<*m  sjm1 


1962  SE« 


GROWTH  AND  DIFFERENTIATION 
IN  APRICOT  TREES 


BY 
H.  S.  REED 


University  of  California  Publications  in  Agricultural  Sciences 
Vol.  5,  No.  1,  pp.  1-55,  18  figures  in  text 


WN?VER$rrv  of  c*  ■ 

COu-4Ul-  'CULTURE 

OAVH 


UNIVERSITY  OF  CALIFORNIA  PRESS 


V*.    iff 


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RARY 


UNIVERSITY  OF  CALIFORNIA  PUBLICATIONS 

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AGRICULTURAL  SCIENCES.— C.  B.  Lipman,  H.  S.  Reed,  R.  E.  Clausen,  Editors.  Price 
per  volume,  $5.  Volume  1  (587  pages),  3  (509  pages),  and  4  (450  pages)  completed. 
Volumes  2  and  5  in  progress. 

Vol.  2.     1.  Studies  in  Juglans.    L  Study  of  a  New  Form  of  Juglans  calif  omica  Watson, 

by  Ernest  B.  Babcock.    Pp.  1-46,  plates  1-12.    December,  1913 „ ?0.60 

2.  Studies  in  Juglans.    II.  Further  Observations  on  a  New  Variety  of  Juglans 

californica  Watson  and  on  Certain  Supposed  Walnut-Oak  Hybrids,  by 
Ernest  B.  Babcock.    Pp.  47-70,  platss  13-19.    October,  1914 _ 35 

3.  Studies  in  Juglans.    III.  (1)  Further  Evidence  that  the  Oak-like  Walnut 

Originates  by  Mutation;  (2)  A  Parallel  Mutation  in  Juglans  hindsii 
(Jepson)  Sargent,  by  Ernest  B.  Babcock.  Pp.  71-80,  plates  20-21.  Sep- 
tember, 1916  _ .10 

4.  Mutation  in  Matthiola,  by  Howard  B.  Frost.     Pp.  81-190,  plates  22-35. 

November,  1919  „ 1.50 

5.  Interspecific  Hybrids  in  Crepis.    I.  Crepis  Capillaris  (L.)  Wallr.  X  O.  Tec- 

torum  L.,  by  Ernest  B.  Babcock  and  Julius  L.  Collins.  Pp.  191-204,  plates 
36-38.    October,  1920 _ _ _ _ _..      .20 

6.  Inbreeding  and  Crossbreeding  in  Crepis  Capillaris  (L.)  Wallr.,  by  Julius  L. 

Collins.    Pp.  205-216,  plates  39-41.    November,  1920  „ _ .30 

7.  Inheritance   of   Some  Morphological   Characters  in   Crepis   capillaris,   by 

Venkata  Rau.    Pp.  217-242,  plates  42-43,  3  figures  in  text.     June,  1923 35 

8.  Microsporogenesis  of   Ginkgo    biloba   L.   with   especial   reference  to   the 

Distribution  of  the  Plastids  and  to  Cell  Wall  Formation,  by  Margaret 
Campbell  Mann.    Pp.  243-248,  plate  52.    September,  1924 25 

Vol.  3.    1.  New  Grasses  for  California.    I.  Phalaris  stenoptera  Hack.,  by  P.  B.  Kennedy. 

Pp.  1-24,  plates  1-8.    July,  1917 _ __ - —      .30 

2.  Optimum  Moisture  Conditions  for  Young  Lemon  Trees  on  a  Loam  Soil,  by 

L.  W.  Fowler  and  C.  B.  Lipman.    Pp.  25-36,  plates  9-11.    September,  1917.      .15 

3.  Some  Abnormal  Water  Relations  in  Citrus  Trees  of  the  Arid  Southwest 

and  Their  Possible  Significance,  by  Robert  W.  Hodgson.    Pp.  37-54,  plate 

12.     September,  1917  _      .20 

4.  A  New  Dendrometer,  by  Donald  Bruce.    Pp.  55-61.    November,  1917 10 

5.  Toxic  and  Antagonistic  Effects  of  Salts  on  Wine  Yeast   (Saccharomyces 

ellipsoideus),  by  S.  K.  Mitra.    Pp.  63-102.    November,  1917 _      .45 

6.  Changes  in  the  Chemical  Composition  of  Grapes  during  Ripening,  by  F.  T. 

Bioletti,  W.  V.  Cruess,  and  H.  Davi.  Pp.  103-130.    March,  1918 25 

7.  A  New  Method  of  Extracting  the  Soil  Solution  (a  Preliminary  Communi- 

cation), by  Charles  B.  Lipman.    Pp.  131-134.    March,  1918  05 

8.  The  Chemical  Composition  of  the  Plant  as  Further  Proof  of  the  Close  Rela- 

tion between  Antagonism  and  Cell  Permeability,  by  Dean  David  Waynick. 

Pp.  132-242,  plates  13-24.     June,  1918 1.25 

9.  Variability  in  Soils  and  Its  Significance  to  Past  and  Future  Soil  Investi- 

gations. I.  A  Statistical  Study  of  Nitrification  in  Soil  by  Dean  David 
Waynick.    Pp.  243-270,  2  text  figures.    June,  1918 SO 

10.  Does  CaCo3  or  CaSo4  Treatment  Affect  the  Solubility  of  the  Soil's  Con- 

stituents?, by  C.  B.  Lipman  and  W.  F.  Gericke.    Pp.  271-282.    June,  1918.      .10 

11.  An  Investigation  of  the  Abnormal  Shedding  of  Young  Fruits  of  the  Wash- 

ington Navel  Orange,  by  J.  Eliot  Coit  and  Robert  W.  Hodgson.  Pp. 
283-368,  plates  25-42,  9  text  figures.    April,  1919  1.00 

12.  Are  Soils  Mapped  under  a  Given  Type  Name  by  the  Bureau  of  Soils  Method 

Closely  Similar  to  One  Another?,  by  Robert  Larimore  Pendleton.  Pp. 
369-498,  plates  43-74,  S3  text  figures.    June,  1919 „ 2.00 

VoL  4.    1.  The  Fermentation  Organisms  of  California  Grapes,  by  W.  V.  Cruess.    Pp. 

1-66,  plates  1-2,  15  text  figures.    December,  1918 _ .76 

2.  Tests  of  Chemical  Means  for  the  Control  of  Weeds.    Report  of  Progress,  by 

George  P.  Gray.    Pp.  67-97,  11  text  figures  _ _.      .30 

8.  On  the  Existence  of  a  Growth-Inhibiting  Substance  in  the  Chinese  Lemon, 

by  H.  S.  Reed  and  F.  F.  Halma.    Pp.  99-112,  plates  3-6.    February,  1919.      .25 


GROWTH  AND  DIFFERENTIATION 
IN  APRICOT   TREES 


BY 
H.  S.  REED 


University  of  California  Publications  in  Agricultural  Sciences 

Volume  5,  No.  1,  pp.  1-55,  18  figures  in  text 

Issued  September  30,  1924 


GROWTH  AND  DIFFERENTIATION  IN 
APRICOT  TREES* 


H.  S.  EEED 


I.  INTRODUCTION 

The  '  habit  of  growth '  of  a  species  or  variety  is  a  character  to  which 
reference  is  often  made  in  botanical  discussions.  The  pattern  of  an 
organism  is  the  result  of  a  process  of  growth  and  differentiation  which 
is  largely  an  expression  of  factors  inherent  in  that  organism.  Growth 
produces  not  only  an  increase  in  size ;  it  is  accompanied  as  well  by  a 
complex  differentiation  of  the  organism.  Nothing  could  be  more 
important  than  an  investigation  of  these  processes  in  order  to  discover 
the  fundamental  principles  which  govern  them.  Those  who  are  inter- 
ested in  the  broader  problems  of  biology  will  be  concerned  with  the 
laws  of  growth,  while  those  who  are  interested  in  the  art  of  horticulture 
may  gather  from  such  a  study  something  that  is  fundamental  in  fruit, 
production. 

There  are  two  well  recognized  methods  of  attacking  the  problem 
of  growth :  the  experimental  and  the  observational.  So  far  as  the 
dynamics  of  growth  are  concerned,  the  experimental  method  of  study, 
dealing  largely  with  factors  which  control  processes,  may  be  expected 
to  yield  useful  information.  But  when  dealing  with  growth  in  relation 
to  differentiation,  and  with  the  problem  of  correlation  of  different  mem- 
bers of  an  organism,  the  observational  method  is  of  great  importance, 
and  it  is  this  method  that  was  employed  in  the  present  investigation. 

The  writer  has  shown  in  earlier  papers  that  the  growth  of  an 
organism,  or  organ,  proceeds  in  a  definite,  orderly  fashion,  and  that 
it  is  possible  to  express  the  rate  of  growth  by  a  mathematical  equation. 
This  contributes  nothing,  of  course,  to  our  knowledge  of  the  causes 
of  growth,  but  does  emphasize  the  fact  that  the  form  and  the  func- 
tion of  organisms,  though  variable,  nevertheless  are  not  outside  the 
realm  of  exact  science.  With  respect  to  apricot  branches,  it  is  known 
that  their  growth  in  length  conforms  to  an  equation  in  which  the  size 
is  shown  to  be  a  definite  function  of  the  time. 


*  Paper  No.  112,  University  of  California,  Graduate  School  of  Tropical  Agri- 
culture and  Citrus  Experiment  Station,  Riverside,  California. 


2  University  of  California  Publications  in  Agricultural  Sciences       [Vol.5 

In  the  present  paper  variability  and  differentiation  in  apricot 
branches  will  be  discussed  at  length.  In  respect  to  length  of  main  axis 
and  percentage  of  buds  which  overcame  dormancy  in  the  first  season, 
variability  was  not  excessive.  In  respect  to  other  characters,  however, 
variability  was  very  great.  Amount  of  growth,  for  example,  is  appar- 
ently largely  determined  by  fortuity  of  position,  because  of  varying 
reaction  to  heat  and  light.  Diverse  types  of  development  are  mani- 
fested by  orthotropic  and  plagiotropic  branches.  A  large  part  of  the 
material  and  energy  at  the  disposal  of  the  branch  is  devoted  to  form- 
ing structures  which,  though  subsidiary,  exceed  in  size  the  main  axis 
of  the  branch.  It  will  be  important,  therefore,  to  investigate  the 
quantitative  relationships  between  branches  and  their  members. 

The  greatest  growth  of  laterals  is  produced  on  the  most  vigorous 
branches.  The  unity  of  the  organism  is  demonstrated  by  the  close 
relationship  between  the  vigor  of  the  branch  and  the  vigor  of  the 
laterals  produced  on  it.  Speaking  in  chemical  terms,  we  might  say 
that  variations  in  the  quantity  of  growth-promoting  substances  or  of 
tissue-forming  materials  are  uniformly  distributed  throughout  a 
branch.  Although  the  terminal  portion  of  a  branch  exerts  a  dominant 
influence  over  the  development  of  the  subterminal  portions,  the  factors 
which  tend  to  promote  growth  in  one  region  tend  also  to  promote 
growth  in  another. 

The  most  casual  observer  cannot  help  noticing,  in  figure  1,  the 
three  distinct  groups  of  laterals  on  the  branches.  Between  adjacent 
groups  there  are  many  buds  whose  dormancy  was  not  broken  during 
the  first  growing  season.  The  quantitative  characters  of  these  groups 
have  been  of  great  interest  in  the  study  of  the  pattern  of  the  apricot 
branches,  because  they  indicate  a  certain  definite  distribution  of  mass 
along  the  axis  of  the  branch. 

A  former  study  of  growth  in  young  pear  trees9  showed  that  the  size 
of  a  shoot  is  a  function  of  its  position  on  the  mother  shoot.  The 
present  study  shows  that  the  shape  and  size  of  these  groups  of  laterals 
is  a  function  of  their  position  on  the  main  axis;  in  other  words,  that 
their  specific  method  of  development  is  a  quantitative  character.  This 
relationship  seems  to  be  highly  important  and  to  support  the  idea  that 
the  growth  process  (in  its  simplest  form)  brings  about  a  definite  dis- 
tribution of  matter  in  space  which  takes  the  form  of  a  characteristic 
pattern.  The  position  and  size  of  the  laterals  on  the  branches  must 
be  regarded  as  the  result  of  a  process  of  differentiation  which  as  yet 
has  been  but  little  studied  with  reference  to  its  quantitative  characters. 


1924] 


Seed:  Growth  and  Differentiation  in  Apricot   Trees 


Herbert  Spencer12  has  stated  the  problem  succinctly. 

The  morphological  differentiation  which  thus  goes  hand  in  hand  with  morpho- 
logical integration  is  clearly  what  the  perpetually-complicating  conditions 
would  lead  us  to  anticipate.  Every  addition  of  a  new  unit  to  an  aggregate  of 
such  units  must  affect  the  circumstances  of  the  other  units  in  all  varieties  of 
ways  and  degrees,  according  to  their  relative  positions,  must  alter  the  distribu- 
tion of  mechanical  strains  throughout  the  mass,  must  modify  the  process  of 
nutrition,  must  affect  the  relations  of  neighboring  parts  to  surrounding  diffused 
actions;  that  is,  must  initiate  a  changed  incidence  of  forces  tending  ever  to 
produce  changed  structural  arrangements. 


Fig.  1.     Diagram  of  a  young  apricot  branch  showing  the  type  of  material 
used  in  the  study.     A  A,  branch  axis;  B,  primary  lateral;  C,  secondary  lateral. 


The  data  to  be  presented  afford  strong  evidence  that  the  number  of 
laterals  per  branch  is  largely  determined  by  factors  which  impose  a 
condition  of  dormancy  upon  the  buds  of  most  of  the  nodes.  The 
greater  number  of  branches  have  relatively  few  laterals.  This  condi- 
tion is  of  obvious  interest  to  horticulturists,  who  find  it  necessary  to 
employ  various  means  of  promoting  the  formation  of  laterals.  So  far 
as  possible,  the  factors  which  influence  the  production  of  laterals  have 
been  studied,  and  the  need  for  further  investigation  indicated. 


4  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  •> 

The  production  of  flower-buds  on  the  branches  is  another  question 
of  biological  interest.  The  number  of  blossoms  on  a  branch  is  neces- 
sarily dependent  upon  the  number  of  laterals  it  produces,  but  long- 
laterals  show  no  tendency  to  be  more  prolific  in  blossoms  than  their 
shorter  neighbors.  One  important  exception  to  this  relation  was  found 
in  the  case  of  primary  laterals,  where  there  appeared  to  be  a  distinct 
group  of  relatively  long  laterals  possessing  from  50  to  110  nodes,  in 
which  the  majority  produced  less  than  five  blossoms  each.  This  group 
might  be  regarded  as  being  predominantly  vegetative  in  activity,  while 
the  other  laterals  were  both  vegetative  and  reproductive  in  function. 
There  is  a  notable  difference  in  the  number  of  blossoms  per  lateral  of 
different  groups,  which  is  probably  caused  in  large  measure  by 
differences  in  age  of  the  several  groups. 

If  we  assume  that  there  is  some  sort  of  an  equilibrium  in  the  tree 
between  forces  producing  vegetative  and  reproductive  growth,  we 
may  understand  better  the  various  correlations  between  blossoms  and 
other  characters  which  are  to  be  studied  in  the  following  pages. 
Speaking  broadly,  we  may  say  that  each  lateral  appeared  to  produce 
about  the  same  number  of  blossoms  as  its  neighbors  of  approximately 
the  same  age,  and  that  the  number  of  blossoms  on  a  lateral  was  more 
or  less  independent  of  the  number  of  nodes  which  the  lateral  possessed. 
In  other  words,  it  may  be  a  matter  of  indifference  to  the  fruit  grower 
whether  the  branches  have  long  laterals  or  short  laterals  so  far  as  the 
capacity  of  the  trees  to  produce  'fruit  buds'  is  concerned. 

In  the  apricot  trees  studied  the  equilibrium  between  forces  influ- 
encing vegetative  and  reproductive  growth  varied,  apparently,  only 
between  limits.  The  variability  in  the  number  of  blossoms  per  branch 
is  large  and  may  possibly  indicate  that  the  equilibrium  between  forces 
is  relatively  unstable.  The  average  number  of  blossoms  per  branch 
was  360,  but  the  actual  numbers  ranged  from  50  to  1200.  This  wide 
variability  may  have  resulted  from  the  fact  that  we  were  dealing  in 
this  case  solely  with  young  branches  produced  in  the  preceding  season. 
The  data  give  some  evidence  on  the  opposition  of  growth  processes  to 
fruit-bud  formation.  It  was  found  that,  while  the  distal  region  of  the 
branch  was  actively  growing,  the  physiological  functions  of  that  region 
were  opposed  to  the  formation  of  energy  centers  which  produce  fruit- 
buds.  In  the  proximal  region,  where  vegetative  growth  had  largely 
ceased  before  the  end  of  the  season,  the  formation  of  fruit  buds  was 
not  opposed  by  other  functions. 


