KMOENCESUBBARY

/§

I LIBRARY

I I/MTVIRSJTY Of VC

•ERNE5T •DRCMN

BABCOCKI BOOK

Duplicate genes for capsule-form in Bursa bursa-pastoris^.

By George Harrison Shull,

Station for Experimental Evolution, Cold Spring Harbor, Long Island, New York. (Eingegangen am 16. Januar 1914.)

The important discovery of NILSSON-EHLE (1908, 1909) and EAST (1910) that the same apparent or "phenotypic" characteristic may be produced independently by any one of several Mendelian factors which are not allelomorphic to each other, causing the alter- native characters (when dominance is complete) to segregate in the Fa in the ratios 15 : 1, 63 : 1, 255 : 1, etc., has opened the way to a Mendelian interpretation of several classes of phenomena which have been rather generally regarded as non-Mendelian , including the inheri- tance of apparently continuous quantitative differences, the apparent modification of unit-characters by selection, the apparent failure to segre- gate in Fa, and the occasional appearance of atavistic or otherwise aberrant individuals which, because of their recessive character, breed true, and which in consequence have been generally considered mutants.

As these phenomena are in the aggregate of very frequent occur- rence, the availability of this Mendelian interpretation for any consid- erable portion of them must depend upon the correctness of the assumption that such duplication of determiners is also frequent. While this may not seem inherently improbable, the number of fully demonstrated cases of this kind can still be counted on the fingers of one hand, and it becomes a matter of considerable importance to add to this list.

To account for certain ratios which have appeared in the hybrids between Bursa bursa-pastoris and B. Heegeri in respect to the form of

x) Read before the American Society of Naturalists in Cleveland, Ohio, January 2, 1913. Extended to include discussions of more recent literature.

98

Shull.

the capsules, I assumed the existence of two independent factors, C and 7), the presence of either resulting in the development of the triangular type of capsule characteristic of B. bursa-pastoris (SHULL 1911). Owing to a rather large fluctuation in the ratios, the truth of my assumption lacked adequate proof, and it remained at the close of the F3 merely an interpretation having1 a certain degree of probability, like a number of similar assumptions made by other investigators. Complete demon-

Fig. 1. Capsules of fiursa bursa-pastoris (above) and of B. Heegeri.

stration of the duplicate genes, C and D, has now been supplied by the results of an ample F4, as will be seen in the tables given below and in the graphic summary presented in Fig. 5.

The superficial differences between the capsules of B. bursa-pastoris and of B. Heegeri are now familiar to most students, but may be re- called more easily by a reference to Fig. 1. The former have a strongly flattened, triangular or obcordate form due to a spur-like inflation

Duplicate genes for capsule.-fonii in Burtifi burna-pastoris. 99

of the valves, while the capsules of B. Heegeri are not at all inflated, and are in consequence slender top-shaped, being circular in cross- section. The valves of the B. Bursa-pastoris capsule drop off at matu- rity, while those of B. Heegeri remain attached, the seeds of the latter being set free by the rupture of the mid-region of the valves. Associated with these externally obvious differences there are also striking internal differences. The inflation of the valves in B. bursa- pastoris permits the seeds to assume a form determined alone by internal forces, the result being that each seed is a nearly perfect spheroid. In B. Heegeri the seeds are so crowded together that they are forced to assume various angular forms (see fig. 2). There are also important histological differences in the walls of the capsules, as might be inferred from the different behavior of the valves at maturity. In B. Heegeri

A B

Fig. 2. Transverse section of the capsule of Bursa bursa-pastoris (A) and of B. Heegeri (B). X IB. Drawn by J. MARION SHULI, from microtome sections.

the walls of the capsules consist of 6 — 8 layers of relatively small, thin- walled cells, while in B. bursa-pastoris the number of cell-layers is about the same, or perhaps on the average about one less, but the cells in the latter are noticeably larger, and the internal epidermis is modified by a thickening of the cell-walls, so that it forms a single layer of stereome covering the entire interior surface of the valve. It is to this layer of mechanical tissue that the resiliency of the valve is due. There is a definite articulation of the valves to the margin of the dissepiment in B. bursa-pastoris, which is wholly wanting in B. Heegeri (Fig. 3). All of these differences, both external and internal, go together and appear to be the product of a single gene acting in conjunction with the genotypic nucleus (XX}1} which is common to both B. bursa-pastoris and B. Heegeri. It is conceivable that this series of associated char- acters may be due to a system of coupled genes, but this can be demonstrated only by the discovery of individuals in which one or more elements of the complex have become detached from the rest.

