted the sums of squares for width and spacing to give 267.23 
182.05 54.75 = 30.43 as the sum of squares for the interaction 
of width X spacing. 

The entire analysis of variance is given in Table 45. 

TABLE 45. ANALYSIS OF VARIANCE OF YIELD IN BUSHELS PER ACRE IN- 
SPACING TRIAL WITH SOYBEANS 



Variation due to 


Degrees of 
freedom 


Sum of 
squares 


Mean 
square 


F 


Blocks 


3 


10 44 


3.48 


1.60 


Width, of row 


5 


182 05 


36 41 


16 78 f 


Error a 


15 


32.56 


2 17 = s z a 














Main plots 


23 


225.05 






Spacing 


3 


54 75 


18 25 


3 67* 


Width X spacing 


15 


30,43 


2.03 




Error b 


54 


268 60 


4 97 = *J 














Total 


95 


578 . 83 

















* Exceeds the 5 per cent point, 
f Exceeds the 1 per cent point. 



The degrees of freedom and sum of squares for error a are 
obtained by subtracting the degrees of freedom and sum of 
squares for blocks and widths from the main plots, which have 
23 degrees of freedom and the sum of squares for which was 
225.05. The degrees of freedom for error 6 will be 95 15 
3 23 = 54. The sum of squares for error b is obtained by 
subtraction in like manner. 

It is noted that the value of F for a comparison of the mean 
squares for widths of row with that of error a was highly signifi- 
cant. The mean square for spacings is compared with that of 
error b and exceeded the 5 per cent point but did not reach the 
1 per cent point. The mean square for interaction of width X 
spacing was numerically less than the mean square for error b and 
clearly not significant. 



RANDOMIZED BLOCKS, LATIN SQUARES, AND x 2 TESTS 319 

From these data one may conclude that the differences in yield 
of soybeans in this test, planted in rows of different width, 
was independent of the spacing within the rows. The planting 
arrangement that would be expected to result in the highest 
yield would be the combination of highest average width per row 
and spacing within the row. 

The standard error of the difference between two means for 
different widths of row would be 



2~X"3_ / 
~~16~ \ 



2X~2l7 

~ 



16 



si being divided by 16, since the means arc based on that number 
of plots and multiplied by 2, since the standard error of a differ- 
ence is desired. Since t at the 5 per cent point for 15 degrees 
of freedom is 2.13, the minimum level of significance would be 
2.13 X 0.521 = 1.11 bu. The average yield of all plots with 
20-in. rows was 22.0 bu., and the average yield for 28-in. rows 
was 19.4 bu. The difference of 1.4 bu. exceeded the minimum 
level of significance and may be judged significant. 

The standard error of the difference between the means of two 
spacings would be 

^ '~~ = 0.644 

Since t at the 5 per cent point and 54 degrees of freedom is 2.00, 
mean differences in excess of 2.00 X 0.644 = 1.30 may be judged 
significant. Spacing of the soybeans 2 in. apart in the row 
resulted in a reduction of 1.8 bu. per acre over J^-in. spacing, a 
significant decrease. 

Split-plot experiments are very useful when two or more factors 
are to be tested in one experiment and planting difficulties make 
it necessary that large plots be used for one factor, the large, or 
main, plots being split up for the second factor. Variety tests 
combined with dates of planting tests would be of this type, the 
dates of planting being the main plots and the varieties the sub- 
plots. Tests of f ungicidal dusts on different varieties would often 
require rather large plots for the different dust treatments in 
order to control "drift" of the dust in application. These could 
well be the main plots and several varieties planted in subplots 



320 



METHODS OF PLANT BREEDING 



within each main or dust treatment plot. For such tests, the 
split-plot design would be well suited. 

CHI-SQUARE (x 2 ) TESTS 

Tests of Goodness of Fit. The x 2 test is a useful method for 
testing goodness of fit of Mendelian ratios, as pointed out by 
Harris (1912). *The methods will be illustrated by various 
examples. 

In the 7^2 generation of a cross between a two-rowed variety of 
barley producing green seedlings (VV LgLg) with a six-rowed 
variety with light-green seedlings (vv Iglg) the following number 
of plants was obtained in the four phenotypic classes: 



VLg 


Vlg 


vLg 


v Ig 


Total 


281 


59 


60 


58 


458 



The general formula for calculating x 2 niay be written as 



2 s(o - 

v * ~~ ' 

x c 



where S refers to summation, is the observed frequency, and 
C is the expected or calculated frequency. 

The test for deviations of the single factor ratio Vv may be 
made as follows : 



Phenotype 


Observed (0) 


Calculated (C) 


n r 


(O - C) 2 




c 


V 

v 
Total 


340 
118 


343.5 

114 5 


-3.5 
3 5 


0.036 
0.107 


458 


458.0 





x 2 = 0.143 



On entering the table of % 2 (Appendix Table III) for 1 degree 
of freedom, it is found that the observed x 2 lies between P = 0.95 
and 0.50. The degrees of freedom are 1 less than the number of 
classes. A x 2 value as great as the observed would be expected 
to occur between 50 and 95 times in 100 trials through errors of 
random sampling. 



RANDOMIZED BLOCKS, LATIN SQUARES, AND % 2 TESTS 321 
X 2 for a 3:1 ratio may be calculated also from 



where A = observed number in the dominant class. 
a = number in the recessive class. 
N = total number. 
For the foregoing problem 

9 [340 - 3(118)] 2 A1 . ,, , ,, ,, , 

X 2 = - .L = 0.143, the same as found by the longer 

o X 4oo 

method. 

Below are listed some formulas that may be useful for two 
class segregations. 

Segregation Expected x 2 Formula 

A:a 

1:1 

2:1 

3:1 

15:1 

9:7 

The agreement between the ratio observed and the ratio 
expected on the basis of independent inheritance of the two factor 
pairs may be tested by calculating x 2 for goodness of fit to a 
9:3:3:1 ratio. The calculations are given in Table 46, with the 
use of the data from the experiment mentioned previously. 

TABLE 46. CALCULATION OF GOODNESS OF FIT TO A 9:3:3:1 RATIO 



x 2 = (A - a) 2 /# 
x 2 = (A - 2a)*/2N 
X 2 (A - 30 



(A - 15a) 2 /15JV 
(7A - 9 



Phenotype 


Observed (0) 


Calculated (C) 


- C 


(0 - C) 2 


c 


V Lg 


a = 281 


257.625 


23.375 


2 121 


Vlg 


6 = 59 


85.875 


-26.875 


8.411 


vLg 


c = 60 


85.875 


-25 875 


7 796 


v Ig 


d = 58 


28 625 


29 375 


30 145 


Total 


N = 458 


458.000 


000 


x 2 - 48 473 



The calculated frequency for the four phenotypic groups will 
be %e? Mf>? Me? an d 3/fe of the total, respectively. On entering 
the table of x 2 (Appendix Table III) for 3 degrees of freedom, it 
is noted that the observed value of %! == 48.473 greatly exceeds 
the 1 per cent point. In goodness-of-fit tests, such as the fore- 



322 METHODS OF PLANT BREEDING 

going, the degrees of freedom are 1 less than the number of 
classes. It may be concluded, therefore, that the deviation 
from a 9:3:3:1 ratio was highly significant. 

A somewhat shorter method may be used for testing goodness 
of fit to a 9 : 3 : 3 : 1 ratio. Thus 



. 16(a 2 + 36 2 + 3c 2 Ar 

X 2 = , - _ -- N 

where a, 6, c, and d = observed frequencies as given in Table 46. 
Ther 

2 - 16[28P + 3(59 2 ) + 3(60 2 ) + 9(58 2 )] _ 

x -- 9 X458 4M ~~ ** A76 

as before. 

The nature of the deviation of the observed ratio from that 
expected on the basis of independent inheritance may be deter- 
mined oy separating x 2 into its components. The 3 degrees of 
freedom for the goodness-of-fit test may be apportioned to: one 
for deviat ons of the Vv segregation from a 3:1 ratio, one for 
deviations of the Lg Ig segregation from a 3:1 ratio, and one 
for detecting association (linkage) of the two factor pairs. Con- 
venient formulas are 

For Vv segregation x 2 = (a + 6 - 3c - 3d) 2 /3N 
For Lg Ig segregation x 2 = (o - 36 + c - 3d)*/3N 
For linkage x 2 = (a - 36 - 3c + 9d) 2 /9N 

The formula for deviations of single-factor ratios will reduce to 
the form given before. Substituting the observed ratios in these 
three formulas gives 

For Vv segregation x 2 = 0.143 for 1 degree of freedom 
For Lg Ig segregation x 2 = 0.073 for 1 degree of freedom 
For linkage x 2 = 48.257 for 1 degree of freedom 



For goodness of fit x 2 =: 48,473 for 3 degrees of freedom 

In referring to the table of x 2 (Appendix Table III), it is noted 
that the agreement of the two single-factor ratios with a 3:1 
ratio is good. The x 2 for linkage exceeds the 1 per cent point. 

With the use of the product method for calculating linkage 
(Fisher 1938) and tables provided by Immer (1930), the per- 



RANDOMIZED BLOCKS, LATIN SQUARES, AND x 2 TESTS 323 



centage of recombination between these two factor pairs was 
30,2 2.7. 

x 2 for Independence. The % 2 test may be used to determine 
whether two characters, classified into two or more groups, are 
independent. The calculations will be illustrated with data 
obtained by Hayes, Moore, and Stakman (1939) in a study of 
inheritance of characters in crosses between varieties of oats. 

Among the characters studied were plumpness of grain and 
type of awn. One of the parents, Bond, produced short, weak 
awns; the other parent, designated Double Cross, produced long, 
heavy awns. The two parents differed in plumpness of grain, 
as may be noted in the following table. Plumpness of grain is a 
visual note taken on a scale of to 100 and has been found to be 
correlated significantly with yield. 

TABLE 47. PERCENTAGE OF PLUMPNESS OF KERNEL OF INDIVIDUAL PLANTS 
OF THE PARENT VARIETIES 



Variety 


Number of plants in plumpness classes 


0-25 


26-50 


51-75 


76-100 


Total 


Bond 


1 

5 


6 

28 


54 
26 


61 


122 
59 


Double Cross . 





In Table 48 are given the number of F 2 plants in different 
classes of plumpness and awn development. 

TABLE 48. FREQUENCY IN CLASSES FOR AWN DEVELOPMENT AND PERCENT 

OF PLUMPNESS OF GRAIN OF F 2 PLANTS IN THE CROSS OF 

BOND X DOUBLE CROSS 



Plumpness, per cent 


Awn classes 


Total 


Weak 


Intermediate 


0-50 

51-75 
76-100 


46 
165 
120 


8 
44 
27 


54 
209 
147 


Total 




331 


79 


410 


Proportion 




0.80732 


. 19268 









To determine whether these two pharacters are independent, 
we may compare the observed frequencies with theoretical fre- 



324 



METHODS OF PLANT BREEDING 



quencies calculated on the assumption of independence. The 
theoretical frequencies for the individual cells of the table are 
calculated so that they are in the same proportion to one another 
as they are in the totals of the rows and columns. 

The theoretical frequency in the upper left-hand cell of the 
table will be the product of the two marginal totals divided by 
the grand total or (331 X 54)/410 = 43.60. The other theoretical 
frequencies are calculated in a similar manner. To expedite the 
computations, the proportion of the grand total in each column 
may be calculated first. This is designated as " proportion" in 
Table 48. The proportion of weak and intermediate awn plants 
may then be multiplied by the margin totals for plumpness 
classes, i.e., 54, 209, and 147, to obtain the theoretical frequencies. 
In Table 49 is given the computation of % 2 for independence. 

TABLE 49. CALCULATION OF % 2 F R INDEPENDENCE OF AWN TYPE AND 
PLUMPNESS OF KERNELS 



Observed 
frequency 


Calculated 
frequency 


C 


(0 - C) 2 


C 


46 


43.60 


2.40 


.132 


165 


168 73 


-3 73 


.082 


120 


118 68 


1 32 


.015 


8 


10.40 


-2.40 


.554 


44 


40 27 


3 73 


.345 


27 


28.32 


-1.32 


.062 


Sum 410 


410.00 


0.00 


x 2 = 1 190 



Since % 2 was calculated from fixed marginal totals, the degrees 
of freedom are (r l)(c 1) = 2, where r and c refer to the 
number of rows and columns, respectively, in Table 48. On 
entering the table of x 2 for 2 degrees of freedom, it is found that 
the observed x 2 gives a value of P between .50 and .70. These 
data indicate, therefore, that there was no association between 
plumpness of kernel and development of awn in this segregating 
population. The x 2 test is frequently useful in testing for inde- 
pendence of different characters in plant-breeding studies, when 
the data for each character are grouped in classes and entered as 
illustrated in Table 48. 



CHAPTER XXI 

CORRELATION AND REGRESSION IN RELATION TO 
PLANT BREEDING 

SIMPLE CORRELATION 

When data on two or more characters of a group of varieties or 
treatments are available, it frequently will be of value to deter- 
mine the degree of association between them. This may be done 
by calculating the correlation coefficient. The coefficient of 
correlation can vary from +1 to 1, being zero when there is no 
association and increasing to + 1 or 1 for complete association. 

A method of computation will be illustrated by using data 
obtained in Minnesota from a study of the relationship between 
number of kernels per spikelet and yield of grain in bushels per 
acre in rod-row trials with spring wheat. Each plot consisted of 
three rows, and the central row only was used for obtaining the 
number of kernels per spikelet and yield. The number of kernels 
per spikelet was obtained from 100 spikes, selected at random, 
from each plot. The yield was computed from the central row 
of each three-row plot. The experiment was a randomized-block 
trial. The data are given in Table 50. 

Before making a study of the extent of correlation between 
yield and number of kernels per spikelet, it will be of value to 
determine whether these strains of wheat differed significantly in 
the two characters being studied. This is accomplished through 
an analysis of variance. The results are given in Table 51. 

The mean squares for varieties compared with error exceeded 
the 1 per cent point, indicating that highly significant differences 
in yield and number of kernels per spikelet existed among these 
21 varieties. For neither character were there significant differ- 
ences between blocks. 

To calculate the correlation coefficient, it is necessary to deter- 
mine the co variance. This is computed from the sums of products 
in a manner analogous to the computation of sums of squares. The 
sums of products are obtained from the sum of the products 

325 



326 



METHODS OF PLANT BREEDING 



TABLE 50. NUMBER OF KERNELS PER SPIKELET AND YIELD IN BUSHELS 

PER ACRE, IN EACH OF THREE REPLICATIONS, IN ROD-ROW TRIALS 

OF SPRING WHEAT 





Kernels per spikelet 


Yield, bu. 




1 


2 


3 


Total 


Mean 


1 


2 


3 


Total 


Mean 


Marquis 


1 5 


1 5 


1 4 


4 4 


1 47 


22 7 


22 3 


28 8 


73 8 


24 6 


Ceres 4 . . .... 


1 9 


1 


1 7 


5 2 


1 73 


32 9 


31 1 


27 4 


91 4 


30 5 


Hope 


1 1 


1 9 


1 1 


3 4 


1 13 


27 1 


21 3 


18 1 


66 5 


22 2 


Ceres X Hope No. 1 ... ... 


1 4 


1 7 


1 4 


4 5 


1 50 


19 4 


19 2 


23 7 


62 3 


20 8 


Ceres X Hope No 2 


1 5 


1 4 


] 4 


4 3 


1 43 


26 4 


35 1 


28 1 


89 6 


29 9 


Ceres X Hope No. 3 


1.5 


1.4 


1.3 


4.2 


1.40 


26.2 


36.4 


29.3 


91.9 


30.6 


Ceres X Hope No. 4 


1.4 


1.5 


1.4 


4.3 


1.43 


24.2 


24.1 


20.0 


68.3 


22.8 


Ceres X Hope No. 5 


1 4 


1 4 


1 3 


4 1 


1 37 


23 g 


26 3 


24 3 


74 4 


24 8 


Double Cross No. 80 


1 3 


1 ' ? 


1 4 


3 9 


1 30 


26 8 


25 7 


30 5 


83 


27 7 


Double Cross No. 85 


1 5 


1 3 


1 4 


4 2 


1 40 


22 6 


26 6 


19 9 


69 1 


23 


Double Cross No. 86 


1.4 


1.5 


1.3 


4.2 


1.40 


23.2 


23.5 


28.8 


75.5 


25.2 


Double Cross No. 97 


1 4 


] 4 


1 4 


4 2 


1 40 


32 4 


27 5 


28 1 


88 


29 3 


Double Cross No. 98 


1 4 


1 3 


1 5 


4 9 


1 40 


26 1 


25 3 


30 7 


82 1 


27 4 


Double Cross No. 99 


1.4 


1.5 


1,3 


4.2 


1.40 


22.1 


28.1 


28.6 


78.8 


26.3 


Double Cross No. 100 


1.5 


1.5 


1.3 


4.3 


1.43 


27.1 


28.3 


26.8 


82.2 


27.4 


Double Cross No. 3 02 


1.4 


1.3 


1.4 


4.1 


.37 


27.1 


30.8 


28.9 


86.8 


28.9 


Double Cross No. 103. ... 


1.4 


1.5 


1.4 


4.3 


.43 


26.9 


29.1 


22.6 


78.6 


26.2 


Marquis X H44, No. 25 


1.2 


1.3 


1.2 


3.7 


.23 


15.9 


18.7 


19.8 


54.4 


18.1 


Marquis X H44, No. 33 


1 1 


1.2 


1 3 


3.6 


.20 


27.9 


27.9 


23.5 


79.3 


26.4 


Marquis X H44, No. 35 


1.2 


1.4 


1.3 


3.9 


.30 


27.0 


21.4 


25.0 


73.4 


24.5 


Marquis X H44, No. 40 


1.3 


1.2 


1.2 


3.7 


23 


22.6 


23.3 


24.0 


69.9 


23.3 


Total 


29.2 


29.3 


28.4 


86.9 




530.4 


552.0 


536.9 


1619.3 







of the deviations of x and y from their means, which may be 
expressed as S(x x)(y g). This is most conveniently cal- 
culated from S(xy) S(x)S(y)/N, and the co variance is found 
by dividing the sum of products by the appropriate degrees of 
freedom. The sums of products may be either positive or 
negative. 

An analysis of covariance is made in the same manner as an 
analysis of variance. Letting y and x represent yield in bushels 
per acre and number of kernels per spikelet, respectively, the 
total sum of products is given by S(xy) S(x)S(y)/N. Mul- 
tiplying each plot yield by the number of kernels per spikelet for 
that plot and summing gives 2242.16. Since S(x) = 86.9 
and S(y) = 1619.3, the correction term will be obtained by 
multiplying 86.9 by 1619.3 and dividing by 63, which gives 
2233.606. The total sum of products will be 2242.16 - 2233.606 
- 8.554. 



CORRELATION AND REGRESSION 327 

Letting x& and yb be the block totals for x and y, the sum of 

products for blocks will be i^M^ - S(x)S(y)/N, or 2233.773 

- 2233.606 = 0.167. 

If x v and y v are the variety totals for x and y, the sum of 

products for varieties will be ^ S(x)S(y')/N t or 2243.937 

- 2233.606 = 10.331. 

TABLE 51. ANALYSIS OP VARIANCE OF YIELD IN BUSHELS PER ACRE AND 

NUMBER OF KERNELS PER SPIKELET OF 21 VARIETIES OF SPRING WHEAT 

IN A RANDOMIZED-BLOCK TRIAL 



Variation due to 


Degrees of 
freedom 


Sum of 
squares 


Mean 
square 


F 


Yield per acre (y) 


Blocks 


2 
20 
40 


11 69 
654.29 
378 04 


5 . 845 
32.714 
9.451 


3.46* 


Varieties . ... 


Error 


Total 


62 


1,044.02 








Kernels per spikelet (x) 


Blocks 


2 
20 
40 


023 
0.930 
330 


0.0115 
0.0465 
0082 


1.40 
5.67* 


Varieties 


Krror 


Total 


62 


1.283 









* Exceeds the 1 per cent point. 

The error sum of products is obtained by subtracting sums of 
products for blocks and varieties from the total. 

In the following table are assembled the sums of squares (from 
Table 51) and sums of products for the different components of 
the total variation together with the correlation coefficients. 

The coefficient of correlation will be given by 






sum of products of xy 



\Xsum of squares of y \/sum of squares of x 



The correlation between varieties is found to be 



10.331 



V654.29 V0.930 



= +.419 



328 



METHODS OF PLANT BREEDING 



The significance of a correlation coefficient may be determined 
by reference to Appendix Table V, where the degrees of freedom 
will be 2 less than the number of pairs. The variety correlation 
+ .419 was slightly less than the value of r = .433 at the 5 per 
cent point for 19 degrees of freedom. 

TABLE 52. SUMS OF SQUARES AND PRODUCTS FOR YIELD IN BUSHELS PER 
ACRE AND KERNELS PER S PIKELET AND THE CORRELATION COEFFICIENTS 



Variation due to 


Degrees 
of 
freedom 


Sums of squares or products 


r 


y* 


xy 


X 2 


Blocks , 


2 

20 
40 


11.69 
654,29 
378 04 


0.167 
10.331 
-1.944 


0.023 
0.930 
0.330 


+ .419 
-.174 


Varieties 


Error .... . 


Total 


62 


1,044.02 


8.554 


1.283 







If it is desired to calculate a correlation coefficient for, say, 
yield and kernels per spikelet of varieties without performing an 
analysis of variance and co variance, a convenient formula is 



r = 



8(xy) - S(x)S(y)/N 



- [S(x)]*/N 



The calculations, with the use of the mean kernels per spikelet 
and yield in bushels for the varieties in Table 50, will be illus- 
trated. Multiplying the mean kernels per spikelet by the mean 
yield for each variety and summing gives S(xy) = 747.773. 
Summing the squares of the means for kernels per spikelet and 
yield in bushels gives S(x*) = 40.2199 and S(y 2 ) = 14,098.53. 
Since the total of the means are S(x) = 28.95 and S(y) = 539.9, 
the correlation coefficient will be 



r = 



747.773 - (28.95) (539.9)/21 



V 40.2199 - (28.95) 2 /21 V 14, 098.53 



(539.9) 2 /21 

= +.423 



This agrees closely with r = +.419 obtained in Table 52, the 
discrepancy being due to rounding off figures in recording the 



means. 



If this formula for the correlation coefficient used above is 
multiplied by N/N 



r = 



CORRELATION AND REGRESSION 329 

N8(xy\- S 



which probably is the best form for rapid machine computation. 
Numerically, this will be 

21(747.773) - (28.95) (539.9) __ 



V2f(402199) - (28.95) 1 V^T^O^^- "(539:9) 2 

= +.423 

LINEAR REGRESSION 

The relationship between two variables may be expressed also 
by means of the regression coefficient. The regression coeffir 
cient gives the rate of change in one variable (the dependent 
variable) per unit rate of change in another (the independent 
variable). The regression coefficient is given by 



v * S(x - x) 2 S(x*) - [8(x)]*/N 

This may be expressed also as 

, _ sum of products of xy 
yx sum of squares of x 

where b yx = regression of y on x. 

Numerically, the regression of yield on number of kernels per 
spikelet for the 21 varieties in Table 52 is 10.331 -4- 0.930 = 
+ 11.109. This means that as the number of kernels per spikelet 
of the varieties increased by 1.0, the yield of the varieties, on the 
average, increased by 11.1 bushels, or with an increase of spikelet 
number of 0.1 yield in bushels increased by 1.11, 

The significance of a regression coefficient may be tested by 
means of an analysis of variance. The total sum of squares 
for varieties is given in Table 52. The test of significance of 
regression is given in Table 53. The sum of squares due to 
regression for varieties will be 

(Sum of products of xyY = (10.331) 2 = 76 
Sum of squares of x 0.930 

The value of F obtained, 4.04, fails to reach the 5 per cent 
point (4.38) for ni = 1 and n<t = 19 degrees of freedom. 



330 



METHODS OF PLANT BREEDING 



It is noted that in testing the significance of both the correla- 
tion coefficient r and the regression coefficient 6, both were non- 
significant. The tests for significance of r and b are equivalent. 
When one is significant the other is significant also and vice 
versa. Exactly the same probabilities are obtained by the two 
tests Of significance. 

TABLE 53. TESTING SIGNIFICANCE OF A REGRESSION COEFFICIENT 



Variation due to 


Degrees 
of freedom 


Sum of 
squares 


Mean 
square 


F 


Regression 


1 


114.76 


114 76 


4.04 


Deviations from regression . . . 


19 


539.53 


28.40 




Total 


20 


654 . 29 

















If the sum of squares due to regression is divided by the total 
sum of squares, we may express this as a percentage of the total 
sum of squares accounted for by regression. Such a quantity is 
r 2 . The square of the correlation coefficient may be used as a 
measure of the percentage of the total variation accounted for. 
The correlation of +.419 indicated that 18 per cent of the 
variability in yield was accounted for by its association with num- 
ber of kernels per spikelet. Little importance can be attached to 
this, however, since the correlation was not significant. 

For prediction purposes, use may be made of the regression 
equation given by 

Y = y + b(x - x) 

where Y = predicted yield. 

y = observed mean yield. 

x = number of kernels per spikelet. 

Since y = 1619.3 -f- 63 = 25.703, x = 86.9 -*- 63 = 1.3794, and 
b for variety regression was +11.109, 



Y = 25.70 + 11.109(* - 1.3794). 

Multiplying 1.3794 by 11.109 and adding 25.70 gives 
Y = 10.38 + ll.WQx 

From this equation, the predicted values of F (yield per acre) 
can be calculated for varieties with different numbers of kernels 
per spikelet. A few such are calculated for illustration. 



CORRELATION AND REGRESSION 



331 





Average number 


Yield per 


acre, bu. 


V&riety 


spikelet (x) 


Observed (y) 


Predicted (7) 


Marquis 


1.47 


24.6 


26.7 


Ceres 


1.73 


30.5 


29.6 


Hope 


1.13 


22.2 


22.9 


Ceres X Hope No. 1 .... 


1.50 


20.8 


27.0 



The observed and predicted yields are given merely as an 
example of procedure. Unless correlation or regression is signifi- 
cant and relatively high, it is apparent that prediction values will 
not be very accurate. 

MEANS AND DIFFERENCES OF CORRELATION COEFFICIENTS 

Frequently it is desired to determine the significance of a 
difference between two correlation coefficients. The method will 
be illustrated with the use of the interannual correlation coeffi- 
cients for loaf volume determined from grain of spring-wheat 
varieties and strains grown in the regular rod-row nurseries in 
four places in the state, as given by Ausemus et. al. (1938). 

Since correlation coefficients cannot be averaged directly, 
it is necessary to transform the coefficients to the statistic z 
(Fisher 1938) and test the significance of the difference between 
the z values by means of its error. The standard error of z is 



The computations for testing the significance of the difference 
between the interannual correlation coefficients for loaf volume 
in 1929-1930, determined from 25 varieties, and in 1931-1932, 
determined from 16 varieties, are carried through in Table 54. 

TABLE 54. TEST OF SIGNIFICANCE OF A DIFFERENCE BETWEEN CORRELA- 

TION COEFFICIENTS 



Yea,rs correlated 


Observed r 


z 


N - 3 


Reciprocal 


1929-1930 


-f .43 


.460 


22 


0455 


1931-1932 


4-. 15 


.151 


13 


0769 













Difference Sum .1224. 

- .309 
.360, 

The observed values of r are first transformed to z with the 
use of Appendix Table IV, The two correlation coefficients were 



332 



METHODS OF PLANT BREEDING 



based on 25 and 16 pairs of observations each; so N 3 was 22 
and 13, respectively. The sum of the reciprocals of JKT 3 
is the variance of the difference between the values of z. The 
square root of .1224 = .350 and is the standard error of the 
difference. The difference was less than its standard error and, 
therefore, it may be concluded that the two values of r were not 
significantly different. 

When several correlation coefficients for the same characters 
are available, it frequently is desirable to determine the average 
correlation. This may be done by transformations of r to z, 
calculating the average value of z and then transforming the 
average z back to r. With the use of data from the same study by 
Ausemus et al., where the correlation coefficients of +.81, +.43, 
and +.15 were based on 11, 25, and 16 determinations, respec- 
tively, the calculations are carried through in Table 55. 
TABLE 55. AVERAGING CORRELATION COEFFICIENTS 



Years correlated 


Observed r 


z 


,V - 3 


(N - 3)z 


1927-1928 


4- 81 


1 127 


8 


9 016 


1929-1930 ... 


4- 43 


460 


22 


10 120 


1931-1932 


+ .15 


.151 


13 


1 .963 














4- 455 


491 


43 


21.099 



The values of r are first transformed to z, with the use of 
Appendix Table IV. Each value of z is multiplied by N 3 
and added to obtain 21.099. Dividing 21.099 by the sum of 
N 3, or 43, gives .491 as the average value of z. This is then 
transformed to r by means of Appendix Table IV to give an 
average correlation coefficient of +.455. The standard error 
of r = +.455 will be l/\/43 or .152. The accuracy of this 
average correlation is equivalent to a single test involving 
43 + 3 = 46 pairs of observations. This average correlation 
is highly significant. 

Before averaging correlation coefficients, it would be desirable 
to test whether they are homogeneous, i.e., whether it can be 
assumed that they could have arisen from a population with the 
mean correlation coefficient through errors of random sampling. 

The procedure in making such a test has been given by Rider 
(1939). The computations are carried through in Table 56 7 
with the use of data given in Table 55, 



CORRELATION AND REGRESSION 333 

TABLE 56. TEST FOB HOMOGENEITY OF COBBELATION COEFFICIENTS 



Years correlated 


r 


z 


N - 3 


(N - 3)2 


(N - 3)z 2 


1927-1928 


-f 81 


1.127 


8 


9.016 


10.161 


1929-1930 


+ .43 


0.460 


22 


10.120 


4.655 


1931-1932 . . . 


+ 15 


151 


13 


1.963 


0.296 














Sum 






43 


21.099 


15 112 















Homogeneity of z can be tested by means of the % 2 test, where 



X 2 = S(N - 3)z 2 - 
for 



- 15.112 - 



S(N - 3) ~ "'"~ 43 

k 1 = 2 degrees of freedom, 



_ 4.759 



where k = number of correlation coefficients. 
In this problem, % 2 does not reach the 5 per cent point of 5.99 
(Appendix Table III) for 2 degrees of freedom. It may be con- 
cluded that these three correlation coefficients could have come 
from equally correlated populations, the mean of which was 
found previously to be r = +.455. 

PARTIAL CORRELATION 

An extension of the idea of correlation leads to its application to 
groups of more than two variables. Partial- and multiple- 
correlation coefficients then become of considerable interest. 
Frequently two characters are related because of a third variable 
that affects both. By means of partial correlation, the relation- 
ship between two variables may be determined when the effect 
of other variables is eliminated. 

High-yielding varieties of grain of high quality are two of the 
major objectives in crop improvement. Resistance to disease 
is of major importance, also, if the disease affects the yield or 
quality of the crop. In order to plan the breeding program, it 
is necessary that the plant breeder have a knowledge of the 
characters that are of greatest value under particular environ- 
mental conditions and the interrelationships between them. 
In determining the interrelationships between a number of 
characters, the method of partial correlation is useful in deter- 
mining the relationship between two characters independent of 
the accompanying variation due to the other variables. 



334 



METHODS OF PLANT BREEDING 



TABLE 57. MEAN YIELD, PLUMPNESS OF KERNEL, DATE HEADING, AND 
CROWN-RUST PERCENTAGE IN ROD-ROW TRIALS WITH OATS 



Variety or strain. 


Nursery 
stock 
number 


Yield 


Plump- 
ness 


Date 
heading 


Crown 

rust 


Victory 


514 


36.5 


3 


7-11 


14 


Minota . .... 


512 


38 


9 


7-11 


17 


Miriota X White Russian 


11-18-37 


60.2 


58 


7-7 


11 


Black Mesdag 




40.2 


13 


7-3 


65 


Double Cross ... 


11-22-35 


36.3 


17 


7-8 


30 


Double Cross 


11-22-36 


40.0 


15 


7-6 


38 


Double Cross . 


11-22-37 


51.8 


43 


7-6 


25 


Double Cross 


11-22-38 


57 3 


28 


7-7 


10 


Double Cross 


11-22-39 


40 6* 


5 


7-6 


60 


Double Cross . .... 


11-22-40 


49.0 


12 


7-5 


60 


Double Cross 


11-22-41 


43.8 


7 


7-5 


57 


Double Cross 


11-22-42 


39.4 


7 


7-5 


60 


Double Cross . . 


11-22-43 


48.5 


13 


7-4 


40 


Double Cross 


11-22-44 


40.7 


2 


7-6 


50 


Double Cross . 


11-22-45 


48.7 


37 


7-4 


28 


Double Cross . 


11-22-46 


51.0 


28 


7-5 


20 


Double Cross 


11-22-47 


40.8 


5 


7-5 


40 


Double Cross 


11-22-48 


38 5 


7 


7-7 


33 


Double Cross. ... 


11-22-49 


40.1 


10 


7-7 


23 


Double Cross 
Double Cross 
Double Cross 
Double Cross 
Double Cross 


11-22-50 
11-22-51 
11-22-52 
11-22-53 
11-22-54 


59.7 
45.7 
33.0 
49 5 
53.9 


30 
5 
7 
48 
37 


7-5 
7-7 
7-7 
7-3 
7-3 


8 
20 
40 
43 
65 


Double Cross 


11-22-55 


54 4* 


50 


7-3 


63 


Double Cross .... 
Double Cross 
Double Cross 


11-22-56 
11-22-57 
11-22-58 


37.2 
40 5 

48.8 


32 
25 
32 


7-4 
7-5 
7-3 


50 
38 
60 


Double Cross 


11-22-59 


47 6 


15 


7-4 


53 


Double Cross .... 


11-22-60 


51.1 


23 


7-4 


50 


Double Cross ... ... 


11-22-61 


53.4 


23 


7-4 


53 


Double Cross 
Double Cross 


11-22-62 
11-22-63 


55.9 
54 . 9 


52 
55 


7-4 
7-4 


27 
18 


Double Cross 


11-22-64 


46.2 


15 


7-3 


47 


Double Cross 


11-22-65 


49 3 


10 


7-3 


30 


Double Cross ... 


11-22-66 


46.4 


35 


7-3 


33 


Double Cross 


11-22-67 


54.4 


23 


7-4 


35 


Double Cross 


11-22-68 


52.1 


23 


7-5 


20 


Double Cross 


11-22-69 


70 5 


67 


7-3 


15 


Double Cross 


11-22-70 


72 9 


67 


7-3 


25 


Double Cross 


11-22-71 


21 2 


7 


7-7 


40 


Double Cross 


11-22-72 


24 6 





7-10 


30 




11-22-73 


53.2 


57 


7-3 


37 


Double Cross 


11-22-74 


50,9 


17 


7-5 


37 


Double Cross 


11-22-75 


61.7 


30 


7-5 


15 




11-22-76 


53.4 


12 


7-7 


12 


Double Cross 


11-22-77 


43.1 


22 


7-4 


25 


Double Cross. 


11-22-78 


54.7 


13 


7-6 


15 


Double Cross. * . . . . , 


11-22-79 


57.2 


47 


7-5 


7 


Double Cross 


11-22-80 


38 8 


10 


7-4 


37 















* Grown in two plots. 



CORRELATION AND REGRESSION 



335 



An illustration of the methods of computation will be made 
with data collected at University Farm, St. Paul, Minnesota, 
from rod-row trials of oats, where three plots of each variety 
or strain were grown and the average of the three replications 
was used. Yield was expressed in bushels per acre, plumpness 
of grain was a visual note taken as a percentage, and the amount 
of crown rust was determined in percentage* 

Plumpness of grain in small grains has been found to be 
directly correlated with yield. Frequently yield is associated 
with earliness. Both yield and plumpness of grain are influenced 
to a considerable extent by rust. By means of partial correla- 
tion, it was possible to determine the degree of association 
between yield and plumpness when the effect of differences in 
rust reaction was eliminated. Data to illustrate the computa- 
tion of partial-correlation coefficients are given in Table 57. 

For a more complete description of partial- and multiple- 
correlation methods, the reader may be referred to Wallace and 
Snedecor (1931). 

In the methods to be given, the first step is the calculation of 
the simple, or total, correlation coefficients. For convenience 
of presentation, the following symbols will be used: 
A = yield in bushel per acre. 
B = plumpness of kernel. 
C = date of heading. 
D = percentage infection with crown rust. 

The total correlation coefficients for all possible relationships 
between these four variables are given in Table 58. 

TABLE 58. TOTAL CORRELATION COEFFICIENTS FOR ALL INTERRELATION- 
SHIPS BETWEEN YIELD, PLUMPNESS, DATE OF HEADING, AND PERCENT- 
AGE OF CROWN RUST 





A 


B 


C 


B 


4-. 7344* 






C 


-.4898* 


-.4968* 




D. 


-.31951 


- . 2320 


.4012* 











* Exceeds the 1 per cent level of significance, 
t Exceeds the 5 per cent level of significance. 

In this study, there were 50 pairs in the sample, and the degrees 
of freedom for testing the significance of a total-correlation 
coefficient would be N ~~ 2 or 48. If Appendix Table V is 



336 



METHODS OP PLANT BREEDING 



referred to, it is noted that all correlation coefficients except 
that between plumpness and crown-rust infection, TBD = .2320, 
exceeded the 5 per cent point and that all but this coefficient and 
r AD = .3195 exceeded the I per cent point. 