1924]  Eeed:  Growth  and  Differentiation  in  Apricot  Trees 


II.    DESCRIPTION  OF  THE  MATERIAL 

The  data  for  the  present  study  were  obtained  from  four-year-old 
apricot  (Primus  armeniaca)  trees  of  the  horticultural  variety  known 
as  Royal.  The  trees  stand  in  an  orchard  at  the  Citrus  Experiment 
Station,  Riverside,  California.  Measurements  were  taken  of  79 
branches  which  had  grown  in  the  preceding1  year.  The  branches  were 
selected  from  36  different  trees  scattered  over  the  orchard  in  such  a 
way  as  to  give  a  fairly  random  distribution.  Figure  1  shows  in  a 
diagrammatic  way  the  morphology  of  a  typical  branch  selected  from 
the  population  studied. 

There  are  advantages  and  disadvantages  in  working  with  material 
from  a  clonal  variety  which,  for  many  years,  has  been  propagated  by 
budding.  A  budded  tree  has  something  of  the  nature  of  a  dual  organ- 
ism, since  it  is  growing  upon  the  root  of  a  seedling  tree.  The  clonal 
quantitative  characteristics  may  be  somewhat  modified  by  the  vigor 
of  the  stock  upon  which  the  variety  is  propagated,  though  it  is  doubt- 
ful whether  a  group  of  trees  like  these  would  have  as  great  variability 
as  a  similar  number  of  unbudded  seedling  trees,  The  Royal  apricot 
probably  originated  in  France.  ' '  This  valuable  sort  was  raised  in  the 
Royal  garden  of  the  Luxembourg,  whence  a  plant  was  sent  to  the 
[Royal  Horticultural]  society  [of  London]  by  M.  Hervy,  the  Director. 
It  fruited  in  the  Garden  in  1828  and  was  then  figured  in  the  Pomo- 
logical  magazine."14 

In  the  discussion,  the  following  terms  will  be  used:  'branches'  are 
the  79  shoots  which  make  up  the  population  under  study;  'mother 
shoots'  are  the  year-old  limbs  on  which  the  population  grew;  'primary 
laterals '  are  the  shoots  which  grew  from  certain  nodes  of  the  branches ; 
'secondary  laterals'  are  shoots  which  grew  on  the  primary  laterals. 

The  mother  shoots  were  pruned  by  the  amputation  of  about  three- 
fourths  of  their  length  in  the  early  spring  of  1920.  The  79  branches 
upon  which  this  study  is  based  grew  during  the  following  season  from 
buds  situated  a  short  distance  back  of  the  points  at  which  the  mother 
shoots  had  been  amputated.  The  favorable  position  of  the  branches,  as 
well  as  the  severe  pruning  of  the  mother  shoots,  unquestionably  had 
much  to  do  with  this  vigorous  growth. 

The  primary  and  secondary  laterals  were  developed  as  the  branch 
grew  and  reached  a  total  length  which  averaged  7  to  8  times  the  length 
of  the  main  axis  on  which  they  were  borne  (fig.  1). 


6  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  .3 

During  the  growing  season  measurements  were  made  each  week  to 
determine  the  length  of  the  branches.  The  length  of  the  primary  and 
secondary  laterals  was  not  determined  during  the  growing  season.  At 
the  end  of  the  growing  season  an  extensive  series  of  measurements  was 
made  covering  the  length  and  circumference  of  the  branches,  number 
of  laterals,  number  of  dormant  buds,  and  number  of  blossoms.  These 
measurements  of  the  shoot  systems  with  their  adherent  laterals  serve  as 
a  basis  for  the  present  study. 

The  vegetative  shoots  of  the  apricot  tree  constitute  very  favorable 
material  for  the  study  of  growth  relationships.  Previous  papers  from 
this  laboratory0' 7- 8  have  presented  some  of  the  salient  features  in  the 
growth  of  shoots  like  those  here  studied.  Except  for  the  vigor  and 
rapidity  of  their  growth  these  shoots  differed  in  no  essential  from  those 
of  other  fruit  trees  which  have  been  under  observation. 

In  the  early  part  of  the  growing  season  the  apricot  shoots  grow  very 
rapidly,  making  about  half  their  season's  growth  in  the  first  seven  to 
nine  weeks.  The  rate  of  growth  usually  attained  its  first  maximum  in 
the  fifth  or  sixth  week  of  the  season,  then  gradually  declined  with 
more  or  less  irregularity  to  about  the  fourteenth  week ;  it  reached  a 
second  maximum  about  the  seventeenth  week  and  fell  to  its  final 
minimum  from  the  twenty-fifth  to  the  twenty-eighth  week.  This 
tendency  to  cyclic  growth  is  characteristic  of  many  trees  and  is  well 
illustrated  by  the  growth  of  the  apricot  shoots. 

The  growing  season  for  apricot  shoots  in  the  locality  mentioned 
usually  begins  in  March  and  extends  to  some  time  late  in  autumn.  It 
is  therefore  necessary  to  make  measurements  of  the  elongation  over  a 
total  period  of  eight  or  nine  months. 

Results  of  an  earlier  investigation0  showed  that  there  were  three 
cycles  in  the  seasonal  growth  of  a  sample  of  vegetative  shoots  and  that 
the  growth  in  each  cycle  could  be  quantitatively  expressed  by  the 
equation 

log-^—=K(t  —  t1). 

a  —  x 

In  this  case  x  is  the  length  of  the  shoots  at  time  t;  a  is  their  final 
length;  ty  is  the  time  at  which  the  shoots  have  been  made  one-half  of 
their  final  length  a;  and  K  is  a  constant.  This  equation  has  been  found 
to  express  the  growth  of  both  plants  and  animals,  and  is  useful  in 
analyzing  the  growth  process.  The  rate  of  growth  of  apricot  shoots 
is  definitely  related  to  the  final  length  a,  with  distinct  quantitative 
differences  between  shoots  of  various  length  through  the  entire  season.7 


1924]  Reed:  Growth  and  Differentiation  in  Apricot  Trees  7 

Pruning  the  trees  severely  in  the  dormant  period  had  a  marked 
influence  upon  the  sap  concentration  and  the  rate  of  growth  of  vegeta- 
tive shoots  in  the  following  season.  Sap  concentration  on  rapidly  grow- 
ing shoots  was  usually  much  less  than  on  slowly  growing  shoots,  and 
showed  a  descending  gradient  from  the  apex  toward  the  base  of  the 
shoots.8 

The  final  measurements  of  the  branches  and  their  parts  were  taken 
with  the  assistance  of  Mr.  F.  F.  Halma  and  Dr.  A.  R.  C.  Haas  in  the 
spring  of  1921  just  before  the  beginning  of  growth.  Not  only  length 
and  number  of  buds  were  recorded  for  each  branch  and  lateral,  but 
the  position  of  each  lateral  on  the  shoot  which  bore  it  was  recorded. 
Table  1  presents  the  data  in  a  condensed  form.* 


*  The  writer  realizes  the  advisability  of  publishing  the  original  data,  but, 
for  reasons  of  economy,  is  unable  to  do  so.  The  original  figures  have  been 
preserved  and  may  be  consulted  by  anyone  who  wishes  to  use  them. 


University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 


TABLE    1 
Summary  op  Data  on  Apricot  Branches 


Branch 
No. 

Angle 
from 
perpen- 
dicular 

(dgrs.) 

Loca- 
tion 

Length 
(cm.) 

Total 
no.  of 
nodes 

No. 

dor- 
mant 
nodes 

No. 

pri- 
mary 
later- 
als 

No. 
second- 
ary 

later- 
als 

Length 
of  all 
pri- 
mary 
later- 
als 
(cm.) 

Length 
of  all 
second- 
ary 
later- 
als 
(cm.) 

No. 

of 
blos- 
soms 

1 

30 

NE 

246 

148 

116 

32 

21 

1029 

198 

320 

2 

50 

S 

257 

130 

101 

29 

59 

1473 

1128 

1066 

3 

50 

SE 

241 

145 

116 

29 

13 

1133 

111 

495 

4 

90 

SE 

235 

138 

103 

35 

20 

1057 

269 

383 

5 

45 

N 

237 

126 

82 

44 

62 

2021 

1124 

714 

6 

80 

SE 

263 

153 

120 

33 

79 

2016 

1304 

347 

7 

50 

W 

195 

114 

86 

28 

41 

1164 

686 

238 

8 

30 

NW 

230 

121 

57 

64 

136 

3078 

1852 

503 

9 

90 

SE 

224 

128 

110 

18 

19 

475 

177 

249 

10 

90 

S 

233 

125 

84 

41 

71 

2011 

1307 

534 

11 

60 

NE 

267 

136 

97 

39 

77 

2765 

1509 

437 

12 

75 

sw 

220 

126 

93 

33 

51 

1626 

715 

235 

13 

90 

NW 

227 

137 

103 

34 

12 

1095 

108 

192 

14 

90 

s 

263 

134 

99 

35 

109 

2635 

1795 

307 

15 

75 

N 

251 

145 

110 

35 

49 

1505 

964 

231 

16 

45 

NE 

267 

149 

92 

57 

133 

2816 

1903 

753 

17 

45 

SE 

289 

164 

100 

64 

127 

2765 

2848 

293 

18 

90 

E 

270 

154 

126 

28 

60 

1659 

775 

527 

19 

30 

VV 

280 

178 

126 

52 

103 

2804 

1755 

391 

20 

45 

s 

305 

148 

92 

56 

117 

3169 

2157 

612 

21 

80 

sw 

231 

127 

96 

31 

30 

1677 

333 

374 

22 

60 

E 

260 

137 

98 

39 

39 

1739 

462 

302 

23 

90 

SE 

223 

144 

120 

24 

19 

1005 

389 

166 

24 

75 

N 

152 

77 

39 

38 

13 

866 

93 

134 

25 

50 

SW 

223 

134 

91 

43 

21 

1248 

227 

358 

26 

0 

SE 

218 

138 

78 

60 

69 

1672 

846 

547 

27 

90 

E 

221 

113 

88 

25 

4 

703 

36 

115 

28 

45 

SW 

227 

121 

98 

26 

18 

1013 

173 

514 

29 

85 

SW 

260 

129 

95 

34 

10 

955 

173 

450 

30 

85 

s 

260 

134 

100 

34 

25 

860 

424 

530 

31 

30 

N 

283 

151 

105 

46 

41 

1608 

536 

645 

32 

90 

s 

137 

82 

64 

18 

8 

338 

57 

298 

33 

85 

NW 

211 

110 

78 

32 

49 

1510 

683 

523 

34 

70 

s 

238 

129 

98 

31 

22 

1199 

206 

468 

35 

80 

w 

202 

111 

76 

35 

19 

1077 

163 

491 

36 

90 

SE 

180 

75 

48 

27 

0 

760 

0 

162 

37 

50 

SE 

191 

112 

96 

16 

1 

371 

14 

185 

38 

90 

SW 

216 

109 

78 

31 

2 

716 

42 

259 

39 

90 

W 

229 

138 

112 

26 

2 

583 

13 

27 

40 

45 

SE 

253 

144 

101 

43 

22 

2004 

288 

104 

1924] 


Reed:  Growth  and  Differentiation  in  Apricot  Trees 


TABLE  1— (Continued) 


Branch 
No. 

Angle 
from 
perpen- 
dicular 

(dgrs.) 

Loca- 
tion 

Length 
(cm.) 

Total 
no.  of 
nodes 

No. 

dor- 
mant 
nodes 

No. 
pri- 
mary 
later- 
als 

No. 
second- 
ary 
later- 
als 

Length 
of  all 
pri- 
mary 
later- 
als 
(cm.) 

Length 
of  all 
second- 
ary 
later- 
als 
(cm.) 

No. 

of 
blos- 
soms 

41 

80 

SE 

235 

141 

108 

33 

13 

1031 

144 

90 

42 

50 

S 

211 

115 

74 

41 

5 

888 

78 

146 

43 

90 

E 

211 

87 

67 

20 

4 

377 

19 

151 

44 

80 

S 

256 

144 

110 

34 

12 

1584 

222 

230 

45 

40 

SE 

312 

157 

103 

54 

100 

2643 

1576 

639 

46 

90 

sw 

218 

117 

104 

13 

0 

262 

0 

159 

47 

80 

E 

225 

122 

95 

27 

0 

578 

0 

285 

48 

70 

E 

258 

135 

98 

37 

31 

1059 

484 

283 

49 

70 

S 

216 

130 

108 

22 

11 

509 

235 

108 

50 

75 

w 

253 

154 

123 

31 

11 

846 

170 

190 

51 

45 

E 

255 

121 

86 

35 

31 

1207 

582 

451 

52 

85 

SE 

263 

133 

104 

29 

15 

1098 

194 

270 

53 

90 

W 

230 

136 

120 

16 

2 

381 

21 

216 

54 

45 

NE 

265 

130 

82 

48 

46 

2148 

778 

899 

55 

90 

SE 

249 

124 

104 

20 

4 

583 

66 

240 

56 

90 

SE 

226 

124 

102 

22 

1 

510 

5 

198 

57 

90 

S 

212 

131 

107 

24 

4 

670 

29 

376 

58 

90 

E 

200 

107 

88 

19 

0 

348 

0 

139 

59 

30 

W 

252 

117 

84 

33 

21 

1279 

231 

258 

60 

45 

NE 

252 

131 

69 

62 

72 

2449 

1081 

1197 

61 

50 

S 

226 

128 

82 

46 

93 

2418 

1069 

574 

62 

30 

s 

209 

117 

71 

46 

37 

1354 

217 

383 

63 

45 

E 

191 

86 

59 

27 

0 

70,6 

0 

129 

64 

80 

E 

225 

115 

68 

47 

16 

1555 

256 

472 

65 

45 

NE 

256, 

124 

76 

48 

30 

1296 

304 

523 

66 

50 

E 

253 

129 

103 

26 

8 

762 

75 

190 

67 

80 

E 

252 

126 

86 

40 

27 

1319 

331 

342 

68 

90 

sw 

217 

109 

84 

25 

7 

606 

88 

252 

69 

45 

SE 

253 

143 

103 

40 

34 

1369 

378 

207 

70 

45 

SE 

274 

150 

95 

55 

63 

2323 

944 

599 

71 

45 

S 

277 

136 

94 

42 

41 

1778 

534 

422 

72 

80 

N 

213 

119 

82 

37 

20 

913 

319 

360 

73 

20 

E 

250 

133 

88 

45 

50 

2239 

492 

346 

74 

15 

N 

260 

144 

98 

46 

78 

2452 

1000 

615 

75 

50 

SE 

261 

134 

103 

31 

18 

909 

264 

86 

76 

90 

S 

211 

126 

108 

18 

5 

454 

35 

44 

77 

90 

SE 

143 

61 

27 

34 

16 

1304 

185 

135 

78 

50 

NE 

229 

102 

71 

31 

0 

433 

o 

56 

79 

30 

E 

271 

128 

77 

51 

14 

1531 

134 

255 

10 


University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 


III.  RATE  OF  GROWTH  OF  THE  BRANCHES 

The  mean  length  of  the  shoots  for  each  week  is  a  convenient  and 
reliable  index  of  their  rate  of  growth.  Measurements  of  the  length  of 
these  79  branches  were  made  at  seven-day  intervals  throughout  the 
growing  season.  Their  rate  of  growth  is  of  interest  in  the  present 
discussion  chiefly  because  it  shows  the  existence  of  two  distinct  cycles 


TABLE  2 

The  Growth  of  the  Main  Axis  of  the  Branches.     Comparison  of  Observed 
Mean  Length  and  Calculated  Values.    Values  for  the  First  Cycle 

x 
Computed  from  Log  ; 


Log 


190  —  x 
a:— 170 
240  —  x 


.147  (t  ■ —  6) ;  for  Second  Cycle 
:.201  ((  —  17.3) 


First  Cycle 

Second  Cycle 

t 

r(obs.) 

i(calc) 

9 

t 

(i-170)  obs. 

(j>170)  calc. 

(wks.) 

(cm.) 

(cm.) 

(cm.) 

(wks.) 

(cm.) 

(cm.) 

(cm.) 

0 

22.0 

29.5 

39.0 

50.5 

64.0 

79.0 

.      95.0 

108.1 

126.0 

139.5 

151   1 

12.0 
6.2 

4.9 
2.3 

-2  6 
0.1 

-0.1 
4.5 
3.6 
4.0 

1.9 
1.7 

13 
15 
17 
19 
21 
25 
38 

2.0 
17.3 

31.3 

47.7 
58.8 
67.3 
68.6 

8.4 
17.9 
32.6 
48.1 
59.3 
68.0 
69.8 

6.4 

1 

2 
3 
4 
5 
6 
7 
8 
9 
10 
11 

17.5 

32.8 

45.6 

61.7 

81.6 

94.9 

108.2 

121  5 

135.9 

147.1 

166.1 
172  0 

0.6 

1.3 
0.4 
0.5 
0.7 
1.2 

Root-mean-square  deviation       2.55 

12 

13 

168.0 
173.7 

Root-mean-square  deviation  4.78 

of  growth,  the  first  covering  the  period  of  13  weeks  in  which  the  most 
rapid  elongation  occurred,  the  second  covering  the  remainder  of  the 
growing  season.  Table  2  shows  the  observed  mean  length  of  the 
branches  at  weekly  or  bi-weekly  intervals  for  38  weeks  and  also  the 
length  computed  from  the  equation13 


log 


K  (t  —  t,). 


1924] 


Seed:  Growth  and  Differentiation  in  Apricot   Trees 


11 


The  actual  equation  for  the  first  cycle  was 


log 


=  .147  (*— 6). 