*) JOHANNSEN, W., Elemente der exakten Erblichkeitslehre. 1st ed., 1900, p. 304; 2nd ed., 1913, p. 387.

100

Shall.

The reappearance of the Heegeri-type of capsule in only 111 indi- viduals out of a total of 2540 plants in the F2 of crosses between B. Heegeri and an American biotype of B. bursa-pastoris was at first accepted as evidence of a non-Mendelian behavior (SHULL 1907, 1909 b). This ratio, 21*9 : 1, did not approximate so closely the ratio 15 : 1 as to suggest clearly by itself the existence of two determiners for the triangular capsule, and it was not until the appearance of NILSSON-

Fig. 3. Anatomical details of the capsule-wall of Bursa bursa-pastoris (A) and of B. Heegeri (B). X 100. Drawn by J. MARION SHULL from microtome sections.

ELBE'S papers in which duplicate determiners were demonstrated for the presence of a ligula in Avena and for red pericarp- color in Triticum that a similar explanation was recognized as possibly available for the unexpected ratio for capsule-form in Bursa.

The phenomena expected in the first four generations following any cross in which duplicate determiners are involved and in which dominance is complete, may be considered with advantage before proceeding to the

Duplicate genes for capsule-form in Bursa bursa-pastoris.

101

actual results of the experiments. The premise that dominance is com- plete fixes the character of the Fi which will be uniform and indistin- guishable from the dominant parent. The expectation in F2 and F3 in the case of a dihybrid will be rendered clear by a careful study of the checker-board shown in Figure 4. Since the recessive character can appear only when all the duplicate genes are absent, the number of such genes involved in the given cross determines the ratio of dominant

o

i

CD

CD

1

Cd

cD

CD . CD

/ : 0

Cd . CD

c D . CD

r.d . CD

15 : I

Cd

I

CD . Cd

1 : 0

Cd . Cd

I : 0

cD . Cd

/5 : /

3 : I

cD

I

CD . cD

/ : 0

Cd . cD

15 : /

/ : 0

3 : I

\

CD. cd

15:1

3 : I

cD . cd

3 : I

cd .c

0 :

Fig. 4. Checker-board diagram to visualize the genetic relations in a dihybrid F2 family of Bursa bursa-pastoris X Heegeri, in respect to the capsule-characters. The capsules figured in each square indicate by their outline their phenotype, and by their oblique ruling their genotype, the gene C being represented by lines from upper right to lower left, and D from upper left to lower right. Homozygotes are densely lined, heterozygotes more sparsely. The ratios indicate the expectation in F3 when a plant having the genotypic constitution indicated in the same square, is self-fertilized.

102 Shull.

and recessive individuals in the Fz. In the dihybrid this ratio is 15 : 1, iu. the trihybrid, 63 : 1, in the tetrahybrid, 255 : 1, &c., or generally, 4n — 1 : 1, in which u is the number of the duplicate determiners which were present in the germ-cells entering into the cross. The occurrence of one of these ratios in the F2 is the first evidence for the existence of duplicate determiners, and is the only evidence yet available in some of the crosses for which the duplication of identical genes has been adopted as an explanation. As the same ratios may be produced by means other than the repetition of Mendelian determiners, the evidence supplied by the F2 ratio is never conclusive. This fact has been strik- ingly illustrated by the studies of KAJANUS (1912, 1913) with beets and turnips.