A simple method of calculating partial-correlation coefficients 
will be illustrated in detail. The partial-correlation coefficients 
will be calculated from the standard parti al-regression coeffi- 
cients by utilizing the fact that r 12.34 = \/fin-u X ^21-34, where 
7*12. 34 means the correlation between variables 1 and 2 with 3 and 4 
eliminated and /3i 2 . 34 and 21.34 are the standard regression coeffi- 
cients. These regression coefficients are calculated by solving 
sets of normal equations as illustrated in Table 59. 

TABLE 59. SOLUTION OF NORMAL EQUATIONS TO OBTAIN STANDAKD 
PARTIAL- REGRESSION ( ^EFFICIENTS 





Line 


D 


C 


B 


A 


Sum 


Enter TDD roc, TDB, TDA D. 
Change signs 


1 

2 


1.0000 
1 . 0000 


- .4012 
+ .4012 


~ .2320 
+ .2320 


-.3195 
+ .3195 


+ .0473 


















3 




1 . 0000 


- .4968 


. 4898 


.3878 


Multiply line 1 by 2.C 


4 




- .1610 


.0931 


. 1282 


+ .0190 


Add lines 3 and 4 
Divide line 5 by 5.C, and change 
signs 


5 
G 




+ -8390 
1 0000 


- .5899 
+ 7031 


-.6180 
+ 7366 


- .3688 
+ 4397 / 
















Enter TBS TBA. . . B, 


7 






1 0000 


+ 7344 


+ 1 0056 


Multiply line 1 by 2.B . . 


8 






0538 


0741 


+ 0110 


Multiply line 5 by 6.B 


9 






- .4148 


.4345 


. 2593 


Add lines 7, 8, and 9 ... 


10 






+ .5314 


+ . 2258 


+ 7573 


Divide line 10 by 10. B, and 


11 






- 1 . 0000 


.4249 


-1. 4251V 
















PAB.CD - +.4249 


I 






-h .4249 


+ .4249 




PAC.BD -.4379 


II 




- .4379 


+ .2987 


- . 7366 




PAD.BC .3966 


III 


- .3966 


- .1757 


+ .0986 


-.3195 





NOTU: In the instructions 2. (7 represents +.4012 in line 2, column C, etc. 



First the correlation coefficients are entered 
added to obtain the sum. The correlation 
obtain the sum for line 3, in the table, add the 
coefficients in this line plus TCD. The sum for 
of the total correlations in this line plus r B c and 
directed in the instructions for each line, 1 to 
The "sum" column serves as a check for all 



in the table and 
of TDD =1. To 
three correlation 
line 7 is the sum 
TBD. Proceed as 
11, in the table, 
preceding work. 



CORRELATION AND REGRESSION 337 

The figures marked \/ must check, within rounding off of deci- 
mals, the sum of the figures in that line to the left of the sum 
column. 

To calculate the partial-regression coefficients, bring down the 
figures in column A, lines 11, G, and 2, in that order, and change 
signs to form I, II, and III, column A. Write figure in LA one 
column to the left. This is PAR- CD. Multiply I.fi by 6.fi and 
2.Bj and write down products under II.fi and III.fi, respectively. 
Thus, ( + .4249) X (+.7031) = +.2987 and (+.4249) X (+.2320) 
= +.0986. Add II. A and II.fi to obtain ILC. This is the par- 
tial-regression coefficient PAC.BD. Then multiply ILC by 2.C, or 
(-.4379) X ( + .4012) = -.1757, and record as III.C. Add 
III.A + III.fi + III.C to obtain III.D. This is the partial- 
regression coefficient PAD.BC. 

It is noted that in Table 59 the partial-regression coefficients 
with A as a dependent variable were determined. The rule is 
that the variable in the last column (if the column of sums is 
omitted) is the first term of the regression coefficients; the second 
term is that in the same vertical column. To obtain all possible 
partial-regression coefficients, each variable must, in turn, be 
placed in the last column and the set of normal equations solved 
anew. To save time, it is best to set up the columns so that the 
characters in the last two come in pairs, i.e., D, C, B, A ; D, C, A, fi 
and A, B, D, C; A, B, C, D. By so doing, part of the computa- 
tions from the first of a pair of characters can be copied off for 
the second. 

Through such calculations, &AB.OD = +.4249 and PBA.CD = 
+ .5102. The partial-correlation coefficient will be 



TAB. CD = VPAW.T/) X PBA.CD 

= V^249"X^5l02 = +.4656 

The significance of the partial-correlation coefficients may be 
determined by reference to Appendix Table V for N 4 or 
46 degrees of freedom. In general, the degrees of freedom are 
N p 2, where N is the number of observations and p is the 
number of variables eliminated. This amounts to the number of 
observations minus the number of variables. 

The more interesting partial-correlation coefficients are given 
with the total-correlation coefficients for comparison. 



338 METHODS OF PLANT BREEDING 

TAB - +.7344* TAB-CD - +.4656* 

TAC - -.4898* r^c.BD - -.4546* 

TAD - -.3195t r^.^c - -.4600* 

* Exceeds the 1 per cent point, 
t Exceeds the 6 per cent point. 

The partial correlation between yield and plumpness was highly 
significant even after the effects of date heading and amount o 
crown rust were eliminated. This strong relationship betweer 
yield and plumpness of grain may be made use of during th< 
segregating generations in a breeding program when yield tests 
are not practical. Selection may be made for plumpness o 
grain, if it is recognized that plumpness is strongly associatec 
with yield. The association between yield and date heading was 
of the same order of magnitude after plumpness and crown-rusl 
differences were eliminated as when these were not. The partia 
correlation between yield and percentage of crown rust was 
highly significant when the effect of date heading and plumpness 
of seed was eliminated. Apparently crown rust significantly 
reduced yields apart from the influence of plumpness of grain 
and date of heading. 

MULTIPLE CORRELATION 

The multiple-correlation coefficient measures the degree tc 
which the dependent variable is influenced by a series of othei 
factors studied. It may be calculated from the total-correlation 
coefficients and the standard partial-regression coefficients. The 
formula is 

R 2 A-BCD = (TAB X $AB-CD) + (TAG X &AC.BD) + (TAD X &AD-BC) 
By substituting the values of r and ft obtained in this problem 

&A.BCD = (.7344 X .4249) + (-.4898 X -.4379) 

+ (-.3195 X -.3966) = .6532 
R = .8082 

The significance of a multiple-correlation coefficient may be 
tested by using Appendix Table V for N 4 = 46 degrees ol 
freedom and entering the column for four variables. The 
multiple-correlation of R = .8082 was highly significant. Squar- 
ing this correlation coefficient gives 65 per cent as the percentage 
of the variability in yield accounted for by its association with 
plumpness of grain, date of heading, and percentage of crown rust, 



CHAPTER XXII 

MULTIPLE EXPERIMENTS, METHODS FOR TESTING A 

LARGE NUMBER OF VARIETIES, AND THE ANALYSIS 

OF DATA EXPRESSED AS PERCENTAGES 

MULTIPLE EXPERIMENTS IN RANDOMIZED BLOCKS 

The same 10 varieties of barley as those used in Chap. XX 
to illustrate the computations for a randomized-block trial at 
University Farm were tested also in five other stations in Minne- 
sota, namely, Waseca, Morris, Crookston, Grand Rapids, and 
Duluth. These tests were conducted in order to determine 
varietal adaptation in different regions of the state. Since 
studies of this nature will be of frequent occurrence in regional 
trials, it will be of interest to illustrate the methods of analysis 
that can be made. 

In Table 60 is given the yields of 5 of the 10 varieties of barley 
in each of 3 randomized blocks at each of 4 stations for each of 
2 years. Since the computations are designed only to illustrate 
the principles involved, the data are reduced from the more 
extended test actually made. The analysis of the data follows 
closely the method outlined by Immer, Hayes, and Powers (1934). 

The degrees of freedom for an individual test at one location in 
1 year would be keyed out as follows: 

Variation Due to Degrees of Freedom 

Blocks 2 

Varieties 4 

Error (blocks X varieties) 8 

Total 14 

For the complete analysis of all data combined, the degrees of 
freedom could be keyed out as given in the summary on page 341 . 

The key to the degrees of freedom on page 341 illustrates the 
analogy between the individual tests and the complete analysis 
for all data combined. It is to be noted that the degrees of 
freedom for blocks within tests, varieties Within tests, and error 

339 



340 



METHODS OF PLANT BREEDING 



TABLE 60. YIELDS OF FIVE VARIETIES OP BARLEY, REPLICATED THREE 
TIMES IN EACH OF FOUR LOCATIONS IN 1932 AND 1935 



Variety 


Block number 


Block number 


Sum 
for 
both 
years 


I 


II 


III 


Sum 


I 


II 


III 


Sum 


Manchuria . . . 
Glabron .... 
Velvet 


University Farm, 1932 


University Farm, 1935 


236.5 
248.4 
251.4 
304 
239.9 


19.7 
28,6 
20 3 
27,9 
22.3 


31.4 
38 3 
27.5 
40 
30.8 


29 6 
43 5 
32.6 
46 1 
31 1 


80.7 
110 4 
80 4 
114.0 
84.2 


45 5 
47.5 
54.2 
62 2 
47 4 


50 3 
41.1 
52.3 
53.1 
57 8 


60.0 
49.4 
64.5 

74.7 
50.5 


155.8 
138.0 
171 
190 
155.7 


Barbless 
Peatland . 


Sum 


118.8 


168 


182.9 


469.7 


256.8 


254 6 


299 1 


810 5 


1280.2 


Manchuria . . . 
Glabron 
Velvet 


Waseca, 1932 


Waseca, 1935 


40.8 
44 4 
44.6 
39 8 

71 5 


29.4 
34.9 
41.4 
39 2 
47 6 


30 2 
33.9 
26 2 
29 1 
55 4 


100.4 
113.2 
112.2 
108 1 
174.5 


53 9 

63.7 
53.9 
74.2 
51.1 


58 8 
61.1 
59 1 
75 6 
47 3 


47 7 
52.2 
56.4 
67.0 
45 


160.4 
177 
169.4 
216.8 
143 4 


260.8 
290.2 
281.6 
324 9 
317.9 


Barbless 
Peatland 


Sum 


241.1 


192 5 


174 8 


608.4 


296.8 


301 9 


268.3 


867 


1475.4 


Manchuria .... 
Glabron 


Crookston, 1932 


Crookston, 1935 


34.7 

28.8 
29 8 
27.7 
43 


29.1 

28.7 
38 4 
27 6 
32 7 


35.1 
21.0 
28.0 
20.4 
32.0 


98.9 
78.5 
96 2 
75.7 
107.7 


42.1 
38.8 
42.1 
44.3 
53.9 


47.1 
29.4 
40.0 
43 5 
51 8 


30 8 
30.5 
39.8 
47 7 
50 3 


120.0 
98 7 
121.9 
135.5 
156 


218.9 
172.2 
218.1 
211.2 
263.7 


Velvet 


Barbless 


Peatland 


Sum 


164.0 


156.5 


136 5 


457.0 


221.2 


211 8 


199.1 


632.1 


1089.1 


Manchuria .... 
Glabron . . 


Grand Rapids, 1932 


Grand Rapids, 1935 


20.2 
13 2 

24.5 
19.0 
27 6 


30 2 
20.5 
41 6 
18.4 
30.0 


16.0 
9.6 
30.6 
24 6 
22 7 


66.4 
43 3 
96.7 
62.0 
80.3 


26.6 
21.4 
20.7 
20.7 
32.6 


26.5 
18 7 
26 8 
23 6 
40.0 


32.7 
24.1 
30 4 
30,9 
34 2 


85.8 
64.2 
77.9 
75.2 
106.8 


152.2 
107.5 
174.6 
137.2 
187.1 


Velvet 


Barbless 


Peatland 


Sum 


104.5 
628.4 


140.7 

657.7 


103.5 
597.7 


348.7 
1883.8 


122.0 
896.8 


135.6 
903.9 


152 3 
918.8 


409.9 
2719.5 


758.6 
4603.3 


Sum of 4 
stations . 



MULTIPLE EXPERIMENTS 341 

are the product of the degrees of freedom in a single test multi- 
plied by the number of tests. 

Degrees of 
Variation Due to Freedom 

Between tests 7 

Stations 3 

Years 1 

Stations X years 3 

Between blocks within tests 16 

Blocks 2 

Blocks X stations 6 

Blocks X years 2 

Blocks X stations X years 6 

Between varieties within tests 32 

Varieties 4 

Varieties X stations 12 

Varieties X years 4 

Varieties X stations X years 12 

Error within tests 64 

Blocks X varieties 8 

Blocks X varieties X stations 24 

Blocks X varieties X years 8 

Blocks X varieties X stations X years 24 

Total Tl9 

The degrees of freedom for the main effects, such as stations, 
years, blocks, and varieties, are 1 less than the number of sta- 
tions, years, blocks, or varieties, respectively. The degrees of 
freedom for the interactions are the product of the degrees of 
freedom for the main effects involved. 

Once the degrees of freedom are keyed out, the calculation of 
the sums of squares must be made in accordance with this plan. 
Before proceeding with the complete analysis, it will be well to 
test the errors of the eight separate tests for homogeneity in 
order to .determine whether they may legitimately be combined 
into a single analysis with a single error. In Table 61 are given 
the sums of squares calculated separately for each of the eight 
tests. 

The % 2 (Chi-square) distribution can be used as an approximate 
test of the homogeneity of several estimates of variance. The 
method proposed by Bartlett (1937) will be used to determine 
whether the variances calculated for the separate tests can be 
considered homogeneous, i.e., whether they can be considered 
random sampling deviates from the mean of these variances. 



342 



METHODS OF PLANT BREEDING 



The formula for x 2 will be x 2 = -^ [n log e s 2 S(n r log c s*)} for 

o 

fc 1 degrees of freedom, where k is the number of variances 
being compared, n r is the degrees of freedom of each variance, 
n is the total degrees of freedom for the separate variances and 

TABLE 61. SUMS OP SQUARES CALCULATED FOR THE SEPARATE TESTS 



Station and year of test 


Sums of squares for 


Total 


Blocks 


Varieties 


Error 


University Farm, 1932 
University Farm, 1935... 
Waseca 1932 


867 30 
1031 71 
1907 14 
1203.56 
487 87 
807 84 
905 56 
509 91 


450 10 
251 62 
471.40 
131 15 
80 83 
49 21 
179.69 
92 13 


375 . 61 
506 36 
1196 33 
993.84 
252 62 
595.82 
536.17 
336 46 


41 59 
273 73 
239 41 

78.57 
154 42 
162.81 
189.70 
81.32 


Waseca, 1935 


Crookstoii, 1932 


Crookston 1935 


Grand Rapids, 1932 


Grand Rapids, 1935 


Sura 


7720 89 


1706 13 


4793 21 


1221.55 



TABLE 62. CALCULATION OF % 2 TEST FOR HOMOGENEITY OF VARIANCES 





Degrees 










Station and year 
of test 


of free- 
dom in 


Lrror 
variance 
of each 


log, si 


n r sl 


n r log, s 2 r 




each 














test, s 2 










test, n r 










University Farm, 1932 


8 


5.20 



1 6487 






University Farm, 1935 


8 


34 22 


3 5328 






Waseca, 1932 


8 


29 93 


3 3989 






Waseca, 1935 


8 


9.82 


2 2844 






Crookston, 1932 


8 


19.30 


2 9601 






Crookston, 1935 


8 


20.35 


3.0131 






Grand Rapids, 1932. . 


8 


23.71 


3 1659 






Grand Rapids, 1935. . 


8 


10 16 


2 3184 






Sum 


64 


152.69 


22 . 3223 


1221.52 


178 5784 















S(n r ), s? refers to the individual variances, s 2 the pooled variance 
calculated from S(n r s%)/n, and C is a correction term denned by 



C= 1 + 



3(* 



=D \ a Q-J - 



MULTIPLE EXPERIMENTS 343 

The estimated variances will be found by dividing the error 
sums of squares in Table 61 by 8 degrees of freedom. Table 62 
may be formed to illustrate the computations. 

Since the degrees of freedom are the same for each test, the 
sum of the products S(n r s*)j and S(n r log e s 2 -) ma 7 be calculated 
from the totals of columns 2, 3, and 4 in Table 62; otherwise each 
value of n r sl and n r log c s? would need to be calculated and the 
column added to obtain the sum. In this problem S(n r $l) = 
1221.52 is found by multiplying 152.69 by 8 and S(n r log e s?) = 
178.5784 is obtained by multiplying 22.3223 by 8. Since 

n = 64 

s2 = 122L52 

t>4 
n log, s 2 = 64 X 2.94891 = 188.7302 

c = i + Hi { (M + H + M + H + H + y s + y s + M) 

- 1^4! = 1-0469 

. 188.7302 - 178.5784 
X = - - = 9.70, tor? degrees ot ireedom. 

-L . 



Referring to the table of % 2 (Appendix Table III) for 7 degrees of 
freedom, we find that x 2 " 9.80 when P = .20. We may con- 
clude, therefore, that deviations between variances as great as 
these observed would occur more than 20 times in 100 through 
errors of random sampling. These 8 error variances may, there- 
fore, be considered homogeneous, and it will be legitimate to 
replace the 8 separate variances by their mean variance (19.09) 
in the analysis of variance of all data. 

The total yield of the 120 plots, as given in Table 60, was 

_ noo , ^ ... , ,_ [S(x)] 2 (4603.3) 2 

4603.3 bu. The correction term S(x)x = AT - = ~ = 

.A/ 1^0 

176,586.42. To obtain the total sum of squares, the squares of 
the individual plots are added to give S(x) 2 = 200,879.35, and 
the correction term S(x)x is subtracted to give 24,292.93. 

Several other tables need to be set up by adding the appropriate 
yields in Table 60. In Table 63 are given the total yields for 
each variety at each station by adding the yields for both years. 

The figures in Table 63 are taken directly from the right-hand 
margin of Table 60. They are assembled here for convenience, 
with the appropriate variety and station totals, 



344 



METHODS OF PLANT BREEDING 



In Table 64 are given the data for comparisons of varieties in 
different years, obtained by adding the yields at the four stations. 

TABLE 63. TOTAL YIELDS GROUPED FOR VARIETIES AND STATIONS 



Variety 


Station. 


Sum 


University 
Farm 


Waseca 


Crookston 


Grand 
Rapids 


Manchuria, . . . 


236.5 
248.4 
251.4 
304.0 
239 9 


260.8 
290.2 
281 6 
324.9 
317 9 


218 9 
177 2 
218.1 
211.2 
263 7 


152 2 
107.5 
174.6 
137.2 

187 1 


868.4 
823.3 
925.7 
977 3 
1008 6 


Glabroii 


Velvet 


Barbless . . 


Peatland 


Sum 


1280 2 


1475 4 


1089 1 


758 6 


4603 3 





TABLE 64. TOTAL YIELDS GROUPED FOR VARIETIES AND YEARS 



Variety 


Year 


Sum 


1932 


1935 


Manchuria 


346 4 
345 4 
385 5 
359 8 

446 7 


522.0 
477.9 
540.2 
617.5 
561.9 


868.4 
823 3 
925.7 
977 3 
1008 6 


Glabron . ... 


Velvet 


Barbless . . . 


Peatland 


Sum ... . ... 


1883 8 


2719.5 


4603 3 





In Table 65 are assembled the data- for comparisons of blocks 
and stations, obtained by adding the block totals for the 2 years 
of each station. 

TABLE 65. TOTAL YIELDS OF BLOCKS AND STATIONS 



Block 


Station 


Sum 


University 
Farm 


Waseca 


Crookston 


Grand 
Rapids 


I 


375.6 

422.6 
482.0 


537.9 
494.4 
443.1 


385.2 
368 3 
335.6 


226 5 
276.3 
255.8 


1525.2 
1561.6 
1516.5 


II 


Ill 


Sum 


1280.2 


1475 4 


1089 1 


758.6 


4603.3 



MULTIPLE EXPERIMENTS 



345 



In Table 66 are the totals for comparison of blocks and years. 
This table is assembled from the totals at the bottom of Table 60. 

TABLE 66. TOTAL YIELDS OF BLOCKS AND YEARS 



Tllrknlr 


Yc 


jar 


Qnrr 




1932 


1935 




I 


628 4 


896 8 


1525 2 


II 


657.7 


903.9 


1561 6 


Ill 


597 7 


918 8 


1516.5 


Sum 


1883.8 


2719.5 


4603 3 











One other table is necessary, that of stations and years. This 
is given as Table 67. The figures for this comparison are assem- 
bled here for convenience, also, but could have been found 
directly in Table 60. 

TABLE 67. TOTAL YIELDS OF STATIONS AND YEARS 



Year 


Station 


Sum 


University 
Farm 


Waseca 


Crooks ton 


Grand 
Rapids 


1932 


469.7 
810.5 


608.4 
867.0 


457.0 
632.1 


348.7 
409 9 


1883.8 
2719.5 


1935 .... 


Sum 


1280.2 


1475.4 


1089.1 


758.6 


4603 3 





The calculation of the sums of squares for the complete analysis 
can be performed with the least difficulty and confusion if the 
steps are carried through in a routine manner. Many of the 
calculations are given in Table 68. The remainder follow easily 
and logically. 

In Table 68, x is used to designate the individual plots and 
x 8 , x v , x vj and Xb, the total yields for each station, year, variety, 
and block, respectively. The symbols x V8 , x vy , etc., refer to the 
totals for each variety at each station, each variety each year, 
etc., as found within Tables 63 to 67. The symbol x vsy refers to 
the total yield of each variety at each station for a single year. 

Column 2 of Table 68 gives the number of figures squared in 
calculating column 1, and column 3 gives the number of plots 



346 



METHODS OF PLANT BREEDING 



in each figure squared. Column 4 is necessary to reduce the 
sums of squares to a single-plot basis. Column 6 gives the sums 
of squares, and column 7 the degrees of freedom. 

TABLE 68. CALCULATION OF SUMS OF SQUARES 









Num- 










Variate 


Total of 
squares 


Num- 
ber of 
figures 
squar- 


ber of 
plots 
in each 
figure 




Correc- 
tion 
term 
S(x)x 


Sum of 
squares 


De- 
grees 
of free- 
dom 






ed 


squar- 
















ed 


(4 = 




(6 - 






(1) 


(2) 


(3) 


1 -5- 3) 


(5) 


4-5) 


(7) 


8(x*) 


200,879.35 


120 


1 


200,879.35 


176,586.42 


24,242.93 


119 


S(xl) 


5,577,329.97 


4 


30 


185,911.00 


176,586.42 


9,324.58 


3 


S(xl) 


10,944,382.69 


2 


60 


182,406.38 


176,586.42 


5,819.96 


1 


8(xl) 


4,261,251.19 


5 


24 


177,552.13 


176,586.42 


965.71 


4 


S(x%) 


7,064,601.85 


3 


40 


176,615.05 


176,586.42 


28.63 


2 


S(xl a ) 


1,129,020.73 


20 


6 


188,170.12 


176,586.42 


11,583.70 


19 


S(xl v ) 


2,206,627.61 


10 


12 


183,885.63 


176,586.42 


7,299.21 


9 


S(xl s ) 


1,871,824.37 


12 


10 


187,182.44 


176,586.42 


10,596.02 


11 


S(xl y ) 


3,650,180.03 


6 


20 


182,509.00 


176,586.42 


5,922.58 


5 


S(x' 2 8y ) 


2,897,377.01 


8 


15 


193,158.47 


176,586.42 


16,572.05 


7 


S(xl av ) 


974,322.93 


24 


5 


194,864.59 


176,586.42 


18,278.17 


23 


S(xl 8V ) 


593,855.03 


40 


3 


197,951.68 


176,586.42 


21,365.26 


39 



The sums of squares for the first-order interactions are obtained 
by subtracting from the sum of squares for the two variables in 
Table 68 the sums of squares for the two main effects. For 
example, the sum of squares for the interaction of varieties X sta- 
tions will be given by the sum of squares for x\ 9 in Table 68 
minus the sum of squares for the main effects of varieties and 
stations x\ and x%. Numerically, this will be: 



Sum of Squares 
11,583.70 

- 965.71 

- 9,324.58 



Degrees of Freedom 
19 

4 (varieties) 
3 (stations) 



1,293 41 12 (varieties X stations) 

The second-order interaction of varieties X stations X years, 
for example, is obtained by subtracting from the sum of squares 
opposite S(xl 8y ) in Table 68 the sums of squares for varieties, 
stations, years, and all possible first-order interactions. Thus: 



MULTIPLE EXPERIMENTS 



347 



Sum of Squares 
21,365.26 

- 965.71 

- 9,324.58 

- 5,819.96 

- 1,293.41 

- 513 54 

- 3,427.51 
2,020.55 



Degrees of Freedom 
39 

4 (varieties) 

3 (stations) 
1 (years) 

12 (varieties X stations) 

4 (varieties X years) 
3 (stations X years) 

12 (varieties X stations X years) 



The complete analysis of variance is now carried through in 
Table 69, the error sum of squares being obtained as a remainder. 
TABLE 69. COMPLETE ANALYSIS OF VARIANCE 



Variation due to 


Degrees 
of freedom 


Sum of 
squares 


Mean 
square 


s 


F 


Stations 


3 

1 
3 
2 

6 
2 

6 

4 
12 
4 
12 
64 


9,324 58 
5,819.96 
1,427 51 
28.63 
1,242 81 
73 99 
360.69 
965 71 
1,293 41 
513 54 
2,020 55 
1,221 55 


3108 19 
5819 96 
475.84 
14 32 
207 14 
37.00 
60 12 
241 43 
107.78 
128 39 
168 38 
19.09 


4.37 


162.82* 
304.87* 
24.93* 

10 85* 
1 94 
3.15* 
12.65* 
5.65* 
6.73* 
8.82* 


Years 


Stations X years 


Blocks 


Blocks X stations ... ..... 


Blocks X years 


Blocks X stations X years .... 
Varieties 


Varieties X stations 


Varieties X years 


Varieties X stations X years. 
Error 


Total 


119 


24,292.93 











* Exceeds the 1 per cent level of significance when compared with error mean square. 

The structure of the complete analysis of variance becomes 
clear when it is compared with the separate analyses of variance 
of the single tests. The sum of squares for error in Table 69 is 
the same as for the sum of all tests calculated separately in 
Table 61. The error mean square in the complete analysis is, 
then, the average of the eight individual error mean squares 
calculated separately in Table 62. Thus, 152.69 -5- 8 = 19.09, 
the mean square for error given in Table 62. Adding the sum 
of squares for varieties, varieties X stations, varieties X years, 
and varieties X stations X years in Table 69 gives 4793.21. 
This agrees with 4793.21 obtained as the sum of the sums of 
squares for varieties within tests given in Table 61. A similar 
comparison holds for blocks. 



348 



METHODS OF PLANT BREEDING 



The manner in which the data can be interpreted will now be 
illustrated. From Table 69, it is seen that the mean square for 
varieties, varieties X stations, varieties X years, and varie- 
ties X stations X years, compared with error mean square, 
exceeded the 1 per cent point. It is plain, therefore, that there 
were significant differences in average yielding ability and that 
some varieties reacted in a differential manner at some stations 
and in some years. 

A summary of the mean yields of the five varieties for 1932 
and 1935 at each of the four stations is given in Table 70. The 
varieties are listed in the order of average yield at all stations. 

TABLE 70. MEAN YIELD OF FIVE VARIETIES OF BAKLEY FOB 1932 AND 1935 
AT EACH OF FOUR STATIONS AND THEIR AVERAGE YIELD AT ALL 

STATIONS 



Variety 


Station 


Average 


University 
Farm 


Waseea 


Crookston 


Grand 
Rapids 


Peatland 


40.0 
50.7 
41.9 
39.4 
41.4 


53.0 
54.2 
46.9 
43.5 

48.4 


44.0 
35.2 
36.4 
36.5 
29.5 


31.2 
22.9 
29.1 
25.4 
17.9 


42.0 
40.7 
38.6 
36.2 
34.3 


Barbless 


Velvet 


Manchuria 


Glabron 





The standard error of a single plot (Table 69) was 4.37 bu. 
Since 24 plots were involved in the variety averages for all sta- 
tions and both years, the standard error of the mean of 24 plots 
would be 4.37/\/24 = 0.89 bu., and the standard error of a differ- 
ence between two variety means would be 0.89 \/2 = 1.26 bu. 

A formula frequently used to obtain the standard error of an 

average of several tests is 1/JV" \/sl 4~ s| + &c + * " " > where N 
is the number of tests and sj, s|, etc., are the variances for error 
of the separate tests. If the variances of the mean of three plots 
were calculated for each of the eight tests by dividing each of the 
error variances, given as si in Table 62, by 3, the standard error 
of the average of all tests would be 



i.20 + 34.22 + 



10.16 



= 0.89 bu., the same as calcu-* 



lated in the preceding paragraph. 



MULTIPLE EXPERIMENTS 349 

With 64 degrees of freedom for error, t 2 at the 5 per cent 
level of significance. If twice the standard error of the difference 
between two means as a minimum level of significance is accepted, 
it may be said that differences in excess of 2 X 1.26 = 2.52 bu. 
would be judged as probably significant. On this basis, Velvet, 
Manchuria, and Glabron would be significantly lower in yield 
than Peatland. Manchuria and Glabron would be significantly 
lower in yield than Barbless. Manchuria and Glabron were 
lowest in yield, and the difference between them was not 
significant. 

The mean square for varieties X stations was significantly 
greater than the mean square for error. It is apparent that some 
varieties reacted in a differential manner at certain stations, A 
first-order interaction involves the difference between two differ- 
ences. The mean yield of Barbless at University Farm, for 
an average of both years, exceeded that of Peatland by 50.7 
40.0 = 10.7 bu. per acre. At Grand Rapids, however, the differ- 
ence between these two varieties was 31.2 22.9 = 8.3 bu. in 
favor of Peatland. The question arises whether these two differ- 
ences are significantly different. This difference between two 
differences will be (50.7 - 40.0) - (22.9 - 31.2) = 19.0 bu. 
Since six plots were involved in each mean being compared, the 

standard error of the cross difference will be ^ \/2 \/2 = 3.57 

V6 

bu. Twice this is 7.14 bu., and any "cross difference " exceeding 
this value is*expected to occur less than once in 20 trials by 
random sampling alone. It is clear, therefore, that the yields of 
the varieties Barbless and Peatland were differential at Uni- 
versity Farm and Grand Rapids. Other differential responses 
can be found also in Table 70. Extensive testing of these and 
other standard varieties of barley in Minnesota for a long period 
of years has shown Peatland to be better adapted at Grand 
Rapids than at any other experiment station in the state. From 
data such as these, carried out at six stations in the state for a 
minimum period of 3 years, general recommendations regarding 
varieties are made to the farmers. In many instances, significant 
interactions of varieties and stations are obtained, and certain 
varieties are recommended only for certain- regions of the state. 
Significant interactions of some varieties in the 2 years could 
be found by applicatioB of the general procedure outli&ed above. 



350 METHODS OF PLANT BREEDING 

Interactions of varieties X years are of less interest to the plant 
breeder than interactions of varieties X stations. 

Although the second-order interaction of varieties X stations X 
years was significant also, this is of minor interest to the plant 
breeder. A significant second-order interaction means that cer- 
tain differential responses of two varieties at each of two stations 
was not the same in each of 2 years. 

For a complete understanding of an analysis of variance, of 
which that given in Table 69 is an example, one further com- 
parison can be set up. Letting V, S 7 and Y represent variances 
due to varieties, stations, and years, respectively, and V X S, 
V X Y, and V X S X Y the interaction variances, we may deter- 
mine whether variance due to 

V>VXS>VXSXY 

yerror 
V>VXY>VXSXY 7 

by means of the F test. The symbol > means "greater than." 
If variance due to varieties significantly exceeds the interaction 
of varieties X stations, we have evidence that varietal perform- 
ance generally was consistent enough to demonstrate that some 
varieties were the best in all stations, as an average of the years 
in which tests were made. If the variety variance significantly 
exceeds that of varieties X years, we may conclude that as an 
average of all stations some varieties were consistently better in 
yield in all years. 

Further, if the interaction of varieties X stations significantly 
exceeds varieties X stations X years, it is plain that the differ- 
ential responses of the varieties at the separate stations were 
sufficiently similar in the different years to warrant the conclusion 
that these differential responses may be permanent features of 
these localities. 

Unless the variance for varieties significantly exceeds that of 
varieties X stations, no general recommendation of a variety for 
the entire state can be made. Extensive tests in the region in 
which the varieties may be grown provide the only sound basis 
for recommendation over wide areas. 

COMPARISON OF VARIETIES IN DIFFERENT EXPERIMENTS, 
WHERE THE SAME CHECK VARIETIES ARE GROWN 

Frequently it may be desirable to compare the yields of varie- 
ties grown in different experiments, If the samQ check varieties 



SIMPLE LATTICE EXPERIMENTS 351 

have been included in the different experiments, comparisons of 
the new varieties may be made by comparing them through the 
checks. Thus, if A and B are the yields of two varieties in 
different experiments and the same check (cK) has been included 
in each test, the relative difference in yield between A and B will 
be given by (A chi) (B c/i 2 ), where chi and c/i 2 are the 
yields of the checks in the experiments involving A and J9, 
respectively. 

The standard error of the foregoing difference will be 
\/2s\ + 2sf, where s\ and s\ are the variance of the mean for the 
two tests. 

If more than one check variety has been included in each test, 
comparisons may be made of (A - ch\) (B ch%), where chi 
and c/?2 are the means of the several checks. The standard error 
of this difference will be 



where sf and sf = variance of the mean for a single variety in 

experiments 1 and 2. 
N = number of checks used in each experiment. 

SIMPLE LATTICE EXPERIMENTS 

When the number of varieties to be tested is small, the random- 
ized block or Latin-square designs provide an efficient method for 
testing the significance of varietal differences. As the number 
of varieties becomes large, the randornized-block design with all 
varieties in the same block becomes less efficient because of 
increasing soil heterogeneity within blocks. The Latin-square 
design for large numbers of varieties cannot be used because of 
the prohibitive number of replications required. 

Yates (1936) suggested a modification of the complete block 
design whereby the number of varieties in a block was less than 
the total number to be tested. The error could then be calcu- 
lated from the variation within the small, or incomplete, blocks 
and would be lower, usually, than the error calculated from 
randomized complete blocks. The methods of analysis appropri- 
ate for such designs have been given by Yates (1936) and Goulden 
(1937, 1939). In these analyses some information about varietal 
difference was lost. As a result, these incomplete block designs 



352 



METHODS OF PLANT BREEDING 



could be less efficient than ordinary randomized complete blocks 
if the soil were relatively homogeneous. Recently Yates (1939) 
and Cox, Eckhardt, and Cochran (1940) have shown how all the 
information regarding differences between varieties in different 
incomplete blocks could be recovered. As a consequence, these 
designs can never be appreciably less efficient than ordinary 
randomized blocks containing the total number of varieties and 
will be considerably more accurate if there is a reduction in the 
error through the use of the small, or incomplete, blocks. 

TABLE 71. RANDOM; ARRANGEMENT OF VARIETIES IN LATTICE EXPERIMENT 

Replication 1 (Group X) Replication 2 (Group Y) 

Block Block 



(1) 


10 


7 


6 


8 


9 


(2) 


14 


13 


11 


15 


12 


(3) 


2 


4 


5 


3 


1 


(4) 


25 


24 


23 


21 


22 


(5) 


18 


16 


17 


20 


19 



(6) 


15 


5 


10 


20 


25 


(7) 


16 


6 


21 


11 


1 


(8) 


2 


17 


7 


22 


12 


(9) 


23 


3 


13 


18 


8 


(10) 


24 


4 


14 


19 


9 



Replication 3 (Group X) 



Block 



Replication 4 (Group Y) 
Block 



(11) 


8 


9 


10 


6 


7 


(12) 


23 


21 


24 


25 


22 


(13) 


12 


14 


11 


13 


15 


(14) 


16 


19 


20 


17 


18 


(15) 


3 


4 


5 


1 


2 



(16) 


13 


8 


3 


23 


18 


(17) 


2 


22 


12 


17 


7 


(18) 


19 


14 


9 


24 


4 


(19) 


21 


11 


16 


1 


6 


(20) 


10 


15 


20 


5 


25 



The design and computation of the data for a lattice 1 experi- 
ment will be illustrated using uniformity trial data given by 
Wiebe (1935). It was assumed that 25 varieties grown in three- 
row plots and the central row harvested were to be tested, with 
four replications. The method of computation will follow 
closely that given by Cox, Eckhardt, and Cochran (1940). 

In the lattice experiments described here, the number of 
varieties is a perfect square. The number of varieties, v = Jfc 2 , 
are tested in incomplete blocks of k varieties each. The varieties 

1 Certain of the lattice designs have been referred to as pseudofactorial 
arrangements in two equal groups of sets, as two-dimensional pseudofactorial 
arrangements with two equal groups of sets, and as two-dimensional quasi- 
factorial desigp in randomized blocks in two equal groups of sets. 