190  —  x 

The  equation  for  the  second  cycle  assumes  that  the  ordinate  and  the 
abscissa  have  been  removed  to  a  new  point  of  origin.    The  new  values 
of  x  were  obtained  by  subtracting  170  from  each  of  the  observed  values 
of  x.    The  actual  equation  was 
x  —  170 


l0£ 


240  —  x 


.201  (f  — 17.3] 


The  graph  (fig.  2)  shows  that  the  agreement  between  the  computed 
and  observed  values  of  the  mean  length  is  satisfactory. 


100 


^^_   Q    ■ o 

o 


Time  in  weeKs 


30 


Fig.    2.      Growth    curve    of    the    population    of    branches.      The    small    circles 
represent  observed  mean  length  of  branches,  the  curves  were  calculated  from 

£  /£ 170 

the  equations:  first  cycle,  log  — — =  .147  (t  —  6);  second  cycle,  log 


190- 


=  .201  (*  —  17.3) 


240- 


It  may  be  of  interest  to  note  that  the  appearance  of  primary 
laterals  was  not  coincident  with  the  termination  of  the  first  growth 
cycle.  The  time  at  which  these  laterals  first  appeared  ranged  from 
the  third  to  the  seventh  week,  the  mean  time  being  4.31  weeks  from 
the  beginning  of  the  growing  season.  The  relations  appear  to  be 
different  from  those  described  for  the  growth  of  roots  by  Priestley 
and  Pearsall,5  who  reported  that  the  appearance  of  secondary  or  of 
tertiary  roots  is  concomitant  with  a  lag  in  the  growth  curve. 


12 


University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 


The  validity  of  the  foregoing  equation  may  be  tested  further  by 
comparing  the  observed  and  computed  increments  in  length  during 
the  growing  season.  The  foregoing  equation,  when  differentiated, 
becomes 

dx 


dt 


kx  (a  —  x) 


K 


where  k=  —   and   the  other  letters  have  their  former   significance. 
a 

dx 
The  computed  values  -7-  and  the  observed  values  of  S  are  given  in 
dt 

table  3.    The  latter  were  smoothed  by  the  method  commonly  used  for 
such  cases  according  to  the  equation 

S  =  Y2  (««_!  + *f+i) 


TABLE  3 

Growth  Rate  of  Apricot  Branches  as  Shown  by  their  Weekly 
Increment  in  Length 


First  Cycle 

Second  Cycle 

t 

dx 
dt 

s 

e 

t 

dt 

s 

e 

(wks.) 

(cm.) 

(cm.) 

(cm.) 

(wks.) 

(cm.) 

(cm.) 

(cm.) 

0 

6.8 

0 

6  8 

13 

3  4 

7  .7 

-4  3 

1 

8.7 

8.8 

-     1 

15 

6.2 

7  5 

-1.3 

2 

10  9 

10.8 

1 

17 

8.1 

7  9 

.2 

3 

13  0 

10.7 

2.3 

19 

7.0 

6.3 

.7 

4 

14.7 

16.4 

-1.7 

21 

4.2 

5.4 

-1.2 

5 

15.8 

14.7 

1.1 

25 

.9 

2.1 

-1.2 

6 

15.9 
15  0 
13.4 

16.6 
13  3 
13.8 

.7 

1.7 

-     4 

38 

1 

1 

0 

7 
8 

Root- 

mean-square  deviation 

1.84 

9 

11.3 

12.3 

1.0 

10 

9.1 

11.9 

-2.8 

11 

7.1 

10.4 

-3.3 

12 

5.4 

7.7 

-2.3 

13 

4  0 

7.7 

-3.7 

14 

2  9 

6.8 

-3.9 

15 

2  1 

7  5 

-5  4 

17 

11 

7.9 

6.8 

19 

.6 

6  3 

-5.7 

21 

.3 

5.4 

-5.1 

Root-mean-square  deviation         3.61 


1924] 


Heed:  Growth  and  Differentiation  in  Apricot  Trees 


13 


The  agreement  of  the  actual  and  computed  values  is  shown  in  figure  3. 
The  curves  for  the  two  cycles  overlap,  indicating  that  the  two  phases 
of  growth  in  these  branches  are  not  sharply  separated  from  each  other. 
Consequently  we  must  add  together  the  computed  values  where  the 
curves  overlap  to  approximate  the  summation  of  the  two  cycles.  The 
course  of  these  summations  is  shown  by  the  dotted  line,  and  the 
observed  values  agree  well  with  them. 


4* 
at 


o     ° 

1°     \ 

1         °  \ 

/               \o 
/                   \  ' 

/  °                 V 

> 
o 

\    °/      \ 

\         /          °\ 

Timi  In  wteKs 

Fig.  3.     Growth    rate    of    apricot   branches,    showing    the    two    overlapping 
cycles.     The  curves  were  calculated  from  the  equations:   first  cycle, 


-^=.00077x  (190- 
at 


■x),  second  cycle,  -jr 


.00084  (x  —  170)  (240— a:). 


The  dotted  line  is  the  sum  of  the  overlapping  portions  of  the  curves.     Small 
circles  represent  mean  weekly  increments  in  length. 


These  considerations  show  that  the  main  axis  of  the  apricot  branches 
grew  during  the  entire  season  in  two  cycles  at  perfectly  definite  rates 
each  of  which  resembles  the  rate  of  an  autocatalytic  reaction.  They 
show  furthermore  that  the  equations  may  be  profitably  used  to  analyze 
the  season's  growth. 


14  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 


IV.  MORPHOLOGY  OF  THE  BRANCHES 

The  branches  under  discussion  (fig.  1  gives  an  idea  of  the  shape 
they  assumed)  were  selected  in  early  spring  at  a  time  when  they  were 
only  a  few  centimeters  long.  They  developed  from  buds  near  the 
distal  ends  of  the  mother  shoots  and  stood  in  positions  where  they  had 
prospects  of  unhampered  development.  We  may  regard  this  popula- 
tion as  representative  of  shoots  which  make  rapid  growth  during  the 
first  season.  Statistics  for  the  salient  characters  of  these  branches 
are  given  in  table  4. 

The  length  of  the  branches  ranged  from  137  to  312  cm.  and  had  a 
mean  of  235.95  ±  2.47  cm.  The  coefficient  of  variability  is  not  greater 
than  that  commonly  encountered  in  the  measurement  of  biological 
material. 

These  branches  were  less  variable  with  respect  to  their  length  than 
to  any  other  character  measured.  The  frequency  distribution  of  the 
branches  with  respect  to  length  is  shown  in  figure  4.  The  frequency 
polygon  is  fairly  symmetrical  with  respect  to  its  mean  and  does  not 
depart  widely  from  the  type  of  polygon  which  represents  a  random 
distribution  of  characters  in  biological  material.  In  certain  respects 
the  variability  in  elongation  is  like  that  previously  described9  for  the 
shoots  of  young  pear  trees. 

The  total  number  of  nodes  on  a  branch  shows  a  mean  of  127.69 
with  a  coefficient  of  variability  of  15.65.  The  number  of  nodes  on  a 
branch  is  closely  related  to  its  length,  consequently  the  coefficients  of 
variability  of  length  and  bud  number  are  not  widely  different. 

The  apricot  branches  have  a  phyllotaxis  of  two-fifths.  Each  node 
produces  from  one  to  three  buds  only  one  of  which  gives  rise  to  a 
vegetative  shoot.  The  central  bud  of  the  group  usually  develops,  the 
others  remain  dormant,  at  least  during  the  first  year. 

The  production  of  primary  and  secondary  laterals  is  one  of  the 
important  activities  of  the  apricot  branch.  The  number  of  primary 
laterals  ranged  from  13  to  64  with  a  mean  of  37.00  ±  1.19.  The  dis- 
tribution of  the  primary  laterals  is  rather  asymmetrical  and  shows  a 
tendency  to  skewness  toward  the  higher  class  values  (fig.  5).  This 
distribution  is  also  reflected  in  the  large  coefficient  of  variability 
(table  4). 


1924] 


Reed:  Growth  and  Differentiation  in  Apricot  Trees 


15 


Scale  for  length  of  branches 


3000 


Scale  for  length  of  lateral; 


Fig.  4.  Frequency  distributions  for  length  of  branches  and  combined  length 
of  laterals  for  each  branch.  The  means  of  the  two  histograms  are  superposed. 
Length  of  branch,  — ;  combined  length  of  laterals, . 


16 


University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 


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1924] 


Reed:  Growth  and  Differentiation  in  Apricot  Trees 


17 


The  number  of  secondary  laterals  produced  on  the  primary  laterals 
ranged  from  0  to  136  with  a  mean  of  35.00  ±  2.57  per  branch.  The 
close  agreement  between  the  mean  number  of  primary  and  of  second- 
ary laterals  may  or  may  not  have  a  significance.  Further  investiga- 
tion is  necessary  before  any  definite  statement  can  be  made.  The  dis- 
tribution of  the  number  of  secondary  laterals  is  more  asymmetric  than 
that  of  the  primary  laterals.  Figure  5  shows  that  the  greatest  fre- 
quency occurs  in  the  class  having  the  lowest  value.  From  this  class 
the  frequencies  are  successively  less  in  the  direction  of  the  higher  class 
values.  The  one-sided  distribution  is  also  reflected  in  the  very  large 
coefficient  of  variability. 


No.  of  UUra.lt  per  branck. 

Fig.  5.     Frequency  distribution  for  primary  and  secondary  laterals.   Primary 
laterals,  — ;  secondary  laterals, . 


The  nature  of  the  variability  in  the  number  of  laterals  directs 
attention  to  the  nature  of  the  factors  which  determine  their  produc- 
tion. An  apricot  shoot  does  not  arise  from  a  lateral  bud  except  where 
the  conditions  which  impose  dormancy  are  overcome,  hence  the  number 
of  laterals  may  be  an  index  of  the  factors  which  overcome  dormancy. 
The  variability  in  the  production  of  laterals  indicates  that  the  forces 
which  overcome  dormancy  in  the  buds  are  conditioned,  not  upon 
factors  of  environment,  but  upon  factors  inherent  in  the  tree.  If 
factors  of  environment  determined  the  release  from  dormancy,  we 
should  expect  to  find  a  more  nearly  normal  type  of  distribution. 

It  is  interesting  to  note  that  there  is  not  a  high  degree  of  associa- 
tion between  the  length  of  branch  and  the  total  number  of  laterals 
which  it  bore.    We  may  designate  number  of  laterals  as  a,  total  length 


18  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 

of  laterals  as  i,  and  length  of  branch  on  which  they  were  borne  as  c. 
The  coefficient  of  gross  correlation  is 

rae  =  .337  ±  .067 

The  coefficient  of  partial  correlation  taking  into  consideration  the 
length  of  the  laterals  is 

acrb  =  —  .313  ±  .013 

which  means  that,  if  all  laterals  were  the  same  length,  there  woidd  be 
a  negative  association  between  length  of  branch  and  number  of  laterals 
produced. 

A  comparison  of  figures  4  and  5  shows  that  the  frequency  distribu- 
tion of  total  length  of  all  laterals  per  branch  is  somewhat  different 
from  that  representing  the  numbers  produced.  The  ratios  of  the 
first  to  the  second  character  have  a  mean  of  7.63  ±  .36  (table  4).  The 
distribution  of  total  length  is  not  strictly  symmetrical,  as  shown  by 
the  graph  in  figure  4,  there  being  a  distinct  tendency  for  the  polygon 
to  skew  toward  the  higher  class  values.  In  figure  4  the  polygon  repre- 
senting distribution  of  total  length  of  laterals  per  branch  is  located  in 
such  a  position  that  its  mean  is  superposed  on  that  of  the  length  of 
branches.    The  two  polygons  show  a  fair  degree  of  correspondence. 

The  correspondence  between  the  two  characters  may  better  be 
determined  by  their  coefficient  of  correlation.  We  may  designate  num- 
ber of  laterals  per  branch  as  a,  length  of  branch  on  which  they  were 
borne  as  c,  and  total  length  of  laterals  as  d. 

rcd  =  .700  ±  .040 

This  indicates  a  high  degree  of  positive  relationship  between  length 
of  branch  and  length  of  laterals  produced  upon  it.  Since  the  number 
of  laterals  on  branches  was  itself  a  variable,  we  may  determine  the 
coefficient  of  partial  correlation,  which  expresses  the  correlation  in 
case  each  branch  had  the  same  number  of  laterals.     This  is 

Cllra  =  .665  ±  .042. 

The  value  of  this  coefficient  indicates  a  very  strong  relationship 
between  the  growth  capacity  of  a  branch  and  that  of  its  laterals. 

The  foregoing  discussion  may  be  summarized  in  the  following  four 
paragraphs : 


1924]  Reed:  Growth  and  Differentiation  in  Apricot  Trees  19 

1.  The  correlations  indicate  that  the  longer  branches  tended  to 
have  more  laterals  and  longer  laterals,  hence  it  is  likely  that  the  posi- 
tion of  these  shoots  on  the  tree  markedly  affected  the  growth  capacity 
of  the  branches  as  wholes. 

2.  The  marked  difference  between  the  frequency  distribution  of 
branches  for  primary  laterals  and  that  for  secondary  laterals  doubtless 
depends  largely  on  the  age  factor  resulting  from  the  position  of  the 
latter  on  primary  laterals;  this  factor  crowded  a  great  part  of  the 
latter  distribution  into  the  zero  class. 

3.  More  generally,  the  skewness  of  several  distributions  suggests 
a  large  effect  on  these  characters  of  a  small  and  unbalanced  group 
of  factors  conditioning  growth. 

4.  Length  of  branch  seems  to  have  been  relatively  free  from  the 
influence  of  highly  potent  factors  of  asymmetrical  effect,  but  this  fact 
is  probably  the  result  in  part  of  the  original  selection  of  branches  for 
uniformity  of  positional  growth  factors.  The  farther  the  members 
produced  get  away  from  the  initial  leveling  effect  of  that  selection,  the 
farther  they  lapse  back  into  a  condition  of  asymmetric  distribution 
Avhich,  as  we  shall  see  later,  seems  to  be  a  general  characteristic  of  the 
differentiation  of  the  tree. 

The  graphs  together  with  the  illustration  (fig.  1)  will  help  to  give 
an  idea  of  the  sort  of  growth  that  characterizes  these  apricot  branches. 
The  discussion  which  follows  will  attempt  to  discover  their  quantita- 
tive relationships  and  to  analyze  growth  in  the  light  of  these  relation- 
ships. The  work  will  proceed  on  the  assumption  that  the  size  and 
development  of  the  branches  is  the  result  of  some  dynamic  agent 
acting  upon  certain  raw  materials  which  the  tree  acquired  from  its 
environment.  Broadly  stated,  the  problem  is  to  discover  something 
about  the  process  by  which  the  tree  forms  its  diverse  parts  out  of 
unorganized  material. 

Data  on  the  influence  of  location  and  of  direction  of  growth  upon 
the  growth  and  differentiation  of  the  branches  are  given  in  table  5. 
The  branches  are  classified  with  respect  to  the  points  of  the  compass. 
The  'north'  class  comprises  branches  which  were  located  on  the  north- 
west, north,  and  northeast  sides  of  the  trees,  and  so  for  other  locations. 
This  broad  classification  necessarily  involves  some  duplication,  because, 
for  example,  shoots  which  were  recorded  as  northeast  were  included 
both  in  the  north  and  in  the  east  classes.  This  duplication  undoubtedly 
operates  to  minimize  differences  between  the  adjoining  classes,  yet  it 
cannot  vitiate  comparisons  between  opposite  sides  of  the  trees. 


20 


University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 


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1924]  Reed:  Growth  mid  Differentiation  in  Apricot   Trees  21 

The  four  classes  of  branches  show  no  striking  differences  in  mean 
length  attributable  to  location.  The  mean  number  of  primary  laterals 
per  branch  ranged  from  33.89  ±  1.90  in  the  west  class  to  42.67  ±  1.79 
in  the  north  class.  Their  difference  is  8.78  ±  2.62  and  may  be  regarded 

as  significant  since  ■=-  =  3.35.     The  means  of  the  other  classes  are 

not  significantly  different. 

The  mean  ratio  of  primary  laterals  to  total  number  of  buds  (index 
of  lateral  production)  in  the  case  of  the  north  class  indicates  a  signifi- 
cant difference  from  those  on  the  other  sides  of  the  tree.  This  differ- 
ence might  have  been  predicted  inasmuch  as  we  have  noted  that  the 
mean  number  of  primary  laterals  on  branches  on  the  north  side  of  the 
trees  was  a  maximum  while  the  mean  length  of  the  branches  on  which 
they  grew  was  approximately  the  same  as  those  in  other  classes. 

The  mean  number  of  blossoms  per  branch  shows  no  significant 
difference  between  different  classes  except  in  the  ease  of  the  north  class. 
The  mean  for  this  class  is  so  much  greater  than  the  others  that  we  must 
recognize  a  real  difference  in  spite  of  the  large  probable  error  attached 
thereto :  the  branches  in  the  north  class  appear  to  differ  from  those  in 
the  other  classes  in  the  possession  of  more  primary  laterals  (both 
relatively  and  absolutely)  and  in  the  production  of  more  blossoms.  In 
other  words,  the  process  of  differentiation  seems  to  have  gone  farther 
in  these  branches.  We  must  not,  however,  lose  sight  of  the  fact  that 
the  north  class  contains  only  15  variants  and  that  the  reliability  of  the 
mean  is  correspondingly  less. 