The F3 gives a much better criterion and if an adequate number of sufficiently large F3 families is grown, the results will be fairly decisive. This is due to the fact that, while all F2 families from a given cross are the same, F3 families produced by selfing the dominant indi- viduals of the F2 are of n -j- 1 different kinds, i.e., there will be, besides a group of families which contain only the dominant type, as many different ratios in the different F3 families as there were duplicate deter- miners involved in the original cross. The ratios placed in the several squares of Fig. 4 represent the ratios expected in the F3 of a dihybrid, and the reason for the expectation in each case will become clear on consideration of the genotypic formula included in the same square. The ratio 1:0, — the pure breeding of the dominant type, - - occurs when any one or more of the repeated determiners are homozygous. When all of the independent genes for the given character are present, but heterozygous, the F3 ratio will be the same as the F2. When one or more of these genes are absent and the remainder heterozygous, one of the Mendelian ratios lower than that of the F2 will be produced. Thus, in a tetrahybrid which produces in the F2 only families present- ing a ratio of 255 : 1, there will be some families in the F3 which will breed true, others which will repeat the 255 : 1 of the F2, and still other families which will consist of the dominant and recessive types in the ratios 63 : 1, 15 : 1, and 3:1. Not only are all of these five kinds of families due to appear in the F3 of a tetrahybrid, but if the number of F3 families is large enough, the relative number of each of these ratios is definitely fixt in the proportion 175 : 16 : 32 : 24 : 8. In the F3 of a trihybrid some families will breed true, and others will give ratios 63 : 1, 15 : 1 and 3 : 1, in the proportion 37 : 8 : 12 : 6. In the dihybrid the F3 families formed by selfing the dominant individuals

Duplicate genes. for capsule-form in Bursa bursa-pastoris. 103

of the Fo will be distributed as follows: Seven-fifteenths or 46'7 per cent will contain only the dominant type; the remaining 53'3 per cent will split into dominants and recessives, half of the families presenting a ratio 15 : 1 and half having the ratio 3:1; in other words, the three kinds of families will appear in the proportion 7:4:4.

It is obvious that, as the number of the repeated determiners increases, both the number and size of the families which will be re- quired to adequately test the inheritance-ratios, will be rapidly increased beyond the numbers practicable to the experimental breeder. Thus, with no more than four independent genes for the same character, only one individual of the recessive type can be expected in 256 F2 offspring, and by chance a much larger number might readily fail to include a recessive individual, in which case the recessive type would appear to have been completely lost or "swamped". If Fs families were grown from such an F2, 68'7 per cent of those families, or more than two- thirds, would continue to breed true, and only one-fourth would give ratios sufficiently low that families of no more than a hundred or two would be adequate for their discovery. For this reason conclusive results may not be secured in certain cases, without the aid of the F4 or even later generations.

The Fi gives an additional criterion of the duplication of deter- miners, for while every sufficiently large series of Fs families must be distributed among n -j- 1 types with respect to the ratios of dominants and recessives (n being as before the number of repeated genes involved in the original cross), the F4 families will exhibit all of these ratios only when they are derived by selfing dominant individuals in an F$ family which repeated the F2 ratio 4n — 1:1. F± families which are formed by selfing dominant individuals in those F3 families which exhibited the lower inheritance-ratios, can present no instance of the high ratio which characterized all the F2 families and some of the F3 families; and, in general, no hybrid family produced by self-fertilization can contain both dominants and recessives in a ratio higher than that which existed among the sibs of its parent, because the ratio is dependent upon the number of heterozygous genes present, and this number can be decreased but not increased by segregation. The formation of negative homozygotes with respect to one after another of the duplicate deter- miners reduces the tetrahybrid to the trihybrid, the dihybrid, the mono- hybrid, and finally, to the recessive, and the units thus omitted could be regained only by a process of positive mutation, or by some sort of rearrangement of determiners such as is discussed later in this paper.

104

Shull.

The distribution of the two types of capsule in the several gener- ations of hybrids between Bursa bursa-pastoris and B. Heegeri may be considered now in relation to the foregoing theoretical expectations.

The original crosses were made reciprocally in March, 1906, and the hybridized seeds were sown as soon as mature, on April 25, 1906.

In the Fi B. bursa-pastoris X Heegeri (ped. No. 0688) produced about 100 offspring, and B. Heegeri X bursa-pastoris (0689) yielded 23 offspring, all of both families having triangular capsules indistinguishable from those of pure B. bursa-pastoris; that is, dominance is complete, and there is no perceptible cumulative effect of the presence of several determiners as compared with but one.