SIMPLE LATTICE EXPERIMENTS 



353 



may be identified by numbers arranged in a square, as follows, 
with the use of k z = 25 varieties : 

12345 

6 7 8 9 10 
11 12 13 14 15 
16 17 18 19 20 
21 22 23 24 25 

TABLE 72. YIELDS OF VARIETIES IN GRAMS PER ROD Row 

Replication 1 (Group X) 
Block Block totals 





1 


2 


3 


4 


5 




(3) 


635 


525 


555 


650 


635 


3,000 




6 


7 


8 


9 


10 




(1) 


495 


730 


810 


775 


710 


3,520 




11 


12 


13 


14 


15 




(2) 


630 


600 


645 


635 


645 


3,155 




16 


17 


18 


19 


20 




(5) 


735 


690 


840 


855 


805 


3,925 




21 


22 


23 


24 


25 




(4) 


620 


795 


590 


660 


615 


3,280 














16,880 



Block 



Replication 2 (Group Y) 



Block totals 





1 


6 


11 


16 


21 




(7) 


530 


490 


595 


495 


540 


2,650 




2 


7 


12 


17 


22 




(8) 


610 


660 


620 


695 


570 


3,155 




3 


8 


13 


18 


23 




(9) 


705 


850 


675 


685 


640 


3,555 




4 


9 


14 


19 


24 




(10) 


840 


905 


785 


860 


875 


4,265 




5 


10 


15 


20 


25 




(6) 


670 


455 


655 


665 


615 


3,060 














16,685 



354 



METHODS OF PLANT BREEDING 



TABLE 72. YIELDS OF VARIETIES IN GRAMS PER HOD Row. (Continued) 

Replication 3 (Group X) 
Block Block totals 





1 


2 


3 


4 


5 




(15) 


635 


700 


640 


640 


645 


3,260 




6 


7 


8 


9 


10 




(ID 


570 


545 


675 


580 


470 


2,840 




11 


12 


13 


14 


15 




(13) 


550 


515 


450 


550 


495 


2,560 




16 


17 


18 


19 


20 




(14) 


505 


620 


700 


570 


575 


2,970 




21 


22 


23 


24 


25 




(12) 


445 


455 


445 


465 


515 


2,325 














13,955 



Block 



Replication 4 (Group F) 



Block totals 





1 


6 


11 


16 


21 




(19) 


550 


655 


545 


515 


550 


2,815 




2 


7 


12 


17 


22 




(17) 


455 


425 


460 


470 


440 


2,250 




3 


8 


13 


18 


23 




(16) 


445 


545 


700 


530 


525 


2,745 




4 


9 


14 


19 


24 




(18) 


510 


525 


515 


395 


425 


2,370 




5 


10 


15 


20 


25 




(20) 


540 


575 


610 


510 


615 


2,850 














13,030 



These 25 varieties are arranged in incomplete blocks of k = 5 
varieties each. In one group, designated as J, the 5 varieties 
for each block are taken from a row of the foregoing square. In a 
second group, designated F, the varieties are taken from a column 
of the foregoing square. The order of the 5 rows, or columns, is 
randomized, and the 5 varieties within each row or column are 



SIMPLE LATTICE EXPERIMENTS 



355 



TABLE 73. COMBINATION OF REPLICATIONS 
Group X (Replication 1 + Replication 3) 



Row totals 





1 


2 


3 


4 


5 






1270 


1225 


1195 


1290 


1280 


6,260 




6 


7 


8 


9 


10 






1065 


1275 


1485 


1355 


1180 


6,360 




11 


12 


13 


14 


15 






1180 


1115 


1095 


1185 


1140 


5,715 




16 


17 


18 


19 


20 






1240 


1310 


1540 


1425 


1380 


6,895 




21 


22 


23 


24 


25 






1065 


1250 


1035 


1125 


1130 


5,605 


Column totals . 


5820 


6175 


6350 


6380 


6110 


30,835 



Group Y (Replication 2 -f Replication 4) 



Row totals 





1 
1080 


6 
1145 


11 
1140 


16 
1010 


21 
1090 


5,465 




2 

1065 


7 
1085 


12 
1080 


17 
1165 


22 

1010 


5,405 




3 
1150 


8 
1395 


13 
1375 


18 
1215 


23 

1165 


6,300 




4 
1350 


9 
1430 


14 
1300 


19 
1255 


24 
1300 


6,635 




5 
1210 


10 
1030 


15 
1265 


20 

1175 


25 
1230 


5,910 


Column totals 


5855 


6085 


6160 


5820 


5795 


29,715 



placed in random order. In Table 71 on page 352 is given the 
random arrangement of the 25 varieties in each of two replica- 
tions of the X and Y groups. 

Varieties 1, 2, 3, 4, and 5 fell in block 3 and again in block 15, 
both in group X. Varieties 1, 6, 11, 16, and 21 fell in blocks 7 
and 19 in group F. All 25 varieties are contained in each com- 
plete replication. 



356 



METHODS OF PLANT BREEDING 



The foregoing random arrangement of varieties was super- 
imposed on the plot yields, in grams per rod row, of Wiebe's 
(1935) data. The plot yields of each variety are given in 
Table 72, assembled according to rows and columns of the original 
square. The variety number is given above each plot yield. 

The data from both replications of groups X and F, for each 
variety, are added next and are given in Table 73. 

The sums of the yields of the two plots each for the X and Y 
groups are combined next to give the total yields of the four plots 
of each variety. These total yields of the varieties are given in 
Table 74, with appropriate row and column totals. 

TABLE 74. TOTAL YIELDS OF VARIETIES 

Row totals 





1 


2 


3 


4 


5 






2,350 


2,290 


2,345 


2,640 


2,490 


12,115 




6 


7 


8 


9 


10 






2,210 


2,360 


2,880 


2,785 


2,210 


12,445 




11 


12 


13 


14 


15 






2,320 


2,195 


2,470 


2,485 


2,405 


11,875 




16 


17 


18 


19 


20 






2,250 


2,475 


2,755 


2,680 


2,555 


12,715 




21 


22 


23 


24 


25 






2,155 


2,260 


2,200 


2,425 


2,360 


11,400 


Column totals 


11,285 


11,580 


12,650 


13,015 


12,020 


60,550 



The total sum of squares is found by adding the squares of 
the 100 plot yields in Table 72 to give 38,012,350 and subtracting 
the correction term (60,550) 2 /100 = 36,663,025 to give 1,349,325 
as the total sum of squares. 

The sum of squares for replications is calculated from the totals 
of the four complete replications, i.e., 

(16,880)' + (16,685) 2 + (13,955)' + (13,030)" _ 36)663)025 

2t& 

= 450,837 
The sum of squares for varieties (ignoring blocks) is calculated 



the variety totals in Table 74. Thus 
(2350)* + (2290)' + + (2360) 



SIMPLE LATTICE EXPERIMENTS 



357 



The sum of squares for blocks (eliminating varieties) is made 
up of two components as follows: 

Component a is calculated from the sum of squares of differ- 
ences between blocks containing identical varieties. These differ- 
ences are found by subtracting the block totals for the same 
group of varieties in replications 1 and 3 and in 2 and 4, taken 
from Table 72. These differences are given below. 



Set X 


Set F 


Replica- 


Replica- 


Differ- 


Replica- 


Replica- 


Differ- 


tion 1 


tion 3 


ence 


tion 2 


tion 4 


ence 


3,000 


3,260 


- 260 


2,650 


2,815 


- 165 


3,520 


2,840 


680 


3,155 


2,250 


905 


3,155 


2,560 


595 


3,555 


2,745 


810 


3,925 


2,970 


955 


4,265 


2,370 


1895 


3,280 


2,325 


955 


3,060 


2,850 


210 


16,880 


13,955 


2925 


16,685 


13,030 


3655 



The sum of squares of the deviations within these two sets of 
differences will give the sum of squares between paired blocks 
within sets. Thus 



(-260) 2 + 



(955) 2 + (-165) 2 



(210) 2 



10 



_ (2925)* + (3655)' = 



The divisors are 2k = 10 and 2k 2 = 50. 1 

Component b is obtained from two sets of differences giving 
estimates of block yields freed of varietal effects. In Table 73, 

1 For six replications, there would be three columns of block totals for 
each set. Component a would then be calculated from an analysis of 
variance for each set, the degrees of freedom for set X being as follows: 

Degrees 
of 

freedom 

Replications 2 

Set X totals k - 1 

Interaction, or component (a) 2(k 1) 

The same would be done for set F, and the degrees of freedom and sums of 
squares of both added to give the complete component a. 



358 METHODS OF PLANT BREEDING 

the row totals are the sums of two blocks of the same group of 
varieties. These row totals cannot be used to calculate block 
sum of squares, since they are confounded with (contain) varietal 
effects as well. The first row total in group X (Table 73), made 
up of the sums of the two blocks containing varieties 1, 2, 3, 4, 
and 5, comes to 6260. The first column total in group Y is 5855 
and is clearly an estimate of the varietal effects alone of the 
same five varieties, since each block in group F is equally repre- 
sented. The difference between these totals, 6260 5855 = 405, 
is an estimate of block effect freed of varietal differences. In a 
similar manner, the first row total in group F (Table 73) minus 
the first column total in group X, 5465 5820 = -355, is an 
estimate of block effect for blocks containing varieties 1, 6, 11, 
16, and 21. 

Since, however, it is easier to add than subtract in making 
adjustments to the average yields of the varieties, it is preferable 
to subtract the un confounded from the confounded totals and 
work with the negative values. Thus, 5855 6260 = 405 
and 5820 5465 = 355. These differences are designated rkc x 
and rkCy, where r is the number of replications and k the number 
of plots per block and c x and c y the mean corrections from the 
X and F groups, respectively. The rkc x values may be deter- 
mined also by subtracting from the row totals of Table 74 twice 
the row totals of group X in Table 73. Thus, 12, 1 15 - 2(6260) = 
405. The rkc y values are obtained by subtracting from the 
column totals in Table 74 twice the row totals for group F in 
Table 73. These values are given below: 

rkc x rkcy 



12,115 - 2(6260) - 405 11,285 - 2(5465) = 355 

12,445 - 2(6360) = - 275 11,580 - 2(5405) - 770 

11,875 - 2(5715) = 445 12,650 - 2(6300) = - 50 

12,715 - 2(6895) - -1075 13,015 - 2(6635) = -255 

11,400 - 2(5605) = 190 12,020 - 2(5910) - 200 

-1120 1120 



The sum of the rkc x and rkc y values will be 0. 

The sum of squares of deviations within sets of rkc x and rkc y 
will be an estimate of variance between blocks (eliminating 
varieties). Thus 



SIMPLE LATTICE EXPERIMENTS 
(-405)'+ + (190) 2 + (355) 2 + + (200) 2 



359 



20 



QQ 



(1120)' _ 

- 97,705 



The divisors will be rk = 20 and rk 2 = 100. 

The analysis of variance table may now be set up. This is 
given in Table 75. 

TABLE 75. ANALYSIS OF VARIANCE OF LATTICE EXPERIMENT 



Variation due to 


Degrees of 
freedom 


Sum of squares 


Mean square 


Replications . . 




3 

16 

24 

56 




450,837 


150,279 00 
43,282.75 
12,213.12 

27,747.94 

10,027.62 
3,818.89 


Component a 


8 
8 


346,262 
97,705 


Component b . 




Blocks (eliminating 
varieties) 


443,967 

240,663 
213,858 


Varieties (ignoring 
blocks) 






Error (intrablock) . . 






Total 








99 




1,349,325 











A test of significance of variety mean square in the form of 
an F test cannot be made from the mean squares for varieties 
and error in Table 75, since variety mean square is partially 
confounded, i.e.j it contains some of the differences between 
blocks. Usually it will be sufficient to apply the test of signifi- 
cance appropriate for an ordinary randomized-complete-block 
test. Although less precise than the exact test, this usually will 
be adequate. A lattice experiment can always be analyzed as 
an ordinary randomized-complete-block test. Such a test is 
given in Table 76. 

TABLE 76. ANALYSIS OF VARIANCE AS RANDOMIZED COMPLETE BLOCKS 



Variation due to 


Degrees of 
freedom 


Sum of 
squares 


Mean 
square 


F 


Replications 


3 


450,837 


150,279.00 




Varieties 


24 


240,663 


10,027.62 


1.10 


Error 


72 


657,825 


9,136.46 




Total 


99 


1,349,325 

















360 METHODS OF PLANT BREEDING 

In the foregoing table, the degrees of freedom and sums of 
squares for replications, varieties, and total are taken directly 
from Table 75 and the error degrees of freedom and sum of 
squares obtained by subtraction. In this case, F = 10,027.62 -f- 
9,136.46 = 1.10, a nonsignificant value for n\ = 24and^ 2 = 72 
degrees of freedom, since uniformity trial data were used. If 
significance of differences between variety means is indicated by 
the test of significance applied to the randomized-complete-block 
analysis, no further test of significance is necessary. Usually, 
when large numbers of varieties are used, it may be expected 
that significant differences between varieties will be found if the 
conditions of the test have been satisfactory. 

The average yield of the varieties, calculated from Table 74, is 
affected by differences in productivity of the blocks. The neces- 
sary corrections are obtained by weighting c x and c v to give c x > 
and Cy'. These corrections are then added to the arithmetic 
averages to give the adjusted mean yields. 

The weighting factor is (w w')/(w + w f ), where w = \/E 
and w' = 3/(4B E), E and B being, respectively, the error 
and block mean squares in Table 75. If B is less than or equal 
to E, no adjustments for blocks are necessary, and the averages 
in Table 77 are the correct variety means. 

The general formulas for estimating w and w f are as follows : 
Two replications : 

E = intrablock error mean square 

B = mean square for component 6, based on 2(k 1) degrees 
of freedom 

w = |, and w' = ^rj 

Four replications : 

E = intrablock error mean square 

B = average mean square of components a and 6, based on 
4(fc 1) degrees of freedom 

3 



Six replications: 

E = intrablock error meai square 

B = mean square for component a, based on 4(fc 1) degrees 
of freedom , Component b need not be 



SIMPLE LATTICE EXPERIMENTS 361 

, 1 



w = -p and 
In this problem 



19 = i = 381^89 = - 0026186 



and 

vf = 



- E 4(27,747.94) - 3818.89 
The weighting factor is 

w - w' 0.00023387 



w + w f " 0.00028985 



= 0.80687 



The rfcc x and rfccj, values are multiplied by this weighting factor 
to secure the c x > and c v > corrections. Thus 



= rk \w + 10') rkCx = 4^ 

^ J 

1 ) 



y rk \w 

In Table 77 are given the average yields of the varieties, 
obtained by dividing the totals in Table 74 by 4. The values of 
C* and c v > are given at the side and bottom, respectively, of 
Table 77. The first c* will be 

(0.040344) (-405) = -16.34 

The other values of c x / and <v & re calculated in a similar manner. 
The adjusted variety means are secured by adding to each 
variety average in Table 77 the corrections in the same row and 
column. Thus, for variety 1, the adjusted (unconfoimded) 
variety mean will be 587.50 - 16.34 + 14.32 = 585.5. Proceed- 
ing in a similar manner, the adjusted means of all varieties are 
calculated and entered in Table 78. 

i As an illustration, consider again the adjustment made for 
variety 1. It was shown previously that varieties, 1, 2,, 3, 4, 5 
yielded 6260 5855 = 405 g. more in the two blocks containing 
this group of varieties than the sum of the yields of the same 
varieties grown in different blocks (see Table 73). In like? 



362 



METHODS OF PLANT BREEDING 



manner, varieties 1, 6, 11, 16, 19 yielded 5465 - 5820 -355 g. 
less in the two blocks containing them than the sum of the yields 
of the same varieties when each was grown in a different block. 

TABLE 77. AVERAGE YIELD OF VARIETIES AND c f VALUES 





1 

587.50 


2 
572.50 


3 
586,25 


4 
660.00 


5 
622.50 


-16.34 




6 
552 50 


7 
590.00 


8 
720.00 


9 
696 25 


10 
552.50 


-11.10 




11 
580.00 


12 
548.75 


13 
617.50 


14 
621.25 


15 
601.25 


17.95 




16 
562.50 


17 
618.75 


18 
688.75 


19 
670.00 


20 
638.75 


-43.37 




21 
538.75 


22 
565.00 


23 

550.00 


24 
606.25 


25 
590 00 


7 67 


c/ 


14 32 


31.06 


2.02 


-10.29 


8.07 



TABLE 78. ADJUSTED VARIETY MEANS 



1 

585.5 


2 

587.2 


3 
571.9 


4 
633.4 


5 
614.2 


6 
555.7 


7 
610.0 


8 
710.9 


9 

674.9 


10 
549.5 


11 
612.3 


12 
597.8 


13 
637.5 


14 
628.9 


15 
627.3 


16 
533.5 


17 
606.4 


18 
647.4 


19 
616.3 


20 
603.5 


21 
560.7 


22 

603.8 


23 

559.7 


24 
603.6 


25 
605.7 



The mean of these differences is (405) + (-355) = g g() 

tracting 2.50 from the average yield of variety 1, 587.50 (see 
Table 77) would give 585.0 as the adjusted mean. This is the 
adjusted mean yield given by the original method of analysis 
developed by Yates (1936) and illustrated by Yates (1936) and 



SIMPLE LATTICE EXPERIMENTS 363 

Goulden (1937, 1939). In the present analysis, the interblock 
information has been recovered, and the correction must be 
multiplied by the weighting factor (w w')/(w + w f ). Sub- 
tracting (2.50) (0.80687) from the average yield of 587.50 gives 
585.5 as the adjusted mean. The method of computation used in 
the problem simplifies the calculation of these correction terms. 

To calculate the standard error of the difference between 
variety means, the intrablock error mean square (Table 75) is 
an estimate of the uncontrolled error variance ($ 2 ) of a single 
plot. 

The standard error of the difference between the means of two 
varieties that have occurred in the same block, such as 1 and 2, 
2 and 7, etc., is 





1(2) (3818.89) r (2) (.00026186) ] 

\ (4) (5) [(.00026186) + (.00002799) """ ( } \ 

= \/2217.58 = 47.1 

The standard error of the difference between the means of two 
varieties that did not occur in the same block, such as 1 and 7, is 




... 

( 



The mean standard error of all comparisons is 



7 + (k - 1) = V2423J30 = 49.2 



Usually, this latter standard error may be used for all compari- 
sons of differences between variety means. 

If the data had been analyzed as a randomized complete block 
(Table 76) the variance of the difference between two variety 
means would have been 



= 4568 . 23 



Assuming the precision obtainable in a randomized-complete- 
block design to be 100 per cent, the lattice design would be 



364 METHODS OF PLANT BREEDING 

4568.23/2423.00 = 189 per cent. This represents a gain of 
89 per cent in precision through the use of incomplete blocks. 

To make an exact test of significance appropriate to the analy- 
sis of a lattice experiment, it is necessary to correct the variety 
mean square so that this can be compared with intrablock 
error. This requires that the variety mean square be freed of 
block differences. To do so, we must first calculate the unad- 
justed sum of squares for component b of the blocks. This is 
calculated from the totals of the two sets of blocks given in 
Table 73. Numerically, this is 



(6260) 2 + ' " + (5605) 2 + (546G) 2 + + (5910) 2 



10 

_ (30,835) 2 + (29,715) 2 
50 



= 222,136 



for 8 degrees of freedom. This may be designated B u . The 
adjusted sum of squares for component b (B a ) was given in 
Table 75 as 97,705. The adjusted sum of square for varieties 
(eliminating blocks) will be the sum of squares for varieties in 

Table 75, which is 240,663, minus ( -^ B u - W 7 W \ B\ 

\ w w + w / 

This becomes 

240 663 - [(^23387) (222 136) _ 000023387) 1 

^u,Qo5 |^ .00026186 ^^ 10U ' .00028985 ^">' UO 'J 

= 121,106 

Dividing this sum of squares by 24 gives 5046.08 as the adjusted 
mean square for varieties. The exact value of F is then 5046. 08/ 
3818.89 = 1.32, 

Lattice experiments can be analyzed as randomized complete 
blocks, although when many treatments are included the error 
may be rather large. If it is found that B is equal to or less 
than E, there would be no advantage in adjusting the variety 
means. The unadjusted variety means should be used and the 
error obtained from a randomized-complete-block analysis. 
When a complete replication is lost the data may be analyzed 
as an ordinary randomized-block test. Methods of analysis 
appropriate for a lattice design may be used for the yield data, 



TRIPLE LATTICE EXPERIMENTS ' 365 

the adjusted means being used, and other characters of less 
interest may be analyzed as ordinary randomized blocks, the 
unadjusted means being used. 

TRIPLE LATTICE EXPERIMENTS 

In triple lattice experiments, 1 the number of groups is three. 
The third group (Z) is added to the X and Y groups used in a 
simple lattice design. The number of replications must be a 
multiple of three. The number of varieties tested is the square 
of some number. 

It is always possible to superimpose a Latin-square arrange- 
ment on a square of variety numbers. Using the five letters A, 
Bj Cj D, E, a Latin square of these letters is superimposed on the 
k 2 = 25 varieties, as given below: 

IA 2E 3D 4(7 5/? 

6# 7A 8E W IOC 

11(7 12B 13A UE 151) 

16D 17(7 18B 19A 20E 

21E 22D 23(7 24B 25A 

These 25 varieties may now be arranged in incomplete blocks of 
k = 5 varieties each. In the first group, designated X, the five 
rows of the square are arranged in random order, and the five 
varieties within each row (block) are randomized. The same pro- 
cedure with the columns of the square produces the Y group. 
For the third, or Z group, the Latin letters are arranged in random 
order and the varieties with the same Latin letter randomized 
within each Latin-letter block. The blocks in group Z were made 
up of varieties with the Latin letters in the order A, E, C, B, D. 

A random arrangement in three such groups is given in Table 
79. 

This random arrangement of "varieties" was superimposed on 
the uniformity trial data with rod rows of wheat given by Wiebe 
(1935). It was assumed that three row plots per variety were 
grown and only the central row harvested. The yields are given 
in grams per rod row. Three complete replications were used. 

Assembling the yields for the X, F, and Z groups according to 
rows, columns, and Latin letters gives Table 80. The block 

1 The triple lattice design has been called a two-dimensional pseudofac- 
torial arrangement in three groups of sets and a two-dimensional quasi-* 
factorial design in randomized blocks in three equal groups of sets, 



366 



METHODS OF PLANT BREEDING 



totals are given also, as well as the total for each complete 
replication. 

TABLE 79. RANDOM ARRANGEMENT OF VARIETIES IN TRIPLE LATTICE 

EXPERIMENT 

Replication 1 (Group X) Replication 2 (Group F) 

Block Block 



(1) 


10 


7 


6 


8 


9 


(2) 


14 


13 


11 


15 


12 


(3) 


2 


4 


5 


3 


1 


(4) 


25 


24 


23 


21 


22 


(5) 


18 


16 


17 


20 


19 



(6) 


15 


5 


10 


20 


25 


(7) 


16 


6 


21 


11 


1 


(8) 


2 


17 


7 


22 


12 


(9) 


23 


3 


13 


18 


8 


(10) 


24 


4 


14 


19 


9 



Replication 3 (Group Z) 



Block 



(11) 


7 


1 


19 


25 


13 


(12) 


14 


21 


8 


2 


20 


(13) 


11 


10 


23 


17 


4 


(14) 


5 


24 


18 


12 


6 


05) 


15 


16 


9 


3 


22 



If six or nine replications were to be used, the X, Y, and Z 
groups would be repeated once or twice, respectively. In 
Table 81 is given the sum of the yields of each variety in a 
5 by 5 table with appropriate row and column totals. To the 



Block 



TABLE 80. YIELDS OF VARIETIES IN GRAMS PER ROD Row 
Replication 1 (Group X) 

Block totals 





1 


2 


3 


4 


5 




(3) 


635 


525 


555 


650 


635 


3,000 




6 


7 


8 


9 


10 




(1) 


495 


730 


810 


775 


710 


3,520 




11 


12 


13 


14 


15 




(2) 


630 


600 


645 


635 


645 


3,155 




16 


17 


18 


19 


20 




(5) 


735 


690 


840 


855 


805 


3,925 




21 


22 


23 


24 


25 




(4) 


620 


795 


590 


660 


615 


3,280 














16,880 



TRIPLE LATTICE EXPERIMENTS 



367 



TABLB 80. YIELDS OF VARIETIES IN GRAMS PER ROD Row, (Continued) 

Replication 2 (Group Y) 
Block Block totals 





1 


6 


11 


16 


21 




(7) 


530 


490 


595 


495 


540 


2,650 




2 


7 


12 


17 


22 




(8) 


610 


660 


620 


695 


570 


3,155 




3 


8 


13 


18 


23 




(9) 


705 


850 


675 


685 


640 


3,555 




4 


9 


14 


19 


24 




(10) 


840 


905 


785 


860 


875 


4,265 




5 


10 


15 


20 


25 




(6) 


670 


455 


655 


665 


615 


3,060 














16,685 



Block 



Replication 3 (Group Z) 



Block totals 





1 


7 


13 


19 


25 




(11) 


580 


675 


545 


470 


570 


2,840 




6 


12 


18 


24 


5 




(14) 


700 


620 


575 


570 


505 


2,970 




11 


17 


23 


4 


10 




(13) 


515 


450 


550 


495 


550 


2,560 




16 


22 


3 


9 


15 




(15) 


640 


700 


635 


645 


640 


3,260 




21 


2 


8 


14 


20 




(12) 


445 


515 


465 


445 


455 


2,325 














13,955 



right of the table are given also the total yields of five varieties 
according to the Latin letters. 

The analysis of variance may now be calculated. This pro- 
cedure will follow closely the form given by Cox, Eckhardt, and 
Cochran (1940). 

The correction term is (47,520) 2 -s- 75 j 30,108,672. Total 
sum of squares is calculated from the sum of the squares of 



368 



METHODS OF PLANT BREEDING 



the 75 individual plot yields minus the correction term. Thus, 
31,090,500 - 30,108,672 = 981,828. 

TABLE 81. TOTAL YIELD OF VARIETIES 

Row Latin 
totals letters Totals 





1 


2 


3 


4 


5 










1745 


1650 


1895 


1985 


1810 


9,085 


A 


9,660 




6 


7 


8 


9 


10 










1685 


2065 


2125 


2325 


1735 


9,915 


B 


9,540 




11 


12 


13 


14 


' 15 










1740 


1840 


1865 


1865 


1940 


9,250 


C 


9,055 




16 


17 


18 


19 


20 










1870 


1835 


2100 


2185 


1925 


9,915 


D 


10,095 




21 


22 


23 


24 


25 










1605 


2065 


1780 


2105 


1800 


9,355 


E 


9,170 


Column 


















totals, . 


8645 


9455 


9765 


10,465 


9190 


47,520 




47,520 



The sum of squares for replications is 
(16,880) 2 + (16,685) 2 + (13,955) 2 



25 



- 30,108,672 = 213,954 



The sum of squares for varieties (ignoring blocks) is calculated 
from the variety totals in Table 81. This is 



(1745) 2 + (1650) 2 + 
3 



+ (1800) 2 



- 30,108,672 = 260,561 



In the triple lattice with three replications, there will be no 
component a for blocks, as described for four replications in 
the simple lattice design. Component b consists of three sets 
of values that may be used to give an estimate of block differ- 
ences freed of varietal effects. The first row total in group 
Z(3000) contains the yields of varieties 1, 2, 3, 4, 5. An uncon- 
founded estimate of the sum of the yield of these five varieties 
can be obtained from the first column (Table 80) in group 
F(3355) and for these same varieties in group Z(2730). An 
estimate of the block effect freed of varietal differences will be 



TRIPLE LATTICE EXPERIMENTS 369 

given by 

2(3000) - 3355 - 2730 = -85 

This value can be calculated more conveniently by subtracting 
the total of the first row in Table 81 from three times the total 
of the first row in Table 80. Thus 

3(3000) - 9085 = -85 

These values are to be used in making the adjustments to the 
variety means. Since it will be easier to add than to subtract, 
in making the adjustments, the negative values are determined. 
These are designated as 2 rkc x} 2 rkc yj 2 rkc z . They are calculated 
as follows: 

2 rkc x = row total of Table 81 3 (row total of group X, Table 

80) 

2rkc y = column total of Table 81 3 (row total of group Y, 

Table 80) 

2 rkc z = Latin-letter total of table 81 3 (row total of group Z, 

Table 80) 
The values of 2 rkc are calculated below: 



2 rkc g 


2 rkcy 


9085 


- 3(3000) 


85 


8,645 


- 3(2650) = 


695 


9915 


- 3(3520) 


= - 645 


9,455 


- 3(3155) = 


- 10 


9250 


- 3(3155) 


= - 215 


9,765 


- 3(3555) = 


- 900 


9915 


- 3(3925) 


= -1860 


10,465 


- 3(4265) = 


-2330 


9355 


- 3(3280) 


= _ 485 


9,190 


- 3(3060) = 


10 






-3120 






-2535 





9,660 - 3(2840) = 1140 

9,540 - 3(2970) = 630 

9,055 - 3(2560) - 1375 

10,095 - 3(3260) = 315 

9,170 - 3(2325) = 2195 

5655 

The sum of the 2 rkc values must be 0. 

(-3120) + (-2535) + (5655) = 



370 



METHODS OF PLANT BREEDING 



The sum of squares of the deviations of the 2 rkc values within 
sets will be 

(85)2 + + (-485)' + (695) 2 + + (10) 2 

+ (1140) 2 + + (2195) 2 

30 
_ (-8120)' + (-2635)' + (6656)' = 

J.OU 

= 325,429 

for 12 degrees of freedom. The divisors are 2 rk and 2 rfc 2 . 
The results are now summarized in Table 82. 

TABLE 82. ANALYSIS OF VARIANCE OF TRIPLE LATTICE EXPERIMENT 



Variation due to 


Degrees of 
freedom 


Sum of 
squares 


Mean square 


Replications 


2 


213,954 


106 977 00 


Component b for blocks (eliminat- 
ing varieties) 


12 


325 429 


27 119 08 


Varieties (ignoring blocks) ... 


24 


260,561 


10,856 71 


Error (intrablock) 


36 


181 , 884 


5,052 33 










Total 


74 


981 , 828 













A test of significance of variety mean square cannot be made 
from the mean squares for varieties and error of the foregoing 
analysis, since variety mean square contains some block effects 
and an exact test requires additional computation and will be 
given later. An approximate test may be made in the form of a 
randomized-complete-block analysis by combining the degrees 
of freedom and sums of squares for blocks and error in Table 82 
to produce Table 83. 

TABLE 83. ANALYSIS OF VARIANCE AS RANDOMIZED COMPLETE BLOCKS 



Variation due to 


Degrees of 
freedom 


Sum of 
squares 


Mean 
square 


F 


Replications 


2 


213,954 


106,977 00 




Varieties 


24 


260,561 


10,856 71 


1 03 


Error 


48 


507,313 


10,569.02 




Total 


74 


981,828 

















TRIPLE LATTICE EXPERIMENTS 371 

F = 1.03 is nonsignificant for HI = 24 and n 2 = 48 degrees 
of freedom, the varieties being hypothetical. If this test of 
significance showed a significant variety mean square, no further 
test would be necessary. If, however, the F value did not reach 
significance and block mean square in Table 82 were above 
error mean square, it would be well to make the exact test of 
significance. 

To calculate the adjusted variety means the values of 2rkc x , 
2rkc y , and 2rkc z must be multiplied by a weighting factor to 
obtain the three sets of corrections <v, ty, arid c z ', respectively. 

The weighting factor is ~ ~, where w = 1/E and w' = 

2/(3B E), E and B being the error and block mean squares, 
respectively, obtained from Table 82. 

The general formulas for estimating w and w' are as follows: 
Three replications : 

E = intrablock error mean square 

B = mean square for component 6, based on 3(fc 1) degrees 
of freedom Component a does not exisv 

1 , , 2 
w jz and w = r-^ ~ 

JLJ O-LJ Ju 

Six replications; 

E = intrablock error mean square 

B = average mean square for components a and b for 6 (k 1) 
degrees of freedom 

1 , , 5 

w = 77 and w = ^-^ r , 

E GB E 

Nine replications : 

E intrablock error mean square 

B = mean square for component a for G(fc 1) degrees of 
freedom. Component b need not be used 

w = -=j and w f = -^ 

If B is less than or equal to E, the randomized-complete-block 
analysis is to be used. The unweighted variety means are then 
tested with the error calculated from the randomized-complete- 
alock analysis. 

In this problem, the mean square for blocks (Table 82) is much 
greater than error mean square, and the weighting of the variety 



372 



METHODS OF PLANT BREEDING 



means will lead to an increase in precision. Referring to the 
mean squares in Table 82, 



w = _. . = 



1 



w = 



E 5052.33 
2 



= 0.00019793 
2 



W - E 3(27,119.08) - 5,052.33 
The weighting factor is then 

' = 0.81370 



= 0.00002621 



w 



The weighted correction terms will be 



w 



= 0.027123(2rtc.) 



<v = 



1 2 <>J^) (2rkc v ) = 0.027l23(2rkc y ) 
2rk 2w + w f v y/ x 

1 2(ti? w 1 



2r/c 



(2rA?c,) = 0. 



In Table 84 are given the average yields of the three replica- 
tions of each variety, found by dividing the total yields in 

TABLE 84. AVERAGE YIELDS AND c f VALUES 





1A 
581 . 67 


2E 
550.00 


3D 
631 67 


4C 

661 . 67 


5B 
603.33 


2.31 




6B 
561.67 


7A 
688.33 


8E 
708.33 


9D 
775.00 


IOC 
571.67 


-17.49 




11C 
580 00 


12B 
613.33 


13 A 

621.67 


14E 

621 . 67 


15D 
646.67 


- 5.83 




16D 
623.33 


17C 
611.67 


18B 
700.00 


19A 
728.33 


20E 
641 . 67 


-50.45 




21E 
535.00 


22D 

688.33 


23C 
593.33 


24B 
701.67 


25A 
600.00 


-13.15 


<y 


18.85 


-0.27 


-24.41 


-63.20 


0.27 




<Y 


A 
30.92 


B 
17.09 


C 
37.29 


D 

8.54 


E 
59,53 





TRIPLE LATTICE EXPERIMENTS 



373 



Table 81 by 3. The weighted corrections c x >, <v, and c z > are 
obtained by multiplying the values of 2rkc XJ 2rkc y and 2rkc z by 
0.027123. The first <v is 

(0.027123) (85) = 2.31 

These are recorded for the proper row, column, or Latin letter in 
Table 84. 

The adjusted mean yields are obtained by adding to the aver- 
age yield of each variety the correction term in the same row, 
column and for the same Latin letter. For variety 1, the 
adjusted mean is 581.67 + 2.31 + 18.85 + 30.92 = 633.8. Pro- 
ceeding in a similar manner for all varieties gives the adjusted 
means in Table 85. 

TABLE 85. ADJUSTED VAKIETY MEANS 



1 

633.8 


2 

611.6 


3 

618.1 


4 
638.1 


5 
623.0 


6 
580.1 


7 
701.5 


8 
726.0 


9 
702.9 


10 
591 7 


11 
630.3 


12 
624.3 


13 
622.4 


14 

612.2 


15 

649 7 


16 
600.3 


17 
598.2 


18 
642.2 


19 
645.6 


20 
651 


21 
600.2 


22 
683.5 


23 

593 1 


24 
642.4 


25 
618 



The mean of the 25 adjusted variety means will be the same as 
the mean of the 25 unadjusted means. Three times the total 
of Table 85 will be the grand total of Table 81. 

Using r 3 replications, k = 5 plots per block, and s 2 = 
5052.33 (the error mean square in Table 82), the standard error 
of the difference between the adjusted mean yields of two varie- 
ties having occured in the same block will be 



2w + w' 



+ /3L 
^/v 



'2(5052.33) 
(3)(5) 



6(.00019793) 



(5- 



\2(.00019793) + .00062621 

= V3916.36 = 62.6 



374 METHODS OF PLANT BREEDING 

The standard error of the difference between two varieties 
that did not occur in the same block is 



>/|{HTT? + <*-}- 

The mean standard error of the difference of all comparisons is 

= 63.7 



n l n--7 
r(k + 1) \2w + w ' 

This latter standard error usually may be used for all compari- 
sons without appreciable error. 

To test the efficiency of the triple lattice design, we may divide 
the error variance of the difference between two variety means 
as calculated from the randomized-complete-block analysis 
by the error variance obtained through use of the triple-lattice 
arrangement. 

The variance of the difference between two means by random- 

. , , . , . . , . 1 , u 2s 2 2(10,569.02) 
ized-complete-block design would be = -= = 

T o 

7046.01. Dividing 7046.01 by 4053.41 gives 174 per cent as the 
precision of the lattice design, when the ordinary randomized 
block is considered 100 per cent. Reducing the block size from 
25 plots per complete block to 5 plots per incomplete block 
resulted in a gain in precision of 74 per cent. 

The exact test of significance appropriate for the triple lattice 
design will now be illustrated. To make this test, it is necessary 
to calculate the variety mean square freed of block effects. The 
sum of squares for varieties (ignoring blocks), given in Table 82, 
must be diminished by 

2(w - w') K __ 2(w - w') 
2w u "~2w + w r a 

where B u and B a are thjs unadjusted and adjusted sums of squares, 
respectively, for component b of the blocks. 