The  direction  which  the  main  axis  of  the  branch  maintains  with 
respect  to  the  perpendicular  is  known  to  exert  a  marked  influence 
upon  its  form  and  function.  The  second  part  of  table  5  presents  some 
determinations  made  upon  branches  classified  according  to  their  posi- 
tion at  the  end  of  the  growing  season.  I  realize  that  the  classification 
is  not  strictly  accurate,  because  many  branches  which  were  vertical 
during  the  first  part  of  the  growing  season  changed  their  direction  as 
time  went  on.  Weight  of  the  branch  and  competition  for  light  are 
among  the  causes  of  change  of  direction.  Indeed  the  greater  number 
of  variants  in  the  most  nearly  horizontal  class  suggests  that  the  popu- 
lation of  this  class  increased  at  the  expense  of  the  more  nearly  vertical 
classes. 

No  definite  statements  can  be  made  with  respect  to  the  mean  length 
of  the  three  classes  of  branches  although  one  is  inclined  to  believe  that 
it  is  actually  shorter  in  the  60°-90°  class  than  in  the  others.     Those 


22  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 

familiar  with  the  training  of  fruit  trees  know  that  horizontally  placed 
shoots  do  not  attain  so  great  a  length,  in  the  same  time,  as  do  upright 
shoots. 

The  number  of  primary  laterals  was  considerably  greater  on  the 
upright  branches  than  upon  those  of  the  other  two  classes,  and  least 
upon  those  in  the  60°-90°  class.  I  think  it  only  logical  to  assume  that 
these  differences  reflect  in  large  measure  the  effects  of  some  growth- 
inhibiting  agency  whose  action  on  horizontal  shoots  and  cuttings 
has  been  previously  described.10' "  The  development  of  laterals  on 
these  branches  would  also  be  influenced  by  the  degree  of  success 
attained  by  the  branch  in  its  competition  for  light  and  by  other  growth 
promoting  agencies. 

The  ratio  of  primary  laterals  to  the  total  number  of  nodes  on  the 
branches  is  considerably  smaller  in  the  60°-90°  class,  indicating  that 
the  development  of  lateral  buds  is  in  some  way  retarded  on  these 
branches. 

Another  relationship  which  shows  the  effect  of  the  direction  of 
growth  is  that  which  exists  between  the  length  of  the  branch  and  the 
total  length  of  all  laterals.  The  ratio  between  these  quantities  ought 
to  indicate  the  relative  differentiation  which  a  branch  has  undergone. 
These  figures  show  that  the  most  nearly  upright  branches  had  the 
highest  ratio.  Those  which  stood  in  the  intermediate  position,  30°-60°, 
had  a  somewhat  smaller  ratio,  but  those  most  nearly  horizontal  had  the 
smallest  ratio.  This  condition  calls  attention  to  the  usual  differences 
in  development  between  orthotropic  and  plagiotropic  branches.  The 
differences  have  been  frequently  mentioned  in  the  literature  and  have 
been  ascribed11  to  the  action  of  a  growth-inhibiting  substance  in  the 
branch.  Plagiotropic  shoots  are  typically  dorsiventral  while  ortho- 
tropic  shoots  are  radial.  This  means  that  the  buds  on  one  side  of  the 
plagiotropic  shoot  are  the  only  ones  which  reach  any  extensive  develop- 
ment. As  a  result,  the  ratio  of  primary  laterals  to  branch  is  smaller 
than  in  the  case  of  upright  shoots.  The  reasons  for  the  smaller  ratio 
may  be  two:  first,  the  actual  number  of  laterals  is  less;  second,  the 
laterals  which  develop  are  shorter.  From  an  inspection  of  the  figures 
in  table  5  it  seems  that  the  first  mentioned  condition  is  principally 
responsible  for  the  smaller  ratio.  It  appears  from  data  given  in  table  6 
that  the  branches  on  the  north  side  of  the  tree  were  somewhat  less 
variable  in  the  ratio  of  active  to  dormant  nodes,  and  that  the  plagio- 
tropic branches  were  more  variable  in  this  character  than  the  ortho- 
tropic  branches. 


1924] 


Meed:  Growth  and  Differentiation  in  Apricot  Trees 


23 


TABLE   6 

Effects  of  Location  and  Position  upon  the  Percentage  of  Nodes  which 
Produced  Primary  Laterals 


Influence  of  Location 

Mean 

Standard 
deviation 

Coefficient  of 
variability 

NW-N-NE 

34.33  ±  1.52 

28.37  ±1.12 
25.90  ±     .95 
25.61  ±  1.35 

33.11  ±  1.97 
30.52  ±     .97 

24.38  ±     .94 

8.73  ±  1.07 
10.46  ±     .78 

9.07  ±     .67 
8.47  ±     .95 

8.75  ±  1.39 
7.44  ±     .68 

9.08  ±     .67 

25.44  ±  3.33 

NE-E-SE 

36.87  ±3.14 

SE-S-SW 

35.02  ±2.91 

SW-W-NW.. 

33.07  ±4.09 

Influence  of  Position 

of  Branches 
0°-30°  from  perpendicular.. 
30°-60°  from  perpendicular. . 
60°-90°  from  perpendicular. 

26.43  ±4.49 
24.38  ±2.37 
37.24  ±3.10 

The  number  of  blossoms  which  each  class  of  branches  produced  in 
the  following  spring  shows  considerable  variation  (table  5).  Here  the 
difference  between  the  60°-90°  branches  and  the  others  is  of  a  magni- 
tude that  seems  to  be  significant.  Clearly,  we  cannot  explain  the  differ- 
ence by  the  fact  that  these  branches  were  somewhat  shorter  than  those 
of  the  other  classes.  Moreover,  the  difference  in  the  number  of  blossoms 
should  not  be  referred  to  the  length  of  the  branch,  but  to  the  total 
length  of  laterals  on  the  branches  of  the  three  classes.  J.  P.  Bennett 
has  suggested  that  the  ratio  of  blossoms  to  unit  of  lateral  is  greater  in 
the  60°-90°  class  than  in  the  others.  The  data  given  in  table  7  show 
this  to  be  true.     The  0°-30°  class  of  branches  produced  a  combined 


TABLE  7 

Eelation  of  the  Direction  of  Growth  of  Branches  on  the  Batio  of 

Shoots  to  Blossoms 


Mean  length  of 

all  laterals  on 

the  branch 


No.  of  blossoms 

per  100  cm.  of 

laterals 


Branches  0°-30°  from  perpendicular 
Branches  30°-60°  from  perpendicular 
Branches  60°-90°  from  perpendicular 


2619 
2455 
1313 


15  4 
18.2 
20.9 


length  of  laterals  which  was  about  twice  that  of  branches  in  the 
60°-90°  class.  The  number  of  blossoms  per  100  cm.  of  laterals  was 
greater,  however,  in  the  60°-90°  class.     This  suggests  that  conditions 


24  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 

in  the  60°-90°  class  were  more  favorable  for  fruit-bud  formation  and 
decidedly  less  favorable  for  vegetative  gTOwth.  The  opposition 
between  the  vegetative  and  the  reproductive  activities  of  plants  is  so 
well  known  that  extended  comment  is  not  necessary.  The  data  here 
presented  give  a  quantitative  expression  of  the  relationship  for  the 
apricot  branches. 


V.  DORMANCY  AND  GROWTH  OF  BUDS  ON  THE  BRANCHES 

The  average  number  of  nodes  on  the  branches  measured  was 
127.69  ±  1.52  and  the  standard  deviation  was  19.95  ±  1.08  (table  4). 
The  type  of  the  distribution  of  nodes  (fig.  6)  and  that  of  branch  length 
are  necessarily  more  or  less  similar,  and  both  are  skewed  toward  the 
lower  class  ranges. 

The  mean  distance  between  nodes  was  approximately  1.85  cm.,  but 
in  certain  regions,  especially  near  the  proximal  end,  they  were  more 
closely  grouped  than  in  others.  There  is  no  doubt  that  the  rate  of 
growth  of  the  main  branch  has  an  effect  in  spacing  the  nodes  on  its 
axis.  The  differences  in  spacing  have  not  been  measured  for  the 
present  study. 

Approximately  30  per  cent  of  the  nodes  on  the  branch  produced 
lateral  shoots  during  the  period  when  the  branch  was  still  making  its 
first  season's  growth,  while  the  rest  remained  dormant.  The  stoichio- 
metry  of  the  branch  depends  to  a  large  extent  upon  the  way  in  which 
the  buds  react,  i.e.,  whether  they  remain  dormant  or  grow.  It  is  there- 
fore important  to  investigate  the  question  of  growth  and  dormancy  in 
these  buds. 

Each  bud  may  be  regarded  as  a  center  of  potential  energy  in  which 
there  is  located  a  quantity  of  labile  compounds  of  carbon  and  nitrogen. 
Under  certain  conditions,  processes  of  growth  are  initiated  in  the 
course  of  which  these  energy  centers  produce  new  structures.  The 
amount  of  material  synthesized  at  each  energy  center  and  its  relation 
to  the  rest  of  the  system  may,  to  some  extent,  serve  as  an  index  of  those 
dynamic  factors  with  which  we  have  to  deal. 

The  ratio  of  primary  laterals  to  all  nodes  expressed  as  a  percentage 
gives  the  most  obvious  expression  of  lateral  production.  This  ratio 
has  been  determined  for  each  branch  (table  4).  The  mean  of  all  ratios 
is  27.51  ±  .70.  The  frequency  distribution  of  these  ratios  is  shown  in 
figure  7. 


1924] 


Seed:  Growth   and  Differentiation  in  Apricot   Trees 


25 


No  of  buoU  per  branch 
Fig.  6.     Frequency  distribution  for  number  of  nodes. 


CI 

M 

>> 

o 

C 

c 

&> 

4 

3 

t 

o- 

*- 

0 

I 

1 

zt 


Percent 


*i 


62 


Fig.  7.     Frequency   distribution  showing  per  cent   of  nodes   from 
which  primary  laterals  were  produced. 


26  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 

This  histogram  shows  some  very  important  things  about  the  varia- 
bility in  the  percentage  of  nodes  which  produce  primary  laterals.  In 
the  first  place,  the  skewness  of  the  figure  is  pretty  good  evidence  that 
the  percentage  of  buds  which  developed  was  not  entirely  due  to  purely 
chance  factors.  Had  that  been  the  case  the  figure  more  nearly  would 
resemble  the  normal  curve  of  errors.  In  the  second  place,  we  find 
upon  referring  to  table  4  that  the  coefficient  of  variability  for  the 
percentage  of  nodes  which  produced  primary  laterals  is  more  than 
twice  as  large  as  the  same  constant  of  variability  for  the  total  number 
of  buds. 

These  relationships  seem  to  indicate  that  this  problem  of  differen- 
tiation is  not  entirely  simple;  that  no  one  factor  determines  whether  a 
bud  shall  grow  or  remain  dormant ;  but  rather  that  the  factors  which 
overcome  dormancy  are  much  more  variable  in  their  effects  than  those 
which  determine  the  formation  of  nodes  upon  the  branch.  It  was 
seldom  that  more  than  50  per  cent  of  the  nodes  on  a  branch  produced 
laterals  and  the  modal  value  was  only  24.29  per  cent.  Some  of  the 
conditions  which  operated  to  cause  this  variability  in  overcoming 
dormancy  of  the  buds  will  be  pointed  out  later. 

In  an  earlier  paragraph  attention  was  called  to  the  effect  which 
location  and  position  of  the  branch  have  on  various  phases  of  develop- 
ment. Table  6  also  shows  the  effect  of  these  factors  upon  the  per- 
centage of  nodes  which  produced  primary  laterals.  It  will  be  seen 
that  the  branches  on  the  north  side  of  the  trees  produced  a  greater 
percentage  of  laterals  than  those  on  the  other  sides  of  the  trees.  The 
mean  is  appreciably  larger  than  the  means  of  other  groups  and  the 
coefficient  of  variability  is  considerably  smaller.  The  mean  percentages 
of  the  other  three  groups  show  no  significant  differences. 

When  the  branches  are  classified  according  to  their  declination 
from  a  perpendicular  line  we  find  differences  in  the  percentages  of 
buds  which  developed.  The  percentages  in  the  classes  0°-30°  and 
30°-60°  are  not  significantly  different  either  in  magnitude  or  varia- 
bility, but  the  60°-90°  class  was  significantly  lower  as  to  its  mean  and 
also  more  variable. 

The  percentage  of  dormancy  in  different  regions  on  the  branches 
is  another  measure  of  the  distribution  of  growth  stimuli.  The  nodes 
on  the  branches  were  tabulated  in  groups  of  20  each  and  the  per- 
centage of  dormancy  determined  for  each  group.  Group  1-20  is  the 
proximal  group  and  group  161-180  is  the  distal  group.  The  figures 
as  given  in  table  8  show  that  great  differences  in  the  percentage  of 


1924] 


Seed:  Growth  and  Differentiation  in  Apricot  Trees 


27 


dormancy  existed  in  different  regions.  The  lowest  percentage  of 
dormancy  existed  in  group  21— 40,  in  which  only  19.05  per  cent  of  the 
buds  failed  to  develop.  From  this  region  the  percentage  of  dormancy 
increased  to  94.59  in  group  81-100,  dropped  slightly  in  the  next 
group,  and  rose  gradually  in  succeeding  groups  to  complete  dormancy 
in  the  last  group. 

TABLE  8 

Percentage  of  Dormancy  in  Nodes  on  Different  Eegions  of  the  Branches 


Groups 

1-20 

21-40 

41-60 

61-80 

81-100 

101-120 

121-140 

141-160 

161-180 

Percentage  of 
dormancy 

79.68 

19.05 

61.96 

76.86 

94.59 

89.49 

96.62 

96.43 

100.0 

It  is  evident  that  the  forces  which  broke  the  dormancy  of  the  buds 
on  these  apricot  shoots  were  not  distributed  in  a  regular  gradient.  The 
lowest  group  had  a  high  percentage  of  dormancy,  while  the  next  group 
had  the  lowest  percentage.  Clearly  we  cannot  refer  the  cause  of  such 
a  distribution  either  to  a  simple  axial  gradient  or  to  an  age  factor, 
except  in  the  distal  part  of  the  branches.  The  data  under  discussion 
lead  directly  to  the  next  point,  viz.,  the  number  and  position  of 
primary  laterals. 

The  relationship  between  the  length  of  the  branch  and  the  number 
of  nodes  from  which  primary  laterals  were  produced  is  a  problem  of 
some  biological  importance.  The  best  method  of  expressing  these 
relationships  is  by  a  series  of  correlations.  The  correlation  coefficients 
ought  to  show  whether  a  long  or  a  short  branch  tends  to  produce  more 
primary  laterals.  If  we  let  /  =  the  length  of  a  branch;  n.  =  the  num- 
ber of  nodes  on  a  branch ;  and  d  =  the  number  of  nodes  which  pro- 
duced primary  laterals,  the  gross  coefficients  of  correlation  are 

rld  =  .479  ±  .058 
rnd  =  .403  ±  .060 
,•^  =  .836  ±  .020 

There  is  a  significant  degree  of  correlation  between  the  number  of 
nodes  which  produced  primary  laterals  and  the  length  of  the  branch. 
This  means  that  longer  branches  have  a  tendency  to  produce  more 
primary  laterals  than  short  branches,  and  speaks  against  the  idea  that 
a  branch  which  attains  more  than  average  length  is  thereby  incapaci- 
tated for  producing  a  proportionally  large  number  of  laterals.  There 
is  nothing  like  a  one  to  one  correlation  between  length  (or  number  of 


28  University  of  California  Publications  in  Agricultural  Sciences       [Vol.5 

nodes)  and  number  of  primary  laterals,  though  the  correlation  is 
positive  and  significant.  The  correlation  between  length  of  branch 
and  number  of  laterals  may  result  largely  from  the  close  correlation 
between  length  of  branch  and  total  number  of  internodes  on  the 
branch.  By  calculating  the  coefficient  of  partial  correlation  we  may 
eliminate  the  effect  of  the  latter  relation.    The  value  is 

Wn  =  .283  ±  .070. 

We  may  interpret  this  coefficient  to  mean  that  the  greater  length  of 
branch  favors  lateral  production,  entirely  apart  from  a  greater  number 
of  nodes.  The  coefficient  of  partial  correlation  has  a  magnitude  four 
times  that  of  its  probable  error  and  may  be  regarded  as  significant. 
We  may  interpret  it  to  mean  that  there  is  a  small,  but  positive,  degree 
of  relationship  between  these  two  variables. 

We  may  ask,  Does  the  proportionate  number  of  nodes  producing 
laterals  tend  to  change  significantly  with  change  in  total  number  of 
nodes?  The  obvious  suggestion,  that  we  find  the  correlation  between 
total  number  of  nodes  and  percentage  of  nodes  producing  laterals, 
seems  to  involve  the  introduction  of  "spurious  correlation  of  indices." 