Six F2 families have been grown, three of which have been reported in earlier papers. On the assumption that the duplicate determiners, C and D, were involved in these crosses, all of these F2 families should have given the ratio 15 : 1. The actual ratios ranged from 16 : 1 to 36'5 : 1, thus in every instance exceeding the expected ratio to a greater or less extent. The detailed results in the several families are presented in the following table:

Table I.

Fed. No. of P,

Ped. No. of Px

Number of bursa-pastoris

Number of Heegeri

Ratio

Percentage dominants

( 06212

507

30

16-9: 1

94-4

0688

| 10446

146

4

36-5 : 1

97-3

1 10447

48

3

10-0: 1

94-1

0689

t 06196 | 06197

179 1743

9

72

19-9: 1 24-2 : 1

95-2 96-0

1 10448

159

7

22-7 : 1

95-8

Total 2782

125

22-3 : 1

95-70

Expected 2725

182

15-0:1

93' 75

Eighteen families have now been grown from self-fertilized bursa- pastoris individuals in the F2, and eleven of these families have been published elsewhere (SHULL 1911). For the sake of completeness the latter are included here with the families more recently grown, in Table II. Owing to the wide range of the ratios and the small number of the families which included both types of capsule, those first eleven families left the question of duplicate genes in doubt, though I believed that the three kinds of families which are expected in the Fa were actually present, their character being obscured by unknown modifying causes, - - possibly selective elimination or selective fertilization. The

Duplicate genes for capsule-form in Bursa bursa-pastoris.

105

additional F3 families which have been grown since, make the case for duplicate determiners much stronger, as will be readily noted in the following table.

Table II.

Fed. No. of P2

Fed. No. of P,

Number of bursa-pastoris

Number of Heegeri

Ratio

Percentage dominants

( 09271

245

—

1:0

100-00

09273

375

—

1:0

100-00

06197

09275 09276

776 474

I

1:0 1:0

100-00 100-00

09281

307

—

1:0

100-00

I 09282

156

—

1:0

100-00

10448

11428

311

—

1:0

100-00 ,

Total 2644

—

1:0

100-00

Expected 2644

—

1:0

100-00

06197

f 09272 I 09274

127

288

2

12

63-5 : 1 24-0 : 1

99-22 96-00

06212

09283

250

16

15-6:1

93-98

10448

f 11426 11430

291 277

22

11

13-2 : 1 25-2 : 1

92-97 96-18

1 11431

293

15

19-5 : 1

95-13

Total 1526

78

19-6:1

95-14

Expected 1504

100

15-0: 1

93-75

06197

09258

— '

1

O'OO : 1

oo-oo

06212

09284

42

9

4'67 : 1

82-35

( 11425

151

40

3-77 : 1

79-06

10448

11427

244

70

3-49 : 1

77-71

' 11429

138

57

2-42 : 1

70-77

Total 575

177

3-25 : 1

76-46

Expected 564

188

3-00:1

75-00

The three kinds of families expected in the Fs are arranged into corresponding groups in this table, and if family 09258 is correctly placed in the third group, as is here done, the numbers of the families in the several groups present the series 7:6:5, the most probable series for eighteen families being 8:5:5.

The families in the first group are expected to breed true in sub- sequent generations, and it was not deemed necessary to test this ex- pectation on an extensive scale, but six F4 families derived from this group were grown incidentally in relation to other problems, and these included in the aggregate 663 B. bursa-pastoris and no B. Heegeri.

Induktive Abstammungs- und Vererbungslehre. XII. g

106

Shull.

The Fs families of the second group, as arranged in Table II, include those which are referable to the expected ratio 15:1, the parents of these families having had both the duplicate genes, C and D, heterozygous. As this was the condition of all the F2 families from which the Fs was derived, the F^ families produced by bursa-pastoris individuals in this group should repeat the conditions found in the Fs, being again distributed among the same three types. Table III includes 27 F4 families derived from this 15 : 1 group of the Fs, and 50 F5 families produced from the corresponding group in F*. No confusion results from tabulating the two generations together in this way, as the expectation is the same in both. If for any reason it should be desired to distinguish between the F4 and Fs families, this may be easily accomplished by reference to the pedigree-numbers.

Table III.