B u will be the sum of squares between blocks, within sets, 
calculated from the block totals in Table 80. Thus 

(3000) 2 + + (3280) 2 + (2650) 2 + ' ' ' + (3060) 2 

+ (2840) 2 + - + (2325) 2 

5 

+ (36,685) 2 

25 



DATA EXPRESSED AS PERCENTAGES 375 

B a was given in Table 82 as 325,429. Then 
2^0 ^ _ ^-) ^ = (0 . 8675?9)(507)404) 

- (0.813704) (325,429) = 175,410 

Subtracting this quantity from the unadjusted sum of squares 
for varieties gives 260,561 - 175,410 = 85,151 as the adjusted 
sum of squares for varieties. Dividing by 24 degrees of freedom 
gives 3547.96 as the corrected mean square. Since this is less 
than the mean square for error (5052.33, Table 82), F will be less 
than 1. A lack of significance is clearly indicated. 

ANALYSIS OF DATA EXPRESSED AS PERCENTAGES 

In the analysis of data expressed in the form of a binomial, 
such as is frequently encountered in studies of the proportion, or 
percentage, of plants diseased, the standard error of the pro- 
portion will be given by \/pq/N, where p is the proportion 
diseased, q = (1 p) is the proportion disease free, and N is the 
total number of plants in the sample. If, for example, one-fourth 
of the plants in a sample of 1 00 were diseased, the standard error 



of p = 0.25 would be = V0.001875 = 0.043. If 



expressed as p = 25 per cent, the standard error would be 
4.3 per cent. 

The standard error of a proportion, or percentage, is clearly 
dependent on the value of p as well as N, being a maximum when 
p, 0.50 and reducing to zero as p becomes or 1.00. Since a 
basic assumption in the use of a generalized error from an analysis 
of variance is that the errors of the separate treatments must be 
independent of the means, data expressed as percentages fre- 
quently need to be transformed before being analyzed by means 
of an analysis of variance. The transformation would need to 
be one for which the variance of each treatment is equalized and 
dependent on N alone. Bliss (1937) suggested an angular 
transformation in which p is replaced by sin 2 0, Tables for 
making such transformations have been given by Bliss (1937, 
1938), Fisher and Yates (1938), and Snedecor (1940) and are 
reproduced as Appendix Table VI. A discussion of some of the 
difficulties in the analysis of data of this type has been given by 
Cochran (1938). 



376 



METHODS OF PLANT BREEDING 



The use of such transformations will be illustrated with data 
taken from a paper by Salmon (1938). Clark and Leonard 
(1939) have given a full analysis of these data. In Table 86 is 
given the percentage of bunt on each of 5 varieties of wheat 
inoculated with 10 different collections of the organism. Two 
replications were used. The percentages were based on counts 
of 200 to 400 heads per plot. 

TABLE 86. PERCENTAGE INFECTION IN DIFFERENT VARIETIES OF WHEAT 
WITH 10 COLLECTIONS OF BUNT, IN EACH OF Two REPLICATIONS 

(FROM SALMON) 



Bunt 


Hybrid 128 


Mmturki 


Turkey 


Albit 


Ridit 




col- 














lec- 






















Total 


tion 
























num- 


I 


II 


I 


II 


I 


II 


I 


II 


I 


II 




ber 
























2 


76 


95 


91 


84 


89 


84 


92 


91 


9 


2 


713 


3 


95 


93 


88 


75 


3 


6 


94 


90 


6 


1 


551 


4 


91 


92 


92 


83 


82 


87 


14 


5 


4 


3 


553 


5 


84 


90 


61 


81 


8 


2 


4 


3 


4 


4 


341 


7 


98 


98 


56 


44 


14 


9 





1 


2 


2 


324 


10 


94 


83 


71 


64 


6 


1 


92 


80 


4 


4 


499 


11 


83 


78 


71 


70 


4 


1 


2 


4 


7 


6 


326 


51 


94 


96 


45 


40 


28 


22 


1 


3 


5 


5 


339 


157 


75 


86 


. 75 


85 


52 


92 


89 


85 


1 


1 


641 


189 


87 


95 


81 


80 


80 


92 


92 


95 


5 


6 


713 


Total 


877 


906 


731 


706 


366 


396 


480 


457 


47 


34 


5000 



These data were transformed into the form p = sin 2 6 by 
means of Appendix Table VI. The transformed data are given 
in Table 87. 

These transformed data in Table 87 may be subjected to an 

(4361. 7) 2 



analysis of variance. The correction term will be 



100 



190,244.27. The total sum of squares will be 269,490.93 - 
190,244.27 = 79,246.66. The sum of squares for replication is 
obtained by adding the totals for replicates 1 and 2, respectively, 
for all five varieties to give 2188.4 and 2173.3. The sum of 

f r .. . (2188.4) 2 + (2173.3) 2 . ., 
squares for replication is ^ "~~^ minus the cor- 



50 



rection term or 2,28. 



DATA EXPRESSED AS PERCENTAGES 



377 



In Table 88 are added the values of the transformations for the 
two replications to give the totals for both. 

TABLE 87. PERCENTAGE DATA FROM TABLE 86 TRANSFORMED TO DEGREES 

BY MEANS OP THE TRANSFORMATION p = siN 2 6 



Bunt 
col- 


Hybrid 128 


Minturki 


Turkey 


Albit 


Ridit 




lec- 












Total 






















tion 
























num- 


I 


II 


I 


II 


I 


II 


I 


II 


I 


II 




ber 
























2 


60 7 


77 1 


72 5 


66.4 


70.6 


66 4 


73 6 


72.5 


17 5 


8 1 


585.4 


3 


77.1 


74 7 


69 7 


60 


10 


14 2 


75 8 


71 6 


14 2 


5 7 


473 


4 


72.5 


73.6 


73 6 


65.7 


64 9 


68 9 


22 


12.9 


11.5 


10.0 


475 6 


5 


66.4 


71.6 


51 4 


64.2 


16.4 


8.1 


11.5 


10.0 


11.5 


11 5 


322.6 


7 


81.9 


81 9 


48.5 


41.6 


22 


17 5 


0.0 


5 7 


8.1 


8 1 


315 3 


10 


75.8 


65.7 


57.4 


53.1 


14.2 


5.7 


73.6 


63.4 


11.5 


11.5 


431.9 


11 


65.7 


62.0 


57 4 


56.8 


11.5 


5 7 


8.1 


11.5 


15.3 


14 2 


308 2 


51 


75 8 


78.5 


42 1 


39 2 


32 


28 


5.7 


10 


12.9 


12.9 


337.1 


157 


60.0 


68 


60.0 


67 2 


46.2 


73.6 


70.6 


67.2 


5.7 


5 7 


524 2 


189 


68 9 


77.1 


64 2 


63.4 


63.4 


73 6 


73 6 


77.1 


12 9 


14.2 


588.4 


Total 


704 8 


730 2 


596.8 


577.6 


351 .2 


361 7 


414 5 


ibT~9 


121.1 


101 9 


4361 7 








I 

















TABLE 88. TOTALS OF Two REPLICATIONS FOR EACH VARIETY AND BUNT 

COLLECTION 



Bunt col- 
lection 


Hybrid 
128 


Minturki 


Turkey 


Albit 


Ridit 


Total 


number 














2 


137 8 


138 9 


137 


146 1 


25.6 


585.4 


3 


151.8 


129 7 


24 2 


147 4 


19 9 


473.0 


4 


146 1 


139 3 


133 8 


34 9 


21 5 


475 . 6 


5 


138.0 


115.6 


24 5 


21 5 


23.0 


322.6 


7 


163.8 


90 1 


39 5 


5 7 


16 2 


315.3 


10 


141.5 


110 5 


19 9 


137.0 


23.0 


431.9 


11 


127.7 


114.2 


17.2 


19 6 


29.5 


308.2 


51 


154 3 


81 3 


60 


15 7 


25 8 


337.1 


157 


128 


127.2 


119 8 


137.8 


11 .4 


524.2 


189 


146.0 


127 6 


137 


150 7 


27.1 


588.4 


Total. . . 


1435.0 


1174.4 


712.9 


816.4 


223.0 


4361 . 7 



The sum of squares for bunt collections will be 
(58S.4) 2 + + (5S8.4) 2 



10 



- 190,244.27 = 10,982.11 



378 



METHODS OF PLANT BREEDING 



The sum of squares for varieties will be 
(1435.0) 2 + + (223.0) 2 



20 



- 190,244.27 = 42,900.97 



The sum of squares for varieties inoculated with the individual 
bunt collections is calculated from the 50 figures within Table 88. 
Thus (137.8)' + (138.9)' + ....+(27.11' _ 190 ,244.27 = 



77,937.02. The sum of squares for interaction of varieties X 
collections will be 

77,937.02 - 10,982.11 - 42,900.97 = 24,053.94 
The analysis of variance is given in Table 89. 

TABLE 89. ANALYSIS OF VARIANCE OP TRANSFORMED DATA 



Variation due to 


Degrees of 
freedom 


Sum of 
squares 


Mean 
square 


F 


Blocks 


1 


2 28 


2 28 




Varieties 


4 


42,900 97 


10,725 24 


402 00* 


Collections, , 


9 


10,982.11 


1,220 23 


45 74* 


Varieties X collection . . . 
Krror 


36 
49 


24,053 94 
1,307.36 


668.17 
26 68 


25.04* 












Total 


99 


79,246 66 

















* Exceeds the 1 per cent point. 

The varieties gave highly significant differences in their average 
reaction to all collections of bunt. The bunt collections differed 
significantly in their ability to produce the disease, as an average of 
all varieties. Furthermore, the interaction of varieties X collec- 
tions was highly significant, indicating clearly that these collec- 
tions produced differential responses on the different varieties. 

The standard error of the difference between the means of varie- 



ties for all bunt collections would be V(2 X 26768) /20 = 1.63. 
The totals in table could be compared also. The standard error 
of the difference between means is \/2s 2 /N, and the standard error 
of the difference between totals is -\/2s 2 N. The standard 
error of the difference between two variety totals would be 
A/2 X 26.68 X 20 = 32.67. 

The standard error for determining significant interactions 
of the totals for two replications would be \/2 X 2 X s 2 X N = 



DATA EXPRESSED AS PERCENTAGES 379 



V2 X 2 X 26.68 X 2 = 12.65. The difference between the dif- 
ferences in reaction of Turkey and Albit to collections 3 and 4 is 
seen to be (24.2 - 133.8) - (147.4 - 34.9) - -221.1. Since 
this difference is 15.1 times its standard error, it is clear that 
these two varieties reacted in a differential manner to collections 
3 and 4. Other comparisons could be made in a similar manner. 
If the range in the percentages is between about 25 and 75, no 
transformation probably would need to be made. In this range, 
the errors of the separate varieties would be sufficiently similar 
so that a transformation would be unnecessary. If, however, 
the range in percentages goes below 25 or above 75, a transforma- 
tion probably would be worth while. Such would be true par- 
ticularly if some of the percentages were very low or very high. 



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BARKER, H. D., 1923. A study of wilt resistance in flax, Minn. Agr. Exp. 

Sta. Tech. Bull. 20. 

381 



382 METHODS OF PLANT BREEDING 

BARTLETT, M. S., 1937. Some examples of statistical methods of research 

in agriculture and applied biology. SuppL Jour. Royal Stat. Soc., 4: 

J 37-1 83. 
BAUR, E., 1931. Masters Memorial Lectures. I. Evolution. II. Scope 

and methods of plant-breeding work at the Kaiser Wilhelm Institute 

fur Ziichtungsforshung, Muncheberg (Mark). Jour. Royal Hort. Soc., 

66: 176-190. 
, 1933. Die heutige Stand der Rebenzuchtung in Deutschland. Der 

Zuchter, 5 : 73-77. 
BEDDOWS, A. R., 1931. Seed setting and flowering in various grasses. 

Welsh Plant Breeding Station Bull., Series H, No. 12, pp. 5-99. 
BIFFIN, R. H., 1905. Mendel's laws of inheritance and wheat breeding. 

Jour. Agr. Sri., 1: 4-48. 
, 1916. The suppression of characters on crossing. Jour. Genetics, 

5:225-228. 
BINDLOSS, ELIZABETH A., 1938. Nuclear size in plumular meristems of 

inbred and hybrid maize. Am. Jour. Bot., 25: 738-743. 
BLAKESLEE, A. F., 1939. The present and potential service of chemistry to 

plant breeding. Am. Jour. Bot., 26: 163-172. 

BLANCHARD, R. A., J. H. BIGGER, and R. O. SWELLING, 1941. The resist- 
ance of corn strains to the corn ear worm. Jour. Am. Soc. Agron., 33: 

344-350. 
BLISS, C. I., 1937. The analysis of field experimental data expressed in 

percentages. Plant Protection Bull. 12, pp. 67-77. U.S.S.R. (In 

Russian, with English summary.) 
, 1938. The transformation of percentages for use in the analysis 

of variance. Ohio Jour. Sci., 38: 9-12. 
BLODGETT, F. M., and KARL FERNOW, 1921. Testing seed potatoes for 

mosaic and leaf roll. Phytopathology, 11 : 58-59. 
BOLLEY, H. L., 1901. Flax and flax seed selection. North Dak. Agr. Exp, 

Sta. Bull 55. 
, 1912. Resistant flax seed for sowing purposes. North Dak. Agr. 

Exp. Sta. Press Bull. 57. 
BORGESON, CARL, and H. K. HAYES, 1941. The Minnesota method of seed 

increase and seed registration for hybrid corn. Jour. Am. Soc. Agron., 

33:70-74. 
BREWBAKER, H. E., 1926. Studies of self-fertilization in rye. Minn. Agr. 

Exp. Sta. Tech. Bull. 40. 

, and F. R. IMMER, 1931. Variations in stand as sources of experi- 
mental error in field tests with corn. Jour. Am. Soc. Agron., 23 : 469- 

480. 
BRIEGER, FRIEDRICH, 1930. Selbststerilitat und Kreuzungssterilitat in 

Pflanzenreich und Tierreich. Julius Springer, Berlin. 
BRIGGS, F. N., 1930. Breeding wheats resistant to bunt by the backcross 

method. Jour. Am. Soc. Agron., 22: 239-244. 

, 1933, A third genetic factor for resistance to bunt, Tilletia tritici, 

in wheat hybrids. Jour. Genetics, 27: 435-441. 



LITERATURE CITATIONS 383 

, 1 934. Inheritance of resistance to bunt, Tilletia tritici, in Sherman 

and Oro wheat hybrids. Genetics, 19 : 73-82. 
, 1935. The backcross method in plant breeding. Jour. Am. Soc. 

Agron., 27 : 971-973. 
, 1938. The use of the backcross in crop improvement. Am. 

Naturalist, 72 : 285-292. 

1940. Linkage between the Martin and Turkey factors for resist- 



ance to bunt, Tilletia tritici, in wheat. Jour. Am. Soc. Agron., 32 : 539- 

541. 
BRINK, R. A., and D. C. COOPER, 1939. Soirmtoplastic sterility in Medicago 

saliva. Science, 90: 545-546. 
BROADFOOT, W. C., 1926. Studies on the parasitism of Fusarium lini 

Bolley. Phytopathology, 16: 951-978. 

BROOKINS, W. W., 1940. Linkage relations of the factors determining reac- 
tion to stem rust in barley. Ph.D. thesis. University of Minnesota. 
BRYAN, A. A., 1933. Factors affecting experimental error in field plot tests 

with corn. Iowa Agr. Exp. Sta., Bull. 163. 
BTJRNHAM, C. R., 1932. The inheritance of Fusarium wilt resistance in flax. 

Jour. Am. Soc. Agron., 24: 734-748. 

, and J. L. CARTLEDE, 1939. Linkage relations between smut resist- 
ance and semi-sterility in maize. Jour. Am. Soc. Agron., 31: 924933. 
BUSHNELL, J. W., 1922. Isolation of uniform typos of Hubbard squash by 

inbreeding. Proc. Amer. Soc. Hort. ScL, 19: 139-144. 
CAMPBELL, H. A., W. L. ROBERTS, W. K. SMITH, and K. P. LINK, 1940. 

Studies on the hemorrhagic sweet clover disease. I. The preparation 

of hemorrhagic concentrates. Jour. Biol. Chem., 136: 47-55. 
CHANG, S. C., 1940. Morphological and physiological causes for varietal 

differences in shattering and after harvest sprouting in cereal crops. 

Ph.D. thesis. University of Minnesota. 
CHRISTIDIS, B. G., 1931. The importance of the shape of plots in field 

experiments. Jour. Agr. ScL, 21: 14-37. 
CHURCHWARD, J. G., 1931. Studies in the inheritance of resistance to bunt 

in a cross between Florence and Hard Federation wheats. Proc. Hoy. 

Soc. N.S.W., 64: 298-319. 
, 1932. Inheritance of resistance to bunt, Tilletia tritici (Bjerk). 

Winter, and other characters in certain crosses of Florence wheat. 

Proc. Linn. Soc. N.S.W., 57: 133-147. 
CLARK, ANDREW, and W. H. LEONARD, 1939. The analysis of variance 

with special reference to data expressed as percentages. Jour. Am. 

Soc. Agron., 31: 55-66. 
CLARK, E. R., and H. K. WILSON, 1933. Lodging in small grains. Jour. 

Am. Soc. Agron., 25: 561-572. 
CLARK, J. A., 1936. Improvement in wheat. U. S. Dept. Agr. Yearbook, 

pp. 207-302. 
, and E. R. AUSEMUS, 1928. Immunity of Hope wheat from black 

stem rust inherited as a dominant character. Jour. Am. Soc. Agron.. 

20: 152-159. 



384 METHODS OF PLANT BREEDING 

CLARKE, S. E., 1927. Self-fertilization in timothy. Sci. Agr., 7: 409-439. 
CLAYTON, J. S., and R. K. LARMOUR, 1935. A comparative color test for 

coumarin and melilotic acid in Melilotus species. Can. Jour. Research, 

13 : 8&-10Q. 
COCHRAN, W. G., 1937. A catalogue of uniformity trial data. Suppl. Jour. 

Roy. Stat. Soc., 4 : 233-253. 
, 1938. Some difficulties in the statistical analysis of replicated 

experiments. Emp. Jour. Exp. Agr., 6: 157-175. 
COFFMAN. F. A., J. H. PARKER, and K. S. QUISENBERRY, 1925. A study of 

variability in the Hurt oat. Jour. Agr. Research, 30: 1-64. 
COLLINS. G, N., 1921. Dominance and the vigor of first generation hybrids. 

Am. Naturalist, 65: 116-133. 
, and J. H. KEMPTON, 1917. Breeding sweet corn resistant to the 

corn ear worm. Jour. Agr. Research, 11: 549-572. 
COLLINS. J. L., arid K. R. KERNS, 1938. Mutations in the pineapple. Jour. 

Heredity, 29: 163-172. 
COOPER, D. C., arid R. A. BRINK, 1940. Partial self-incompatibility and the 

collapse of fertile ovules as factors affecting seed formation in alfalfa. 

Jour. Agr. Research, 60: 453-472. 
COOPER, H. P., 1923. The inheritance of spring and winter habit in crosses 

between typical spring and typical winter wheats and the response of 

wheat to artificial lights. Jour. Am. Soc. Agron,, 16: 15-25. 
Cox, GERTRUDE M., R. C. ECKHARDT, and W. G. COCHRAN, 1940. The 

analysis of lattice and triple lattice experiments in corn variety trials. 

Iowa Agr. Exp. Sta. Res. Bull. 281. 
CRAIGIE, J. H., 1940. The origin of physiologic races of rust fungi through 

hybridization. The Genetics of Pathogenic Organisms, Publication of 

the American Association for the Advancement of Science, No. 12, pp. 

66-72. The Science Press. 
CRANE, M. B., and W. J. C. LAWRENCE, 1934. The Genetics of Garden 

Plants. Macmillan & Company, Ltd., London. 
CUMMINGS, M. B., and E. W. JENKINS, 1928. Pure line studies with ten 

generations of Hubbard squash. Vermont Agr. Exp. Sta., Bull. 280. 
CURTIS, L. C., 1939. Heterosis in summer squash (Cucurbita pepo) and 

the possibilities of producing F\ hybrid seed for commercial planting. 

Proc. Am. Soc. Hort. Sci., 37: 827-828. 
CUTLER, G. H., and W. W. WORZELLA, 1931. A modification of the 

Saunders' test for measuring "quality" of wheats for different pur- 
poses. Jour. Am. Soc. Agron. , 32: 1000-1009. 
, and W. W. WORZELLA, 1933. The wheat-meal fermentation time 

test of "quality " in wheat as adapted for small plant breeding samples. 

Cereal Chemistry, 10 : 250-262. 
DARLINGTON, C. D., 1927. The behavior of polyploids. Nature, 119 : 390- 

391. 
DARWIN, CHARLES, 1876. The Effects of Cross- and Self-fertilization in the 

Vegetable Kingdom. D. Appleton-Century Company, Inc., New York. 
DAVIS, R. L., 1929. Report of the plant breeder. Porto Rico Agr. Exp. 

Sta., Ann. Rept. 1927: 14-15. 



LITERATURE CITATIONS 385 

DEEMBN, HAIG, 1940. Colchicine polyploidy and technique. Botanical 

Review, 6 : 599-635. 
DICKSQN, J. G., 1939. Diseases of Cereal and Forage Crops. Burgess 

Publishing Co., Minneapolis, Minn. 
DILLMAN, A. C., 1936. Improvement in flax. U. 8. Dept. Agr. Yearbook, 

pp. 745-784. 
DOXTATOE, C. W., and I. J. JOHNSON, 1936. Prediction of double cross 

yields in corn. Jour. Am. Soc. Agron,, 28 : 460-462. 
EAST, E. M., 1909. A note concerning inheritance in sweet corn. Science 

29:465-467. 

, 1929. Self-sterility. BMiog. Gwetica, 5: 331-370. 

, 1934. The reaction of the stigmatic tissue against pollen-tube 

growth in self -sterile plants. Proc. Nat. Acad. Sci., 20: 364-368. 
, 1935a. Genetic reactions in Nicotiana. I. Compatibility. 

Genetics, 20: 403-413. 
, 19356. Genetic reactions in Nicotiana. IT. Phenotypic reaction 

patterns, (rentes, 20: 414-442. 
, 1935r. Genetic reactions in Nicotiana. III. Dominance. 

Genetics, 20: 443-451. 
, 1936a. Genetic aspects of certain problems of evolution. Am. 

Naturalist, 70: 143-158. 

, 19366. Heterosis. Genetics, 21: 375-397. 

, and H. K. HAYES, 1912. Heterozygosis in evolution and in plant 

breeding. U.S. Dept. Agr., Bur. Plant Ind. Bull. 243. 
, and D. F. Jones, 1919. Inbreeding and Outbreeding. J. B. Lippin- 

cott Company, Philadelphia. 
-, and D. F. JONES, 1921. Genetic studies on the protein content of 



maize. Genetics, 5: 543-610. 
ECKHARDT, R. C., and A. A. BRYAN, 1940. Effect of method of combining 

the four inbred lines of a double cross of maize upon the yield and 

variability of the resulting hybrid. Jour. Am. Soc. Agron., 32 : 347-353. 
EDGERTON, C. W., 1918. A study of wilt resistance in the seedbed. 

Phytopathology, 8: 5-14. 
EMERSON, R. A., G. W. BEADLE, and A. C. FRASER, 1935. A summary of 

linkage studies in maize. N.Y. (Cornell) Agr. Exp. Sta., Mem. 180. 
, and E. M. EAST, 1913. The inheritance of quantitative characters 

in maize. Nebr. Agr. Exp. Sta. Res. Bull. 2. 
EMSWELLER, S. L., and PHILIP BRIE RLE Y, 1940. Colchicine-induced 

tetraploidy in Lilium. Jour. Heredity, 31 : 223-230. 
, and H. A. JONES, 1934. The inheritance of resistance to rust in the 

snapdragon. Hilgardia, 8: 197-211. 
ENGLEDOW, F. L., 1914. A case of repulsion in wheat. Proc. Cambridge 

Phil. Soc., 17:433-435. 
, 1920. The inheritance of glume length and grain length in a wheat 

cross. Jour. Genetics^ 10: 109-134. 
, 1924. Inheritance in barley. III. The awn and the lateral floret 

(cont/d): Fluctuation: A linkage: Multiple allelomorphs. Jour. 

Genetics, 14 : 49-87. 



386 METHODS OF PLANT BREEDING 

FISHER, R. A., 1937. The Design of Experiments, Ed. 2. Oliver & Boyd, 

Edinburgh. 
, 1938. Statistical Methods for Research Workers, Ed. 7. Oliver <fe 

Boyd, Edinburgh. 
, and F. YATBS, 1938. Statistical Tables for Biological, Agricultural 

and Medical Research. Oliver & Boyd, Edinburgh. 
FLOR, H. H., 1940. New physiologic races of flax rust. Jour. Agr. 

Research, 60: 575-591. 
FRASEB, A. C., 1919. The inheritance of weak awn in certain Avena crosses 

and its relation to other characters of the oat grain. N.Y. (Cornell) 

Agr. Exp. 8ta. Mem,, 23, pp. 635-676. 
FREEMAN, G. F., 1918. Producing breadmaking wheats in warm climates. 

Jour. Heredity, 9: 211-226. 
GATNKS, E. F., 1917. Inheritance in wheat, barley, and oat hybrids. 

Wash. Agr. Exp. Sta. Bull 135. 
, 1934. The results of recent research in genetics. Proc. 5th Par. 

Sci. Cong., pp. 2627-2629. The Toronto Press. 
~, and HANNAH C. AASE, 1926. A haploid wheat plant. Am. Jour. 

BoL, 13:375-385. 
GARBKR, R. J., 1922. Inheritance and yield with particular reference to rust 

resistance and panicle type in oats. Minn. Agr. Exp. Sta. Tech. Bull. 7. 
, and M. M. HOOVER, 1930. Persistence of soil differences with 

respect to productivity. Jour. Am. Soc. Agron., 2: 883-890. 
, T. C. MclLVAiNE, and M. M. HOOVER, 1926. A study of soil 

heterogeneity in experiment plots. Jour. Agr. Research, 33 : 255-268. 
-, and K. S. QUISKNBERRY, 1925. Breeding corn for resistance to 



smut (Ustilago zeae). Jour. Am. Soc. Agron., 17: 132-140. 

GARNER, W. W., II. A. ALLARD, and E. E. CLAYTON, 1936. Superior germ- 
plasm in tobacco. U.S. Dept. Agr. Yearbook, pp. 785-830. 

GARRISON, H. S., and F. D. RICHEY, 1925. Effects of continuous selection 
for ear type in corn. U.S. Dept. Agr. Bull. 1341. 

GOULDEN, C. H., 1931. Modern methods in field experimentation. Sci. 
Agr., 11:681-701. 

, 1937. Modern methods of testing a large number of varieties. 

Dominion of Canada Dept. of Agr. Tech. Bull. 9. 

, 1939. Methods of Statistical Analysis. John Wiley & Sons, Inc , 

New York. 

, K. W. NEATBY, and J. W. WELSH, 1928. The inheritance of resist- 
ance to Puccinia graminis tritici in a cross between two varieties of 
Triticum vulgare. Phytopathology, 18 : 631-658. 

GRIFFEE, FRED, 1925. Correlated inheritance of botanical characters in 
barley, and manner of reaction to Helminthosporium sativum. Jour. 
Agr. 'Research, 30: 915-933. 

HABBR, E. S., 1929. Inbreeding the table queen (Des Moines) squash. 
Proc. Amer. Soc. Hort. ScL, 25: 111-114. 

^ ] 938 A study of drought resistance in inbred strains of sweet corn, 

Zea mays var. Rugosa. Iowa Agr. Exp. Sta. Res. Bull 243. 



LITERATURE CITATIONS 387 

HALL, D. M., 1934. The relationship between certain morphological 

characters and lodging in corn. Minn. Agr. Exp. Sta. Tech. Bull. 103. 
HAMILTON, R. I,, 1926. Improving sunflowers by inbreeding, $a. Agr., 6: 

190-192. 
HARLAN, H. V., 1918. The identification of varieties of barley. U.S. Dept. 

Agr. Bull 622. 
, and H. K. HAYES, 1919. Breeding small grains in Minnesota. 

II. Barley investigations. Minn. Agr. Exp. Sta. Bull. 182. 
, and H. K. HAYES, 1920. Occurrence of the fixed intermedium, 

Hordeum intermedium haxtoni, in crosses between //. vulgare pallidum 

and II. distichon palmella. Jour. Agr. Research, 19: 575591. 
-, and M. L. MARTINI, 1936. Problems and results in barley breeding. 

U.8. Dept. Agr. Yearbook, pp. 303-346. 
,_ ^ am i M. L. MARTINI, 1940. A study of methods in barley breeding. 

U.8. Dept. Agr. Tech. Bull. 720. 

and M. N. POPE, 1922. The use and value of backcrosses in small 



grain breeding. Jour. Heredity, 13: 319-322. 

HARRINGTON, J. B., 1932. Predicting the value of a cross from an F 2 
analysis. Canadian Jour. Research, 6: 21-37. 

-, 1937. The mass-pedigree method in the hybridization improve- 
ment of cereals. Jour. Am. 8oc. Argon., 29: 379-384. 

, 1940. Yielding capacity of wheat crosses as indicated by bulk 

hybrid tests. Canadian Jour. Research, 18: 578584. 

, and O. S. AAMODT, 1923. Mode of inheritance of resistance to 

Puccinia graminis with relation to seed color in crosses between varieties 
of durum wheat. Jour. Agr. Research, 24: 979-996. 

, and P. F. KNOWLES, 1940a. Dormancy in wheat and barley varie- 
ties in relation to breeding. Set. Agr., 20: 355-364. 

, and P. F. KNOWLES, 19406. The breeding significance of after- 
harvest sprouting in wheat. Sci. Agr., 20: 402-413. 

HARRIS, J. A., 1 91 2. A simple test of the goodness of fit of Mendelian ratios. 
Am. Naturalist, 46: 741-745. 

_ , y 1915. On a criterion of substratum homogeneity (or heterogeneity) 

in field experiments. Am. Naturalist, 49: 430-454. 

, 1920. Practical universality of field heterogeneity as a factor influ- 
encing plot yields. Jour. Agr. Research, 19: 279-314. 

-, and C. S. SCOFIELD, 1920. Permanence of differences m the plots 

of an experimental field. Jour. Agr. Research, 20: 335-356. 

, and C. S. SCOFIELD, 1928. Further studies on the permanence of 

differences in the plots of an experimental field. Jour. Agr. Research, 
36; 15-40. 

HARVEY, P. H., 1939. Hereditary variation in plant nutrition. Genetics, 
24:437-461. 

HAUGE, S. M., and J. F. TROST, 1930. An inheritance study of the distri- 
bution of vitamin A in maize. Jour. Biol. Chemistry, 86 : 167-172. 

HAYES, H. K., 1922. Production of high protein maize by Mendelian 
methods. Genetics, 1 : 237-257. 



388 METHODS OF PLANT BREEDING 



, 1926. Breeding improved varieties of smooth-awned barleys. 

Jour. Heredity, 17: 370-381. 

, and O. B. AAMODT, 1927. Inheritance of winter hardiness and 

growth habit in crosses of Marquis with Minhardi and Minturki wheats. 
Jour. Agr. Research, 36: 223-236. 

, and C. L. ALEXANDER, 1924. Methods of corn breeding. Minn. 

Agr. Exp. Sta. Bull. 210. 

, and A. C. ARNY, 1917. Experiments in field technics in rod row 

tests. Jour. Agr. Research, 11: 399-419. 

, E. R. AUSEMUS, E. C. STAKMAN, C. H. BAILEY, H, K. WILSON, 

R. H. BAMBERO, M. C. MARKLEY, R. F. CRIM, and M. N. LEVINE, 
1936. Thatcher wheat. Minn. Agr. Exp. Sta. Bull. 325. 

, and E. M. EAST, 1915. Further experiments on inheritance in 

maize. Conn. Agr. Exp. Sta. Bull. 188. 

, and R. J. GARBER, 1919. Synthetic production of high-protein 

corn in relation to breeding. Jour. Am. Soc. Agron., 11 : 309-318. 

, and R. J. GARBER, 1927. Breeding Crop Plants, Ed. 2. McGraw- 
Hill Book Company, Inc., New York. 

, FRED GRIPFEE, F. J. STEVENSON, and A. P. LTINDEN, 1928. Corre- 
lated studies in oats of the inheritance of reaction to stem rust and smuts 
and of other differential characters. Jour. Agr. Research, 36 : 437-457. 

, and H. V. HARLAN, 1920, The inheritance of the length of inter- 
node in the rachis of the barley spike. U.S. Dept. Agr. Bull. 869. 

, and I. J. JOHNSON, 1939. The breeding of improved selfed lines of 

corn. Jour. Am. Soc. Agron., 31: 710-724. 

f M. B. MOORE, arid E. C. STAKMAN, 1939. Studies of inheritance 

in crosses between Bond, A vena byzantina, and varieties of A. saliva. 
Minn. Agr. Exp. Sta. Tech. Bull. 137. 

, J. H. PARKER, and CARL KTJRTXWEIL, 1920. Genetics of rust 

resistance in crosses of Tnticum vulgare with varieties of T. durum and 
T. dicoccum. Jour. Agr. Research, 19: 523-542. 

, E. C. STAKMAN, and O. S. AAMODT, 1925. Inheritance in wheat of 

resistance to black stem rust. Phytopathology, 15 : 371-387. 

, E. C. STAKMAN, FRED GRIFFEE, and J. J. CHRISTENSEN, 1923. 

Reaction of barley varieties to Helminthosporium sativum. Minn* Agr. 
Exp. Sta. Tech. Bull. 21. 

, E. C. STAKMAN, FRED GRIFFEE, and J. J. CHRISTENSEN, 1924. 

Reaction of selfed lines of maize to Ustilago zeae. Phytopathology, 14 : 
268-280. 

HENKEMEYEF^ A., 1915. Untersuchungen liber die Spaltungen von Weizen- 
bastarden in der F% and F$ Generationen. Jour, fur experimentalle 
Landwirtschaft 63 : 97-124. 

HENRY, A. W., 1930. Inheritance of immunity from flax rust. Phyto- 
pathology, 20:707-721. 

HERIBERT-NILSSON, N., 1916. Populationsanalysen und Erblichkeits- 
vereuche fiber die Selbssterilitat, Selbstfertilitat, und Sterilitat bei dem 
Roggen. Zeit. fur Pflanzenzucht 4 : 1-44. 



LITERATURE CITATIONS 389 

, 1919. Ragforadlingens Methodik och Principer. Saertryk af 
Nordisk Jorbrugsforskning. 

1921. Selektive Verschlebung der Gametenfrequenz in einer Kreu- 



zungspopulation von Roggen. Hereditas, 2: 364-369. 
HEYNE, E. G., and A. M. BRUNSON, 1940. Genetic studies of heat and 

drought tolerance in maize. Jour. Am. Soc. Agron., 32: 803-814. 
, and H. H. LAUDE, 1940. Resistance of corn seedlings to high tem- 
peratures in laboratory tests. Jour. Am. Soc. Agron., 32: 116-126. 
HITCHCOCK, A. S., 1935. Manual of the grasses of the United States. U.S. 

Dept. Agr. Misc. Pub. 200. 
HOLBERT, J. R., 1924. Anchorage arid extent of corn root system. Jour. 

Agr. Research, 27: 71-78. 
, and W. L. BTJRLISON, 1928. Corn breeding for resistance to cold 

yields good results. U.S. Dept. Agr. Yearbook, pp. 227-229. 
HOOVER, M. M., 1932. Inheritance studies of the reaction of selfcd lines of 

maize to smut (Ustilago zeae). West Va. Agr. Exp. Sta. Bull. 253. 
HOPKINS, C. G., 1899. Improvement in the chemical composition of the 

corn kernel. III. Agr. Exp. Sta. Bull, 55. 
HOR, K. S., 1924. Interrelations of genetic factors in barley. Genetics, 9: 

151-180. 
HOWARD, A., and G. L. C. HOWARD, 1915. On the inheritance of 

some characters in wheat. II. Mem. Dept. Agr. India Bot. Ser. 7: 

273-285. 
HUMPHREY, L. M., 1940. Effects of inbreeding cotton with special reference 

to staple length and lint percentage. Ark. Agr. Exp. Sta. Bull. 387. 
, and A. V. TULLBR, 1938. Improvement in the technique of cotton 

hybridization. Ark. Agr. Exp. Sta. Bull. 359. 
HUNTER, H., and H. M. LEAKE, 1933. Recent Advances in Agricultural 

Plant Brooding. The Blakiston Company, Philadelphia. 
HUNTER, J. W., H. H. LAUDE, and A. M. BRUNSON, 1936. A method for 

studying resistance to drought injury in inbred lines of maize. Jour. 

Am. Soc. Agron., 28: 694-698. 
HUTCHINS, A. E., 1938. Heterosis in the cucumber. Proc. Amer.Soc.HorL 

Sri., 36:660-664. 
IMMER, F. R., 1927. The inheritance of reaction to Ustilago zeae in rnaize. 

Minn. Agr. Exp. Sta., Tech. Bull. 51. 
~, 1930. Formulae and tables for calculating linkage intensities. 

Genetics, 16: 81-98. 
-, 1934. Varietal competition as a factor in yield trials with sugar 

beets. Jour. Am. Soc. Agron., 26: 259-261. 
, 1941. Relation between yielding ability and homozygosis in 

barley crosses. Jour. Am. Soc. Agron., 33: 200-206. 
, H. K. HAYES, and LfiRoy POWERS, 1934. Statistical determination 

of barley varietal adaptation. Jour. Am. Soc. Agron., 26: 403-4J9. 
, and S. M. RALEIGH, 1933. Further studies on size and shape of 

plot in relation to field experiments with sugar beets. Jour. Agr. 