We  may  therefore  compute  the  correlation  between  the  number  of 
primary  laterals  and  the  deviation  of  this  number  from  its  probable 
value 


Tnz 


r"d~vd 


\  1  —  r2nd  +  (  ?•„,/  —  tt  J 


In  this  case  Y„  and  Vd  are  the  coefficients  of  variability  of  the  number 
of  nodes  and  of  the  numbers  of  primary  laterals  respectively. 

r„,  =  —  .082  ±  .075 

The  value  of  this  coefficient  is  close  to  zero  and,  in  view  of  the 
magnitude  of  its  probable  error,  cannot  be  regarded  as  indicative  of 
any  correlation.  It  shows  that  there  is  little  or  no  real  difference  in 
the  proportionate  capacity  of  branches  with  different  numbers  of 
nodes  to  produce  primary  laterals.  In  other  words,  there  is  no  cor- 
relation between  the  number  of  primary  laterals  and  the  deviation 
from  their  probable  number. 

The  lack  of  any  marked  causal  relationship  between  the  percentage 
of  dormancy  and  the  length  of  primary  laterals  is  also  indicated  by  the 
coefficient  of  correlation  between  these  two  characters.    It  has  the  very 


1924]  Heed:  Growth  and  Differentiation  in  Apricot  Trees  29 

low  value  of  r=.061  ±  .076  and  cannot  be  regarded  as  significant. 
In  figure  18,  there  is  a  presentation  of  the  general  problem  of 
correlation  in  the  apricot  branch.  The  length  and  the  number  of 
primary  laterals  show  a  fairly  high  positive  correlation  with  the  length 
of  the  branches,  and  about  the  same  degree  of  correlation  with  similar 
characters  of  the  secondary  laterals.  The  total  length  of  all  laterals 
bears  a  very  high  degree  of  positive  correlation  with  the  length  of  the 
branch. 

VI.  DIFFERENTIATION 
1.  Configuration  of  Laterals  on  Branches 

The  process  of  differentiation  as  manifested  by  the  growth  of 
primary  and  secondary  laterals  is  one  of  the  important  aspects  of 
this  study.  We  are  concerned,  not  alone  with  the  activities  which 
result  in  the  formation  of  the  main  axis  of  the  branch,  but  with  the 
formation  of  its  subsidiary  shoots.  These  subsidiary  shoots  are 
morphological  characters  which  go  to  make  up  the  entities  with  which 
we  are  dealing.  From  the  standpoint  of  the  fruit  grower  they  are  of 
primary  interest  because  they  determine,  to  a  large  extent,  the  capacity 
of  a  branch  to  produce  fruit.  The  importance  of  this  process  in  Sea 
Island  cotton  has  recently  been  discussed  by  Mason.4 

The  various  groups  of  primary  laterals  on  the  apricot  branches 
were  so  well  delimited  that  it  was  an  easy  matter  to  determine  and 
measure  their  salient  characters.  The  data  are  summarized  in  table  9. 
Group  I  refers  to  the  group  nearest  the  proximal  end  of  the  branch, 
and  group  III  to  the  group  nearest  the  distal  end  (fig.  1).  The  length 
of  the  groups  diminishes  as  we  pass  toward  the  distal  end  of  the 
branches,  and  the  space  between  groups  increases. 

The  superior  development  of  the  laterals  in  Group  I  is  most  strik- 
ingly shown  by  a  comparison  of  the  total  length  of  all  primary  laterals 
in  that  group  with  the  length  of  primary  laterals  in  other  groups.  In 
this  respect  Group  I  produced  six  times  as  much  as  Group  II  and 
seventeen  times  as  much  as  Group  III,  while  Group  II  produced  only 
three  times  as  much  as  Group  III.  The  total  number  of  nodes  on 
primary  laterals  follows  rather  closely  the  ratios  of  total  length. 

The  number  of  secondary  laterals  per  branch  borne  upon  the 
primary  laterals  of  each  group  differs  still  more  widely,  as  might  be 
expected,  since  primary  laterals  must  attain  a  certain  size  and  stage 
of  maturity  before  they  produce  secondary  laterals. 


30 


University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 


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1924] 


Meed:  Growth  and  Differentiation  in  Apricot  Trees 


31 


The  time  at  which  the  first  primary  laterals  were  found  upon  the 
branches  was  recorded  only  for  those  of  Group  I.  At  that  time 
(4.31  weeks)  the  mean  length  of  the  branches  was  about  70  cm.  and 
they  were  approaching  their  period  of  most  rapid  growth. 


15  I0S  ISO  210 

Length  of  primary  laterals  in  cm 

Fig.  8.     Frequency  distributions  for  length  of  primary  laterals  in  the  three 

groups  plotted  on  logarithmic  scales.     Group  I,  ;  Group  II,  -----  ;  Group 

III, . 


2.  Primary  Laterals 

The  frequency  with  which  laterals  of  various  lengths  were  produced 
is  a  matter  of  importance  because  it  shows  something  of  the  ability  of 
the  main  axis  of  the  branches  to  produce  new  material.  It  is  plain 
that  the  kind  as  well  as  the  number  of  laterals  produced  is  an  index 
of  the  differentiation  which  occurred. 

It  has  already  been  shown  (figure  4)  that  the  total  length  of  all 
laterals,  primary  and  secondary,  per  branch  gives  a  skewed  distribu- 
tion. The  figures  in  table  4  show  that  the  coefficient  of  variability  of 
the  measurements  of  total  length  was  rather  high  and  indicate  that 
the  length  distribution  is  subject  to  considerable  fluctuation. 

The  histograms  of  length  distribution  for  2528  individual  primary 
laterals  (fig.  8)   in  the  three  groups  are  extremely  asymmetric  with 


32 


University  of  California  Publications  in  Agricultural  Sciences       [Vol.  o 


very  high  frequencies  in  the  classes  of  shorter  laterals.  To  appreciate 
fully  the  asymmetry  of  these  distributions  the  reader  must  recollect 
that  the  frequencies  are  plotted  on  a  logarithmic  scale.  The  asymmetry 
appears  to  increase  as  one  passes  from  Group  I  to  Group  III.  Having 
seen  the  graphs  representing  the  frequency  distritmtion  of  laterals, 
the  reader  will  appreciate  the  data  in  table  10  showing  the  mean 
length  and  variability  of  laterals  of  the  various  groups.  The  distribu- 
tions show  that  the  numbers  of  short  laterals  in  the  several  groups  are 
not  governed  by  the  laws  of  chance — they  are  indeed  so  far  from  what 
would  occur  in  an  approximately  normal  curve  of  errors  that  we  must 
conclude  that  length  of  primary  laterals  is  determined  by  some  very 
definite  factor  so  fixed  in  its  action  that  the  law  of  chance  is  prac- 
tically eliminated.  It  is  evident  that  more  short  laterals  occurred  in 
Groups  II  and  III  than  in  Group  I,  a  result  due  in  part,  undoubtedly, 
to  the  age  factor.  Many  of  the  laterals  in  these  groups  might  have 
become  longer  if  the  growth  cycle  of  the  tree  had  not  terminated  when 
it  did. 

TABLE  10 
Length  of  Laterals  ox  Apricot  Branches 


No.  of 

vari- 
ants 

Mean 
(cm.) 

Standard 

deviation 

(cm.) 

Coefficient 
of  variability 

Primary  laterals,  Group  I. 

1796 

49.20  ±      80 

50.36  ±    .57 

102.36  ±2.38 

Primary  laterals,  Group  II 

538 

26.91  ±     .92 

31  52  ±  .65 

117.13  ±4.65 

Primary  laterals,  Group  III 

194 

18.09  ±1.10 

22.75  ±  .78 

125.76  ±8.79 

Primary  laterals,  all  groups. 

2528 

42.07  ±     .62 

46.50  ±  .44 

110.53  ±  1.95 

Secondary  laterals,  Group  I 

2276 

17.00  ±     .29 

20.22  ±  .20 

118.94  ±2.33 

Secondary  laterals,  Group  II 

156 

17  00  ±     .74 

13  72  ±  .52 

80  70  ±4.68 

As  a  further  measure  of  the  amount  of  differentiation  we  may 
determine  the  cases  in  which  primary  laterals  produced  secondary 
laterals.  We  have  seen  in  table  4  that  the  mean  number  of  secondary 
laterals  per  branch  was  35  and  table  9  shows  that  practically  all  of 
them  arose  on  primary  laterals  of  Group  I.  The  number  of  primary 
laterals  which  produced  secondary  laterals  was  5.11  ±  .31  per  branch, 
and  the  average  number  of  secondary  laterals  on  each  was  about  six. 
As  will  be  shown  later,  there  is  a  high  degree  of  positive  correlation 
between  the  mean  numbers  per  branch  of  primary  and  secondary 
laterals,  which  indicates  that  the  same  tendency  toward  differentiation 
is  shared  bv  branches  and  their  laterals. 


1924] 


Reed:  Growth  and  Differentiation  in  Apricot  Trees 


33 


The  total  number  of  blossoms  on  the  primary  laterals  shows 
differences  somewhat  similar  to  those  of  other  characters.  The  number 
of  blossoms  on  Group  I  was  about  four  times  as  great  as  on  Group  II, 
and  about  eighteen  times  as  great  as  on  Group  III. 


TABLE  11 

Length  of  Primary  L 

ATERALS  ON  EACH 

Daughter  Shoot 

x  = 

=  ordinal  position  of  the  laterals. 

T  = 

-  average  length  of  yx-i,  Vx, 

Vx+i- 

X 

Y                               X 

Y 

X 

Y 

(cm.) 

(cm.) 

(cm.) 

2 

0                           53 

10.95 

104 

1  05 

5 

.19                         56 

9.58 

107 

2.87 

8 

1.94                        59 

18.08 

110 

1.88 

11 

11  42                        62 

13  28 

113 

1.00 

14 

12  50                         65 

9.13 

116 

1.21 

17 

18.22                         68 

6.00 

119 

.98 

20 

26.36                         71 

2.92 

122 

.74 

23 

41.64                         74 

1.46 

125 

.38 

26 

52.40                         77 

1.08 

128 

.54 

29 

55  59                         80 

.58 

131 

.20 

32 

42.50                        83 

1.78 

134 

.0 

35 

29.60                         86 

.84 

137 

.08 

38 

21.80                         89 

1  51 

140 

.05 

41 

15.01                         92 

1.40 

143 

.04 

44 

8.72                         95 

1.22 

146 

.0 

47 

7.78                         98 

.63 

149 

.05 

50 

8.37                       101 

2  41 

152 

.05 

We  may  attempt  first  to  get  a  general  idea  of  the  number,  position, 
and  length  of  the  primary  laterals  upon  the  branches  under  considera- 
tion. It  has  already  been  stated  that  the  number  of  primary  laterals 
ranged  from  13  to  64  per  branch  with  a  mean  of  37.  The  position  of 
the  primary  laterals  and  the  mean  length  of  laterals  in  various  posi- 
tions may  next  be  ascertained.  These  data  are  presented  in  table  11. 
The  ordinal  number  of  each  primary  lateral  was  determined  by  ascer- 
taining the  number  of  the  node  from  which  it  grew,  counting  from  the 
proximal  (basal)  end  of  the  branch.  The  value  of  1*  (the  length  of 
successive  laterals)  is  recorded  for  the  lateral  in  position  X.  In  order 
to  simplify  the  table,  the  mean  length  of  three  laterals  is  given  for 
every  third  lateral ;  for  example,  the  length  Y  was  obtained  by  taking 
the  average  of  y.,.j,  y.r  and  j/.,+1.  The  length  of  lateral  17  is  accord- 
ingly the  average  length  of  laterals  16,  17,  and  18. 

The  nodes  at  the  base  of  the  branches  produced  no  laterals,  or  very 
short  laterals.     The  length  of  the  laterals  was  progressively  longer  as 


34  University  of  California  Publications  in  Agricultural  Sciences       [Vol.5 

the  distance  from  the  proximal  end  increased  up  to  approximately 
lateral  30,  then  decreased  rather  rapidly  to  lateral  45.  A  second 
maximum  occurred  near  lateral  60.  From  lateral  70  on  to  the  distal 
end  of  the  branch,  the  laterals  were  exceedingly  variable  in  length, 
and  the  average  for  any  given  position  is  small.  This  may  be,  in  part, 
because  of  the  fact  that  they  were  produced  later  in  the  growing 
season  and  their  growth  was  therefore  terminated  sooner  by  the 
approach  of  winter  dormancy. 

Casual  observation  will  show  that  the  primary  laterals  occur  in 
well  denned  groups  on  each  branch  and  that  a  true  impression  of  the 
differentiation  is  not  to  be  obtained  readily  from  the  figures  presented 
in  table  11.  Most  of  the  branches  had  three  groups  of  primary  laterals. 
The  group  nearest  the  proximal  end  of  the  branch  was  the  largest,  and, 
as  already  intimated,  produced  the  longest  primary  laterals  (cf.  fig.  1). 
Above  the  first  group,  about  20  buds  remained-  dormant,  and  the 
second  group  was  inferior  both  in  number  and  in  length  of  laterals. 

An  analysis  of  the  mean  length  of  the  primary  laterals  will  be 
presented  later  in  a  discussion  of  certain  dynamical  aspects  of  their 
growth.  We  will  now  compare  the  primary  laterals  in  the  several 
groups  with  respect  to  their  more  obvious  features. 

The  primary  laterals  in  a  group  are  rather  symmetrically  arranged 
according  to  length.  The  longest  laterals  are  at  the  center  of  the 
groups  and  the  lengths  of  other  laterals  diminish  as  one  passes  from 
the  center  to  either  end  of  the  group.  The  rate  at  which  the  lengths 
of  successive  laterals  diminish  suggests  a  logarithmic  curve. 

All  the  groups  were  now  superposed  in  such  a  way  that  the  central 
lateral  of  each  Group  I  fell  upon  the  same  point.  If  we  take  node  48 
as  the  midpoint  for  the  laterals  of  Group  I,  and  arrange  the  data  so 
that  the  actual  centers  of  Group  I  coincide  for  all  branches,  we  can 
easily  get  the  mean  length  of  the  primary  laterals  for  each  node,  upon 
the  basis  of  a  uniform  arrangement.  Table  12  gives  the  values  so 
obtained.  If  this  adjustment  also  results  in  placing  the  laterals  of 
Groups  II  and  III  in  symmetrically  shaped  groups,  it  might  lend 
additional  support  to  the  assumption  that  the  development  of  primary 
laterals  is  the  outcome  of  a  definite  physiological  function  of  growth. 
As  a  matter  of  fact,  this  is  just  what  happens.  The  grouping  of 
laterals  in  Group  II  results,  on  a  smaller  scale  in  the  same  arrange- 
ment as  that  in  Group  I.  The  arrangement  of  laterals  in  Group  III 
is  less  striking  on  account  of  their  shortness  and  because  of  their  great 
variability,  yet  it  is  fairly  definite. 


1924] 


Reed:  Groicth  and  Differentiation  in  Apricot  Trees 


35 


TABLE  12 

Mean  Length  of  Primary  Laterals  after  Adjusting  Positions  so  that 
Bud-position  48  was  the  Center  of  Group  I 


x= 

ordinal  but 

-position. 

Y  = 

mean  of  yx 

-i,  Vx,  and  yx+1. 

X 

Y 

X 

Y 

X 

Y 

5 

0.0 

59 

16.69 

113 

1.08 

8 

0.09 

62 

12.52 

116 

1.49 

11 

0.46 

65 

10  00 

119 

1.54 

14 

1.57 

68 

7.65 

122 

1.09 

17 

2.12 

71 

11.10 

125 

1.97 

20 

3.26 

74 

7.57 

128 

1.79 

23 

6.36 

77 

10.02 

131 

1.36 

26 

7.68 

80 

10.09 

134 

1.06 

29 

10.60 

83 

8.08 

137 

1.40 

32 

22  64 

86 

7.12 

140 

0.32 

35 

28.92 

89 

2.88 

143 

0.28 

38 

26.49 

92 

1.40 

146 

0.0 

41 

39.11 

95 

2.51 

149 

0.0 

44 

44.03 

98 

1.11 

152 

0.12 

47 

44.61 

101 

1.31 

155 

0.12 

50 

38.86 

104 

1.27 

158 

0.0 

53 

28.39 

107 

1.20 

161 

0.08 

56 

17.07 

110 

1.00 

i« 

-o 

2 

/  ° 

\° 

«i 

Jo 

iO*tf^ 

oV) 

V5 

3  ^^fr&i  n  a  a  a  o  en 

Fig.  9.  Curves  showing  the  cyclic  nature  of  the  three  groups  of  primary 
laterals.  X,  ordinal  position  of  laterals;  Z,  length  of  laterals.  The  curves  were 
computed  from  the  equations: 

Group  I Z,  —  . 000177  y,  (380 — y,) 

Group  II Z2  =  .0017i/2(58  —  y.) 

Group  III Z3  =  .0024  2/3(20  —  y3) 

The  broken  line  represents  the  summation  of  overlapping  portions  of  the  curves 
of  Groups  I  and  II.  Small  circles  represent  mean  lengths  of  laterals  in  the 
various  ordinal  positions  after  positions  had  been  shifted  to  bring  the  center 
of  each  Group  I  to  the  same  point. 