Fed. No. of P8

Fed. No. of P,

Number of bursa-pastoris

Number of Heegeri

Ratio

Percentage dominants

10380

325

—

1:0

100-00

10382

322

—

1:0

100-00

09274

10387

312

—

1:0

100-00

10388

306

—

1:0

100-00

10389

278

—

1:0

100-00

10399

293

—

1:0

100-00

10402

320

—

1:0

100-00

10403

325

—

1:0

100-00

10404

277

—

1:0

100-00

10407

307

—

1:0

100-00

10408

266

—

1:0

100-00

09283

10409

325

—

1:0

100-00

10410

264

—

1:0

100-00

10411

311

—

1:0

100-00

10412

205

—

1:0

100-00

10413

117

—

1:0

100-00

10414

321

—

1:0

100-00

11448

290

—

1:0

100-00

11450

aia

—

1:0

100-00

11451

314

—

1:0

100-00

11453

312

—

1:0

100-00

10398

11456

313

—

1:0

100-00

11457

311

—

1:0

100-00

11458

313

—

1:0

100-00

11462

229

—

1:0

100-00

11463

311

—

1:0 | 100-00

Duplicate genes for capsule-form in Bursa bursa-pastoris.

Table ni (continued).

107

Fed. No.

Fed. No.

Number of

Number of

Ratio

Percentage

of P2

of P±

bursa-pastoris

Heegeri

dominants

11465

104

1:0

100-00

11466

307

—

1:0

100-00

11468

310

' —

1:0

100-00

11470

315

—

1:0

100-00

11472

291

—

1:0

100-00

11477

313

—

1:0

100-00

10398

11478

312

—

1:0

100-00

11479

310

—

1 :0

100-00

11481

305

—

1:0

100-00

11482

309

—

1:0

100-00

11488

126

—

1:0

100-00

11490

216

—

1:0

100-00

11495

282

—

1:0

100-00

Total 11080

—

1:0

100-00

Expected 11080

—

1:0

100-00

10381

287

15

^19-1 : 1

95-03

10385

305

16

19-1 : 1

95-01

09274

10386

278

24 I

114461)

292

22 1

-12-4:,!

92-53

10398

216

21

-10-3:1

91-14

10400

290

22

- 13-2 : 1

92-95

10401

310

15 1

09283

114451)

289

21 I

-16-6: 1

94-33

10405

268

15

-17-9 : 1

94-70

10406

300

22

-13-6:1

93-17

11447

268

20

- 13-4 : 1

93-06

11449

288

27

10-7:1

91-43

11452

304

11

27-6 : 1

96-51

11455

290

24

12-1 : 1

92-36

11459

257

16

-16-1:1

94-14

11461

217

10

-21-7: 1

95-59

11464

289

17

-17-0: 1

94-44

10398

11467

291

21

- 13-9 : 1

93-27

11469

289

24

12-0 : 1

92-33

11480

284

21

• 13-5 : 1

93-11

11484

299

15

- 19-9:1

95-22

11485

298

16

- 18-6 : 1

94-90

11486

294

18

16-3:1

94-23

11487

293

12

-24-4 : 1

96-07

A second sowing from the same lot of seeds used for the preceding pedigree.

108

Shull. Table III (continued).

Fed. No.

Fed. No.