Research, 47 : 591-598. 



390 METHODS OF PLANT BREEDING 

IVANOFF, S. S., and A. J. HIKER, 1936. Resistance to bacterial wilt of 
inbred strains and crosses of sweet corn, Jour. Agr. Research, 53 : 927- 
954. 

JENKIN, T. J., 1924. The artificial hybridization of grasses. Welsh Plant 
Breeding Station Bull., Series H, No. 2. 

, 1931a. Self-fertility in perennial rye-grass (LoUum perenne L.). 

Welsh Plant Breeding Station Bull, Series H, No. 12, pp. 100-119. 

, 19316. Fertility in plants of the genus Phleum. Welsh Plant Breed- 
ing Station Bull., Series II, No. 12, pp. 148-159. 

1931e. The method of selection, breeding and strain building in 



grasses. Imp. Bur. of Plant Genetics: Herbage Plants Bull. 3. 
JENKINS, M. T., 1929. Correlation studies with inbred and cross-bred 

strains of maize. Jour. Agr. Research, 39: 677-721. 
, 1932. Differential resistance of inbred and crossbred strains of 

corn to drought and heat injury. Jour. Am. Soc. Agron., 24: 504-506. 
, 1934. Methods of estimating the performance of double crosses in 

corn. Jour. Am. Soc. Agron., 26: 199-204. 
, 1935. The effect of inbreeding and selection within inbred lines of 

maize upon the hybrids made after successive generations of selling. 

Iowa State College \Iour. Sci., 9: 429-450. 

~ , 1936. Corn improvement. U.S. Dept. Agr. Yearbook, pp. 455-522. 

- , 1940. The segregation of genes affecting yield of gram in maize. 

Jour. Am. Soc. Agron,, 32: 55-63. 

arid A. M. BRUNRON, 1932. Methods of testing inbred lines of 



make in crossbred combinations. Jour. Am. Soc. Agro?i., 24: 523-530. 
JODON, N. E., 1938. Experiments on artificial hybridization of rice. Jour. 

Am. Soc. Agron., 30: 294-305. 
JOHANNWEN, W., 1903. Ucber Krblichkeit in Populationen und in reinen 

Linien. Gustav Fischer, Jena. 
, 1909. Elemente der exakten Erblichkeitslehre. Gustav Fischer, 

Jena. 
JOHNSON, I. J., 1932. Correlation studies with strains of flax with particular 

reference to the quantity and quality of the oil. Jour. A m. Soc. Agron., 

24: 537-544. 
, and H. K. HAYES, 1936. The combining ability of inbred lines of 

Golden Bantam sweet corn. Jour. Am, Soc. Agron., 28: 246-252. 
, and H. K. HAYES, 1938. The inheritance of pericarp tenderness in 

sweet corn. Jour Am. Soc. Agron., 30: 220-231. 

and H. K. HAYKR, 1940. The value in hybrid combinations of 



inbred lines of corn selected from single crosses by the pedigree method 

of breeding. Jour. Am. Soc. Agron., 32: 479-485. 
JOHNSON, T., and M ABO ABET NEWTON, 1940. Mendelian inheritance of 

certain pathogenic characters of Puccinia graminis tritici. Canadian 

Jour. Research, C. 18: 599-611. 
JONES, D. F., 1916. Natural cross-pollination in the tomato. Science, 

43 : 509-510. 
, 1917. Dominance of linked factors as a means of accounting for 

heterosis. Genetics, 2 : 466-479. 



LITERATURE CITATIONS 391 

, 1918. The effects of inbreeding and crossbreeding upon develop- 
ment. Conn. Agr. Exp. Sta. Bull. 207. 

, 1920. Selection in self fertilized lines as the basis for corn improve- 
ment. Jour. Am. Soc. Agron., 12: 77-100. 

, 1924. The origin of flint and dent corn. Jour. Heredity, 16: 417- 

419. 

, 1939. Continued inbreeding in maize. Genetics, 24: 462-473. 

-, and W. R. SINGLETON, 1935. The improvement of naturally 



cross-pollinated plants by selection in self-fertilized lines. II. The 

testing and utilization of inbred strains of corn. Conn, Agr. Exp. Sta. 

Bull. 375. 
JONES, H. A., 1932. Vegetable breeding at the University of California. 

Proc. Amer. Soc. Hort. Science, 29: 572-581. 
, and S. L. EMSWELLER, 1933. Methods of breeding onions. II il- 

gardia, 1 : 625-042. 
JONES, J. W., 1936. Improvement in rice. U.S. Dept. Agr. Yearbook, 

pp. 415-454. 
JONES, L. R., and J. C. OILMAN, 1915. The control of cabbage yellows 

through disease resistance. Wis. Agr. Exv. Sta. Res. Bull. 38. 
JORGENSON, Locus, and H. E. BREXVKAKER, 1927. A comparison of selfed 

lines of corn and first generation crosses between them. Jour. Am. 

Soc. Agron., 19: 819-830. 
KEARNEY, T. 11., 1923. Self fertilization and cross fertilization in Pima 

cotton. U.S. Dept, Agr. Bull. 1134. 
KEEBLE, FREDERICK, and C. PELLEW, 1910. The mode of inheritance of 

stature arid of time of flowering in peas (Pisum sativum). Jour. Genetics, 

1 : 47-56. 
KEMPTON, J. K., 1924. Inheritance of proterogyny in maize. Am. 

Naturalist, 58: 182-187. 
KEZEK, ALVIN, and BREEZE BOYACK, 1918. Mcndelian inheritance in 

wheat and barley crosses. Colo. Agr. Exp. Sta. Bull. 249. 
KIESWELBAOH, T. A., 1918. Studies concerning the elimination of experi- 
mental error in comparative crop tests. Ncbr. Agr. Exp. Sta. Res. 

Bull. 13. 

, 1922. Corn investigations. Ncbr. Agr. Exp. Sta. Res. Bull. 20. 

, 1923. Competition as a source of error in comparative corn yields. 

Jour-. Am. Soc. Agron., 16: 199-215. 
, 1930. The use of advanced-generation hybrids as parents of double 

cross seed corn. Jour. Am. Soc. Agron., 22: 614-626. 
-, and 11, M. WEIHING, 1933. Effect of stand irregularities upon the 



acre yield and plant variability in corn. Jour. Agr. Research, 47: 

399-416. 
KIHARA, H., and I. NISIIIYAMA, 1932. The genetics and cytology of certain 

cereals, III. Different compatibility in reciprocal crosses of A vena with 

special reference to tetraploid hybrids between hexaploid and diploid 

species. Japan. Jour. Bot., 6: 245-305. 
KIRK, L. E., 1927. Self-fertilization in relation to forage crop improvement. 

Sci. Agr., 8: 1-40. 



392 METHODS OF PLANT BREEDING 



, 1930. Abnormal seed development in sweet clover species crosses. 

A new technique for emasculating sweet clover flowers. Sci. Agr., 10 : 
321-327. 

, 1 932. Methods employed in the breeding of biennial sweet clover, 

Melilotus, and brief notes on the breeding of Lucerne, Medicago saliva, 
bronie grass, Bromus inermis, and slender wheat grass, Agropyron 
tenerum. Imp. Bur. Plant Genetics: Herbage Plants. Bull. 7. 

1933. The progeny test and methods of breeding appropriate to 



certain species of crop plants. Am. Naturalist, 67; 515531. 
KOSTOFF, DONOHO, 1937. Cytological studies on certain progenies of the 

hybrid Triticum timopheevi X Triticum persicum. Cytologia, Fujii 

Jubilee Vol., pp. 262-277. 
LARSON, A. H., R. B. HARVEY, and JOHN LARSON, 1936. Length of the 

dormancy period in cereal seeds. Jour. Agr. Research, 62: 811-836. 
LEONARD, W. H., 1940. Inheritance of fertility in the lateral spikelets of 

barley. Ph.D. thesis. University of Minnesota. 
LEVY, E. B., 1933. Strain testing and strain building. Technique employed 

in grassland research in New Zealand. Imp. Bur. of Plant Genetics: 

Herbage Plants. Bull. 11, pp. 6-16. 
LILIENFELD, F., and H. KIHARA, 1934. Genomarialyse bei Triticum und 

Aegilops. V. Triticum timopheevi Zhuk. Cytologia, 6: 87-122. 
LINDSTROM, E. W., 1931. Genetic tests for linkage between row number 

genes and certain qualitative genes in maize. Iowa Agr. Exp. Sta. 

Res. Bull. 142. 
, 1935. Genetic experiments on hybrid vigor in maize. Am. 

Naturalist, 69: 311-322. 
LOVE, H. H., and W. T. CRAIG, 1918a. Methods used and results obtained 

in cereal investigations at the Cornell station. Jour. Am. 8oc. Agr on., 

10:145-157. 
, and W. T. CRAIG, 19186. The relation between color and other 

characters in certain Avena crosses. A m. Naturalist, 52 : 369-383. 
and W. T. CRAIG, 1924. Methods now in use in cereal breeding 



and testing at the Cornell Agricultural Experiment Station. Jour. Am. 

Soc. Agron., 16: 109-127. 
, and G. P. McRosTiB, 1919. The inheritance of hull-lessness in oat 

hybrids. Am. Naturalist, 63: 5-32. 
LOVE, R. M., 1938. Somatic variation of chromosome numbers in hybrid 

wheats. Genetics, 23 : 517-523. 

LUCKWILL, L. C., 1937. Studies on the inheritance of physiological char- 
acters. IV. Hybrid vigour in the tomato. Part 2. Manifestation of 

hybrid vigour during the flowering period. Ann. Bot. (N.S.), 1: 379- 

408. 
MACATJLEY, T. B., 1928. The improvement of corn by selection and plot 

inbreeding. Jour. Heredity, 19: 57-72. 
MACINDOE, S. L., 1931. Stem rust of wheat. Agr. Gazette N.S. W., 42 : 475- 

484. 
MAINS, B. B., 1931. Inheritance of resistance to rust, Puccinia sorghi, in 

maize. Jour. Agr. Research, 43: 419-430. 



LITERATURE CITATIONS 393 

MANGBLSDORF, P. C., 1926. The genetics and morphology of some endo- 
sperm characters in maize. Conn. Agr. Exp. Sta. Bull. 279. 

, and G. S. FRAPS, 1931. A direct quantitative relationship between 

vitamin A in corn and the number of genes for yellow endosperm. 
Science, 73:241-242. 
-, and R. G. REEVES, 1939. The origin of Indian corn and its rela- 



tives. Texas Agr. Exp. Sta. Bull. 574 (monograph). 
MARSTON, A. R., 1930. Breeding corn for resistance to the European corn 

borer. Jour. Am. Sac. Agron., 22: 986-992. 
MCFADDEN, E. S., 1 930. A successful transfer of emmer characters to vulgare 

wheat. Jour. Am. Soc. Agron., 22: 1020-1034. 
MERCER, W. B., and A. D. HALL, 1911. The experimental error of field 

trials. Jour. Agr. Sri., 4: 107-127. 
MEYERS, M. T., L. L. HUBER, C. R. NEISWANDER, F. D. RICKEY, and G. H. 

STRING FIELD, 1937. Experiments on breeding corn resistant to the 

European corn borer. U.S. Dept. Agr, Tech. Bull. 583. 
MILLER, H. ,!., 1936. Out of the Night. Victor Gollancz, Ltd., London. 
MONTGOMERY, E. G., 1909. Experiments with corn. Nebr. Agr. Exp. Sta. 

Bull. 112. 
MORSE, W. J., and J. L. CARTTER, 1937. Improvement in soybeans. U.S. 

Dept. Agr. Yearbook, pp. 1154-1189. 

MURPHY, H. C., T. R. STANTON, and F. A. COFFMAN, 1936. Hybrid selec- 
tions of oats resistant to smuts and rusts. Jour. Am. Soc. Agron., 28: 

370-373. 
MURPHY, R. P., 1941. Convergent improvement with four inbred lines of 

corn. Part B of Ph.D. thesis. University of Minnesota, 
MYERS, W. M., 1936. A correlated study of the inheritance of seed size and 

botanical characters in the flax cross, Redwing X Ottawa 770B. Jour. 

Am. Soc. Agron., 28: 623-635. 
, 1937. The nature and interaction of genes conditioning reaction to 

rust in flax. Jour. Agr. Research, 66: 631-666. 

and LER.OY POWERS, 1938. Meiotic instability as an inherited 



character in varieties of Triticum aestivum. Jour. Agr. Research, 66: 

441-452. 

NEAL, N. P., 1935. The decrease in yielding capacity in advanced genera- 
tions of hybrid corn. Jour. Am. Soc. Agron., 27: 666-670. 
NEBEL, B. R., and M. L. RUTTLE, 1938. Colchicine and its place in fruit 

breeding. New York (Geneva) Agr. Exp. Sta. Circ. 183. 
NEWMAN, L. H., 1912. Plant breeding in Scandinavia. Canadian Seed 

Growers' Association, Ottawa, Canada. 
NILSSON-EHLE, H., 1909. Kreuzungsuntersuchungen an Hafer und Weizen. 

Lunds Univ. Arsskr. N.F. Afd. 2. Bd. 5. Nr. 2, pp. 1-122. 
, 191 la. Kreuzungsuntersuchungen an Hafer und Weizen. Lunds 

Univ. Arsskr. N.F. Afd. 2, Bd. 7. Nr. 6, pp. 3-84. 
-, 19116. Ueber Falle spontanen Wegf aliens eines Hemmungsfaktors 



beim Hafer. Zeitschr. fur Induk. Abstamm. u. Vererb., 6: 1-37. 
NILSSON-LEISSNEB, GUNNAR, 1925. Beitrage zur Genetik von Triticum 
spelta und Triticum vulgare. Hereditas, 7 : 174. 



394 METHODS OF PLANT BREEDING 



, 1927. Relation of selfed strains of corn to F\ crosses between them. 

Jour. Am, Soc. Agron., 19: 440-454. 
NISHIYAMA, I., 1929. The genetics and cytology of certain cereals. I. 

Morphological and cytological studies on triploid, pentaploid, and 

hcxaploid Avena hybrids. Japan. Jour, Genetics, 6: 1-48. 
NOLL, C. P., 1927. Mechanical operations of small grain breeding. Jour. 

Am. Soc. Agron., 19: 713-721. 
NOWOSAD, F. S., and R. M. MAOVICAR, 1940. Adaptation of the "picric 

acid test" method for selecting HCN free lines in sudan grass. Sci. 

Agr., 20: 566-569. 
ORTON, W. A., 1913. The development of disease resistant varieties of 

plants. IV. Conference Internationale de G6n6tique, Paris, 1911. 
PAINTER, R. H., E. T. JONES, C. O. JOHNSON, and J. H. PARKER, 1940. 

Transference of Hessian fly resistance and other characteristics of 

Marquillo spring wheat to winter wheat. Kan. Agr. Exp. 8ta. Tech. 

Bull, 49. 
PAN, C. L., 1940. A genetic study of mature plant resistance in spring wheat 

to black stern rust, Puccinia graminis tritici, and reaction to black chaff, 

Bacterium translucens var. undulosum. Jour. Am. Soc. Agron., 32: 

107-115. 
PARKER, W. H., 1914. Lax and dense eared wheats. Jour, Agr. Sci., 6: 

371-386. 
PEARSON, KARL, 1924. Tables for Statisticians and Biometricians, Part I, 

Ed. 2. Cambridge University Press, London. 
PEARSON, O. H., 1932. Breeding plants of the cabbage group. Calif. Agr. 

Exp. Sta. Bull. 532. 
PELSHENKE, P., 1930. Beitriige zur Bestimmung der Backfahigkeit von 

Weizen und Weizemnehlen. Arch. Pfianzcnbau, 5: 108-151. 
, 1933. A short method for the determination of gluten quality in 

wheat. Cereal Chemistry, 10 : 90-96. 
PERCIVAL, J., 1921 . The wheat plant: A monograph. Gerald Duckworth & 

Company, Ltd., London. 
PETERSON, R. F., 1934. Improvement of rye through inbreeding. Sci. 

Agr., 14: 651-668. 
, T. JOHNSON, and MARGARET NEWTON, 1940. Varieties of Triticum 

vulgare practically immune in all stages of growth to stem rust. Science, 

91:313. 
PHILP, JAMES, 1933. The genetics and cytology of some interspecific 

hybrids of Avena. Jour. Genetics, 27: 133-179, 
PIETERH, A. J., and E. A. HOLLOWELL, 1937. Clover improvement. U.S. 

Dept. Agr. Yearbook, pp. 1190-1214. 

PORTER, D. R., 1933. Watermelon breeding. Hilgardia, 1: 585-624. 
POWERS, LsRoY, 1932, Cytologic and genetic studies of variability of 

strains of wheat derived from interspecific crosses. Jour. Agr. Research. 

44:797-831. 
, 1934. The nature and interaction of genes differentiating habit c 

growth in a cross between varieties of Triticum vulgare. Jour. Agr. 

Research, 49 : 573-605. 



LITERATURE CITATIONS 395 

-, 1936. The nature of the interaction of genes affecting four quan- 
titative characters in a cross between Hordeum deficiens and vulgare. 
Genetics, 21 : 398-420. 

-, and LEE HINES, 1933. Inheritance of reaction to 'stem rust and 



barbing of awns in barley crosses. Jour. Agr. Research, 46: 1121-1129. 

PRELL, II., 1921. Das Problem der Unbefruchtbarkeit. Naturwiss t 20: 
440-446. 

QUISENBERRY, K. S., and J. A. CLARK, 1933. Inheritance of awn develop- 
ment in Sonera wheat crosses. Jour. Am. Soc. Agron., 25 : 482-492. 

RASMUSSON, J., 1935. Studies on the inheritance of quantitative characters 
in Pisum. Hereditas, 20: 161-180. 

REED, G. M., 1935. Physiological specialization of the parasitic fungi. 
Botanical Review, 1: 119-137. 

, 1940. Physiologic races of oat smuts. Am. Jour. BoL, 27: 

135-143. 

REID, D. A., 1938. A study of the inheritance of seedling and mature plant 
reaction to Puccinia graminis tritici in a cross of Wisconsin 38 X 
Peatland barley. M.S. thesis, University of Minnesota. 

RICKEY, F. D., 1922. The experimental basis for the present status of corn 
breeding. Jour. Am. Soc. Agron., 14: 117. 

, 1924. Effects of selection on the yield of a cross between varieties 

of corn. U.S. DepL Agr. Bull. 1209. 

, 1927. The convergent improvement of selfed lines of corn. Am. 

Naturalist, 61 : 430-449. 

, and L. S. MAYER, 1925. The productiveness of successive genera- 
tions of self-fertilized lines of corn and of crosses between them. U.S. 
Dept. Agr. Bull. 1354. 

, and G. F. SPRAGUE, 1931. Experiments on hybrid vigor and con- 
vergent improvement in corn. U.S. Dept. Agr. Tech. Bull. 267. 
-, G. H. STRINGFIELD, and G. F. SPRAGUE, 1934. The loss in yield 



that may be expected from planting second generation double-crossed 

seed corn. Jour. Am. Soc. Agron., 26: 196-199. 
RIDER, PAUL R., 1939. An Introduction to Modern Statistical Methods. 

John Wiley & Sons, Inc., New York. 
RIEMAN, G. H., 1939. The importance of disease resistant varieties in a 

programme of vegetable seed production. Annual Rept. Canadian Seed 

Growers' Assoc., Ottawa. 
RILEY, H. P., 1934. A further test showing the dominance of self-fertility to 

self-sterility in shepherd's purse. Am. Naturalist, 68: 60-64. 
, 1936. The genetics and physiology of self -sterility in the genus 

Capsella. Genetics, 21 : 24-39. 
ROBERTS, W. L., aDd K. P. LINK, 1937. Determination of coumarin and 

mclilotic acid. Ind. and Eng, Chem., 9: 438-441. 

ROBERTSON, D. W., 1933. Inheritance in barley. Genetics, 18: 148-158. 
, G. A. WIEBE, and F. R. IMMER, 1941. A summary of linkage studies 

in barley. Jour. Am. Soc. Agron., 33: 47-64. 
ROSA, J. T., 1927. Results of inbreeding melons, Proc. Amer, Soc, Hort, 

ScL } 24:79-84, 



396 METHODS OF PLANT BREEDING 

SABOE, L. C., and H. K. HAYES, 1941. Genetic studies of reactions to smut 

and firing in maize by means of chromosomal interchanges. Jour. Am. 

Soc. Agron., 33 : 463-470. 
SALMON, S. C.,' 1931. An instrument for determining the breaking strength 

of straw and a preliminary report on the relation between breaking 

strength and lodging. Jour. Agr. Research, 43: 73-82. 
, 1 938. Generalized standard errors for evaluating bunt experiments 

with wheat. Jour. Am. Soc. Agron., 30: 647-663. 
SANSOME, F. W., and J. PHILP, 1939. Recent Advances in Plant Genetics, 

Ed. 2. The Blakiston Company, Philadelphia. 
SAUNDEBS, H. A., and S. HUMPHRIES, 1928. The Saunders test. Jour. 

Inst. Agr. Bot., 2 : 34. 
SCOTT, G. W., 1932. Inbreeding studies with Cucumis melo. Proc. Amer. 

Soc. Hort. Sci., 29: 485. 
SHAMEL, A. D., and C. S. POMEROY, 1932. Bud variations in apples. Jour. 

Heredity, 23: 173-180, 213-220. 
, L. B. SCOTT, and C. S. POMKROY, 1918a. Citrus-fruit improvement: 

A study of bud variation in the Washington navel orange. U.S. Dept. 

Agr. Bull. 623. 
, L. B. SCOTT, and C. S. POMEROY, 19186. Citrus-fruit improvement: 

A study of bud variation in the Valencia orange. U.S. Dept. Agr. Bull. 

624. 
-, L. B. SCOTT, and C. S. POMKROY, 1918c. Citrus-fruit improvement: 



A study of bud variation in the Marsh grapefruit. U.S. Dept. Agr. 

Bull. 697. 
SHAW, F. J. F., A. R. KHAN, and M. A LAM, 1931. Studies in Indian oil 

seeds. V. The inheritance of characters in Indian linseed. Indian 

Jour. Agr. Sci., 1 : 1-57. 
SHULL, G. H., 1909. A pure line method of corn breeding. Am. Breeders 

Assoc. Rept. 5: 51-59. 
, 1910. Hybridization methods in corn breeding. Am. Breeders 

Magazine 1 : 98-107. 

1914. Duplicate genes for capsule form in Bursa bursa-pastoris. 



Zietschr. fur Induk. Abstamm. u. Vererb., 12: 97149. 
SMITH, D. C., 1934. Correlated inheritance in oats of reaction to diseases 

and other characters. Minn. Agr. Exp. Sta. Tech. Bull. 102. 
SMITH, II. H., 1939. The induction of polyploidy in Nicotiarui species and 

species hybrids. Jour. Heredity, 30: 291-306. 
SMITH, L. H., and A. M. BRUNSON, 1925. An experiment in selecting corn 

for yield by the method of the ear-row breeding plot. 111. Agr. Exp. 

Sta. Bull. 271. 
SNEDECOR, G. W., 1940. Statistical Methods, Ed. 3. Iowa State College 

Press, Ames, Iowa. 
SNELLING, R. O., R. A. BLANCH ARD, and J. H. BIGGER, 1940. Resistance 

of corn strains to the leaf aphid, Aphis maidis Fitch. Jour. Am. Soc. 

Agron., 32: 371-381. 
, and R. G. DAHMS, 1937. Resistant varieties of sorghum and corn in 

relation to chinch bug control in Oklahoma. Okla. Agr. Exp. Sta. Bull, 

232, 



LITERATURE CITATIONS 397 

SPILLMAN, W. J., 1909. The hybrid wheats. Wash. Agr. Exp. Sta. Bull. 89. 
SPRAGUE, G. F., 1936. Hybrid vigor and growth rate in a maize cross and 

its reciprocal. Jour. Agr. Research, 63: 81^-830. 
, and A. A. BRYAN, 1941. The segregation for genes affecting yield 

prepotency, lodging and disease resistance in F$ and ^4 lines of corn. 

Jour. Am. Soc. Agron., 33: 207-214. 
STADLEB, L. J., 1928. Mutations in barley induced by x-rays and radium. 

Science, 68: 186-187. 
, 1929. Chromosome numbers and the mutation rate in Avena and 

Triticum. Proc. Nat. Acad. Sci., 16: 876-381. 
STAKMAN, E. C., 1914. A study of cereal rusts: physiological races. Minn. 

Agr. Exp. Sta. Bvll. 138. 

, L. O. KUNKEL, A. J. RlKER, J. H. CRAIGIE, H. A. RODENHISER, 

and J. J. CHRISTENSEN, 1940. The genetics of pathogenic organisms, 
pp. 9-17, 22-27, 46-56, and 66-90. Publication of American Associa- 
tion for the Advancement of Science, No. 12. Science Press. 
-, M. N. LEVINE, J. J. CHRISTENSEN, and K. ISENBECK, 1935. Die 



Bestimmung physiologischer Rassen pflanzenpathogener Pilze. Nova 

Acta Leopoldina (N.S.), 3: 281-336. 
STANFORD, E. H., and F. N. BRIGGS, 1940, Two additional factors for 

resistance to mildew in barley. Jour. Agr. Research, 61: 231-236. 
STANTON, T. R., 1933. Navarro oats. Jour. Am. Soc. Agron., 26 : 108-1 12. 
, 1936. Superior germ plasm in oats. U. S. Dept. Agr. Yearbook, 

pp. 347-414. 
, and H. C. MURPHY, 1933. Oat varieties highly resistant to crown 

rust and their probable value. Jour. Am. Soc. Agron., 26 : 674683. 
, H. C. MURPHY, F. A. COFFMAN, and H. B. HUMPHREY, 1934. 

Development of oats resistant to smuts and rusts. Phytopathology, 24 : 

165-167. 
, G. M. REED, and F. A. COFFMAN, 1934. Inheritance of resistance 

to loose smut and covered smut in some oat hybrids. Jour. Agr. 

Research, 48: 1073-1083. 
STAPLEDON, R. G., 1931. Self- and cross-fertility and vigour in cocksfoot 

grass (Dactylis glomerata L.). Welsh Plant Breeding Station Bull., 

Series H, No. 12, pp. 161-180. 
STEPHENS, J. C., and J. R. QUINSY, 1933. Bulk emasculation of sorghum 

flowers. Jour. Am. Soc. Agron., 26: 233-234. 
STEVENSON, F. J., 1928. Natural crossing in barley. Jour. Am. Soc. 

Agron., 28: 1193-1196. 
STEVENSON, T. M., and J. S. CLAYTON, 1936. Investigations relative to the 

breeding of coumarin-free sweet clover, Melilotus. Can. Jour. Research, 

14: 153-165. 
, and W. J. WHITE, 1940. Investigations concerning the coumarin 

content of sweet clover. Sci. Agr., 21 : 18-28. 
STEWART, GEORGE, 1926. Correlated inheritance in wheat. Jour. Agr. 

Research, 33: 1163-1192. 
STURTEVANT, E. L., 1899. Varieties of corn, U.S. Dept. Agr. Office Exp. 

Sta. Butt. 57. 



398 METHODS OF PLANT BREEDING 

SUMMERBY, R., 1934. The value of preliminary uniformity trials in increas- 
ing the precision of field experiments. MacDonald College (McGill 

University) Tech. Bull. 15. 
SUNESON, C. A., 1937. Emasculation of wheat by chilling. Jour. Am. Soc. 

Agron., 29: 247-249. 
SURFACE, F. M., 1916. Studies on oat breeding. III. On the inheritance 

of certain glume characters in the cross of Avenafatua X A. saliva var. 

Kherson. Genetics, 1 : 252-286. 
TAMMES, TINE, 1928. The genetics of the genus Linum. Bibliog. Genetica 

4; 1-36. 
TEDIN, OLOF, 1931. The influence of systematic arrangement upon the 

estimate of error in field experiments. Jour. Agr. Sci., 21: 191-208. 
TIPPETT, L. H. C., 1927. Tracts for Computers. No. XV. Random 

Sampling Numbers. Cambridge University Press, London. 
TISDALE, W. H., 1916. Relation of soil temperature to infection of flax by 

Fusarium lini. Phytopathology, 6: 412-413. 
, 1917. Flax wilt. A study of the nature and inheritance of wilt 

resistance. Jour. Agr. Research, 11: 573-605. 
TORRIE, J. H,, 1939. Correlated inheritance in oats of reaction to smuts, 

crown rust, stem rust, and other characters. Jour. Agr. Research, 69: 

783-804. 
TYSDAL, H. M., 1941. Effect of self-pollination upon seed and forage yield 

in alfalfa. Unpublished. 
, and J. R. GAEL, 1938. A new method for alfalfa emasculation. 

Jour. Am. Soc. Agron., 32: 405-407. 

and T. A. KIEBSELBACH, 1939. Alfalfa nursery technic. Jour. 



Am. Soc. Agron., 31: 83-98. 

U.S. Dept. Agr. Yearbook of Agriculture, 1936. 

U.S. Dept. Agr. Yearbook of Agriculture, 1937. 

VALLE, O., 1931. Untersuchungen liber die Selbststerilitat und Selbstfer- 
tilitat des Timothes (Phleurn pratense L.) und die Einwirkund der 
Selbstbefruchtuiig auf die Nachkommenschaft. Eine ziichtungs- 
methodische Studie. Acta Agralia Fennica, 24: 1-257. 

VAVILOV, N. L, 1939. Genetics in the U.S.S.R. Chron. BoL, 6: 14-15. 

, and E. S. KOUZNETSOV, 1921. On the genetic nature of winter and 

spring varieties of plagts. Izvestii Agron. Facul'tete Saratovskogo Univ. 
(Bull. Agron. Faculty Saratov Univ.), pp. 1-25. (In Russian; English 
summary, pp. 23-25.) 

VILMORIN, Louis DE, 1856. Note sur la creation d'une nouvelle race de 
betterave a sucre, pp. 25-29. Notices sur 1 'amelioration des plantes, 
by Louis Levque de Vilmorin and Andre* Lev^que de Vilmorin. Vil- 
morin- Andrieux, Paris. 

VOGEL, O. A., 1938. The relation of lignification of the outer glume to 
resistance to shattering in wheat. Jour. Am. Soc. Agron. , 30 : 599-603. 

WADE, B. L., 1937. Breeding and improvement of peas and beans. U.S. 
Dept. Agr. Yearbook, pp. 251-282. 

WALKEK, J. C., 1935. Types of disease resistance. Zesde Internationaal 
Botanisch Congress Proc. 2 : 200-208, 



LITERATURE CITATIONS 399 

WALLACE, H. A,, and E. N. BRESSMAN, 1928. Corn and Corn Growing. 

John Wiley & Sons, Inc., New York. 
, and G. W. SNEDECOR, 1931, Correlation and machine calculation. 

Revised. Iowa State College Pub. 30. 
WANG, K. W., 1939. Some phases of heterosis in corn. Ph.D. thesis. 

University of Minnesota. 
WARMKE, H. E., and A. F. BLAKESLEE, 1939. Induction of simple and 

multiple polyploidy in Nicotiana by colchicine treatment. Jour. 

Heredity, 30: 419-432. 
W ATKINS, A. E., 1940. The inheritance of glume shape in Triticum. Jour. 

Genetics 39 : 249-264. 
, and SYDNEY ELLERTON, 1940. Variation and genetics of the awn 

in Triticum. Jour. Genetics, 40 : 243-270. 

WEIBEL, R. O., and K. S. QUISENBERRY, 1941. Field versus controlled freez- 
ing as a measure of cold resistance of winter wheat varieties. Jour. 

Am. Soc. Agr on., 33: 336-343. 
WELLHATJSEN, E. J., 1937. Genetics of resistance to bacterial wilt in maize. 

Iowa Agr. Exp. Sta. Res. Bull. 224. 
WELSH, J. N., 1931. The inheritance of stem rust reaction and lemma 

colour in oats. Sci. Agr. 12 : 209-242. 
, 1937. The synthetic production of oat varieties resistant to race 6 

and certain oilier physiologic races of oat stem rust. Canadian Jour. 

Research, 16 : 58-69. 
WEXELSEN, H., 1934. Quantitative inheritance and linkage in barley. 

Hereditas, 18 : 307-348. 
WHALEY, W. G., 1939a. A development analysis of heterosis in Lycoper- 

sicum. I. The relation of growth rate to heterosis. Am. Jour. Botany, 

26:609-616. 
, 19396. A development analysis of heterosis in Ly coper si cum. II. 

The role of the apical meristem in heterosis. Am. Jour. Botany, 26: 

682-690. 
WHITAKER, T. W., and I. C. JAGGER, 1937. Breeding and improvement of 

cucurbits. U.S. Dept. Agr. Yearbook, pp. 207-232. 
WIEBE, G. A., 1935. Variation and correlation in grain yields among 1500 

wheat nursery plots. Jour. Agr. Research, 50: 331-357. 
WIENER, W. T. G. ? 1937. The Canadian Seed Growers' Association. Her- 
bage Reviews, 5: 14-18. Imp. Bur. Plant Genetics: Herbage Plants. 
WILLIAMS, C. G., 1905. Pedigreed seed corn. Ohio Agr, Exp. Sta. 

Circ. 42. 
, 1907. Corn breeding and registration. Ohio Agr. Exp. Sta. Circ. 

66. 
, and F. A. WELTON, 1915. Corn experiments. Ohio Agr. Exp. Sta. 

Bull. 282. 
WILLIAMS, R. D,, 1931 a. Self- and cross-sterility in red clover. Welsh 

Plant Breeding Station Bull, Series H, No. 12, pp. 181-208. 
, 19316. Self- and cross-sterility in white clover. Welsh Plant 

Breeding Station Bull., Series H. No. 12, pp. 209-216. 



400 METHODS OF PLANT BREEDING 



, 1931c. Methods and techniques of breeding red clover, white 

clover and lucerne. Imp. Bur. Plant Genetics: Herbage Plants Bull. 3, 

pp. 46-76. 
WRIGHT, SEWALL, 1921. 'Systems of mating. V, General considerations. 

Genetics, 6: 167-178. 
Wu, SHAO-KWEI, 1939. The relationship between the origin of selfed lines 

of corn and their value in hybrid combination. Jour. Am. Soc. Agron., 

31 : 131-140. 
YASTTDA, S., 1934. Physiological research on self-incompatibility in Petunia 

violacea. Bull. Imp. Col. Agri. and Forestry Morioka, 20: 1095. 
YATES, F., 1933. The analysis of replicated experiments when the field 

results are incomplete. Empire Jour. Exp. Agr., 2: 129-142. 
, 1936. A new method of arranging variety trials involving a large 

number of varieties. Jour. Agr. Sci.j 26: 424-455. 
, 1939. The recovery of inter-block information in variety trials 

arranged in three-dimensional lattices. Ann. Eugenics, 9: 136-156. 



GLOSSARY 

Allele, allel, allelomorph: adjective forms: allelic, allelomorph ic. One of a 
pair, or of a series of factors, that occur at similar loci of homologous 
chromosomes and for this reason are inherited in alternative pairs. 
One alternative form of a gene. 

Aleurone. The protein grains found in the endosperm of ripe seeds. 

Aleurone layer. In wheat and maize, the outer differentiated layer of cells 
of the endosperm; named thus because these cells are filled with aleurone 
grains. 

Allopolyploid. A polyploid having chromosome sets from different sources, 
such as different species. A polyploid containing genetically different 
chromosome sets; for example, from two or more species. 

Amphidiploid. A plant possessing the sum of the somatic chromosome 
numbers of two species. 

Andromonoecious. A plant bearing bisexual or complete flowers instead of 
strictly pistillate ones in addition to staminate flowers. 

Aneuploid. An organism or cell having a chromosome number other than 
an exact multiple of the nionoploid or basic number. Hyperploid 
higher. Hypoploid = lower. 

Anthesis. The period or act of flowering. 

Apogamy. The development of a sporophyte from some other cell or cells 
of the gametophyte (embryo sac) instead of from a gamete (egg). 

Apomixis. The development of an individual from an unfertilized egg 
without sexual fusion, whether the egg be normally haploid or abnor- 
mally diploid through failure of reduction division. 

Autogamous. Self-fertilizing. 

Autopolyploid. A polyploid arising through the multiplication of the com- 
plete genom complement of a species; e.g.j an autotetraploid has four 
identical sets of chromosomes. 

Awn. A bristle-shaped elongated appendage or extension to a glume, 
akene, anther, etc. 

Backcross. The cross of a hybrid to one of the parental types. The off- 
spring of such a cross is referred to as the backcross generation. 

Backcross method of breeding. A system of breeding carried out by several 
generations of backcrossing and subsequent selection. The characters 
of the recurrent parent are retained for the most part, and a few charac- 
ters from the nonrecurrent parent are added. 

Biometry. The application of statistical methods to the study of biological 
problems. 

Biotype. A population of individuals with identical genetic constitution. 
A biotype may be homozygous or heterozygous. 

401 



402 METHODS OF PLANT BREEDING 

Bivalent. A pair of synapsed or associated homologous chromosomes. 
Bud-sport* A branch, flower, or fruit that differs genetically from the 

remainder of the plant. 
Bulk method of breeding. The growing of segregating generations of a 

hybrid of self-pollinated crops in a bulk plot, with or without mass 

selection, followed by individual plant selection in Fe or later 

generations. 
Caryopsis. A one-seeded dry fruit with the thin pericarp adherent to the 

seed, as in most grasses. 
Chaff. The floral parts of cereals, generally separated from the grain in 

threshing or winnowing. 