36  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 

Group  I  laterals  had  a  maximum  mean  length  of  44.6  cm.  at  node 
48.  The  upper  range  of  Group  I  overlaps  the  lower  range  of  Group  II, 
and  it  is  necessary  to  recognize  the  overlapping  values  in  studying  the 
groups.  This  aspect  will  be  discussed  below.  Node  70  probably  marks 
the  point  near  which  Group  I  ends  and  Group  II  begins. 

Group  II  laterals  appear  to  reach  a  maximum  mean  length  of  about 
10  cm.  near  node  80,  from  which  point  the  length  decreases  to  another 
minimum  near  node  98. 

Group  III  appears  to  have  a  maximum  mean  length  of  laterals  near 
node  119  from  which  the  length  decreases  to  near  node  160. 

The  important  feature,  for  our  present  purposes,  is  that  the  mean 
lengths  of  primary  laterals  fall  into  three  distinct  groups.  When  the 
values  are  plotted  on  a  scale  in  which  ordinates  are  the  lengths  of  the 
several  laterals  and  abscissae  are  the  ordinal  positions  of  laterals  on 
the  branch,  they  form  three  symmetrical,  overlapping  curves  (fig.  9). 

If  we  assume  that  the  cyclic  growth  of  the  primary  laterals  is  in 
some  way  similar  to  the  cyclic  growth  in  length  of  the  branch  which 
bears  them,  we  may  proceed  to  examine  the  data  by  the  method  already 
used.  The  situation  may  be  simplified  by  assuming  that  the  forces 
which  produce  the  branches  produce  in  the  same  way  the  primary 
laterals.  The  summations  of  length  of  laterals,  beginning  at  the  base 
of  the  branch,  should  therefore  give  a  curve  somewhat  like  that  repre- 
senting the  increasing  length  of  the  branches,  shown  in  figure  2.  This 
was  found  actually  to  be  the  case,  and  the  three  groups  of  laterals 
could  readily  be  distinguished.  The  observed  values  agreed  closely 
with  an  equation  of  the  general  form 

log^—  =K(x  —  xx) 

a  —  y 

where  y  =  length  at  any  node  x ;  xl  =  the  node  at  which  i/  had  attained 
half*the  length  of  a  for  the  cycle;  a==the  maximum  (limiting)  value 
of  y ;  and  K  =  a  constant. 

If  the  lengths  of  the  laterals  be  regarded  as  increments  at  unit 
distances  on  the  branch,  starting  at  the  proximal  end,  then  the  differ- 
ential form  of  the  foregoing  equation  ought  to  express  their  lengths  for 
each  nodal  position.    The  differential  form  of  the  above  equation  is 


*=!-»»<—»> 


Here  k  =  — 
a 


1924]  Heed:  Growth  and  Differentiation  in  Apricot  Trees  37 

With  the  aid  of  the  table  prepared  by  Robertson,13  the  values  of  Z 
shown  in  table  13  were  computed. 

Group  I  Z1  =  .000my1  (380  — j/J 

Group  II Z2=^.0017y2  (58  —  y2) 

Group  III Z,  =  .0024ys  (20  —  y3) 

TABLE  13 

Mean  Length  of  Primary  Laterals  Showing  their  Cyclic  Arrangement. 
Values  of  Z  were  Calculated  from  the  Equations: 

Z,  —  .000177  yt  (380  —  1/,) 
Z2  =  . 0017  ya  (58  —  y,) 
Z3=.0024i/3  (2O  —  1/3) 


Group  I 

Group  II 

Group  III 

A 

A 

A 

X 

observed 
Y 

calc. 
Zi 

X 

observed 
Y 

calc. 
Z2 

X 

observed 
Y 

calc. 
Z3 

(cm.) 

(cm.) 

(cm.) 

(cm.) 

(cm.) 

(cm 

..) 

8 

.09 

53 

.1 

92 

0 

14 

1.57 

1.8 

56 

.2 

98 

1.1 

.3 

20 

3.26 

4.2 

59 

.4 

101 

1.3 

.6 

26 

7.68 

9.6 

65 

1.6 

104 

13 

.9 

32 

22.6 

20.7 

71 

11    1 

4.8 

110 

1.0 

1.2 

38 

26  5 

35.7 

74 

7.6 

8  1 

116 

1.5 

1.5 

44 

44.0 

44.1 

78.8 

9.9 

119 

15 

1.8 

50 

38.9 

35.7 

80 

10.1 

9  6 

122 

1.1 

1.5 

56 

17.1 

20.7 

86 

7.1 

5.4 

128 

1.8 

1.2 

62 

12.5 

9.6 

92 

1.4 

1.8 

134 

1.1 

.9 

68 

7.7 

4.2 

98 

1.1 

.6 

140 

.3 

.6 

71 

2.7 

146 
152 

.0 
.1 

.3 
.0 

The  values  obtained  from  these  equations  indicate  the  cyclic  nature 
of  the  growth  process  which  governs  the  production  of  primary 
laterals.  The  curve  (fig.  9)  which  represents  the  mean  length  of 
laterals  in  any  group  is  symmetrical  about  the  maximum  value.  The 
margins  of  the  second  group  overlap  those  of  the  adjoining  groups, 
and  the  calculated  values  of  the  overlapping  portions  must  be  added 
to  approximate  the  observed  values. 

The  satisfactory  agreement  between  observed  and  calculated  values 
seems  to  justify  the  conclusion  that  the  length  of  each  primary  lateral 
was  a  function  of  its  position  in  its  group,  and,  consequently,  of  its 
position  on  the  branch.  The  size  of  the  group  may  depend  to  an  even 
greater  extent  upon  its  position  on  the  branch.  The  growth  processes 
concerned  with  the  production  of  laterals  therefore  bring  about  a 
definite  spatial  distribution  of  mass. 


38  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 

The  decreasing  amplitude  of  the  three  curves  suggests  that  the 
successive  groups  of  laterals  may  represent  damped  oscillations  of  the 
growth  process.  The  limits  of  the  third  group  are  too  poorly  defined, 
however,  to  afford  satisfactory  material  for  the  study  of  this  possibility. 

3.  Secondary  Laterals 

The  secondary  laterals  are  another  distinct  feature  of  the  differen- 
tiation process  in  growth.  Arising  on  the  primary  laterals,  their 
existence  is  naturally  conditioned  to  some  extent  by  the  factors  which 
govern  the  production  of  primary  laterals  and  determine  their  length. 

Figure  5  gives  a  graphical  comparison  of  the  frequency  distribu- 
tions of  primary  and  secondary  laterals.  The  frequency  polygon 
representing  the  distribution  of  the  secondary  laterals  has  much  the 
same  range  as  that  representing  the  primary  laterals,  but  is  completely 
asymmetrical.  The  figures  given  in  table  4  show  that  the  standard 
deviation  of  the  population  as  computed  very  nearly  equals  the  mean. 
In  such  a  case  the  mean  fails  to  represent  the  population.  It  seems 
logical  to  conclude  from  these  facts  that  the  number  of  secondary 
laterals  per  branch  is  strongly  affected  by  some  factor  which  tends  to 
keep  the  number  at  a  minimum,  for  while  the  number  per  branch 
ranged  from  0  to  136,  more  than  two-fifths  of  the  branches  had  less 
than  15  secondary  laterals  each. 

A  classification  of  2831  primary  laterals  with  respect  to  the  number 
of  secondary  laterals  which  each  produced  shows  a  still  more  asym- 
metrical distribution.  The  483  secondary  laterals  on  these  branches 
were  produced  on  17.06  per  cent  of  the  primary  laterals,  leaving  82.94 
per  cent  which  produced  none.  The  majority  of  primary  laterals 
which  produced  secondary  laterals  produced  less  than  five  each. 

The  production  of  secondary  laterals  with  respect  to  the  groups  of 
primary  laterals,  elsewhere  described,  may  also  be  noted.  The  average 
number  of  secondary  laterals  per  branch  on  the  primary  laterals  of 
Group  I  was  33.61  ±  2.53 ;  on  those  of  Group  II,  1.86  ±  .26 ;  and  on 
those  of  Group  III,  .19  ±  .08.  It  is  more  than  probable  that  the  age 
factor  was  dominant  in  causing  this  distribution. 

Viewed  from  either  standpoint  there  is  no  evidence  that  the  num- 
bers of  secondary  laterals  on  these  branches  wore  governed  by  the  laws 
of  chance.  On  the  contrary,  there  is  evidence  of  some  definite,  active 
factor  which  tends  to  keep  the  buds  on  the  primary  laterals  in  a  condi- 
tion of  dormancy  until  the  end  of  the  first  year.     The  number  of 


1924] 


Reed:  Growth  and  Differentiation  in  Apricot  Trees 


39 


primary  laterals  on  a  branch  does  not  depart  widely  from  the  values 
to  be  expected  from  the  normal-curve  type  of  variability,  although  it 
is  modified  by  the  location  and  position  of  the  branch  (see  tables  5 
and  6).  The  distribution  of  secondary  laterals  appears,  however,  to 
be  widely  different  from  that  of  the  primary  laterals. 

The  influence  of  the  position  of  the  branch  upon  the  mean  number 
of  secondary  laterals  produced  was  found  to  be  important,  although 
subject  to  considerable  variability.  The  figures  given  (table  14)  show 
little  difference  in  the  numbers  produced  on  branches  which  made  an 
angle  of  less  than  60  degrees  from  the  perpendicular,  but  there  was  a 
much  smaller  number  produced  on  branches  which  approached  a  hori- 
zontal position.  The  variability  in  the  number  of  secondary  laterals 
produced  by  all  classes  of  branches  is  very  great  and  gives  support  to 
a  suggestion,  for  which  I  am  indebted  to  Dr.  H.  B.  Frost,  viz.,  that 
the  physiological  processes  were  very  sensitive  and  were  readily  turned 
in  either  direction  by  factors  of  an  external  or  of  an  internal  nature. 

TABLE   14 

Influence  of  Position  of  Branch  upon  Number  of  Secondary 
Laterals  Produced 


Position  of  Branch 

Mean 

Standard 
deviation 

Coefficient  of 
variability 

0°-30°  from  perpendicular 

30°-60°  from  perpendicular 

60°— 90°  from  perpendicular   

54.67  ±8 .72 
48.11  ±4.82 
21.19  ±2.26 

38.82  ±6  17 
37.10  ±3.40 
21  70  ±  1.60 

71.01  ±  16.02 

77  11  ±  10.55 

102.41  ±13.10 

In  addition  to  the  data  showing  the  influence  of  the  position  of  the 
branch,  there  are  certain  correlations  which  show  something  of  the 
influence  of  internal  factors  upon  the  formation  of  secondary  laterals. 
The  coefficient  of  correlation  between  the  mean  numbers  of  primary 
and  secondary  laterals  per  branch  is 

r  =  .549  ±  .053. 

This  relationship  might  be  expected  on  a  priori  grounds,  since  second- 
ary laterals  are  produced  only  on  primary  laterals.  It  is  logical  to 
expect  that  an  increase  in  the  mean  number  of  primary  laterals  per 
branch  would,  ceteris  paribus,  be  followed  by  an  increase  in  the  number 
of  secondary  laterals  (fig.  10). 


40 


University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 


The  production  of  secondary  laterals  is  obviously  dependent  upon  the 
ability  of  the  branch  to  overcome  the  conditions  which  determine 
dormancy.  This  concept  relates  merely  to  the  number  of  buds  which 
grew  into  secondary  laterals,  not  to  the  size  of  laterals  produced.  So 
far  as  problems  of  differentiation  are  concerned  release  from  dormancy 
is  a  matter  of  prime  importance.  Unless  the  potentiality  of  the  bud 
can  find  kinetic  expression,  it  counts  for  nothing  in  the  further 
differentiation  of  the  branch. 


x. 
c 


153- 


c 


Mi- 


ls 35  JS  bi 

rUan  no  o[  primary  laterals  per  branch 

Fig.  10.     Regression  line  of  mean  number  of  secondary  laterals  per 
branch  on  mean  number  of  primary  laterals. 


The  lengths  of  secondary  laterals  in  Groups  I  and  II  have  been 
studied  with  reference  to  their  frequency  and  variability.  So  few 
secondary  laterals  were  produced  in  Group  III,  that  they  were  not 
included  in  the  study.  The  frequency  distributions  are  shown  in 
figure  11  and  exemplify  a  case  of  pronounced  asymmetry.  It  will  be 
remembered  that  the  length  distributions  of  primary  laterals  show  a 
similar  type  of  distribution.  In  both  cases  it  is  apparent  that,  among 
the  factors  which  determine  the  length  of  a  lateral,  the  chance 
variations  of  the  environment  play  a  small  part. 


1924] 


Reed:  Growth  and  Differentiation  in  Apricot  Trees 


41 


It  is  very  interesting  to  note  (table  9)  that  the  mean  length  of 
secondary  laterals  in  Groups  I  and  II  is  the  same  in  spite  of  the 
difference  in  age  and  position.  The  absence  of  any  such  relation  in 
the  primary  laterals  makes  it  doubtful  whether  there  is  any  significance 
in  this  relationship,  although  it  suggests  that  the  forces  involved  in 
the  growth  of  secondary  laterals  tend  to  come  to  a  rather  definite 
equilibrium. 

2000 


66 

length  in  cm 

Fig    11.     frequency  distributions  for  length  of  secondary  laterals  in  Groups  I 
and  II,  plotted  on  logarithmic  scales.    Group  I,  ,  Group  II, . 


The  relation  of  the  mean  number  of  secondary  laterals  on  a  branch 
to  their  mean  length  expressed  as  a  coefficient  of  correlation  is 

r  =  .148±  .078. 

This  coefficient  is  not  large  and,  moreover,  is  only  twice  its  probable 
error;  consequently  it  fails  to  denote  any  significant  correlation 
between  the  two  variables.  If  the  amount  of  unformed  materials  in 
the  branch  were  more  or  less  constant,  we  should  then  expect  to  find 
a  definite  negative  correlation  between  these  two  variables,  because 


42 


University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 


where  few  laterals  were  produced  they  would  have  more  material  to 
draw  upon  and  consequently  attain  a  greater  size.  The  lack  of  any 
strong  correlation  shows  that  the  size  of  the  laterals  is  independent  of 
any  such  factor.  Indeed,  if  any  weight  be  laid  upon  the  coefficient,  it 
must  be  interpreted  in  quite  the  opposite  direction,  i.e.,  the  more 
laterals  produced,  the  greater  will  be  their  average  length.  Doubtless 
this  tendency  would  be  more  pronounced  were  it  not  for  the  fact  that 
the  manufacture  of  sufficient  photosynthates  is  limited  by  the  crowding 
and  consequent  shading  of  laterals  during  the  growing  season. 


.5  S- 


£ 

c 


10  - 


10  30  10  SO 

/•Veaa  Ungth^uem)-  primary  laterals 

Fig.  12.     Kegression  line  of  mean  length  (per  branch)   of  secondary 
laterals  on  mean  length  of  primary  laterals. 

Another  important  correlation  is  that  which  exists  between  the 
mean  length  of  primary  and  secondary  laterals  of  each  branch.  The 
coefficient  expressing  this  correlation  is 

r  =  .467  ±  .062. 
This  expresses  a  strong  positive  correlation  between  the  two  variables 
and  may  be  taken  as  evidence  that  the  factors  which  determine  the 
size  of  primary  laterals  on  a  branch  operate  in  the  same  way  on  the 
secondary  laterals.  The  validity  of  the  correlation  is  shown  by  the 
linearity  of  regression  (fig.  12). 

This  coefficient  of  correlation  expresses  concisely  a  relationship 
which  was  suggested  by  the  rough  parallelism  of  the  polygons  (fig.  5) 
showing  the  frequency  distributions  of  the  numbers  of  primary  and 
secondary  laterals  per  branch.  Both  distributions  have  the  greatest 
frequencies  in  the  region  of  the  smaller  numbers  of  laterals  per  branch. 


1924] 


Heed:  Growth  and  Differentiation  in  Apricot  Trees 


43 


4.  Blossoms 

The  formation  of  blossoms  is  an  important  stage  in  growth  and 
differentiation.  The  blossom  bud  is  a  highly  energized  center  on  the 
vegetative  organs  toward  which  flow  some  of  the  most  important  syn- 
thetic materials  from  other  parts  of  the  tree.  So  far  as  the  perpetua- 
tion of  the  species  is  concerned,  the  formation  of  a  sufficient  number  of 
viable  fruit  buds  is  one  of  the  factors  of  success  in  the  struggle  for 
existence.  The  horticulturist  has  an  obvious  interest  in  the  factors 
which  govern  the  formation  of  a  maximum  number  of  buds  on  fruit 
trees. 


IS 

L_ 

11- 

I 

2 

1    '" 

1 

,         1.        1                 1 

O  400  800  1200 

No  of  blossoms  ptrbrnnch 
Fig.  13.     Frequency  distribution  for  number  of  blossoms  on  apricot  brandies. 


The  problem  of  fruit-bud  formation  on  the  apricot  tree  is  broader 
than  the  aspects  dealt  with  here,  because  most  of  the  fruit  buds  are 
produced  on  laterals  which  appear  after  the  branch  is  one  year  old. 
It  is  well  known  that  such  conditions  are  not  favorable  for  the  pro- 
duction of  a  maximum  number  of  blossom  buds.  The  problem  here 
attacked  is  the  production  of  fruit  buds  on  branches  which  are  making 
rapid  vegetative  growth  in  the  first  season. 