Character. One of the many details of structure, form, substance, or func- 
tion that make up an individual organism. The Mendel ian characters 

of genetics represent the end products of development, during which the 

entire complex of genes interacts within itself and with the environment. 
Chimera. A mixture of tissues of genetically different constitution in the 

same part of an organism. It may result from mutation, irregular 

mitosis, somatic crossing over, or artificial fusion (grafting) . There are 

two main types, periclinial with parallel layers of genetically different 

tissues and sectorial. 
Chi-square (x 2 ) test. A statistical comparison of observed with theoretical 

ratios. 
Goodness of fit. Comparison of observed Mendelian ratio with a 

theoretical. 

Independence. A test for association between two series of variables. 
Chromatids. Half chromosomes, resulting from longitudinal division, that 

later became daughter chromosomes. 
Chromosomes. Microscopically small, dark-staining bodies visible in the 

nucleus of the cell at the time of nuclear division. The number in any 

species is usually constant. They carry the genes, arranged in linear 

order. 

Class. A group that includes variates of similar magnitude. 
Clon. All the individuals derived by vegetative propagation from a single 

original individual. 

Coefficient of variability. A measure of variability expressed in percentage. 
Combining ability. The relative ability of a biotype to transmit desirable 

performance to its crosses. 

Complementary genes. Genes that interact to produce a new character. 
Convergent improvement. A system of double backcrossing for the purpose 

of improving each of two inbred lines without greatly modifying the 

yield of their F\ cross, 
Correlation coefficient. A statistical measure of relationship between 

two or more series of variables. 

Simple. The total correlation between two series of variables. 
Partial. The correlation between two series of variables independent of 

the accompanying variation due to other variables. 
Multiple. A coefficient that measures the degree to which the dependent 

variable is influenced by a series of other factors studied. 



GLOSSARY 403 

Coupling* The condition in linked inheritance in which an individual 
heterozygous for two pairs of factors received the two dominant mem- 
bers from one parent and the two recessives from the other parent; 
y/e.0., A ABB X aabb. 

Crossing over. The exchange of corresponding segments between the 
chromatids of paired (homologous) chromosomes. It is a process 
inferred genetically from new associations of linked factors and inferred 
cytologically from new associations of parts of chromosomes, both of 
which may be observed in heterozygotes. It results in an exchange of 
factors and therefore in combinations of factors differing from those 
that came in with the parents. The term genetic crossover may be 
applied to these new gene combinations. 

Cross-pollination. The pollination of a plant by pollen of a different 
plant. 

Deficiency, The absence, "deletion," or inactivatkm of a segment of a 
chromosome. 

Deletion. The absence of a segment of a chromosome involving one or more 
genes, 

Detassel. To remove the tassel, as in maize. 

Dioecious. Having male and female flowers on different plants. 

Diploid. An organism with two sets of chromosomes. 

Disease garden. A special nursery for the study of reaction to specific 
pathogens. 

Dominant. A term applied to one member of an allelic pair of characters 
-that has the quality of manifesting itself wholly or largely to the exclu- 
v sion of the other member. 

Double cross. A term used particularly in corn, where four inbred lines 
are used as parents. The double cross is the F\ cross between two single 
v' crosses. 

Duplicate genes. Two separately inherited factors, either alone or together, 
giving similar effects. 

Duplication.- The occurrence of a segment more than once in the same 
chromosome or genom. 

Ear. A large, dense, or heavy spike or spike-like inflorescence, as the ear 
of maize. Popularly applied also to the spike-like panicle of such 
grasses as wheat, barley, timothy, and rye. 

Emasculation. The act of removing the anthers from a flower. 

Endosperm. The nutritive tissue formed within the embryo sac in seed 
plants. It commonly arises following the fertilization of the two 
primary endosperm nuclei of the embryo sac by one of the two male 
"' sperms. In a diploid organism, the endosperm is triploid. 

Epistasis. The suppression of a character dependent upon the action of 
a gene or genes by a gene or genes not allelic to those suppressed. 
Those characters suppressed are said to be hypostatic. Distinguished 
from dominance that refers to the members of one allelic pair. 

Euploid. An organism or cell having a chromosome number which is an 
exact multiple of the monoploid or haploid number. Terms used for a 
euploid series are haploid, diploid, triploid, tetraploid, etc. 



404 METHODS OF PLANT BREEDING 

Fi* The first filial generation. The first generation of a given mating, 
F*. The second filial generation, produced by crossing inter se or by self- 
pollinating the Fi. 
Factor. The same as gene. 
Fatuoids. Mutants occurring in cultures of cultivated oats and possessing 

characters of A vena fat ua, wild oats. 
Fertility. The ability to produce viable offspring. 

Fertilization. The fusion of a male gamete (sperm) with a female gamete 
(egg) and of their nuclei, without which their later development is 

usually impossible. 
Floret. A small flower, especially one of an inflorescence, as in grasses and 

Compositae. 
Foundation stock seed. Seed that has descended from a selection of 

recorded origin, under the direct control of the original breeder, a 

delegated representative, or of a state or federal experiment station. 
Gamete. A mature male or female reproductive coll (sperm or egg). 
Gene.- The hypothetical unit of inheritance located in the chromosome, 

which by interaction with the other genes and the environment controls 

the development of a character. Genes arc believed to be arranged 

linearly in the chromosomes. 
Genom. A complete set of chromosomes (hence of genes), inherited as a 

unit from one parent. 

" Genotype. The fundamental hereditary constitution of an organism. 
Glabrous. Smooth, without hairs. 
Glume. One of the two empty chaffy bracts at the base of each spikelet 

in grasses. 

Grain. Cereal seeds in bulk. Seed-like fruit of any cereal grass. 
Haploid. An organism or cell having only one complete set of chromosomes. 
Head. A dense, short cluster of sessile or nearly sessile flowers on a very 

short axis or receptacle, as in red clover or sunflower. 
Heteroploid. An organism characterized by a chromosome number other 

than the true euploid number. 
Heterosis. Hybrid vigor. 
Heterozygous. The condition in which the homologous chromosomes of an 

individual possess different genes of the same allelic series. 
Homologous. Chromosomes occur in somatic cells in pairs that are similar 

in size, shape, and supposedly in function, one being derived from the 

male and one from the female parent. The two members of such a 

pair are spoken of as homologous chromosomes. 
Homozygous. Possessing identical genes with respect to any given pair or 

series of alleles. 
Hull. The term applied to include the lemma and palea when they remain 

attached to the caryopsis after threshing. 
Hybrid vigor. The phenomenon in which the cross of two stocks produces 

hybrids that show increased vigor. 
Hybrids. The progeny of a cross-fertilization of parents belonging to 

different genotypes. 
Hypostasis. See Epistasis. 



GLOSSARY 405 

Inbred Line. A relatively homozygous line produced by inbreeding and 

selection. 

Inbred-variety Cross. The F\ cross of an inbred line with a variety. 
Inflorescence. The flowering part of a plant. 

Interchange. An exchange of segments of nonhomologous chromosomes. 
Interference. The property by which the occurrence of one crossover 

reduces the chance of occurrence of another in its neighborhood. 
Inversion. A rearrangement of a group of genes in a chromosome in such 

a way that their order in the chromosome is re versed. 
Keel. A central ridge resembling the keel of a boat, as in the glumes of 

some grasses, etc. ; also, the inferior petal in the legume flowers. 
Kernel. The inner portion of a seed within the integuments. Also the 
t whole grain of a cereal. 
Latin square. An experimental design for comparing treatments where the 

number of replications is the same as the number of treatments and 

each treatment occurs only once in each row and column. Especially 

adapted for accurate comparisons with a small number of treatments. 
Lattice designs. Designs developed for testing a large number of treat- 
ments, in which the number of blocks exceeds the number of complete 

replications. 
Lethal gene. A gene that renders in viable an organism or a cell possessing 

j it. 
Linkage. Association of characters in inheritance, due to the fact that the 

genes determining them are physically located in the same chromosomes. 

Such a group of linked genes is called a linkage group. 
Lodicule. A minute scale at the base of the ovary opposite the palea in 

grasses, usually two in number, probably representing the reduced 

perianth. 
Mass selection. Selection for some desired character, or characters, where 

progeny of the plants or heads selected are grown in bulk. 
Mature-plant resistance. A term applied particularly to resistance to stem 

rust in the stages from heading to maturity where this resistance is not 

correlated with seedling reaction. 
Mean. The arithmetic average. 
Megaspore (macrospore). A spore having the property of giving rise to a 

gametophyte (embryo sac) bearing only a female gamete. One of the 

four cells produced by two meiotic divisions of the megaspore- 

mother-cell (megasporoeyte). 
Meiosis. The process by which the chromatin material becomes reduced 

qualitatively and quantitatively to half the somatic number. It is 

completed in the two divisions, meiotic mitoses, which precede the 

formation of gametes in animals, or of spores in plants. 
Microspore. One of the four cells produced by the two meiotic divisions 

(mitoses) of the microspore-mother-cell (microsporocyte). A spore 

having the property of giving rise to a gametophyte bearing only male 

gametes. 
Mitosis. The process by which the nucleus is divided into two daughter 

nuclei. 



406 METHODS OF PLANT BREEDING 

Somatic mitosis. The process by which the daughter nuclei are identical, 

quantitatively and qualitatively. 
Meiotic mitoses. Two nuclear divisions that result in spores in higher 

plants and in gametes in animals. Both divisions are necessary to 

complete reduction. 

Mode. The class of greatest frequency in a frequency distribution. 
Modifier or modifying Gene. A gene that affects the expression of another 

nonallclic gene. 

Monoecious. With separate male and female flowers on the same plant. 
Multiple alleles. A series of alleles in similar loci of homologous chromo- 
somes of related races. 
Multiple cross. A cross between more than two parental lines of different 

origin. 
Multiple -factor hypothesis. -The type of inheritance in which a character 

is dependent on many different genes or factors. 
Mutation. A sudden variation that is inherited. The term is used loosely 

to include "point mutations" of a single gene and chromosomal changes. 
Nonrecurrent parent. -IT sec I in backcrosses to refer to the original parent 

not used in backcross generations. 

Ovary. The swollen part of the pistil that contains the ovules. 
Ovule. The macrosporangium of flowering plants, consisting of the nucellus 

plus the integuments. 

Pi, P^ etc. The first, second, etc., parental generation of a parent. 
Palea. The upper of the two bracts immediately enclosing each floret in 

grasses. 
Panicle. A compound inflorescence with pedicel ed flowers, usually loose 

and irregular, as in oats, rice, proso, etc. 
Parthenogenesis. The development of a new individual from a germ cell 

without fertilization. 

Pedicel. A stalk on which an individual blossom is borne. 
Pedigree method of breeding. A system of individual plant selection during 

the segregating generations of a cross where the progeny plants usually 

are separately spaced and the pedigree of particular selections is known. 
Peduncle. The primary stalk supporting either an inflorescence or a solitary 

flower. In grasses, the uppermost iriternode of the culm. 
Pericarp. The mature or ripened ovary wall around the ovule. 
Phenotype. The observed character of an individual without reference to 

its genetic nature. Individuals of the same phenotype look alike but 

may not breed alike. 
Physiologic races. Biotypes or groups of biotypes within species that 

behave more or less consistently in pathogenicity on certain differ- 
ential varieties or host plants. Physiologic races sometimes are 

differentiated on the basis of cultural or physiochemical characters. 
Physiological resistance. A type of resistance due to physiological or 

protoplasmic incompatibility between the host plant and the pathogen. 
Pistil. That part of the flower consisting of ovary plus style and stigma. 
Polyploid. An organism with more than two sets of a basic or rnonoploid 

number of chromosomes, e.g., triploid, tetraploid, pentaploid, hexaploid, 

heptaploid, octoploid, etc. 



GLOSSARY 407 

Proterandry. The maturing and functioning of stamens before pistils in 

hermaphroditic flowers or in different flowers of the same plant in a 

monoecious species. 

Proterogyny. The reverse of proterandry. 
Pubescent. Hairy, in a general sense; in special use, covered with short 

soft hairs. 
Pure line. A strain of organisms that is comparatively pure genetically 

(homozygous) because of continued inbreeding or through other means. 
Quadrivalent. Association of homologous chromosomes in groups of four. 
Qualitative characters.- Characters that are qualitatively different, so that 

separation is relatively easy. 
Quantitative characters. Characters that show a continuous range in 

variability, making separation into distinct classes difficult. 
Randomized blocks. An experimental design in which the treatments are 

arranged in random order within the blocks or replicates. 
Recessive. -A term applied to one member of an allelic pair lacking 

the ability to manifest itself wholly or in part when the other or domi- 
nant member is present. 
Recombination. The observed new combinations of characters different 

from those combinations exhibited by the parents. Percentage of 

recombination equals percentage of crossing over only when the genes 

are relatively close together. Cytological crossing over refers to the 

process; recombination or genetic crossing over refers to the observed 

genetic result. 
Reciprocal crosses.- Crosses where the parental plants or lines are used as 

both male and female. 
Recurrent parent. Used in backcrosses to refer to the parent to which the 

first cross and backcrossed plants are crossed. 
Reduction division; heterotypic division. Terms formerly applied to the 

one of the mciotic mitoses at which a particular author thought reduc- 
\ tion and segregation occurred. 
"Registered seed. Seed of a variety or strain that is the multiplied progeny 

of foundation stock seed and traces directly to it and that complies with 
J certain standards of purity and quality. 
Regression coefficient. A coefficient that gives the rate of change in one 

variable (dependent variable) per unit rate of change in another 

(independent variable) . 

Replication. Repetition of treatments in experiments. 
Repulsion. The condition in linked inheritance in which an individual 

heterozygous for two pairs of linked factors received the dominant 

member of one pair and the recessive member of the other pair from one 

parent and the reverse condition from the other parent; e.g., 

A Abb X aaBB. 

Rod row. A type of field plot approximately 1 rod long. Used particularly 
\ with small grains where the seed is sown without definite spacing. 
Roguing. The act of removing undesirable individuals from a varietal 

mixture in the field by hand selection. 
Seed. The mature ovule, consisting of the kernel and its integuments. 

Also used for the seedlike fruits of cereals. 



408 METHODS OF PLANT BREEDING 

Segregation. The separation of the paternal from maternal chromosomes 

at meiosis and the consequent separation of differences as observed 

genetically in the offspring. 
Self-fertilization. The union of the egg cell of one individual with a sperm 

cell of the same individual. 

Self -incompatibility. Some physiological hindrance to self-fertilization. 
Sib mating. Crossing of siblings, two or more individuals of the same 

parentage (brother-sister mating). 
Single cross. A cross between two inbred lines. 
Somatic. Referring to body tissues; having two sets of chromosomes, one 

set normally coming from the female parent and one from the male, as 

contrasted with germinal tissue that will give rise to germ cells. 
Somatoplastic sterility. The collapse of fertilized ovules during the early 

developmental stages. 
Species. A group of individuals so much alike that it may reasonably be 

assumed that they have arisen from a common ancestor. 
Speltoid. Mutants occurring in cultures of common wheat, Triticum 

vulgare, and possessing characters of T. spelta, spelt wheat. 
Spike. A simple inflorescence with the flowers sessile or nearly so on a 

more or less elongated common axis or rachis. 
Spikelet. A small or secondary spike, especially in the inflorescence of 

grasses. 
Standard deviation. A measure of variability in terms of the units of 

measurement. Frequently refers to the infinite population. 
1 Standard error. Similar to standard deviation, except that it is calculated 

from a sample. 

Sterility. Inability to produce viable offspring, 
Strain. A group within a variety that constantly differs in genetic factors 

or a single genetic-factor difference from other strains of the same 

variety. 
Strain building. The improvement of cross-pollinated plants by any one of 

several methods of selection. 

Synapsis. The conjugation of homologous chromosomes. 
Synthetic variety. A term used particularly with cross-pollinated plants to 

refer to a variety produced by the combination of selected lines or 

plants and subsequent normal pollination. 
t test. A method for testing the significance of a difference. 
Three-way cross. A cross between a single cross and an inbred line. 
Top-cross. See Inbred-variety cross. 
Transgressive segregation. The appearance in the F 2 (or later) generations 

of individuals showing a more extreme development of a character than 

either parent. Assumed to be due to cumulative and complementary 

effects of genes contributed by the parents of the original hybrid. 

Adequate testing of variation in the parents is required to establish its 

occurrence. 
Translocation. The change in position of a segment of a chromosome to 

another part of the same chromosome or of a different chromosome. 



GLOSSARY 409 

Triploid. An organism whose cells contain three haploid (monoploid) sets 
of chromosomes. 

Trivalent. An association of three homologous chromosomes at meiosis. 

Unit character. Term used for a character believed to be determined by 
the alleles at a single-gene locus. The term is now largely abandoned. 

Univalent. A chromosome unpaired at meiosis. 

Variance. The square of the standard deviation or standard error. 

Xenia. The immediate effect of pollen on the endosperm, due to the 
phenomenon of double fertilization in the seed plants. 

Zygote. The cell produced by the union of two cells (gametes) in reproduc- 
tion; also, the individual developing from such a cell. 



APPENDIX 



TABLE I. TABLE OF /* 



Degrees of 
freedom 


Probability (7*) 


Degree? of 
freedom 


Probability (P) 


.05 


.01 


.05 


.01 


1. 

2 

3 


12 71 
4 30 
3 18 


63,66 
9 92 
5 84 


26 
27 

28 


2 06 

| 2 05 
2 05 


2 78 
2 77 
2.76 


4 


2 78 


4 60 


29 2 04 


2.76 


5 


2 57 


4 03 


30 


2 04 


2.75 


6 


2 45 


3 71 


35 


2 03 


2.72 


7 


2 36 


3 50 


40 


2.02 


2.70 


8 


2 31 


3 36 


45 


2 01 


2.69 


9 


2 26 


3 25 


50 


2 01 


2 68 


10 


2 23 


3 17 


60 


2 00 


2.66 


11 


2 20 


3 11 


70 


1 99 


2 65 


12 


2 18 


3 06 


80 


1.99 


2.64 


13 


2.16 


3 01 


90 


1 99 


2 63 


14 


2 14 


2 98 


100 


1.98 


2.63 


15 


2 13 


2 95 


125 


1 98 


2 62 


16 


2 12 


2 92 


150 


1 98 


2 61 


17 


2.11 


2.90 


200 


1 97 


2.60 


18 


2 10 


2 88 


300 


1 97 


2.59 


19 


2 09 


2 86 


400 


1 97 


2 59 


20 


2 09 


2 84 


500 


1 96 


2.59 


21 


2 08 


2 83 


1000 


1 96 


2 . 58 


22 


2 07 


2 82 


OC 


1.96 


2.58 


23 


2 07 


2 81 








24 


2 06 


2 80 








25 


2 06 


2 79 









'"Abridged from Table IV of Fiwhei's "Statistical Methods tor ileseareh Workers," 
Oliver & Boyd, Edinburgh, and from Table 16 of Wallace and Siiedecor's "Correlation and 
Machine Calculation," by kind penmasion of the authors and publishers. 



411 



412 



METHODS OF PLANT BREEDING 









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CO 


TH 


-t cn 


co to 


CO 10 


CM 


CM * 






o 


$ % 


33 


t- b- 
o eo 


ss 


CM b 

HH rH 


ss 


CD 00 

CM b- 





^ IS 






t- 


to" 


C en 


oo to 
eo 


to eo 

TH 


t cn 


eo b- 


eo 10 


CO IO 


CM <* 


a 

\^t 







CM eo 

.0 o 

CM CO^ 


'"" * 

28 


00 W 

to eo 

00 tO 


o cn 
t>. to 

6 eo* 

rH 


*t en 


co* b- 


CM IO 

CO 00 
CO W 


CO tO 

q o 

co" id 


0? 10 


o 




o 


1 rH (0 
S S 


ft 3 


-H 
CD If 


h- b 


co cn 


I- * 
JT- TH 


'f O 

co cn 


IO TH 
O TH 


CM tO 
00 IO 


rt2 




^ 


,0" 


CD cn 
rH cn 


00 tO 
CO 


to eo 


^ cn 


CO b- 


CO IO 


co 10 


CM "* 


"3 







o oo 

iO IO 


CO b- 


CM O 

co 10 


t- 00 


^8 


oo eo 


00 00 

co <n 


00 O 
CO 


CO ^ 

oo to 


* G 






to" 


CD cn 
rH cn 


oo to 
eo 


to eo 

TH 


*t cn 


CO b* 


eo 10 


CO IO 


CM ** 


^ 'Z 





^ 


3S 


10 to 


CO tO 


l^. CO 

t^ cn 


5 


** TH 
00 CO 


^ 


CM 00 


o co 


fe G 
o o 


C" 


CM 


to" 


CD en 


oo to 
eo 


o eo 

rH 


^ cn 


CO b 


CO tO 


CO IO 


CM * 


u o 

X u, 


(fi 

C 





3 


-H 10 

-t ^ 


co cn 
cr to 


s 


CD 10 
tO IO 


K cn 
oo eo 


^ 2 


2 eo 


CO O 
CD 00 




C3 
<t 


CM 


to" 


CD cn 
-H cn 


oo to 
eo 


tO <# 


t cn 


co f 


co to 


CO IO 


CM < 


b T-H 




S-. 


CO 


co cn 

Tt O 

CM TH 


CO ^l 

-t ^* 


CD CO 
CO 00 


** IO 

00 rH 


9 
to 


CM CO 
CD IO 


CD b- 

^ eo 


O 00 

CM <* 


oo eo 
CD cn 




"^ 




to" 




eo 


rH 












fe 

-4 O 
-s G 


0) 
t-. 

bC 

O 


-f 


>o eo 
to" 


CD cn 
rH cn 


".s 

oo" to 


00 CO 

TH 


HH b- 


CD tO 
CO b^ 


CM IO 

O CO 

co to' 


co to 

CM IO 

eo id 


CM O 



co id 


p> 



o 


2 


-t tO 

to" 


-t <* 

2 * 


-f IO 
00 t* 

eo 


CD CO 


oo en 

CO 00 

"* cn 


o eo 

b; 


CO ) 


00 b- 
CM tO 

co" id 


r- TH 

O TH 

co id 


a oJ 




rH 


co eo 

-t* 00 


5 3 


CD CO 


eo 10 

CD ^ 


o to 
r- en 


co en 

O b- 


o *# 

CO 10 


CO b- 


00 

rH rH 




s~l 


rH 




CD cn 


00 eo 


rH 


rf cn 


-t* b- 


CO tO 


eo 10 


CO IO 


/} "*"* 


o 


o 


CM tO 

-H IO 


eo n* 


00 CO 


co ^*t 

CD IO 


bt 


CO b- 
O 00 


co eo 

CD tO 


-t< eo 
eo oo 


co to 

rH CO 


H 0^ 









CD cn 


oo b- 


'0 * 


rH 


"t b- 


co to 


CO 10 


eo w 


^ -+-' 


bC 

cu 




-f CO 


00 00 

eo eo 


oo eo 


o to 

o to 


00 IO 


O CO 

rH cn 


00 rH 

co b- 


CD TH 

co cn 


00 10 

rH CO 


bC 


- 






rH cn 


GO b- 
CO 


o * 

rH 


^ 


^ f 


eo to 


eo 10 


CO 10 


H 






CO 00 


CO CO 


GO <<* 




CM t- 

00 


>0 

i ( rH 


CO -^ 

b* co 


38 


co b 








o" 


CD cn 

rH W 


00 b- 

eo 


CO "* 
rH 


-* 
rH 


*t 00 


CO tO 


co to 


co 10 


J G 






t- CO 

CO CO 


O * 

co eo 


oo 5 


o en 


00 IO 
00 * 


rH tO 

CM CO 


88 


8S 


CD CO 
CM tO 


1} o 

-I rH 






10" 


CD cn 
rH cn 


00 N 


CD *H 

rH 


't O 
rH 


-* 00 


co b- 


co to 


CO IO 










CO CO 


CD en 


rH CO 


CD tO 


CM * 


i> en 

00 rH 


00 b- 

to eo 


eo 00 


LO 






10" 


TH cn 


00 


CO IO 


rH 


t oo 


co b* 


co to 


CO IO 


*H 

o 






o <* 
eo to 



co eo 


o eo 


CO CO 
CM 10 


O b- 

o en 


CD IO 
CO b- 


r>. to 


CD CO 

co to 


oo to 

<* o 


+H 

02 






10" 


rH cn 


CD 00 


CO iO 


o o 


^ 00 


co b- 


co to 


co to 


0> 






>0 IO 
CM 


tO IO 
CM CO 





CO S 


CD cn 

rH CO 


CO IO 

O TH 


CM IO 

rH 00 


*f TH 

00 O 


co eo 

CD ^ 


^ 






10" 


CD en 
-H cn 


CD 00 


CO IO 

rH 


>O TH 
rH 


-* cn 




CO b- 


co to 


"*" 






CO CO 

rH O 


CD t- 


00 IO 
CM * 


S8 


rH tO 


CO 00 

r e- 


85 


b- cn 

O 10 


00 8 








to" 


2S 


og 


co to 

H 


>O CO 


^ en 


-* oo 


-* b- 


CO tO 








o en 
o cn 


83 


*O TH 

'O 00 


CD 8 


CD b" 
t- CO 


rt CO 

rH cn 


I- M3 


s 


co eo 

CM 










CD cn 


" S 


CO 00 


>o eo 

rH 


10 o 

rH 


<* en 


~* * 


"* 00 








S 


io 3 


CO CO 

rH rH 


8 


CO CO 


CD S 


CD IO 
'O CO 


CM tO 

CO CO 


CM tO 

rH IO 








^ S" 


oo oo 
rH cn 


O ^f 

rH CO 


c 


CO tO 
rH 


o eo 

rH 


' rH 


tO TH 
rH 


'O O 




9 

C 




- 





CO 


, 


. 


CO 


- 


00 


Oi 



APPENDIX 



413 



ST* 
cn 


s 


88 


CM IH 


eo g 


fe 


rH IO 

O b 


s 


01 b- 

O5 IO 


285 


S8S 


rH (O 

00 CO 


CO 


CN W 


CM CO 


01 eo 


CM CO 


04 CO 


CN 04 


Ol 04 


rH 04 


rH 04 


rH 04 


rH O4 


TH* 04 




Jo en 


^8 


rH CO 

co eo 


CM 00 

CM TH 


rf 


g 


o 


05 5 


co en 

05 10 


O5 IO 


>O * 
00 <# 


00 CO 


& 


CM CO 


CM CO 


04 eo 


oi' co' 


01 eo 


O4 04 


O4 O4 


rH 04 


rH 04 


rH 04 


rH 04 


rH O4 


ft 


co to 
10 en 


CM tO 

*# to 


04 TH 

CO ^ 


Ol O4 


28 


O C4 


O CO 


05 O 


a tfi 


O5 IO 


00 5 


00 ^ 




CN CO 


CM CO 


O4 CO 


CM CO 


CM CO 


04 C4 


O4 04 


rH CN 


rH 04 


rH 04 


rH O4 


rH 04 


o3 


o o 


iO O 


o to 

CO * 


CO b 
04 04 


05 TH 

rH TH 


Ol b- 


t- to 

O CO 


01 tO 
C b- 


00 00 
Oi O 


-t O 
OS tO 


S 


l^. b" 

00 ^ 





CM * 


CM CO 


CM CO 


O4 CO 


CM eo 


O4 04 


O4 04 


CM 04 


rH 04 


rH 04 


rH 04 


rH 04 


~3 


CO O 


rP i 


CD en 

CO <* 


00 O 
O4 CO 


CM TH 


2 


00 


3? 


TH 
b- 


co eo 

05 tO 


04 tO 

O5 IO 


/ 


cu 

rj 


CN *# 


CM CO 


CM eo 


CM CO 


Ol CO 


04 CO 


OJ 04 


O4 04 


04 O4 


rH O4 


rH 04 


rH 04 




CO TH 

CM' * 



04 CO 


oi eo 


OJ b- 

CO CO 
O4 CO* 


O4 O4 
CM* CO 


* 

CM eo' 


CO tO 
C4 04 


DO tO 
O 00 
04 04* 


O C^ 

oi w 


O4 04 


CO CO 
O3 tO 
rH' 04 


CO 00 
O5 IO 




I 


CO TH 




~f <0 




Cl 04 


Ol TH 






O 00 


O b- 


05 tO 


O5 tO 


'3 


CM "# 


CM CO 


04 eo 


04 CO 


ot eo 


Ol CO 


CM CO 


04 04 


Ol 04 


04 04 


rH 04 


rH C4 


5 


8 


i o en 





00 TH 


co eo 


ic o 

04 04 


^ S 


12 


^ en 


t- *p 

O CO 


O b- 


04 
b- 


T.J 


CM * 


CM CO 


04 CO 


O4 CO 


CM CO 


04 CO 


O4 CO 


oj eo 


04 04 


CM 


O4 04 


O4 O4 


-3 


K w 

CN <* 


rH C4 

CD O 

04 * 


O 00 
iq t-; 
oi co* 


04 cn 

O4 CO 


10 eo 

CO ^J 

oi co 


CT< cn 

O4 CO* 


-f 00 
04 TH 

Ol CO* 


Ol *> 
OJ CO 


28 

oi n 


rH C4 

rH q 

Ol 04 


oo to 
O 00 
04 0* 


c o 

O 00 
O4 04 


of 


CM" ^ 

CM 04 
00 10 

CM" ^ 


cgS 

s$T 

t en 


C 00 
04 CO 

cToo~ 

co en 

04 CO 


CO b 

"t to 

OJ CO 
04 CO* 


CO IO 

c-i eo 

01 CO* 


co to 

CO CO 
04 CO 

co 5 

04 CO 


00 IO 
O4 04 

oi eo 
co eo 

04 CO* 


co to 

CM TH 

oi eo 

"8 5 

O4 CO 


rH" O 

OJ CO 
01 CO 


iC O 

ri O 

04 CO 

04 TH 
CM CO* 


CJ ^ 

rn en 
oi 04 

CO tO~ 

rH O 

O4 CO 


00 
00 

oi O4 

io cn 
rH en 

04 O4* 

O t- 


o 
<u 

s 

r/T 


oo to 

CM i* 


oi * 




oj eo 


O4 CO 


04 CO 


CM eo 


OJ CO 


04 CO 


Ol CO 


OJ CO 


OJ 
Ol CO 


a> 

(M 


O5 b-; 
CM <# 


3 

oi * 


O5 tO 

CO TH 
01 * 


o to 

co q 

O4 CO 


CO O 

oi eo' 


00 b- 

t to 
oi eo* 


OJ 10 

"f 10 

oi co 


00 10 

CO ^f 
04 CO 


-t b 
CO CO 
04 CO 


CO CO 
04 CO 


00 CO 
04 04 

04" eo 


>0 b- 

04 TH 

O4 CO 


1 


"? 00 
O5 b- 
CM 


04 tO 

00 <# 


04 O4 
I- 04 
04* **" 


CO 04 
CO 
04 "** 


;J 


rH CO 

O4 CO* 


01 eo" 


Tf O 

<N* CO 


CO <* 
Ol CO 


-H tO 
CO CO 

01 eo" 


co co 
oi co 


00 ^H 
01 04 

oi eo" 


u 

cu 


l> 10 

O5 00 
CM "* 


O ^ 
oo 10 

CM* ^ 


8 

01 ""** 


b, o 

CO TH 

oi -* 


s 

O4 CO 


>c o 
ic oo 

O4 CO 


?? 

O4 CO 


>c en 

't IO 

oj eo 


oi co" 


GO CO 
CO <* 
04 CO 


iC b- 
CC CO 
01 CO 


Ol t-4 
CO CO 

oi co 


m 

<A 


CM 10 

o q 

CO* * 


o eo 

o> q 


00 CO 
04 ^ 


04 cn 

04 * 


o eo 

co q 

01 * 


p5 en 

01 CO 


f CO 
CM CO* 


C no 
>o to 
oi co 


CO O 

Hi tO 

04' co 


CO 04 
~V 10 
04 CO 


C IO 

oi eo 


r^ O 

O4 CO 


o 
cu 


o q 

CO 10 


O5 b^ 

CM* "* 


>o o 

00 IO 

04 ^ 


t- O 

1^ CO 

o" *' 


o ** 
r- TH 

O4 * 


co q 

O4 *# 


CM" co' 


>C b 
04 CO* 


CM* CO* 


01 co" 


c to 
oi co' 


04 TH 

*t 10 
oi co 




t TH 
CO 10 


rH 00 

O 00 

co tj* 


04 IO 

O4 "J 


00 ^ 
O4 -^ 


t^ 00 

Ol d 


O "* 

t^ TH 

01 -"di 


CO CO 

co q 

O4 T}i 


oj eo 

co q 

O4 CO 


00 IO 

>c oo 

CM* CO 


Ol CO 


04 TH 
>O t; 

oi co 


O5 IO 

Tf! (^ 

oi co 


o 

OJ 


CM en 
04 eo 


O5 b- 




O 04 
O 00 


Si 2 


.0 to 

00 <# 


C5 04 
t>. CO 


f O 


C O 


CO TH 
CO O 


co en 


b- 

co oo 


iC 00 


Is 




























CO ^< 
CO tO 


O 04 

O4 CO 


rH tO 


01 to 
o oo 


s 


o to 

O3 10 


00 * 


00 CO 


(-- IO 


t^ TH 


rH O 
J>> TH 


00 "* 

CO 


aS 


























f/) 


oo en 


85 


CO TH 

04 *# 


% 8 


^ s 


co en 
o oo 


O b 


CO b- 
O5 tO 


CO 00 
05 IO 


o o 

05 10 


3 


t b 

QO eo 




























o 


rH IO 

IO 


38 


% cn 


* 


-H tO 
CO IO 


83 


04 04 


O 00 

O4 TH 


co cn 

rH O 


Or, ,H 
rH O 


o ^* 
TH cn 


O 00 




o 
T3 


oo to 


co to 


CO IO 


CO IO 


CO IO 


CO IO 


CO IO 


CO IO 


co 10 


CO IO 


co ^ 


CO ^l 





28 

** b-' 


00 O 
05 04 
CO* b-" 


00 CO 

oq en 
co" to 



GO b 

co to 


"t TH 

l> 10 

co to 


oo to 

CO CO 

co to" 


CO CO 
CO O4 
co % to 


O5 TH 
CO* tO 


'"q O 

co" to" 


01 eo 
10 cn 
co ui 


O5 IO 

""t n . 

CO IO 


N. 00 

CO 10 


G 

(_l 


CO "* 

05 O 
-f 6 


"f IO 
GO tO 


to eo 

t>- CO 


co q 


CO 00 


3 & 

~t< CO 


t CO 


"* 06 


^ 00 


00 00 

CO TH 


10 O 

CO TH 


OJ Cf4 

CO O 


a> 

"c 




rH 


Y-H 
rH 


Cl 


ro 


3 


rH 


CO 

T t 


rH 


00 


05 


s 


O4 


a 

OJ 



414 



METHODS OF PLANT BREEDING 









| SS 


co to 


S 


^ S 




K O 


CO 8 


CO 


O O 








1 *HM 


rH Od 


rH Cd 


rH Cd 


rH Cd 




rH Od 


rH (N 


rH Cd 






O 


oo eo 


fcS 


-t CO 


CM O) 


O IO 


00 Cd 





tO tO 

CO O 


** CO 

CO O 










rH Cd 


rH Cd 


rH Cd 


rH Cd 






rH Cd 


rH Cd 






o 


rH |> 


" CO 


CD to- 


't CO 


CM O 


rH tO 


Ol CO 


oo o 


CO t- 








rHCd 


rH Cd 


rn cd 


rH'c4 


rH Cd' 


rH Cd 


rH Cd" 


rH Cd 











00 ^** 


CJ to- 

oo eo 


00 CO 


t^. en 


CO IO 


1> Cd 


cj co 

l> rH 


!> TH 


01 eo 

CO H 






rH 


rH Cd 


rH Cd 


rH 01 


rH (N 


rH 09 


TH <N 


rH Cd 


rH Cd 


rH Od 


CD 







t- to 

oo ^Jj 

rH Od* 


HH TH 
00 O 


&S 


O Cd 

oo eo 


2 


co to 

rH Cd 


rH Cd* 


CO O> 

rH Cd' 


CM tO 
O TH 

rH Od 


PH 
r>J 




o 


rH eo 
Ol IO 


00 3 


S3 


"t O 

oo ^< 


01 tO 

oo eo 


O eo 
oo eo 


00 O 

t*. eo 


r^ c- 

1- Cd 


CO -^ 
t^ Cd 










rH Cd 


TH Cd 




rH Cd 


rH Cd 


rH Cd 






O 

-v d 







00 00 

5s 10 


rH CO 

Oi IO 


a o 
oo -^ 


I- IO 

oo -i 


IO TH 

CO ^ 


oo eo 


rH IO 

oo eo 


O Cd 

oo eo 


R S 


S T= 


x-v 










rH Cd 




rH Cd 








* n 


d 


o 

CO 


00 to- 
Ol to 


22 


~t 00 


CM * 
Ol IO 



Oi IO 


00 t- 

00 * 


00 <# 

rH Cd 


tO TH 
00 * 

TH Cd 


oo eo 

rH* Cd 


5 "* 
-> 

-' su 


C 
a! 


Cl 


CO iO 

o t- 

01 Od 


g 

Cl Cd 


oo to 

Ol tO 


is 

rH Cd 


S3 


C*i IO 
O5 IO 
rH Cd* 


05 IO 

rH Cd* 


3 

rH Od 


%$ 

rH Cd 


o 

rH 

' CD 

* ft 


Cw 
1 


o 

Cl 


b eo 

o oq 

CM Cd 


-t CO 
l> 


CM * 
O to- 
Ol Cd" 




c i> 

01 Cd 


rn" Cd 


t>- eo 


CO O 


Ol IO 

rH Cd 


CO IO 
01 10 
rn" Od 


t, ^ 

5 O 


bC 

o 


co 


CO * 
rH <* 

cj cd 


O 

rH 00 

Cl Cd 


o oq 


q oq 


'0 t- 

q t-^ 

CJ Cd' 


CO <** 

q i> 

Cl" Cd' 


q to^ 

CJ Cd* 


o oo 

tO 
OJ Cd 


Ol to 
01 to 

rH Od' 


>> 4X 
* 

D 



c 

-c 




00 Cd 

cj eo 


"t to- 


co eo 

CM Cd" 


01 Cd* 


S oq 

Cl Od 


00 CO 

o oq 

CJ Cd' 


CO O 

o oq 

Cl Cd' 


q l> 


SS 

Oj' Od 


a -s 

5 ^> 
* 

Q 


0) 


2 


CO Cd 

CM TH 

CM" eo" 


to- 
ci q 

CM eo 


oo eo 

rH O 


old 


SS 


T3 CO 

rH O> 

CJ* Cd' 


01 o 

rH Cft 

ci c4 


O to- 
rn oq 

CJ Cd" 


ci Od" 


^ S. 

3 >. 


a- 
be 


^ 


co eo 

CJ TH 

CM eo' 


CJ CO 


CM q 
cj eo' 


C4 CO 


00 Cd 

01 eo' 


CO 00 
OJ* Cd' 


>0 10 
01 Cd* 


"t Cd 
CM Cd 


01 O 
CJ Od" 




CP 

tJ 


o 


o to 

CO Cd 


00 TH 


CD to- 
CJ rH 


HM eo 

Cl rH 


CM <n 

01 


g 


ss 


S 


co eo 

rH 9> 


s S 


C 




Cl CO 


cj eo 


01 CO 


Ol CO 


oj eo 


OJ CO 


OJ CO 


Ol CO 


CM Od 


' "c 

H ..H 






o o 
co eo 


co eo 


o o 

CO Cd 


Cl Cd 


t- to- 
ci TH 


o *# 

Ol TH 


CM TH 


01 00 
OJ O 


<N 


D bC 






CM eo 


CM CO 


cj eo 


Cl CO 


01 eo 


CJ eo 


ci eo 


ci eo 


ci eo 


5 "H 




00 


S?J5 

cj eo" 


00 TH 

co ^ 
oi eo 


co eo 


'f Ct 
CO CO 

cj eo* 


CM eo 


o to 
co cd 

CM CO* 


en eo 

OJ Cd 
CJ CO* 


00 O 
01 Cd 
OJ CO 


04 TH 

oi eo* 








t>- a> 


>o ^ 


5 S 


rH & 


Ol Cd 


r- at 


co yj 


CO 


*t o 


. o 

H 




*- 


cj eo" 


CJ CO 


cj eo 


CJ CO* 


01' eo* 


oj'eo" 


ci eo 


oi eo 


ci eo 


< 0) 






iO to- 


CO TH 
iO C- 


S 5 


a eo 

f tO 


t- o> 


CO tO 


H? eo 


CO O 


tj 


I 
i j_, 

' o 






CM eo 


cj eo 

co at 


ci eo 

Cl 


cj eo 

CO 00 


cj eo 

iO 00 


cj eo 
tO to- 


CJ CO 

~~cc~to 
to to- 


oj eo 

Hn CO 

to t- 


cj eo 

~co~0 
to to- 


cc 






CM eo 


cj eo 


CM CO 


cj eo 


CM eo 


Cl eo 


ol eo 


cj eo 


cj eo 


2 






oo eo 


06 cd 


00 (N 


CO 00 


tot TH 


CO TH 

t- TH 


i-^. o 


o ^ 


Ol Cd 

CO O 


crj 






Cl ^ 


CM ^ 


OJ * 


CM * 


OJ ^ 


04 -s*i 


CJ -^ 


CM ^ 


CJ ^ 


K" 




CO 


00 


CO tO 

o t-. 


to- 


01 CO 

oj 5 


00 ^ 


g 


>O to- 


CO ^ 
Ol 10 


CJ TH 
Oi 10 
































3 to2 


sjs S 


O TH 


oo to- 
co 10 


b. eo 

CO IO 


C?^ 


H^ IO 

CO # 


83 


01 en 

CO CO 








CO 10 


CO IO 


CO IO 


CO 10 


co 10 


CO IO 


CO IO 


CO IO 


CO 10 






rH 


CO 9* 


oo oo 

CM 00 


CO Cd 
04 CO 


"f fr- 

ci to" 


OJ Cd 
d fr- 


S 


c *# 
04 to 


oo o 


i> to 








<* to- 




















S 




CM 


CO 
CM 


a 


to 

CM 


01 


CM 


00 


Ol 

04 


o 

CO 



APPENDIX 



415 



Oi tO 

tO en 


b* H 

<o en 


Ift fr- 

iO 00 


ee H 
10 oo 


rH ^ 

10 00 


Ol 00 

T^ t- 


oo to 

Tf O 


ee 64 

^ l> 


1C O 
* t* 


^ co 

"# tO 


rH ^( 

^ to 


a> o 
co S 


f 


























J3 


r-< 00 
CO en 


OS ^K 
10 en 


CO O 
10 en 


Tf <O 

O 00 


CO i* 
HO 00 


rH O 

to co 


^S 


oo to 


t> CO 


CO ^ 


CO O 


rH CO 

-t o 







rH TH 


rH TH 


rH ^ 


rH T-l 


rH *S 


rH <H 




rH rH 


rH TH 


rH TH 


rH T-l 


J3 
3 
D. 


Tti en 

CD O 


rH 00 

CO en 


Ol ^ 

o 


^ O 
>o o> 


IO 00 

to oo 


*t IO 
tO 00 


01 en 

iO 00 


rH O 

iO 00 


Sg 


00 <O 

Tt t* 


CO *4 

<* e 


T(1 00 

^ to 


-T! 
pj 


iH C* 
























c 


b- 00 

CO O 


rf* * 

CO O 


w o 

CO O 


CO CJ> 


O5 ^ 
10 0> 


r- i-i 

iO O> 


CO 00 
10 CO 


-# to 

>0 00 


CO -^ 
iO 00 


01 04 

tO 00 


CO 

o t- 


^2 


O 

*d 


rH O4 


rH 04 


rH 09 


rH rHI 


rH rH 


rH ,H 


rH *H 


rH T-l 


rH T-l 


rH TH 


T-H T-l 


rH T-l 


rJ 


Ol O4 

CO TH 


t- 00 

CO O 


>o ^ 

CO O 


CO O 
CO 5 


rH C- 

co cr 


ss 


oo 04 
>o en 


I- O 

to en 


CO' 00 
tO 00 


to to 

tO 00 


^s 


S? 


r 




























t O 
b- 04 


1^ TH 


01 ca 

CO T-l 


C0 


co to 
CO O 


co O 


s 


O4 00 

co en 


S 


o ^ 

co en 


00 O 

to en 


CO t- 
>O 00 




c; 


"CD no ~ 
I>- 04 


~ "+T TH ~ 

!> 04 


o7~i>" 
r^ *-< 


"^T^T"" 

r>- rH 


~cT <H 

CO iH 


"~ 00^00~ 

CO O 


~I8~ 


~! s" 


~S 8 


co~cT 
co o 


rH~ &~ 

CD O> 


oT""co 
o <n 


2 


1-4 04 


r-< en 






















CD 


01 * 

00 CO 




'00 eo 


00 (O 
1- 0<l 


CO N 
r- cxi 


Z3 


C5 


Cl IO 

f-^ t-l 


rH CO 
t- TH 


O T-l 

t^ <H 


01 o 

CD H 


r>- to 

CO O 


iO CO 

CO O 


O- 
TJ 


T-( 04 


rH 04 


iH W 








rH 




rH 04 


rH 04 


rH 04 


TH 04 




tO 04 

00 < 


Tf CO 

oo eo 


(M IO 

QO eo 


O N 

oo eo 


O5 cr> 
i- 


00 IO 

i en 


CO * 
t^. Ol 


'O 04 
>. 04 


-t O 
t^- C4 


^ 00 

t T*l 


01 to 

IN. -H 


04 

I> rH 


">> 


rH 04 

T-T~TH~ 

as 10 


rH 0) 

00 * 


~^ "eo" 

00 ^ 


~~7~~o ~~ 

00 ^ 


^~t- 
oo eo 


(N~W~~ 
00 CO 


ii Ofl 
00 CO 


__^_- 

oo eo 


Q^Q^ 

t- O4 


" 00"^"" 

t- 04 


~_____ 
J^ 04 


LCTO 
t^. 04 


of 

if 
o 


I~~e4~^ 

05 10 


"o ob~ 

O5 O 


cr o 


^j~^i ~ 
o; to 


O~CT>" 
Oi * 


~~o~to 
at. ^t 


oo~^i~~ 

00 ff 


__^,___ 

00 T 


""C 1 "o" 
00 * 


o~ o~ 
oo co 


P0~" 

oo eo 


T-H 04 
00 CO 


8 

2 
























rH 04 


<j 


CM O 

O t> 


c to 




00 N 
0> 9 


co er 

Ci 


>o to 
a 10 


^ ^ 
a> w 


Ol N 
C- 10 


si 


O CO 

^ 


o to 

a> * 


00 CO 

oo * 


5 


8 


r^~o^ 

q co 


5=r to~ 
o t> 


~~co cT" 

O b; 


ci~oT ~ 
o to 


to 


c^ ""* ~ 
a> <o 


~oo~~ci ~ 

05 tO 


___^___.-_. 

OS tO 


"co^oo 

OS 10 


"~S3 T" 
OS 10 


coTeo ~~ 

O5 10 


~w b 

O5 IO 


a* 
<t> 

bC 
























rH 04 




2$ 


00 04 
O 00 


CO CO 
t- 


in IO 
O f 


o t- 


c-j o 

o t- 


rH CO 

o to 


tO 
to 


a ^ 

01 tO 


00 04 

Oi to 


r^ en 

Ol IO 


to to 

Oi 10 





01 04 


CM 04 


M e* 


CN M 


O4 N 


04 N 


01 CXI 


01 e* 


rH 04 


rH 04 


rH 04 


rH 04 


S 

oS 


"tf 5* 

rH Cn 

oi 04* 


<N en 

rH 09 

Ol 04 


2? 

C Oil 


C: Od 
O 00 
(N Ofl 


r- o 

O 00 

<>i CA 


co fr. 
O l> 

<N N 


id IO 
O fr- % 

01 en* 


^ eo 
O C^ 
OJ 04 


CO -r* 

o t> 

01 O4 


<N 
t-. 
Ol 04 


o to 
o to 
oi 04" 


ss 


5 

1 


ss 


rH Cf 


rH O 


rH O> 




rH 00 


S 5 


O 00 


O CO 


oS 


t 


3S 


O 


Ol CO 


(M 04 


<M exi 


<M CXI 


cj exi 


<N <SI 


OJ 04 


01 04 


CM 04 


01 04 


01 O4 


01 04 




-d 


tO 04 
01 i* 


co oo 

01 


<N O 


28 


00 CT> 

rH CT 


N- tO 

T-H en 


CO ^ 

r-i Cft 


"t 04 

rH 0> 


t 

rn 0> 


CO CO 

rH 00 


rH CO 


O O4 

rH CO 


H 


CM CO 


Ol CO 


<M eo 


<>j eo 


(N Od 


CJ C* 


01 04 


01 O4 


Ol O4 


01 04 


01 O4 


Ol 04 


of 


01 D 
CO O4 


O T-l 
CO 04 


oo co 

^4 T-l 


10 
C4 tH 


10 


-f O 
CM i-H 


CO l> 

01 O 


Ol IO 

01 O 


rH ^ 

Ol O 


O 04 

01 O 


00 00 

rH en 


t- IO 

rn en 


O 
^J 


<M eo 


01 eo 


co eo 


<N eo 


(M CO 


cq eo 


OJ CO 


01 CO 


Ol CO 


01 eo 


01 04 


Ol 04 


OJ 


O 04 

-t ^J 

oi eo 


00 00 
CO CO 

<M eo 


CO 10 

co_ eo 
c4 eo" 


tO CH 

co eo 

<N CO 


t Oi 

CO 

oi eo 


04 tO 

CO 

oi eo' 


^H <()< 

co en 
oi eo" 


O O4 

CO 04 

oi co" 


s 

01 co' 


Oi 00 

01 T-l 

oi co* 


b> IO 

01 T-l 

oi eo 


>O 04 
Ol TH 

oi co 


"e5 

o 
'*3 


rH (O 

>O (O 


Ol rH 
<* 


^ 


CO ^ 

Tf U9 


tO rH 


^5 


c^ to 

f ^ 


01 ** 

^ *x 


%% 


O T-l 

*K * 


oo e 

CO CO 


t-. ^ 

co eo 




co eo 


01 eo 


CM CO 


<N eo 


<M eo 


w eo 


CM CO 


01 eo 


Ol CO 


01 CO 


01 eo 


M eo 


OQ 


*- t- 

CO 04 
Ol CO 


10 eo 

co en 
oi co* 


co en 

CD CO 

<M" co 


(N IO 

CD CO 

ci eo 


r-4 CO 

CO 00 

ci co' 


OJ O 

>q co 
ci co" 


00 00 
iO fr^ 
01 CO 


r- to 

to t- 

oi co" 


CO -^ 

q i> 
oi co 


CO N 
tO fc- 

oi co" 


"t CO 
10 S 

oi eo" 


Ol IO 

iq <o 

oi eo' 


^05 
""-( 

o 


o to 

01 * 


oo 04 
QO * 


O 00 

oo eo 


>o * 

00 CO 


^ rH 
00 CO 


CO O> 
00 04 


01 to 

00 04 


rH * 

00 04 


O O4 

00 04 


o> o 
i-* en 


oo to 

l> T^ 


co eo 

l> TH 




cu 

T3 


(M <# 
























c 


o -^ 

CO OS 


00 Cn 
<M 04 


CO 10 

CM e* 


IO T-l 

CN <N 


CO 00 

(N Y-l 


0^ IO 

<N t- 


S3 


O O 
01 -l 


OS 00 

rH O 


oo to 

^H O 


^s 


>O 00 

rH en 


CO 

r) 


CO IO 


CO IO 


CO HO 


CO IO 


CO IO 


co 10 


CO IO 


CO tO 


CO IO 


CO 10 


CO IO 


CO * 


2 


2 


CO ^ 
rH TJ* 


38 


o o 

rH CO 


oo *-i 

O CO 


N. t 

O <M 


CO * 

o en 


O -l 
04 


"f en 

O ** 


CO t 

THI 


01 04 

*4 


00 



TJ 


^ l> 


Tjl fr 


^* fr- 


^ t 


Tt< t- 


^ b- 


f fr- 


TH |> 


"*l t> 


rH C- 


*# fr- 


* fr 






416 



METHODS OF PLANT BREEDING 





8 co to 


10 eo 
eo 10 


c^5 


S3 


iO t- 
01 eo 


O) CO 

CM eo 


OS 00 
TH 04 


W 

rH rH 


00 i-l 
O *H 


88 


E 
























0) 




o SS 


IN. tO 

CO IO 


o e 

CO 10 


33 


S3 


iO If 

01 eo 


01 eo 
oj eo 


CO ^ 
TH 04 


co en 

TH rH 


rH \[ 


a 




1C r " 1 ** 


1-1 1-1 


!-< 1-1 


TH iH 


TH "H 


TH t-4 


TH rH 


rH rH 


TH rH 


rH rH 


a 

Gi 




, ^ ^ 

^ ^ 


o 

TP 


00 If 

CO IO 


t - 

CO O 


rH tO 

CO ^* 


S3 


co cn 
01 eo 


O4 O4 

01 eo 


28 


Is. 11 


13 




(M TH TH 


TH 1-| 


















d 




_ CO rH 

% *+.*". 


>o o> 

^ D 


01 IO 

"t W 


o> o> 


CO <* 


^ H 


04 00 


00 04 


CO 00 


HH tO 


O 

X3 




2 TH rH 


rH 1-1 














rn rH 


TH rH 


"5 




as o 
10 -f t- 

* TH* 1H 


t- * 

"^ ^ 
r4 i-H 


iO O 

t ^ 

r4 <H 


01 * 

"*. *? 

t-H 1-J 


os en 

CO US 


C0 


o eo 

co 10 

TH* TH 


01 If 

CO ^J 

rH rH 


gs 

rH rH 


00 rH 
01 ^ 


0) 

rC5 


p, 

\*t 


Tfl ^) 

o iO 00 

>o ,_| ,4 


CO N 
'O 00 


i-H 00 

o t> 


00 CO 

Tft f 


00 

^ <, 


* IO 

T}J UJ 


Ol 04 
^ O 


00 t- 
CO IO 


CO *# 
CO 10 


'O 64 
CO IO 


O 




--> 
























o 
s o3 

? % 


o ^ o 

^ rH' rH 


CD 00 

CO 

r-I r4 


-t ^t 

q 00 

T-H 4 


rH O> 

>o t- 

i-i -i 


o to 

"t ^ 

TH 4 


l>- M 

't ^ 

TH T-i 


-. s 

rH i4 


01 # 

~& o 

rH rH 


TH rH 
"* * 
TH rH 


o en 

H^ W 


.2 
2 
* 


"o 
s: ^ 


CO Q 

co 5 
co ,_< ej 


(N 00 
O tf 


o * 

CO 0> 


t^ en 

>O 00 


IO 

ic oq 


'f CO 

to co 


01 cn 

tf 


OS Tt 
t_ t- 


O rH 
"t* t- 


co cn 
t to 


T3 

fl 


c - 






















'**! 


- 

O *-' 3 


oo o> 

44 CC O 

CM rJ 4 


t^ t- 

o o 

Y-H* C9 


o eo 

o q 

,-J Qjj 


CO 00 

co en 


o ^ 
e o 


OS - 
^ i 


t- 00 

iO 00 


't ^ 
>C CO 


CO rH 

*o eo 


01 en 

tO t- 


I>v 

-D 


o o 4 






















- 


U? 


eo co 

t- t-< 

01 rH C4 


01 IO 
K -H 

T-H ci 


O r^ 
t^ rH 
rH C<l 


oo to 

CO 

1 CNJ 


o eo 

co 

r-H OJ 


38 

TH ci 


01 t- 

co cn 

rH TH 


co en 


oo en 

'O 00 


jr^ t 

tc oo 


EC 

O 


: i 

^ C 3 


1 O O 
to I oo eo 


C5 eo 

J^ OQ 
rH M 


1^ -^ 

> N 

rH C4 


o en 

I- r^ 
r-4 04 


01 10 

(> 1-1 

i-l c4 


jqa 

TH e4 


o; cn 


TH 04 


s 

rH 04* 


>O rH 

co- q 

rn" 04 


-t cn 

cc_ en 




6 

<! 


^ gi 

H g M 


'O If 

^ 00 W 


*f IO 

oq n 


(M W 

oq eo 


Ci O 
t- M 


K eo 
r- N 


ID O 
b- 


t If 

t^ *H 


Ol C4 

t^. rH 


o cn 
** 9 


a> b- 

CO O 


m 
co 
OJ 


& % <3 
















C4 


04 




fl* 


!>i 

!/) - ' i 


01 Oi "* 

.H _ N 


cr. 10 

00 * 

rH 04 


00 i-H 

00 "* 

T-H W 


o to 

00 CO 

T-H 


co eo 
oo eo 
TH c4 


01 o 
oq eo 
TH ei 


O 00 
00 04 


oo eo 
r- C4 

TH 04 


CO O 

ts ; N . 

TH 04* 


tc oo 
r- i" 

TH' 04 


S 
0> 


5 a 1 

3 > ** 


HH ^1 

T-l OS IO 

T- 1 TH 04 


CO H 
CJi 10 


T-t 00 

Qi ^ 

r^ Oi 


oo eo 

00 ^ 

TH 


CO O 
00 * 
TH' o4 


ic e- 
oo eo 
TH c4 


CO * 

oo eo 

TH' 04 


00 04 
TH 04* 


o to 
oq 04 

rH 04 


OS <* 

r>. e> 

TH 


o 

0? 
c3 


3 HH o 

^ ^ & 


00 rH 
O OS tO 


K en 

o 10 


>t IO 

Ci 10 


Ol i-l 
OS 


5 



OS <* 
00 <* 


t^ 1-1 

oq ^ 


tO If 

oq eo 


SS5 


CO 04 

oo e* 


W 


* % g 






w 






en 


C4 


N 









2S 1 


01 o 

-, f 
a rvi 04 


qo 


O5 <* 
C- CO 


i> en 
a 10 


iO O 

a to 


HH CO 

q 10 


gs 


O *0 

q ^j 


a eo 

oq ^ 


00 rH 
00 * 


O 

r 1 

cu 


be - 
















04 


C4 




A 


r^ 

H C 


00 Cn 

00 ^ ^ 


fef: 


t* 

O l> 


co en 
o o 


oS 


O 

O <O 


?8 


CO IO 
0> W 


to eo 

a 10 


^S 


H 


3 '^ 
. +j 


00 01 en 


04 CM 


Ol [ 


Ol W 


04 


01 04 


TH 04 


TH 04 


rH 04 


TH 04 


to" 

T3 


H c 

<D 
. C3 

3 H 


tO eo 

^ o> 
oi 04 


Tf< f- 
rH OJ 

tN 


Ol l> 

^ *. 

01 


W 

TH 00 

04 ' 


oo en 

If 

01 e4 


t- (O 

q if 
oi C4 


to eo 

O If 
04 04 


^o en 


Ol 04* 


01 tO 

q co 

01 04 


ss 

oi 




0) 
rH 


; a 


"f O 

N - ^ 


CO C- 
CN 


r-i ^ 

01 o 


28 


JN *e 

rH 0) 


cr oi 
TH en 


-t O 

TH cn 


04 IO 

rH CO 


O C4 

rH CO 


s 




o 10 


oi eo 


a eo 


01 eo 


01 d 


Ol 04 


01 04 


01 04 


01 04 


01 04 


01 04 





3 tH 



CD 


CO T-l 

co w 
esj w 


>o en 

CO W 

w eo' 


CO IO 
CO N 

<N eo 


o o 

CO CS| 

oi eo 


01 t- 

Ol i-< 

oi eo 


r^ -^ 

O4 H 

oi eo 


CO i-l 
01 i-J 

oj eo' 


co <o 
oi q 

oi eo 


04 ^ 

01 o 
oi eo 



04 CO 


.a 

cfl 
t 


<L> 
j3 

13 


^ eo 

iO U) 

"^ cs eo 



04 eo' 


00 <O 
~f IO 

01 eo* 


CO 1- 

"* IO 

01 eo' 


t t- 
"t "^ 
oi eo' 


CO * 

^ ^ 

oi eo* 


rH rH 

*f * 
oi eo" 


o <o 
co eo 
oi eo' 


00 ^ 

co eo 
oi eo' 


l> M 

co eo 
01 eo* 


**IU 

o 




iO O 
CO ^ ^ 


t 00 
I- O 


01 * 
t* G 


O 00 

t^ <n 


00 <# 

CD en 


t- Y"t 

CD 


ss 


01 CO 

CD CO 


S 00 


O 00 
CO If 


8 




05 (M 


OJ * 


Ol ^K 


01 eo 


01 eo 


04 eo 


M eo 


O4 CO 


oi eo 


O4 CO 


o 

C 




^ IO 

d M . J 


CO M 
tH 0> 


S3 


a 

00 


r- oo 

t- 


g 


t rH 

O h* 


04 O 

o o 


C4 
to 


Os O 
Oi tO 


Ctt 

p 




























Oi ^ 

^ * 


00 i-l 

OS O 


CO (0 

ci o 


^ o 
a en 


Ol <* 
Oi 00 


TH T-l 

a> co 


Oi 

00 f 


CD 
00 t 


>O CO 

oo to 


* * 

oo to 


T3 




CO t^ 


CO t- 


CO (0 


co to 


CO 


CO (O 


CO (O 


CO O 


co to 


co to 


H% 


s 


iO 
CO 


o 
l> 


i 


o 

o 


iO 

01 





8 


8 

nf 


1 


8 


i-i 
&. 

eu 
PH 
)* 



APPENDIX 
TABLE III. TABLE OF x 2 * 



417 



Degrees of 
freedom 


Probability (P) 


.99 


.95 


.50 


.20 


.10 


.05 


.02 


,01 


1 


0.0002 


0.004 


0.46 


1 64 


2.71 


3.84 


5.41 


6.64 


2 


020 


103 


1.39 


3.22 


4.6( 


5.99 


7.82 


9.21 


3 


0.115 


0.35 


2.37 


4.64 


6.25 


7.82 


9.84 


11 34 


4 


0.30 


0.71 


3.3b 


5,91 


7.78 


9.49 


11.67 


13.28 


5 


0.55 


1.14 


4.35 


7.29 


9.24 


11.07 


13.39 


15.09 


6 


87 


1.64 


5.35 


8.56 


10.64 


12 59 


15.03 


16.81 


7 


1 24 


2.17 


6.35 


9.80 


12.02 


14.07 


16.62 


18 48 


8 


1.65 


2.73 


7.34 


11.03 


13 36 


15.51 


18 17 


20.09 


9 


2 09 


3.32 


8.34 


12.24 


14.68 


16 92 


19.68 


21 . 67 


10 


2.56 


3.94 


9.34 


13.44 


15.99 


18.31 


21.16 


23.21 


11 


3.05 


4.58 


10.34 


14.63 


17.28 


19 68 


22 62 


24.72 


12 


3.57 


5.23 


11.34 


15.81 


18 55 


21.03 


24.05 


26.22 


13 


4 11 


5 89 


12 34 


16 98 


19 81 


22 36 


25 47 


27 69 


14 


4.66 


6.57 


13 34 


18.15 


21 06 


23 68 


26 87 


29 14 


15 


5 23 


7.26 


14.34 


19 31 


22.31 


25 00 


28 26 


30.58 


16 


5 81 


7.96 


15.34 


20.46 


23.54 


26.30 


29.63 


32.00 


17 


6.41 


8.67 


16.34 


21.62 


24.77 


27.59 


31 00 


33.41 


18 


7 02 


9 39 


17 34 


22.76 


25.99 


28.87 


32 35 


34.80 


19 


7.63 


10 12 


18.34 


23.90 


27.20 


30.14 


33.69 


36.19 


20 


8.26 


10 85 


19.34 


25.04 


28.41 


31.41 


35.02 


37.57 


21 


8.90 


11 59 


20.34 


26.17 


29.62 


32.67 


36.34 


38.93 


22 


9.54 


12 34 


21.34 


27.30 


30.81 


33.92 


37.66 


40 29 


23 


10 20 


13 09 


22.34 


28.43 


32 01 


35.17 


38.97 


41.64 


24 


10.86 


13.85 


23.34 


29.55 


33.20 


36.42 


40.27 


42.98 


25 


11 52 


14.61 


24.34 


30.68 


34.38 


37.65 


41 57 


44.31 


26 


12.20 


15.38 


25.34 


31.80 


35.56 


38.88 


42,86 


45.64 


27 


12.88 


16 15 


26.34 


32.91 


36.74 


40.11 


44.14 


46 96 


28 


13.56 


16 93 


27 34 


34.03 


37.92 


41.34 


45.42 


48.28 


29 


14.26 


17.71 


28.34 


35.14 


39.09 


42.56 


46.69 


49.59 


30 


14.95 


18.49 


29.34 


36.25 


40.26 


43.77 


47.96 


50.89 



For larger values of n, the expression -\/2x 2 ~~ "\/'2n 1 may be used as a normal deviate 
with unit variance. 

* Abridged from Table III of Fisher's "Statistical Methods for Research Workers," 
Oliver & Boyd, Edinburgh, by kind permission of the author and publishers. 



418 METHODS OF PLANT BREEDING 

TABLE TV. TABLE OF r, FOR VALUES OF z FROM TO 3* 



K 


.01 


.02 


i 
.03 


.04 


.05 


.06 


.07 


.08 


.09 


.10 





0100 


0200 


. 0300 


.0400 


. 0500 


. 0599 


. 0699 


. 0798 


. 0898 


0997 


1 


. 1090 


.1194 


.1293 


.1391 


.1489 


.1586 


.1684 


.1781 


.1877 


1974 


f) 2 


2070 


2105 


2260 


. 2355 


2449 


2543 


2636 


2729 


.2821 


2913 


. 3 


3004 


. 3095 


3185 


.3275 


3364 


3152 


3540 


.3627 


.3714 


3800 


i 


3885 


3969 


4053 


4136 


1219 


.4301 


. 4382 


4462 


.4542 


4621 


5 


4099 


4777 


.4854 


. 4930 


. 5005 


,5080 


.5154 


.5227 


. 5299 


5370 





5441 


551 I 


5580 


.5649 


. 571 7 


5784 


5850 


.5915 


. 5980 


. 6044 


7 


0107 


.01(59 


6231 


.(')291 


6351 


.6111 


6469 


. 6527 


6584 


0640 


8 


(51.90 


0751 


6805 


6858 


.6911 


6963 


.7014 


. 7064 


.7114 


7163 


9 


721 1 


7259 


. 7306 7352 


. 7398 


.7443 


.7487 


.7531 


7574 


7616 


1 


7658 


7699 


. 7739 


7779 


7818 | 7857 


. 7895 


. 7932 


7969 


8005 


1 1 


804 1 


80 70 


8110 


8144 


8178 


8210 


8243 


. 8275 


. 8306 


8337 


1 2 


8367 


8397 


8426 


8455 


.8483 


.8511 


. 8538 


. 8565 


.8591 


8617 


i ,3 


8043 


8008 


. 8692 


.8717 


.8741 


8704 


.8787 


.8810 


. 8832 


8854 


] 1 


8875 


8890 


8917 


8937 


8957 


. 8977 


8996 


.9015 


9033 


.9051 


I 5 


9069 


9087 


9104 


.9121 


9138 


9154 


9 1 70 


9186 


.9201 


9217 


1 (i 


9232 


924(5 


9261 


. 9275 


. 9289 


9302 


9316 


9329 


. 934 1 


9354 


1 7 


9360 


.9379 


.9391 


. 9 102 


. 94 1 4 


9425 


9436 


.9417 


9458 


94681 


1 8 


94783 


94884 


91983 


95080 


.95175 


95268 


95359 


. 95449 


95537 


95624 


I 9 


95709 


95792 


95873 


95953 


. 96032 


96 1 09 


96185 


. 96259 


.96331 


96403 


2.0 


904 73 


96541 


96609 


96675 


96739 


96803 


. 96865 


. 96926 


96986 


97045 


2.1 


97103 


97159 


97215 


97269 


97323 


.97375 


.97426 


.97477 


. 97526 


. 97574 


2 2 


97022 


97608 


97714 


97759 


97803 


97846 


97888 


97929 


. 97970 


98010 


2 3 


98049 


98087 


98124 


,98161 


98197 


. 98233 


98267 


98301 


98335 


98307 


2 4 


98399 


98431 


98462 


.98492 


98522 


.98551 


. 98579 


. 98607 


98635 


.98661 


o r 


98088 


.98714 


98739 


98764 


98788 


98812 


98835 


. 98858 


.98881 


98903 


2 6 


98924 


98945 


98966 


98987 


. 99007 


99026 


.99015 


99064 


. 99083 


99101 


2.7 


99118 


99 1 36 


99153 


.99170 


99180 


99202 


99218 


. 99233 


99248 


. 99263 


2 8 


99278 


. 99292 


. 9J300 


99320 


99333 


99346 


. 99359 


.99372 


. 99384 


. 99396 


2.9 


.99408 


99420 


99431 


99443 


.99454 


. 99464 


99475 


99485 


.99195 


.99505 



For great/or accuracy, arid for values beyond the table, r = (e iz 1 ) -f- (e~ z -\ 1); 
z = KfloK (1 + r) - lug (1 - r)} 

* RepiinU'd from Table V.B. of Fishei's "Statistical Methods for Reseat ch Workers," 
Oliver & Royd, Edinburgh, by kind peimiHHion of the author and pubhsheiN. 



APPENDIX 



419 



TABLE V. SIGNIFICANT VALUES OF r AND 72. * 
Values for P = .05 in lightfacc type. Values for P .01 in boldface type 



Degi ee,B of 
freedom 


Number of variables 


2 


3 
999 
1.000 


4 
999 
1.000 


5 
.999 
1.000 





7 


9 


13 


25 
1 000 
1.000 


1 


907 
1.000 


1 000 
1.000 


1 000 
1.000 


1 000 
1.000 


1 000 
1.000 


2 


950 
.990 


975 
.995 


983 
.997 


.987 
.998 


990 
.998 


992 
.998 


994 
.999 


990 
.999 


998 
1.000 


3 


.878 
.959 


930 
.976 


950 
.983 


901 
.987 


.908 
.990 


973 
.991 


979 
.993 


980 
.995 


993 
.998 


4 


.811 
.917 


881 
.949 


912 
.962 


.930 
.970 


.942 
.975 


950 
.979 


901 
.984 


973 
.989 


980 
.994 


5 


. 754 
.874 


830 
.917 


874 
.937 


898 
.949 


.914 
.957 


.925 
.963 


.941 
.971 


958 
.980 


978 
.989 


6 


707 
.834 


795 
.886 


839 
.911 


807 
.927 


.880 
.938 


.900 
.946 


920 
.967 


943 
.969 


909 
.983 


7 


000 
.798 


758 
.855 


807 
.885 


838 
.904 


800 
.918 


876 
.928 


900 
.942 


927 
.958 


960 
.977 


8 


032 
.765 


720 
.827 


777 
.860 


811 
.882 


835 
.898 


854 
.909 


880 
.926 


912 
.946 


950 
.970 


9 


602 
.735 


(597 
.800 


750 
.836 


.780 
.861 


812 
.878 


832 
.891 


.801 
.911 


.897 
.934 


941 
.963 


10 


570 
.708 


071 
.776 


720 
.814 


703 
.840 


.790 
.859 


812 
.874 


843 
.895 


882 
.922 


932 
.955 


11 


553 
.684 


048 
.753 


703 
.793 


741 
.821 


.770 
.841 


792 
.857 


820 
.880 


80S 
.910 


922 
.948 


12 


532 
.661 


<>27 
.732 


083 
.773 


722 
.802 


751 
.824 


774 
.841 


.809 
.866 


. 854 
.898 


913 
.940 


13 


511 
.641 


008 
.712 


.004 
.755 


703 
.785 


.733 
.807 


.757 
.825 


.794 
.852 


.840 
.886 


904 
.932 


14 


197 
.623 


590 
.694 


. 040 
.737 


. 080 
.768 


.717 
.792 


741 
.810 


779 
.838 


.828 
.875 


. 895 
.924 


15 


482 
.606 


574 
.677 


. 030 
.721 


.070 
.752 


.701 
.776 


720 
.796 


705 
.825 


815 
.864 


880 
.917 


10 


.408 
.590 


559 
.662 


.015 
.706 


055 
.738 


. 080 
.762 


712 
.782 


751 
.813 


.803 
.853 


.878 
.909 


17 


.450 
.576 


545 
.647 


.001 
.691 


.041 
.724 


.073 
.749 


.098 
.769 


738 
.800 


792 
.842 


869 
.902 


18 


.444 
.561 


. 532 
.633 


. 587 
.678 


.028 
.710 


. 000 
.736 


. 080 
.756 


.720 
.789 


781 
.832 


801 
.894 


19 


. 433 
.549 


.520 
.620 


.575 
.665 


.015 
.698 


.047 
.723 


.074 
.744 


.714 
.778 


.770 
.822 


853 
.887 


20 


. 423 
.537 


509 
.608 


. 503 
.652 


.004 
.685 


.036 
.712 


.002 
.733 


. 703 
.767 


.700 
.812 


. 845 
.880 


21 


.413 
.526 


198 
.596 


. 552 
.641 


.592 
.674 


.024 
t 700 


.051 
.722 


.093 
.756 


.750 
.803 


.837 
.873 


22 


404 
.515 


188 
.585 


542 
.630 


582 
.663 


.014 
.690 


040 
.712 


.082 
.746 


.740 
.794 


.830 
.866 


23 


.390 
.505 


.479 
.574 


532 
.619 


.572 
.652 


004 
.679 


. 080 
.701 


073 
.736 


.731 
.785 


. 823 
.859 


24 


. 388 
.496 


.470 
.565 


523 
.609 


. 502 
.642 


. 594 
.669 


.021 
.692 


.003 
.727 


.722 
.776 


.815 
.852 



* Reprinted by kind permission of Dr. George W. Snedecor from 
Machine Calculation" (1931). 



' Correlation and 



420 



METHODS OF PLANT BREEDING 



TABLE V. -SicNiFirANT VALUES OF r AND R.* (Continued^ 
Values for P = .05 in lightfaoc type. Values for P = .01 in boldface type 



Degrees of 
freedom 


_. 