The  salient  features  of  the  number  and  variability  of  blossoms  are 
shown  in  table  15  and  in  figure  13.  The  number  of  blossoms  per  branch 
ranged  from  50  to  1200  with  the  mean  at  360.26  ±  16.62.  The  great 
variability  in  the  number  of  blossoms  per  branch  is  shown  by  the  fre- 
quency polygon  and  by  the  coefficient  of  variability  of  60.39  ±  4.28. 
This  frequency  polygon  bears  a  certain  resemblance  to  those  represent- 
ing the  distribution  of  laterals,  since  it  also  has  the  highest  frequencies 
in  the  region  of  a  minimum  number  of  blossoms  per  branch. 


44 


University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 


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1924]  Beed:  Growth  and  Differentiation  in  Apricot  Trees  45 

The  main  axis  of  the  branch  bore  very  few  blossoms,  the  majority 
of  them  being  produced  upon  primary  laterals. 

The  primary  laterals  of  Group  I  produced  the  greater  part  of  the 
blossoms  and  the  variability  of  the  mean  number  per  lateral  is  less  than 
in  the  more  distally  located  groups.  The  variability  of  the  means  in 
all  these  groups  is  relatively  enormous. 

The  decrease  in  the  number  and  the  increase  in  the  variability  of 
the  numbers  of  blossoms  in  the  distal  regions  of  the  branches  may  be 
due  to  a  number  of  causes,  among  which  we  must  recognize  growth. 
While  the  distal  region  was  growing,  the  physiological  functions  of 
that  part  were  opposed  to  the  formation  of  the  energy  centers  which 
form  blossom  rudiments.  In  the  proximal  region,  growth  in  mass  had 
largely  ceased  so  long  before  the  end  of  the  season  that  the  develop- 
ment of  blossom  rudiments  was  not  opposed  by  other  functions.  The 
effect  of  the  migration  and  localization  of  materials  in  the  branch  is 
a  biochemical  question  which  will  not  be  discussed  here.  Hooker2,  3 
has  made  a  significant  beginning  in  the  study  of  these  factors  and 
Barker  and  Lees1  have  approached  the  problem  by  a  somewhat  different 
route. 

Since  blossoms  were  produced  mainly  upon  laterals,  any  factor 
which  increases  the  production  of  laterals  may  also  increase  the  produc- 
tion of  blossoms.  The  coefficient  of  correlation  between  the  number  of 
blossoms  per  branch  and  the  ratio  of  primary  laterals  to  total  number 

of  nodes  per  branch  is  _n„        „„_ 

r  =  .dob  ±  .Obo. 

This  coefficient  might  be  expected  to  measure  the  effect  of  the  factors 
which  overcome  dormancy  on  the  production  of  blossoms.  One  may 
assume  that  substances  moving  into  the  branch  go  either  to  the  produc- 
tion of  laterals  or  to  the  formation  of  flower  rudiments.  If,  from  any 
cause,  the  number  of  primary  laterals  were  relatively  small,  the  mate- 
rial might  be  vised  in  forming  flower  rudiments.  If  the  number  of 
laterals  were  relatively  large,  they  might  so  compete  with  flower-bud 
formation  as  to  lessen  the  number  of  flowers  formed ;  but  this  correla- 
tion coefficient  speaks  against  the  validity  of  such  an  assumption.  The 
coefficient  is  positive  and  indicates  that  factors  which  cause  the  form- 
ation of  numerous  laterals  also  tend  to  form  a  larger  number  of  flower 
buds.  It  is  not  improbable  that  the  formation  of  primary  laterals, 
through  their  ability  to  increase  the  amount  of  photosynthates, 
increases  the  formation  of  flower  buds.  Again,  it  is  possible  that  the 
formation  of  the  two  kinds  of  units  (laterals  and  flower  buds)  is  an 
expression  of  the  same  tendency  to  differentiation. 


46  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 

The  next  step  in  this  study  was  designed  to  answer  the  question, 
Is  there  any  relation  between  the  length  of  a  lateral  and  the  number 
of  blossoms  it  bears?  There  is  an  opinion  current  that  short  laterals 
are  the  most  precocious  in  fruiting  habits.  This  opinion,  however, 
may  be  due  to  the  fact  thai  the  blossoms  on  them  must  of  necessity 
be  close  together  and  are  therefore  more  conspicuous.  A  more  accurate 
idea  of  the  relationship  may  be  obtained  by  ascertaining  the  correlation 
coefficient  between  the  number  of  blossoms  and  the  number  of  nodes 
of  the  laterals. 

Correlation  coefficients  were  determined  for  972  primary  laterals 
in  Group  I,  since  this  is  the  largest  and  most  representative  group  of 
laterals.    If 

a'  =  number  of  blossoms  on  primary  laterals 
b'  =  number  of  nodes  on  primary  laterals 
c'  =  length  of  primary  laterals 

the  coefficients  of  correlation  are 

ra.b.  =  .089  ±  .020 
ra.c.  =  .077  ±  .020 
r6V  =  .969  ±  .014 

The  coefficient  representing  the  correlation  between  the  numbers  of 
blossoms  and  nodes  is  small,  and  of  very  doubtful  significance;  the 
same  holds  true  of  the  correlation  between  number  of  blossoms  and 
length  of  lateral.  The  third  coefficient  shows,  as  one  might  predict,  a 
very  high  correlation  between  the  length  of  a  lateral  and  the  number 
of  nodes  it  bears. 

On  the  face  of  these  coefficients  of  gross  correlation,  we  should 
conclude  that  there  is  practically  no  association  between  the  number 
of  nodes  and  the  number  of  blossoms  a  lateral  may  bear.  The  problem 
is  a  bit  complicated  by  the  fact  that  the  laterals  are  of  different  lengths, 
but  this  factor  may  be  eliminated  by  making  the  partial  correlation 
between  the  numbers  of  buds  and  nodes. 

a,b,rc,  —  .059  ±  .021 

This  coefficient  shows  very  plainly  that  there  is  no  correlation  between 
the  number  of  blossoms  and  the  number  of  nodes  on  the  laterals.  That 
is  to  say,  a  short  lateral  may  have  as  many  blossoms  as  a  long  lateral. 
The  character  of  the  correlation  coefficient  may  be  made  a  bit 
plainer  by  referring  to  the  curve  of  means  of  yx  in  figure  14,  which 
shows   the   mean    number    of    blossoms   produced    upon   the    laterals 


1924] 


Reed:  Growth  and  Differentiation  in  Apricot  Trees 


47 


possessing  varying  numbers  of  nodes.  The  curve  of  the  means  of 
blossoms  for  primary  laterals  shows  that  we  are  not  here  dealing  with 
a  case  of  linear  regression  and  that  the  coefficient  of  gross  correlation 
is  therefore  somewhat  lacking  in  reliability.  It  is  interesting  to  note 
that  the  greatest  mean  number  of  blossoms  occurred  on  laterals  bearing 
from  30  to  60  nodes. 


Nodes    -    scale  for  secondary   laterals 
4  11  60  74 


5  60 

Nodes  -  scale  [or  primary  laterals 

Fig.  14.     Relation  of  the  number  of  blossoms  to  the  number  of  nodes.   Curves  of 
the  means  of  yx.    Primary  laterals, ;  secondary  laterals, . 

A  better  idea  of  the  relations  between  the  two  characters  may  be 
grasped  from  the  representation  of  the  blossom-node  distribution  as 
shown  in  figure  15.  This  blossom-node  surface  shows  that  there  are 
two  kinds  of  primary  laterals  on  apricot  branches.  The  larger  class 
has  a  tendency  toward  a  linear  regression  of  blossoms  on  nodes,  i.e., 
the  more  nodes  the  more  blossoms.  It  is  true  that  the  ellipses  showing 
the  distribution  values  are  imperfect,  but  that  is  because  the  frequency 
distributions  of  these  values  are  so  asymmetrical  (fig.  13).  The  smaller 
class  of  laterals  is  indicated  by  the  partial  ellipses  in  the  upper  right 
portion  of  the  blossom-node  surface.  These  laterals  were  characterized 
by  many  nodes  and  few  blossoms.     This  blossom-node  surface  there- 


48 


University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 


fore  shows  clearly  that  the  apricot  branches  possessed  a  large  number 
of  fruiting  laterals  and  a  smaller  number  of  vegetative  laterals.  It 
also  shows  why  the  curve  of  means  of  yx  has  an  upward  trend  in  the 
nodal  classes  of  high  values. 

Nodes  on  primary  laterals   (group  l) 

_S lb 27  i&  19  60  71  82 


Fig.  15.     Blossom-node  surface  for  primary  laterals. 

The  blossoms  on  the  secondary  laterals  borne  on  primary  laterals 
of  Group  I  were  also  studied  in  somewhat  the  same  manner.  The 
frequency  distributions  of  blossoms  and  nodes  on  the  secondary  laterals 
were  of  the  same  asymmetrical  types  as  on  the  primary  laterals  and 
the  coefficients  of  gross  correlation  were  similar. 

The  following  notation  was  used : 

a"  =  number  of  blossoms  on  secondary  laterals 
b"  =  number  of  nodes  on  secondary  lateral 
c"  =  length  of  secondary  lateral 

The  coefficients  of  correlation  as  determined  for  a  population  of  1370 

secondary  laterals  were 

tVb»  =  .118±.018 
ra»c''  =  .122±.018 
n,.c„  =  .971  ±  .001 


1924] 


Eeed:  Growth  and  Differentiation  in  Apricot  Trees 


49 


The  first  two  coefficients  are  somewhat  more  reliable  than  the  corre- 
sponding determinations  on  primary  laterals,  but  they  cannot  be 
regarded  as  indicating  any  strong  degree  of  association  between  the 
characters  concerned.  Indeed,  it  is  evident  from  other  relations  that 
the  number  of  blossoms  a  secondary  lateral  bore  was  quite  independent 
of  the  number  of  nodes  or  of  its  length.  The  coefficient  of  partial 
correlation  is 

a„v,rd,  =  —  .002  ±  .018 

In  view  of  the  fact  that  the  value  of  this  coefficient  is  practically  zero, 
it  is  evident  that  if  all  the  secondary  laterals  were  of  equal  length, 
there  would  be  no  correlation  between  the  numbers  of  blossoms  and 
nodes  upon  them. 


Nodes  on  stconda.r*  laterals   (group  l) 


Pig.  16.     Blossom-node  surface  for  secondary  laterals. 


50 


University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 


The  curve  of  the  means  of  yx  (fig.  14)  shows  that  the  mean  numbers 
of  blossoms  on  classes  of  laterals  with  varying  numbers  of  nodes  were 
not  significantly  different,  in  fact,  they  were  remarkably  constant. 
The  actual  range  for  values  of  yx  was  0  to  8.16.  It  is  evident  from 
these  values  that  we  are  not  dealing  with  a  case  of  linear  regression 
between  these  two  characters. 


10  - 


Ua  - 


14  $  II  16 

Ordinal  position  o|  laterals 

Fig.  17.     Relation  of  the  number  of  blossoms  to  the  position  of  the  secondary 
lateral  on  which  they  were  borne.    Curve  of  the  means  of  f/j-. 


The  actual  distribution  of  blossoms  on  the  secondary  laterals  is 
well  shown  by  figure  16.  Here,  again,  we  see  that  there  are  two  rather 
distinct  classes  of  laterals,  one  of  which  bore  many  more  blossoms  in 
proportion  to  the  number  of  nodes  than  the  other.  The  first  class 
includes  laterals  having  less  than  40  nodes  and  the  partial  ellipses 
representing  their  distribution  have  axes  sloping  rather  steeply  down- 
ward. The  other  group  which  contains  long  laterals  appears  to  be 
distinctly  vegetative  in  character;  at  least,  it  bore  relatively  few 
blossoms  in  proportion  to  its  number  of  nodes. 

One  further  aspect  of  the  distribution  of  blossoms  was  investigated. 
viz.,  the  correlation  between  the  position  of  a  secondary  lateral  and 
the  number  of  blossoms  it  bore.  It  is  interesting  to  know  whether  the 
lower  laterals  in  a  group  produced  more  or  less  blossoms  than  the 
upper  laterals.  The  records  of  2011  secondary  laterals  on  primary 
laterals  of  Group  I  were  used  in  making  the  correlation  table.  They 
were  counted  in  succession,  the  lateral  nearest  the  base  of  the  primary 
lateral  on  which  they  were  borne  being  designated  as  number  one. 
The  coefficient  of  correlation  between  these  variables  was 

r  =  —  .109  ±  .022. 


1924]  Beed:  Growth  and  Differentiation  in  Apricot  Trees  51 

It  indicates  only  a  small  degree  of  negative  correlation  and  may  be 
interpreted  to  mean  that  the  lower  laterals  were  only  slightly  if  at  all 
superior  to  others  in  the  production  of  blossoms. 

The  remarkable  uniformity  in  the  mean  number  of  blossoms  on 
laterals  is  shown  by  the  means  of  yx  (fig.  17).  From  this  we  may  infer 
that  it  was  neither  the  number  of  nodes  on  a  lateral  nor  the  ordinal 
position  of  the  lateral  which  determined  the  number  of  blossoms  it 
bore,  but  some  other,  as  yet,  unknown  factor. 


VII.  GENERAL  SURVEY  OF  CORRELATED  VARIABILITY  IN 
THE  APRICOT  BRANCH 

The  method  of  presenting  correlations  employed  in  figure  18  gives 
a  comprehensive  idea  of  the  relations  existing  between  the  variables 
whose  correlation  has  been  discussed  on  widely  separated  pages.  The 
manner  in  which  the  coefficients  are  shown  on  the  lines  which  connect 
the  names  of  the  characters  whose  correlation  was  determined  calls  for 
little  additional  discussion. 

The  length  of  the  branch  was  employed  as  the  central  character 
from  which  others  radiate,  since  the  length  of  that  member  seems  to 
be  an  excellent  index  of  growth.  The  majority  of  the  coefficients  are 
large  enough  in  comparison  with  their  probable  errors  to  be  significant. 
In  the  cases  where  one  variable  is  very  dependent  upon  another,  e.g., 
Avhere  the  number  of  nodes  depends  almost  entirely  upon  the  length  of 
the  laterals,  the  coefficient  of  correlation  between  the  two  variables  is 
very  high. 

VIII.  SUMMARY 

1.  The  pattern  of  the  organism  is  the  result  of  a  process  of  growth 
and  differentiation  which  is  largely  an  expression  of  inherent  factors. 
Growth  and  differentiation  lead  to  a  quantitative  distribution  of 
matter  in  space  that  makes  it  necessary  to  regard  the  position  and 
size  of  members  of  the  branches  as  the  expression  of  an  inherent  tend- 
ency Avhich  varies  within  limits  under  the  influence  of  the  ever- varying 
environment. 

2.  The  main  axis  of  the  apricot  branch  shows  distinct  cycles  of 
growth  during  the  first  season,  each  of  which  may  be  expressed  by  a 
logarithmic  equation  similar  to  that  of  autocatalysis.  The  maximum 
rate  of  growth  was  reached  in  the  fifth  and  sixth  weeks. 


52  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  5 

3.  The  branches  in  the  population  studied  were  less  variable  in 
length  than  in  any  other  character.  Their  frequency  polygon  for 
length  is  fairly  symmetrical  with  respect  to  its  mean  and  does  not 
depart  widely  from  the  type  of  polygon  which  represents  a  chance 
distribution  of  characters  in  biological  material.  The  mean  length  of 
all  laterals  was  more  than  seven  times  that  of  the  branches  on  which 
they  were  borne.  The  degree  of  association  between  number  of 
laterals  per  branch  and  the  length  of  the  branch  was  not  high ;  but  it 
was  high  between  the  length  of  branch  and  length  of  laterals  it  bore. 
The  location  of  the  branches  and  their  angle  with  the  perpendicular 
had  certain  effects  upon  their  growth  and  differentiation.  Branches 
on  the  north  side  of  the  tree  produced  the  maximum  number  of 
primary  laterals  and  blossoms.  Branches  which  made  an  angle  of 
60  to  90  degrees  with  the  perpendicular  had  fewer  laterals  and  blossoms 
than  those  which  were  more  nearly  upright,  although  the  ratio  of 
blossoms  to  unit  length  of  lateral  was  greater  on  the  horizontal 
branches. 

•4.  The  distribution  of  laterals  and  blossoms  showed  wide  divergence 
from  the  normal  frequency  distribution  of  variables.  Groups  con- 
taining the  smaller  numbers  of  laterals  and  blossoms  per  branch  had 
by  far  the  greatest  frequencies.  The  types  of  distribution  here  studied 
appear  to  depend,  not  upon  the  chance  factors  of  the  environment,  but 
upon  fundamental  internal  conditions  of  differentiation.  These 
internal  conditions  are  obviously  grounded  in  the  basic  growth 
tendencies  of  the  cells,  that  is  to  say,  in  their  genetic  constitution,  and 
are  especially  conditioned  by  certain  inescapable  spatial  limitations. 
A  striking  result  of  these  conditions  is  that  relatively  large  growth 
occurs  in  a  few  buds  and  shoots,  while  relatively  slight  growth  (or 
none)  occurs  in  many  buds  and  shoots.  We  find,  therefore,  a  general 
tendency  toward  distributions  showing  positive  skewness,  with  or 
without  zero  classes.  The  close  approach  in  this  study  to  a  Gaussian 
distribution  for  'branch'  length  is  doubtless  due  to  the  method  of 
initial  sampling;  only  shoots  in  favorable  locations  were  selected  for 
study,  and  the  feebler  majority  was  thus  eliminated. 