Number of variables 


3 


4 


5 


6 


7 


9 


13 


25 


. __ ^ 


~381 
.487 


46 2~ 
.555 


' "ini 

.600 


553" 
.633 


585 
.660 


.612 
.682 


654 
.718 


- 714- 
.768 


". 80 8 " 
.846 


26 


374 
.478 


.454 
.546 


506 
.590 


545 
.624 


576 
.651 


.603 
.673 


645 
.709 


706 
.760 


.802 
.839 


27 


367 
.470 


446 
.538 


,498 
.682 


. 536 
.615 


. 568 
.642 


594 
.664 


637 
.701 


698 
.752 


.795 
.833 


28 


361 
.463 


439 
.530 


. 490 
.573 


529 
.606 


560 
.634 


586 
.656 


.629 
.692 


.690 
.744 


.788 
.827 


29 


.355 
.456 


432 
.522 


.482 
.665 


521 
.598 


552 
.625 


.579 
.648 


.621 
.685 


.682 
.737 


.782 
.821 


30 


349 
.449 


.426 
.514 


.476 
.558 


.514 
.591 


. 545 
.618 


571 
.640 


.614 
.677 


675 
.729 


776 
.815 


35 


.325 
.418 


397 
.481 


445 
.523 


482 
.556 


512 
.582 


538 
.605 


580 
.642 


642 
.696 


746 
.786 


40 


301 
.393 


373 
.454 


419 
.494 


455 
.526 


484 
.552 


. 509 
.576 


.551 
.612 


613 
.667 


720 
.761 


45 


288 
.372 


353 
.430 


397 
.470 


. 432 
.501 


. 460 
.527 


.485 
.549 


.526 
.586 


. 587 
.640 


. 696 
.737 


50 


273 
.354 


336 
.410 


. 379 
.449 


412 
.479 


440 
.504 


464 
.526 


.504 
.562 


. 565 
.617 


.674 
.716 


60 


250 
.325 


308 
.377 


.348 
.414 


380 
.442 


.406 
.466 


.429 
.488 


.467 
.523 


.526 
.577 


.636 
.677 


70 


232 
.302 


286 
.351 


324 
.386 


354 
.413 


379 
.436 


401 
.456 


438 
.491 


.495 
.544 


004 
.644 


80 


.217 
.283 


.269 
.330 


.304 
.362 


. 332 
.389 


. 356 
.411 


.377 
.431 


.413 
.464 


.469 
.516 


576 
.615 


90 


205 
.267 


254 
.312 


288 
.343 


.315 
.368 


338 
.390 


358 
.409 


392 
.441 


446 
.492 


552 
.690 


100 


195 
.254 


241 
.297 


.274 
.327 


.300 
.351 


.322 
.372 


.341 
.390 


.374 
.421 


426 
.470 


530 
.668 


125 


.174 
.228 


.216 
.266 


246 
.294 


.269 
.316 


. 290 
.335 


.307 
.352 


.338 
.381 


387 
.428 


485 
.521 


150 


.159 
.208 


.198 
.244 


.225 
.270 


.247 
.290 


.266 
.308 


.282 
.324 


.310 
.351 


.356 
.395 


.450 
.484 


200 


.138 
.181 


.172 
.212 


.196 
.234 


.215 
.253 


.231 
.269 


246 
.283 


.271 
.307 


312 
.347 


398 
.430 


300 


.113 
.148 


.141 
.174 


J60 
.192 


.176 
.208 


.190 
.221 


.202 
.233 


.223 
.253 


.258 
.287 


.332 
.359 


400 


.098 
.128 


.122 
.151 


. 1 39 
.167 


. 153 
.180 


.165 
.192 


.176 
.202 


.194 
.220 


.225 
.250 


291 
.315 


500 


.088 
.116 


. 109 
.135 


.124 
.150 


.137 
.162 


.148 
.172 


.157 
.182 


.174 
.198 


.202 
.225 


. 262 
.284 


1000 


.062 
.081 


.077 
.096 


.088 
.106 


.097 
.115 


.105 
.122 


.112 
.129 


.124 
.141 


.144 
.160 


.188 
.204 



For total and partial coirelation coefficients, use column for 2 variables in table for 5 and 1 
per eerit points. Degrees of freedom = (number of observations) (number of variables). 

For multiple-correlation coefficients, use the column corresponding to the number of 
variables. Degrees of freedom = (number of observations) (number of variables). 

* Reprinted by kind permission of Dr. George W. Snedecor from "Correlation and 
Machine Calculation" (1931). 



APPENDIX 



421 



TABLE VI. TRANSFORMATION OF PERCENTAGE TO DEGREES 
Percentage (p) = sin 2 0* 



Per cent 


0.0 


0.1 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


0.0 





1 8 


2 6 


3 1 


3 6 


4 1 


4 4 


4.8 


5 1 


5 4 


1 


5 7 


6 


6 3 


6.5 


6 8 


7.0 


7 3 


7 5 


7 7 


7 9 


2 


8 1 


8.3 


8 5 


8 7 


8 9 


9 1 


9 3 


9 5 


9.6 


9 8 


3 


10.0 


10.1 


10.3 


10.5 


10.6 


10.8 


10.9 


11.1 


11.2 


11 4 


4 


11.5 


11.7 


11.8 


12.0 


12.] 


12.2 


12 4 


12.5 


12.7 


12 8 


5 


12 9 


13 1 


13 2 


13.3 


13.4 


13.6 


13.7 


13.8 


13 9 


14 1 


6 


14 2 


14.3 


14.4 


14 5 


14 7 


14.8 


14 9 


15.0 


15 1 


15 2 


7 


15 3 


15 5 


15 6 


15 7 


15 8 


15 9 


16 


16 1 


16 2 


16 3 


8 


16 4 


16 5 


16 6 


16 7 


16 8 


17 


17.1 


17.2 


17 3 


17 4 


9 


17.5 


17.6 


17.7 


17 8 


17 9 


18 


18 


18.1 


18 2 


18 3 


10 


18.4 


18 5 


18.6 


18.7 


18.8 


18.9 


19.0 


19.1 


19.2 


19 3 


11 


19 4 


19 5 


19.6 


19.6 


19.7 


19.8 


19.9 


20 


20.1 


20.2 


12 


20 3 


20 4 


20.4 


20.5 


20.6 


20.7 


20 8 


20.9 


21.0 


21.0 


13 


21 1 


21 2 


21.3 


21 4 


21.5 


21.6 


21.6 


21.7 


21.8 


21.9 


14 


22 


22 I 


22 1 


22.2 


22.3 


22 4 


22 . 5 


22 5 


22.6 


22 7 


15 


22 8 


22 9 


22 9 


23.0 


23.1 


23.2 


23.3 


23 3 


23.4 


23.5 


16 


23 6 


23 7 


23 7 


23.8 


23.9 


24.0 


24 


24.1 


24.2 


24 3 


17 


24 4 


24 4 


24.5 


24 6 


24.7 


24.7 


24.8 


24.9 


25 


25 


18 


25 1 


25.2 


25 3 


25.3 


25.4 


25 . 5 


25 5 


25 6 


25 7 


25 8 


19 


25 8 


25 9 


26 


26 1 


26.1 


26.2 


26 3 


26.3 


26 4 


26 5 


20 


26 6 


26 6 


26 7 


26.8 


26.9 


26.9 


27.0 


27.1 


27.1 


27 2 


21 


27 3 


27 3 


27.4 


27 5 


27.6 


27 6 


27.7 


27 8 


27.8 


27 9 


22 


28 


28 


28 1 


28.2 


28.2 


28 3 


28 4 


28.5 


28 5 


28 6 


23 


28.7 


28.7 


28 8 


28 9 


28.9 


29.0 


29 1 


29 1 


29 2 


29 3 


24 


29 3 


29.4 


29.5 


29 5 


29.6 


29.7 


29.7 


29.8 


29.9 


29.9 


25 


30 


30.1 


30.1 


30.2 


30.3 


30.3 


30.4 


30.5 


30.5 


30.6 


26 


30.7 


30 7 


30.8 


30.9 


30.9 


31.0 


31.0 


31.1 


31.2 


31 2 


27 


31 3 


31.4 


31.4 


31.5 


31.6 


31.6 


31.7 


31.8 


31.8 


31 9 


28 


31 9 


32.0 


32 1 


32 1 


32.2 


32 3 


32.3 


32 4 


32.5 


32 5 


29 


32.6 


32 6 


32.7 


32.8 


32.8 


32.9 


33.0 


33.0 


33.1 


33 1 


30 


33 2 


33.3 


33.3 


33.4 


33.5 


33.5 


33.6 


33.6 


33.7 


33 8 


31 


33 8 


33.9 


34.0 


34.0 


34.1 


34.1 


34 2 


34.3 


34.3 


34 4 


32 


34 4 


34.5 


34 6 


34.6 


34.7 


34.8 


34.8 


34.9 


34.9 


35 


33 


35.1 


35.1 


35.2 


35 2 


35.3 


35.4 


35.4 


35.5 


35.5 


35 6 


34 


35 7 


35 7 


35.8 


35 8 


35.9 


36.0 


36 


36.1 


36.2 


36 2 


35 


36.3 


36.3 


36 4 


36.5 


36.5 


36 6 


36 6 


36.7 


36.8 


36 8 



* Published by kind permission of Dr. C. I. Bliss (1937). 



422 METHODS OF PLANT BREEDING 

TABLE VI. TRANSFORMATION OF PERCENTAGE TO DEGREES. (Continued) 



Per cent 


0.0 


0.1 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


36 


36 9 


36 9 


37 


37 


37 1 


37 2 


37 2 


37 3 


37 3 


37 4 


37 


37 5 


37 5 


37.6 


37.6 


37.7 


37.8 


37.8 


37.9 


37.9 


38.0 


38 


38 1 


38 1 


38 2 


38 2 


38 3 


38 4 


38.4 


38.5 


38.5 


38.6 


39 


38.6 


38 7 


38 8 


38.8 


38 9 


38 9 


39.0 


39.1 


39 1 


39 2 


40 


39.2 


39 3 


39.3 


39 4 


39.5 


39.5 


39.6 


39 6 


39.7 


39.8 


41 


39 8 


39 9 


39 9 


40.0 


40.0 


40 1 


40.2 


40.2 


40 3 


40.3 


42 


40 4 


40 5 


40 5 


40 6 


40 6 


40.7 


40.7 


40.8 


40 9 


40 9 


43 


41 


41 


41 1 


41 1 


41.2 


41 3 


41 3 


41 4 


41 4 


41 5 


44 


41 6 


41 6 


41 7 


41 7 


41.8 


41.8 


41 9 


42 


42.0 


42 1 


45 


42.1 


42.2 


42 2 


42.3 


42 4 


42 4 


42 5 


42 5 


42 6 


42 6 


46 


42 7 


42 8 


42 8 


42 9 


42.9 


43 


43 


43.1 


43 2 


43 2 


47 


43 3 


43 3 


43 4 


43 5 


43 5 


43 6 


43 


43 7 


43 7 


43 8 


48 


43 9 


43 9 


44 


44 


44 1 


44 1 


44 2 


44 3 


44 3 


44 4 


49 


44 4 


44 5 


44 5 


44 6 


44 7 


44.7 


44.8 


44 8 


44 9 


44 9 


50 


45 


45.1 


45.1 


45.2 


45.2 


45 3 


45 3 


45 4 


45 5 


45 5 


51 


45.6 


45 6 


45.7 


45.7 


45 8 


45 9 


45 9 


46.0 


46 


46 1 


52 


46 1 


46 2 


46 3 


46 3 


46.4 


46.4 


46.5 


46 . 5 


46 6 


46 7 


53 


46 7 


46 8 


46 8 


46 9 


47 


47 


47.1 


47 1 


47 2 


47 2 


54 


47.3 


47 4 


47.4 


47.5 


47 5 


47 6 


47.6 


47 7 


47 8 


47 8 


55 


47.9 


47 9 


48 


48.0 


48.1 


48.2 


48.2 


48.3 


48.3 


48 4 


56 


48 4 


48 5 


48 6 


48.6 


48.7 


48 7 


48 8 


48.9 


48 9 


49 


57 


49 


49 1 


49 1 


49 2 


49.3 


49.3 


49 4 


49.4 


49.5 


49 5 


58 


49 6 


49 7 


49 7 


49.8 


49 8 


49 9 


50.0 


50.0 


50.1 


50 1 


59 


50 2 


50 2 


50 3 


50 4 


50.4 


50.5 


50.5 


50 6 


50.7 


50.7 


60 


50.8 


50.8 


50 9 


50.9 


51.0 


51.1 


51.1 


51.2 


51.2 


51 3 


61 


51 4 


51 4 


51.5 


51 5 


51.6 


51.6 


51.7 


51.8 


51.8 


51.9 


62 


51 9 


52 


52 1 


52.1 


52.2 


52 2 


52.3 


52.4 


52.4 


52.5 


63 


52 5 


52 6 


52 7 


52 7 


52.8 


52.8 


52.9 


53.0 


53.0 


53 1 


64 


53.1 


53.2 


53.2 


53 3 


53.4 


53.4 


53.5 


53.5 


53 6 


53 7 


65 


53.7 


53 8 


53.8 


53.9 


54.0 


54.0 


54.1 


54.2 


54.2 


54.3 


66 


54.3 


54 4 


54 5 


54.5 


54 6 


54 6 


54.7 


54.8 


54.8 


54.9 


67 


54 9 


55.0 


55 ] 


55 1 


55 2 


55 2 


55.3 


55.4 


55 4 


55.5 


68 


55 6 


55.6 


55 7 


55.7 


55 8 


55 9 


55 9 


56 


56.0 


56 1 


69 


56.2 


56 2 


56.3 


56.4 


56.4 


56.5 


56.5 


56.6 


56.7 


56.7 


70 


56.8 


56.9 


56.9 


57.0 


57.0 


57.1 


57.2 


57.2 


57.3 


57.4 



APPENDIX 423 

TABLE VI. TRANSFORMATION OF PERCENTAGE TO DEGREES. (Continued} 



Per cent 


0.0 


0.1 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


71 


57.4 


57.5 


57.5 


57.6 


57.7 


57.7 


57.8 


57.9 


57 9 


58 


72 


58.1 


58.1 


58.2 


58.2 


58 3 


58.4 


58.4 


58.5 


58.6 


58 6 


73 


58 7 


58.8 


58 8 


58 9 


59 


59. ( 


59 1 


59 . 1 


59.2 


59 3 


74 


59 3 


59 4 


59 . 5 


59 5 


59 . ( 


59.7 


59.7 


59.8 


59 9 


59 9 


75 


60 


60 1 


60.1 


60 2 


60.3 


60 3 


60.4 


60 . 5 


60 5 


60 6 


76 


60 7 


60.7 


60.8 


60.9 


60 9 


61.0 


61.1 


61.1 


61 2 


61 3 


77 


61 3 


61 4 


61 5 


61 5 


61 


61.7 


61 8 


61 8 


61.9 


62 


78 


62 


62 . 1 


62.2 


62 2 


62 . 3 


62 4 


62 4 


62.5 


62.6 


62.7 


79 
80 


62 7 
63 . 4 


62 . 8 
63 5 


62.9 
63.6 


62.9 
63.7 


63 . 

63 . 7 


63.1 
63.8 


63 1 
63 9 


63 . 2 
63 9 


63 3 
64 


63 4 
64 1 


81 


64.2 


64.2 


64.3 


64.4 


64.5 


64.5 


64.6 


64.7 


64.7 


64 8 


82 


64 9 


65 


65 


65 1 


65 . 2 


65 3 


65 . 3 


0.5 4 


65 5 


65 6 


83 


05 


65 . 7 


05 8 


65 . 9 


66.0 


60 


66 1 


66.2 


66 3 


66 3 


84 


66 4 


66 . 5 


66 6 


GO 7 


66.7 


66.8 


66.9 


67.0 


67.1 


67 1 


85 


07 2 


67.3 


67 4 


67 5 


67.5 


67.6 


67 7 


67 8 


67.9 


67.9 


86 

87 


68 
08 9 


08 1 
09 


08 2 
09 


68 3 
69 1 


08 4 

09 2 


68.4 
69 3 


68.5 
09 4 


68 
69 5 


68 7 
69.6 


68.8 
69 6 


88 


09 7 


69.8 


09 9 


70 


70 1 


70.2 


70 3 


70.4 


70.4 


70 5 


89 


70 


70 7 


70 8 


70 9 


7J .0 


71 I 


71.2 


71.3 


71 4 


71 5 


90 


71 6 


71 7 


71.8 


71 9 


72.0 


72 


72.1 


72.2 


72.3 


72 4 


91 


72 5 


72 


72 7 


72 8 


72 . 9 


73.0 


73 2 


73 3 


73 4 


73 5 


92 


73 6 


73 7 


73 8 


73 9 


74.0 


74 1 


74 2 


74 3 


74 4 


74 5 


93 


74.7 


74 8 


74 9 


75 


75 . 1 


75.2 


75 3 


75 5 


75 6 


75.7 


94 


75 8 


75 9 


76 1 


76 2 


76 . 3 


76.4 


76 . 


76 7 


76.8 


76 9 


95 


77.1 


77 2 


77.3 


77.5 


77.6 


77.8 


77.9 


78.0 


78 2 


78 3 


96 


78.5 


78 


78. S 


78 9 


79.1 


79 2 


79.4 


79.5 


79.7 


79 9 


97 


80.0 


80.2 


80.4 


80 5 


80 7 


80.9 


81.1 


81.3 


81.5 


81.7 


98 


81.9 


82.1 


82 3 


82 5 


82 7 


83 


83 2 


83 5 


83 7 


84 


99 


84.3 


84.6 


84.9 


85.2 


85 6 


85 9 


86 4 


86 9 


87 4 


88 2 


100 


90 





















INDEX 



Aamodt, 134-136, 138 
Aase, 20 
Ahlgren, 185 
Alexander, 188 

Alfalfa, effects of self-fertilization, 
243-247 

inflorescence, 68-69 

selfing and crossing, 69 
Allard, 85 
Anderson, 203 
Arny, 170, 171, 297, 298 
Ashhy, 54 
Atkins, 180 
Atwood, 69, 249 
Ausermis, 139, 331, 332 



B 



Barker, 173 

Barley, artificial epiphytotics, fusar- 

ial head blight, 120 
smuts, 120 
stem rust, 118 
breeding, 88-91 
chromosome numbers, 155 
cross-pollination, 42 
crossing methods, 63 
effects of selling, 99-100 
inheritance, internode length, 155 
quantitative characters, 163 
reaction to Ilelminthosporium 

nativum, 159 
reaction to mildew, 162 
reaction to stem rust, 160 
in species crosses, 152-153 
linkage groups, 155-156 
species, 152-153 
Bartlett, 341 



Bateson, 11 

Baur, 114 

Beadle, 224 

Beans, mosaic resistance, 115 

Beddows, 249 

Biffin, 132, 133 

Bindloss, 56 

Blakeslee, 34-36 

Blanchard, 241 

Bliss, 375, 421 

Blodgett, 41 

Bolley, 114, 172 

Borgeson, 268 

Boyack, 132, 133 

Bressman, 218 

Brewhaker, 194, 247, 301 

Brieger, 251 

Bnerley, 35 

Bnggs, 104, 139, 140, 162 

Brink, 255 

Broadfoot, 171 

Brookms, 89, 117, 127, 162 

Brtmson, 189, 197, 236, 239 

Bryan, 209, 237, 238, 304 

Burlison, 239 

Burnham, 110, 173, 224, 235 

Bushnell, 250 



Cabbage, wilt resistance, 115 

yellows, 126 
Campbell, 182 
Cantaloupe, resistance to mildew, 

104 

Cartledge, 1 10, 235 
Cartter, 85 
Chang, 178, 179 
Christidis, 303 
Chromosome numbers, in cereals, 1? 



425 



426 



METHODS OF PLANT BREEDING 



Chromosome numbers, in fiber 

plants, 13 

in* forage grasses, 12-13 
m fruits, 14 
in legumes, 13 
in oats, 141 
in oil plants, 13 
in stimulants, 13 
in sugar plants, 13 
in vegetables, 14 
Churchward, 139 
Clark, Andrew 376 
Clark, E. R., 181 
Clark, J. A., 83, 131, 132, 139 
Clarke, 247 
Clayton, 85, 182 
Cochran, 292, 352, 367, 375 
Coffman, 143, 150 
Collins, G. N., 52, 241 
Collins, J. L., 40 
Combining ability, in corn, 236-239 

in small grains, 98 
Cooper, D. C., 255 
Cooper, II. P., 134 
Corn, artificial epiphytotics, smuts, 

121, 122 

breeding improved inbred linos, 
by baekcross method, 210 
by convergent improvement, 

52-53, 210-214 
by pedigree method, 207 
breeding methods, 6-8, 187-214 
combining ability, 236-239 
controlled pollination methods, 

193-214 

drought resistance, 181 
effects of selfing, 48-50 
inheritance, of chlorophyll varia- 
tions, 221 

of endosperm characters, 218 
of glossy seedlings, 223 
of plant colors, 222 
linkage map, 225 
linkage studies, 224-231, 233-236 
origin and classification, 215-218 
pericarp tenderness, 108, 240 
protein content, 239 
quantitative inheritance, 231 



Corn, resistance of, to bacterial wilt, 

241 

to cold, 239 
to drought, 239 
to insects, 241 
to rust, 241 
to smut, 109, 234 
seed increase of inbreds and F\ 

crosses, 268-269 

selection without controlled pol- 
lination, 187-191 
selfing and crossing technics, 61 
Cotton, effects of self-pollination, 47 

selfing and crossing, 64 
Cox, 352, 367 
Craig, 81, 145, 148 
Craigie, 136 
Crane, 251 
Cummmgs, 48, 250 
Curtis, 250 
(Hitler, 176 

Cytogenetics, nllopolyploids, 16 
autopoiyploids, 16 



D 



Dahms, 241 

Darlington, 130 

Darwin, 242 

Davis, 236 

Derm an, 34 

Dickson, 135, 148 

Dillman, 85, 165, 167, 169 

Disease resistance, in barley, 90 

in beans, 115 

in cabbage, 115 
types of, 126 

in cantaloupe's, powdery mildew, 
104 

in corn, smut, 109 

in flax, wilt-, 114 

in grapes, 1 1 4 

importance of, 113-116 

methods of breeding for, 122 124 

nursery methods, 82 

in oats, crown rust, 27, 149 
smuts, 29, 150 
stem rust, 28, 148 



INDEX 



427 



Disease resistance, production of 

epiphytotics, 118-122 
reaction to bacterial wilt of corn, 

241 
reaction to Hehninthosporium sati- 

vum, 159 

reaction to insect attacks, 241 
reaction to rust of corn, 240 
reaction to smut of corn, 234 
in snapdragons, rust resistance, 

106 

in tomatoes, 115 
in vegetables, 115 
in watermelons, 115 
in wheat, bunt, 104 
Hessian fly, 127 
leai rust, 107 
mature-plant resistance, 4, 117, 

127 
physiological resistance, 4, 117, 

126 

stem rust, 107 
Doxtator, 202 



E 



East, 45, 49-51, 53, 77, 193, 218, 

221, 232, 239, 242, 251, 254 
Eckhardt, 209, 237, 352, 307 
Edgerlon, 1J5 
Ellerton, 131 

Emerson, 219, 222, 224, 231, 232 
Emsweller, 35, 60, 106, 251 
Engledow, 130, 133, 152 

F 

Fairer, 87, 139 

Fernow, 41 

Field plot methods, Latin squares, 

312-313 
lattice, simple, 351-365 

triple, 365 -375 

multiple experiments, 339-350 
randomized blocks, 307-312 
replication, 304 
size and shape of plots, 302 
split-plot designs, 315-320 
yield trials in Minnesota, 304-306 



Field plot teehnic, competition, 297 
crop rotation, 289-291 
soil heterogeneity, 291 
Fisher, 287, 295, 307, 308, 312, 322, 

331, 375, 411, 417, 418 
Flax, artificial epipliytotic, rust, 120 

wilt, 120 

chromosome numbers, 165 
crossing methods, 64 
dehiscence of bolls, 168 
inflorescence, 166 
inheritance, of flower and seed 

color, 167 

of quality of oil, 170 
of resistance to rust, 174 
of resistance to wilt, 171 
smooth vs. cihate septa, 169 
of weight of seed and oil con- 
tent, 169 

of wilt resistance, 114, 171 
Flor, 174 
Fraps, 219 

Eraser, 143, 145, 224 
Freeman, 133 

G 

Gaines, 2, 20, 134, 139, 147 
Garber, 39, 60, 147, 157, 158, 218, 

236, 239, 293, 296 
Garl, 70 
Garner, 85 
Garrison, 189, 190 
Genetics, application of, to plant 
breeding, 25-34 

of barley, 152-164 

of bunt resistance, 140 

of flax, 165-174 

genomes in wheat, 20-21 

of maize, 215-241 

of oats, 141-151 

of plant pathogens, 125-126 

of self-incompatibility, 251-257 

of wheat, 12&-140 
Oilman, 115 
Glossary, 381-389 
Goulden, 81, 136, 139, 351, 363 
Grapes, resistance of, to vine louse 
and vine mildew, 114 



428 



METHODS OF PLANT BREEDING 



Grasses, iffects of selfing, 249 

selfing, methods, 71 
Griffee, 89, 160, 161 

II 

Haber, 239, 250 

Hall, A. D., 281 

Hall, D. M., 180 

Hamilton, 247 

Harlan, 84, 88, 97, 98, 101, 152, 153, 
155, 157 

Harrington, 98, 99, 136, 179, 180 

Harris, 292, 293, 296, 320 

Harvey, 240 

Hauge, 219 

Hayes, 5, 23, 39, 49-51, 54, 60, 88, 
89, 108, 135, 138, 143, 144, 145, 
150-153, 157, 158, 188, 193, 199, 
207, 208, 218, 221, 235, 236, 
239, 240, 268 7 293, 297, 298, 
308, 323, 339 

Hays, 76 

Henkemeyer, 133 

Henry, 174 

Heribert-Nilsson, 247 

Heterosis, explanation of, 50-56 

Heyne, 181, 239 

Hines, 89, 160 

Hitchcock, 216 

Hogg, 185 

Holbert, 180, 239 

Hollowell, 69 

Hoover, 234, 296 

Hopkins, 187 

Hor, 152 

Howards, 131, 132 

Humphrey, 47, 65 

Humphries, 176 

Hunter, H., 57 

Hunter, J. W., 181 

Huskins, 24 

Hutchins, 250 



Immer, 99, 155, 234, 292, 299, 301, 

308, 322, 339 
Ivanoff, 241 



Jagger, 250 

Jenkm, 71, 73, 247, 249 

Jenkins, E. W., 48, 250 

Jenkins, M. T., 61, 195, 197, 201, 

202, 206, 236, 237, 239 
Jodon, 65 
Johaimseii, 76 
Johnson, I. J., 54, 108, 169, 199, 202, 

207, 208, 236, 239, 240 
Johnson, T., 135, 138 
Jones, D. F., 42, 45, 46, 49, 51, 52, 

193, 206, 218, 236, 239, 242 
Jones, H. A., 66, 104, 106 
Jones, J. W., 85 
Jones, L. II., 115 
Jorgenson, 194 



K 



Kearney, 47 

Kechle, 50 

Kempton, 240, 241 

Kerns, 40 

Kezer, 132, 133 

Kicsselbach, 55, 187, 195, 298-300, 

302 

Kihara, 20, 141 
Kirk, 69, 71, 244, 249 
Knowlcs, 179, 180 
Kostoff, 20 
Kouznetsov, 134 
Kurtzweil, 138 

L 

Larmour, 182 
Larson, 179 
Latin squares, 312-313 
Laudc, 181 
Lawrence, 251 
Leake, 57 
Leith, 89 
Leonard, 153, 376 
Levy, 259 
Lilienfeld, 20 
Lindstrom, 55, 233 



INDEX 



429 



Link, 185 

Love, H. H., 81, 145, 147, 148 

Love, R. M., 23 

Luckwill, 55 

M 

Macaulcy, 259 

McFadden, 6, 22, 138 

Mclllvaine, 296 

Macindoe, 137, 138 

McRostie, 147 

Mac Vicar, 185 

Mains, 240 

Mangelsdorf, 215, 216, 219, 221 

Marston, 241 

Martini, 84, 98 

Mayer, 194 

Mendel, 11, 86 

Mercer, 281 

Meyers, 241 

Missing plots, estimating yield of, 

314 

Montgomery, 187 
Moore, 23, 143, 144, 323 
Morse, 85 
Muller, 2 

Murphy, H. C., 150 
Murphy, R. P., 213 
Mutations, induced in wheat, oats, 

and barley, 21 
nondefective, 78 
Myers, 22, 169, 174, 241 

N 

Neal, 195 

Neatby, 136, 139 

Nebel, 36 

Newman, 75 

Newton, 135, 138 

Nilsson, H. N., 75 

Nilsson-Ehle, 133, 134, 145, 148 

Nilsson-Leissner, 134, 194 

Nishiyama, 141, 143 

Noll, 81 

Nowosad, 185 



O 



Oats, artificial epiphytotics, crown 

rust, 118 
smuts, 120 
stem rust, 118 

breeding of, 25-34, 92 

crossing methods, 63 

fatuoids, 24 

inflorescence, 146 

inheritance, of awn development, 

144 
of byzantina-sativa characters, 

23, 30-33 

of color of grain, 145 
of crown rust reaction, 27, 149 
of hulled vs. hull-less, 147 
of pubescence, 148 
of quantitative characters, 151 
of smut reaction, 29, 150 
of spreading vs. side panicle, 147 
of stem rust reaction, 28, 148 

loose smut, 124 

quantitative characters, 33, 151 

species crosses, 141-144 

stem rust, 28, 117, 123 
Onion, selfing and crossing, 66 



Painter, 127 

Pan, 139 

Parker, J. H., 138, 143 

Parker, W. H., 134 

Pearl, 3 

Pearson, Karl, 283 

Pearson, O. H., 258 

Pellew, 50 

Pelskcnkc, 176 

Pcrcival, 132 

Peterson, 138, 247 

Philp, 24, 143, 147, 148 

Physiologic races, Hessian fly, 122 

loose smut of oats, 124 

rust in flax, 174 

stem rust, of oats, 123 
of wheat, 4-6, 123, 135 

wilt of flax, 171 



430 



METHODS OF PLANT BREEDING 



Pieters, 69 

Plant breeding, applications of gene- 
tics, 25-34 
colchicine in, 34-38 
hybridization methods in self- 
pollinated plants, 86-100 
outline of procedure, 91-98 
important phases, 1 
methods, asexual groups, 39-41 
backcross, 97, 101-112 
bulk, 96 

classification, 56 
convergent improvement, 52-53 
corn breeding, 6-8, 187-214 
cross-pollinated plants, 257262 
disease and insect resistance, 

113-128 

multiple crosses, 97 
pedigree, 95 

potato improvement, 8-10 
pure line, 74-85 

outline of procedure, 79-83 
in Scandinavia, 75 
sexual group, 41-50 
technics in selfing and crossing, 

60-73 
value of, 2 
Vilmorin's isolation principle, 

75 

polyploids in relation to, 15-25 
selection methods, for cold re- 
sistance, 177 
for oouraarin content in sweet 

clover, 182 

for dormancy in wheat, 179 
for drought resistance in corn, 

181 

for HCN in sudan grass, 185 
for lodging resistance in small 

grains and corn, 180 
for quality in wheat, 175 
for shattering resistance in 

wheat, 178 
for wheat-meal fermentation 

time test, 176 

of wheat, rust resistance, 3-6 
Polyploids, autopolyploid inherit- 
ance, 18-19 



Polyploids, origin of, 16 

in relation to plant breeding, 

15-25 

Pomeroy, 40 
Poole, 250 
Pope, 101 
Porter, 250 
Potatoes, breeding methods, 8-10 

crossing methods, 66 
Powers, 22, 23, 43, 89, 135, 160, 163, 

164, 308, 339 
Prell, 251 

Pumpkin, selfing and crossing, 66 
Punnett, 11 



Q 



Quinby, 65 

Quiscnbcrry, 131, 132, 143, 177, 236 



R 



Raleigh, 292 

Randomized blocks, 307-312 

multiple experiments, 339-350 
Rasmussen, 161 
Red clover, effects of sclfing, 249 

selfing and crossing methods, 67 
Reed, 124, 125, 148, 150 
Reeves, 215, 216 
Reid, 89, 161 

Rice, crossing methods, 65 
Richey, 52, 53, 102, 189-191, 194, 

195, 197, 210 
Rider, 332 
Hi GUI an, 115 
Riker, 241 
Riley, 253, 254 
Roberts, 185 
Robertson, 152, 153, 155 
Rosa, 250 
Ruttle, 36 
Rye, effects of selfing, 247 

selfing and crossing methods, 64 



Saboe, 235 
Salmon, 180, 376 



INDEX 



431 



Sansome, 24 

Saunders, 176 

Scofield, 296 

Scott, G. W., 250 

Scott, L. B., 39 

Seed certification, 263-279 

Canadian Seed Growers' Associa- 
tion, 265, 269 
increase by Minnesota method, 

266 
International Crop Improvement 

Association, 270 
Minnesota method, 272-277 
potatoes, 277 

Maine method, 278- 279 
recommended varieties, 264 
selecting the variety, 263 
Self-fertilization, effects of, in al- 
falfa, 244-247 
in corn, 48, 242 
in cotton, 47 
in cross- pollinated plants, 48 

50 

formulas, 4546 
in often cross-pollinated plants, 

16-47 

in rye, 247 
in sunflowers, 247 
in timothy, 247 
Shamel, 39, 40 
Shaw, 168 
Shull, 50, 192, 193 
Singleton, 206 

Smith, D. C., 117, 123, 127, 148, 150 
Smith, H. H., 36 
Smith, L. II., 189 
Snapdragons, rust resistance, 106 

tetraploid, 35 

Snetlecor, 310, 335, 375, 412, 419 
Snelling, 241 
Sorghum, artificial epiphytotics, 

smut, 121-122 
crossing methods, 65 
Spillman, 134 

Sprague, 52, 53, 55, 210, 238 
Squash, selfing and crossing meth- 
ods, 66 
Stadler, 21 



Stakman, 23, 125, 126, 135, 138, 143, 

144, 323 
Stanford, 162 
Stan ton, 84, 92, 141, 150 
Statistics, applied to data in per- 
centages, 375-379 
Chi square tests, 320-324 
comparison of varieties through 

check, 350-351 
correlation, multiple, 338 
partial, 333-338 
simple, 284, 325-329 

means and differences of, 

331-333 

definition of constants, 280-281 
mean, mode, standard error, vari- 
ance, coefficient of variation, 
281-284 

regression, 329-331 
t test, 285-288 
tables of P\ 412-416 
tables of p = sin 2 0, 421-423 
tables of r and R, 419-420 
tables of r to z, 418 
tables of /, 411 
tables of x 2 , 417 
Stephens, 65 
Stevenson, F. J., 42 
Stevenson, T M., 69, 182, 185 
Sturtevant, 217 
Summerby, 297 
Suneson, 64 

Sunflowers, effects of selfing, 247 
Surface, 143, 145, 148 
Sweet clover, coumarin content, 182 
inducing biennial habit, 182 
selfing and crossing methods, 69 

T 

Tammes, 165, 167 
Tedin, 307 

Timothy, selfing effects, 247 
Tmgcy, 92 
Tippett, 308 
Tisdale, 171 

Tomatoes, cross-pollination, 42 
wilt resistance, 115 



432 



METHODS OF PLANT BREEDING 



Torrie, 143, 144, 147, 150 

Trost, 219 

Tuller, 65 

Tysdal, 70, 244, 246, 299 



Valle, 247 

Vavilov, 34, 88, 134, 215 

Vegetables, disease resistance, 115 

Vilmorin, 75 

Vogel, 178 

W 

Wade, 85 
Walker, 126 
Wallace, 218, 335 
Wang, 56 
Warmke, 35 

Watermelons, wilt resistance, 115 
Watkins, 129, 131 
Weibel, 177 
Weihing, 302 
Wellhausen, 241 
Welsh, 136, 139, 148, 149 
Wclton, 189 
Wexelsen, 159 
Whaley, 56 

Wheat, artificial epiphytotics, bunt, 
119 

fusarial head blight, 120 

Hessian fly, 122 

leaf rust, 118 

stem rust, 118 
bunt resistance, 104 
crossing methods, 63 



Wheat, cross-pollination, 43 
genomes, 20-21, 129 
germinal instability, 22-23 
Hope and H44, 6, 23 
inflorescence, 62 
inheritance, of awnedness, 130 
of bunt resistance, 139 
of chaff characters, 132 
of glume shape, 129 
of quantitative characters, 140 
of seed characters, 133 
of spike density, 134 
of spring vs. winter habit, 134 
of stem rust reaction, 135 
kernel color, 17 
leaf rust, 107 

resistance to Hessian fly, 127 
spcltoids, 24 
Thatcher, 5-6 
Whitaker, 250 
White, 185 

Wiebe, 155, 352, 356, 365 
Wiener, 269 

Williams, C. G., 187, 189 
Williams, R. P., 67, 249 
Wilson, 181 
Wmge, 19, 24 
Woodward, 92 
Worzella, 176 
Wright, 45 
Wu, 208, 236 



Yasuda, 255 

Yates, 308, 312, 314, 351, 352, 362, 
375