5.  Most  of  the  nodes  remained  dormant  through  the  first  season. 
The  ratio  of  nodes  which  produced  laterals  is  such  that  it  indicates  a 
cyclic  distribution  of  the  forces  which  break  the  dormancy  of  lateral 
buds. 


1924] 


Eeed:  Growth  and  Differentiation  in  Apricot  Trees 


53 


Number 

of 
blossoms 

.706 

Num 
secon 

»tr  of 

dar  v 

.148 

Mean  length 
of  secondary 
laterals 

laterals 

.4ft* 

i 

L 

JSJ 

.549 

i 
J 

Number 

of 
blossoms 

.318 

Nunibe  r  of 

pmuary 

laterals 

Mean  leugth 

of  primary 

la  ferals 

.700 

L 

•473 

J 

.337 

Length  of  branch 

Total  Number 
of  all 
laterals 

Total  length 
of  all 
laterals 

-9fifl 

1 

1 

i 

L 

.62*      . 

.445 

J 

Number 
blossoms 

.077 

Length  of 

primary 

laterals 

Number 

of 
nodes 

.971 

I , 

L 

•i83_         . 

.467 

J 

Number 

of 
blossoms 

.122 

Length  of 
secondary 
laterals 

Number 

of 
nodes 

l 

1 

I I1& I 

Fig.  18.    Diagram  representing  correlations  between  certain  characters. 


54  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  3 

6.  The  configuration  of  primary  laterals  on  the  branch  afforded 
suitable  material  for  the  study  of  the  statics  of  cyclic  growth  and 
gave  satisfactory  evidence  of  a  definite  distribution  of  matter  in  space. 
The  production  of  material  for  the  formation  of  laterals  appears  to 
follow  the  same  mathematical  relations  as  does  the  growth  of  the 
branch.  A  method  is  described  by  which  it  was  possible  to  compute 
the  length  of  a  lateral  situated  at  a  given  node. 

7.  The  general  form  of  frequency  distribution  of  the  numbers  and 
lengths  of  secondary  laterals  does  not  appear  to  be  conditioned  to  any 
great  extent  by  the  factors  located  in  the  environment.  The  mean 
number  of  secondary  laterals  per  branch  showed  rather  a  high  positive 
correlation  with  the  mean  number  of  primary  laterals.  The  correla- 
tion between  the  mean  number  of  secondary  laterals  and  their  mean 
length  indicated  that  the  size  of  the  laterals  is  not  dependent  upon 
the  factors  which  determine  their  numbers.  The  mean  lengths  of 
primary  and  secondary  laterals  on  a  branch  showed  a  correlation  which 
indicated  that  the  factors  which  operated  to  determine  the  length  of 
one  order  of  laterals  acted  similarly  on  the  other  class. 

8.  The  main  axis  of  the  branch  produced  very  few  blossoms  in  the 
following  season ;  the  primary  laterals  bore  the  majority  of  those  pro- 
duced. The  mean  number  of  blossoms  per  lateral  tended  to  be  rather 
constant  regardless  of  the  length  of  the  lateral,  and  indicates  that 
random  factors  of  the  environment  were  less  important  than  internal 
factors  of  differentiation  in  determining  distribution.  The  blossom- 
node  surface  gave  good  evidence  of  the  occurrence  of  two  classes  of 
laterals  on  apricot  branches ;  the  larger  class  showed  a  tendency  toward 
a  linear  regression  of  blossoms  on  nodes,  while  the  smaller  class  was 
characterized  by  the  possession  of  many  nodes  and  few  blossoms,  and 
showed  no  definite  tendency  toward  linear  regression. 


1924]  Eeed:  Growth  and  Differentiation  in  Apricot  Trees  55 


LITERATURE  CITED 

i  Barker,  B.  T.  P.,  and  Lees,  A.  H. 

1916,  1919.     Factors  governing  fruit-bud  formation.     Agr.  and  Hort.  Ees. 
Sta.,  Bristol,  Ann.  Kept.  1916,  pp.  46-64;  1919,  pp.  85-98. 
2  Hooker,  H.  D. 

1921.  Localization  of  the  factors  determining  fruit-bud  formation.    Missouri 

Agr.  Exp.  Sta.,  Bes.  Bull.  47. 
a  Hooker,  H.  D. 

1922.  Certain  responses  of  apple  trees  to  nitrogen  applications  of  different 

kinds  and  at  different  seasons.    Ibid.,  50. 
*  Mason,  T.  G. 

1922.     Growth  and   correlation  in  Sea  Island  cotton.     West  Indian  Bull., 
vol.  19,  pp.  214-238. 
s  Priestley,  J.  H.,  and  Pearsall,  W.  H. 

1922.     Growth  studies.  II.    An  interpretation  of  some  growth-curves.    Ann. 
Bot.,  vol.  36,  pp.  239-249. 
«  Eeed,  H.  S. 

1920.     The  dynamics  of  fluctuating  growth   rate.     Proc.   Nat.   Acad.   Sci., 
vol.  6,  pp.  397-410. 
i  Reed,  H.  S. 

1920.  Slow  and  rapid  growth.     Am.  Jour.  Bot.,  vol.  7,  pp.  327-332. 

s  Reed,  H.  S. 

1921.  Growth  and  sap  concentration.    Jour.  Agr.  Res.,  vol.  21,  pp.  81-98. 

s  Reed,  H.  S. 

1921.     Correlation  and  growth  in  the  branches  of  young  pear  trees.     Jour. 
Agr.  Res.  vol.  21,  pp.  849-876. 
io  Reed,  H.  S.,  and  Halma,  F.  F. 

1919.     On  the  existence  of  a  growth-inhibiting  substance  in  the  Chinese 
lemon.    Univ.  Calif.  Publ.  Agr.  Sci.,  vol.  4,  pp.  90-112. 
ii  Reed,  H.  S.,  and  Halma,  F.  F. 

1919.     The   evidence  for  a  growth-inhibiting  substance   in   the   pear  tree. 
Plant  World,  vol.  22,  pp.  239-247. 
i-  Spencer,  H. 

1893.     Principles  of  biology,  vol.  2,  p.  215. 

13  ROEERTSON,  T.  B. 

1915.     Tables  for  the  computation  of  curves  of  autocatalysis,  with  especial 

reference  to  curves  of  growth.    Univ.  Calif.  Publ.  Physiol.,  vol.  4, 

pp.  211-228. 
i*  Thompson,  R. 

1835.     A  report  upon  the  varieties  of  apricot  cultivated  in  the  garden  of 

the  horticultural  society.    Read  Feb.  15,  1831.    Trans.  Roy.  Hort. 

Soc,  London,  ser.  2,  vol.  1,  p.  63. 


UNIVERSITY  OF  CALIFORNIA  PUBLICATIONS— (Continued) 

4.  Further  Studies  on  the  Distribution  and  Activities  of  Certain  Groups  of 
Bacteria  in  California  Soil  Columns  by  Charles  B.  Lipman.  Pp.  113-120. 
April,   1919 _ _ _ J.0 

6.  Variability  in  Soils  and  Its  Significance  to  Past  and  Future  Soil  Investi- 
gations. II.  Variations  in  Nitrogen  and  Carbon  in  Field  Soils  and  Their 
Relation  to  the  Accuracy  of  Field  Trials,  by  D.  D.  Waynick  and  L.  T. 
Sharp.    Pp.  121-139,  1  text  figure.    May,  1919  i .20 

6.  The  Effect  of  Several  Types  of  Irrigation  Water  on  the  Ph  Value  and  Freez- 

ing Point  Depression  of  Various  Types  of  Soils,  by  D.  R.  Hoagland  and 

A.  W.  Christie.    Pp.  141-157.    November,  1919  _ _      .26 

7.  A  New  and  Simplified  Method  for  the  Statistical  Interpretation  of  Bio- 

metrical  Data,  by  George  A.  Linhart.    Pp.  159-181,  12  text  figures.    Sep- 
tember, 1920  „.      .25 

8.  The  Temperature  Relations  of  Growth  in  Certain  Parasitic  Fungi,   by 

Howard  S.  Fawcett.    Pp.  183-232,  11  text  figures.    March,  1921 .76 

9.  The  Alinement  Chart  Method  of  Preparing  Tree  Volume  Tables,  by  Donald 

Bruce.    Pp.  233-243.    December,  1921 „ _ .20 

10.  Equilibrium  Studies  with  Certain  Acids  and  Minerals  and  their  Probable 

Relation  to  the  Decomposition  of   Minerals  by  Bacteria,   by  Douglas 
Wright,  Jr.    Pp.  245-337,  35  text  figures.    March,  1922 __..    1.25 

11.  Studies  on  a  Drained  Marsh  Soil  Unproductive  for  Peas,  by  Paul  S.  Burgess. 

Pp.  339-396,  21  text  figures.    June,  1922 65 

12.  The  Effect  of  Reaction  on  the  Fixation  of  Nitrogen  by  Azotobacter,  by 

Harlan  W.  Johnson  and  Charles  B.  Lipman.    Pp.  397-405,  3  text  figures. 
December,  1922  25 

13.  The  Toxicity  of  Copper  Sulfate  to  the  Spores  of  Tilletia  tritici  (Bjerk.) 

Winter,  by  Fred  N.  Briggs.    Pp.  407-412,  1  figure  in  text.    November, 
1923    __       .26 

14.  Influence  of  Reaction  on  Inter-Relations  Between  the  Plant  and  its  Culture 

Medium,  by  J.  J.  Theron.    Pp.  413-144,  12  figures  in  text.    January,  1924       .45 

Vol.  5.     1.  Growth  and  Differentiation  in  Apricot  Trees,  by  H.  S.  E«ed.     Pp.  1-55, 

18  figures  in  text.    September,  1924 75 

AGRICULTURE. — The  Publications  of  the  Agricultural  Experiment  station  consist  of  Bul- 
letins and  Biennial  Reports  edited  by  Professor  Thomas  Forsyth  Hunt,  Director  of 
the  Station.  These  are  sent  gratis  to  citizens  of  the  State  of  California.  For 
detailed  information  regarding  them  address  the  Agricultural  Experiment  Station, 
Berkeley,  California. 

BOTANY. — W.  A.  Setchell  and  R.  C.  Holman,  Editors.  Volumes  I-IV  $3.50  per  volume ; 
volume  V  and  following  $5.00  per  volume.  Volumes  I  (pp.  418),  II  (pp.  360), 
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pleted.   Volumes  VII,  VIII,  X,  XI,  and  XII  in  progress. 

VoL  7.  1.  Notes  on  the  California  Species  of  Trillium  L.  A  Report  on  the  General 
Results  of  Field  and  Garden  Studies,  1911-1916,  by  Thomas  Harper  Good- 
and  Robert  Percy  Brandt.    Pp.  1-24,  plates  1-4.    October,  1916 _      .25 

2.  (The  same.)     The  Nature  and  Occurrence  of  Undeveloped  Flowers,  by 

Thomas  Harper  Goodspeed  and  Robert  Percy  Brandt.    Pp.  25-38,  plates 

5-6.    October,  1916  „ _ - —      .16 

3.  (The  same.)     Seasonal  Changes  in  Trillium  Species  with  Special  Reference 

to  the  Reproductive  Tissues,  by  Robert  Percy  Brandt.  Pp.  39-68,  plates 
7-10.     December,  1916  _ .30 

4.  (The  same.)    Teratological  Variations  of  Trillium  sessile  var.  giganteum,  by 

Thomas  Harper  Goodspeed.    Pp.  69-100,  plates  11-17.    January,  1917 „      .30 

5.  A  Preliminary  List  of  the  Uredinales  of  California,  by  Walter  C.  Blasdale. 

Pp.  101-157.  .August,  1919 —       .50 

6.  A  Rubber  Plant  Survey  of  Western  North  America.     I.  Chrysothamnus 

nauseosus  and  Its  Varieties,  by  Harvey  Monroe  Hall  and  Thomas  Harper 
Goodspeed.    Pp.  159-181. 

7.  (The  same.)     II,  Chrysil  a  New  Rubber  from  Chrysothamnus  nauseosus,  by 

Harvey  Monroe  Hall.    Pp.  183-264,  plates  18-20,  6  figures  in  text. 

8.  (The  same.)     HI.  The  Occurrence  of  Rubber  in  Certain  West  American 

Shrubs,  by  Harvey  Monroe  Hall  and  Thomas  Harper  Goodspeed.     Pp. 
265-278,  2  figures  in  text. 

Nos.  6,  7,  and  8  in  one  cover.    November,  1919 1.25 

9.  Phycological  Contributions.    I,  by  William  Albert  Setchell  and  Nathaniel 

Lyon  Gardner.    Pp.  279-324,  plates  21-31.    July,  1920  50 


UNIVERSITY  OF  CALIFORNIA  PUBLICATIONS— (Continued) 

10.  Plantae  Mexicanae  Purpusianae.    X,  by  Townshend  Stith  Brandegee.    De- 

cember, 1920  _ _ .10 

11.  Phycologlcal  Contributions,  II  to  VI.     II,  New  Species  of  Myrionema; 

ITT,  New  Species  of  Composonema;  TV,  New  Species  of  Hecatonema; 
V,  New  Species  of  Pylaiella  and  Streblonema;  VI,  New  Species  of  Ecto- 
carpus,  by  William  Albert  Setchell  and  Nathaniel  Lyon  Gardner,  Pp. 
333-426,  plates  32-39.    May,  1922 _ 1.50 

12.  Notes  on  Pacific  Coast  Algae.    II,  On  tbe  Calif ornian  "Delesseria  Querci- 

folia,"  by  Carl  Skottsberg.    Pp.  427-436,  plate  50.    June,  1922 .25 

13.  Undescribed  Plants  mostly  from  Baja  California,  by  Ivan  Murray  John- 

ston.   Pp.  437-446.    August,  1922 „ .25 

14.  The  Morphology,  Development,  and  Economic  Aspects  of  Schizophyllum 

commune  Fries,  by  Frederick  Monroe  Essig.  Pp.  447-498,  plates  51-6L 
August,  1922  „ „ _       .80 

VoL  8.  1.  The  Marine  Algae  of  the  Pacific  Coast  of  North  America.  Part  I.  Myxo- 
phyceae,  by  William  Albert  Setchell  and  Nathaniel  Lyon  Gardner.     Pp. 

1-138,  plates  1-8.    November,  1919  _ 1.50 

2.  (The  same.)     Part  n.  Chlorophyceae,   by  William  Albert  Setchell   and 

Nathaniel  Lyon  Gardner.    Pp.  139-374,  plates  9-33.    July,  1920 „    2.75 

VoL  9.    A  Report  upon  the  Boreal  Flora  of  the  Sierra  Nevada  of  California,  by  Frank 

Jason  Smiley.    423  pages,  7  plates.    October,  1921 „ „    5.00 

VoL  10.   1.  The  Genus  Fucus  on  the  Pacific  Coast  of  North  America,  by  Nathaniel 

Lyon  Gardner.    Pp.  1-180,  pis.  1-60.    April  1922 _ 2.25 

2.  Plantae   Mexicanae   Purpusianae,   XI,   by   Townshend   Stith   Brandegee. 

Pp.  181-188.    November,  1922 .16 

3.  A  Revision  of  the  Californian  Species  of  Lotus,  by  Alice  M.   Ottley. 

Pp.  189-305,  plates  61-82,  10  maps.    August,  1923 _ 2.00 

4.  Notes  on  a  Collection  of  New  Zealand  Hepaticae,  by  William  Henry  Pear- 

son.   Pp.  307-370,  plates  83-103. 

5.  More  New  Zealand  Hepaticae,  by  William  Henry  Pearson.     Pp.  373-392, 

plates  104-109. 

Nos.  4  and  5  in  one  cover.    June,  1923 1.25 

6.  Parasitic  Florideae  II,  by  William  Albert  SetchelL    Pp.  393-396. 

7.  A  Revision  of  the  West  North  American   Species  of  Callophyllis,   by 

William  Albert  SetchelL    Pp.  397-401. 

Nos.  6  and  7  in  one  cover.    May,  1923 _ 25 

VOL  11.  X.  Diterspecific  Hybridization  in  Nicotiana.  On  the  Results  of  Eackcrossing 
the  F,  Sylvestris-Tabacum  Hybrids  to  Sylvestris,  by  Thomas  Harper 
Goodspeed  and  Roy  Elwood  Clausen.  Pp.  1-30,  12  figures  in  text. 
August,  1922  _ .45 

VoL  12.   1.  Lichenes  a  W.  A  Setchell  et  H.  E.  Parks  in  Insula  Tahiti  a  1922  Collecti, 

scripsit  Edv.  A  Vainio.     Pp.  1-16,  January,  1924 35 

2.  Report  upon  a  Collection  of  Ferns  from  Tahiti,  by  William  A  Maxon. 

Pp.  17-44,  plates  1-6.     May,  1924 45 

3.  Tahitian  Mosses,  Collected  by  W.  A  Setchell  and  H.  E.  Parks,  Determined 

by  V.  F.  Brotherus.    Pp.  45-48.    September,  1924 , 25