Number of

Number of

Percentage

of P2

of Pj

bursa-pastoris

Heegeri

Eatio

dominants

11489

253

11

23-0: 1

95-83

10398

11492

301

14

21-5: 1

95-56

11494

288

25

11-5 : 1

92-01

11496

305

11

27-7 : 1

96-52

Total 7943

506

15-7 : 1

94-01

Expected 7921

528

15-0:1

93-75

10383

229

75

3-05 : 1

75-33

09274

10384

221

92

- 2-40 : J

70-61

11454

210

72

* 2-92 : 1

74-47

11460

239

72

- 3-32 : 1

76-85

11471

235

79

2-97 : 1

74-84

11473

208

63

- 3-30 : 1

76-75

11474

238

77

^3-09: 1

75-56

10398

11475

235

80

2 94 : 1

74-60

11476

240

71

- 3-38 : 1

77-17

11483

218

59

- 3-69 : 1

78-70

11491

229

51

4-49 : 1

81-79

11493

231

65

.3-55:1

78-40

Total 2733

856

3-19: 1

76-15

Expected 2692

897

3-00:1

75-00

The three expected groups appear among the 77 families in this table with great clearness, there being 39 families in the first or homo- zygous group, 26 in the 15 : 1 group, and 12 in the 3 : 1 group. The expected grouping for 75 families (the nearest multiple of 15) forms the series, 35 : 20 : 20. The deficiency in the third group and the corre- sponding excess in the other two groups may be significant of nothing but the chance variation usually found when we deal with relatively small numbers, though it will be noticed that the third or 3 : 1 group is numerically smaller than the second or 15 : 1 group in all of the three generations, Fs, F4 and Fs, included in Tables II and III. If these generations are thrown together to make a grand total, the series is 46 : 32 : 17, as compared with the nearest expected series 44 : 25 : 25.

It is seen therefore that the F4 and Fs families derived from the 15 : 1 group of the preceding generation, present a complete repetition of the conditions in the Fs, adding to the evidence for duplicate deter- miners nothing new in kind but only in quantity. A new kind of

Duplicate genes for capsule-form in Bursa bursa-pastoris.

109

evidence is made available, however, when we breed from the dominant individuals of the third group of F3 families, namely, from those which are referable to the expected ratio 3:1. This monohybrid ratio indi- cates that one of the duplicate determiners, either C or D, has been omitted, and that the other was heterozygous in the parents of these families. As the omitted gene cannot be reinstated when the dominant members of these families are self- fertilized, there can be no repetition of the 15 : 1 ratio in the F4 or any later generation derived from the 3 : 1 group of families of the preceding generation. Only two kinds of dominant individuals may be supposed to occur in any one of these families, those which are homozygous and those which are hetero- zygous for the single remaining gene, and the F4 families derived by selfing these individuals should likewise be of but two kinds, containing either nothing but bursa-pastoris, or bursa-pastoris and Heegeri in the ratio 3:1. The 39 families included in the following table were all produced by selfing a like number of bursa-pastoris plants in family No. 09284 recorded in the third section of Table II.

Table IV.

Fed. No. of P!

Number of bursa-pastoris

Number of Heegeri

Ratio

Percentage dominants

10420

113

— .

1:0

100-00

10424

112

—

1:0

100-00

10435

108

—

1:0

100-00

10438

110

—

1:0

100-00

10441

110

—

1:0

100-00

11432

149

—

1:0

100-00

11433

261

—

1:0

100-00

11435

315

—

1:0

100-00

Total 1278

—

1:0

100-00

Expected 1278

—

1:0

100-00

10415

79

28

- 2-82 : 1

73-83

10416

82

23

s 3-57 : 1

78-10

10417

85

25

- 3-40 : 1

77-27

10418

80

26

3-08 : 1

75-47

10419

74

38 )

114481)

224

86 1

2-40 : 1

70-62

10421

88

26

3-38 : 1

77-19

10422

75

38

_ 1-97 : 1

66-37

A second sowing from same lot of seeds that produced the preceding family.

110

Shull. Table IV (continued).

Fed. No. Of P1

Number of bursa-pastoris

Number of

Heegeri

Ratio

Percentage dominants

10423

81

28

2-89 : 1

74-31

10425

82

31

- 2-65 : 1

72-57

10426

76

30

- 2-53 : 1

71-70

10427

82

28

-2-93 : 1

74-55

10428

85

25

- 3-40 : 1

77-27

10429

78

31

-2-52: 1

71-56

10430

76

33

2-30 : 1

69-72

10431

80

'30

2-67: 1

72-73

10432 114421)

87 229

23 \

75 J

3-22 : 1

76-33

10433

91

19

4-79 : 1

82-73

10434

73

33

2-21 : 1

68-87

10436

76

30

-2-53 : 1

71-70

10437

80

28

-2-86: 1

74-07

10439

83

26

3-19 : 1

76-15

10440

81

29

2-79: 1

73-64

10442

81

28

^•89 : 1

74-31

10443

65

28

- 2-32 : 1

69-89

11434

134

59

2-27 : 1

69-43

11436

111

43

2-58 : 1

72-08

11437

196

74

2-65 : 1

72-59

11438

218

92

-2-37:1

70-32

11439

220

93

- 2-37 : 1

70-29

11440

81

25

3-24 : 1

76-42

11441

233

75

8-11:1

75-65

Total 3566

1306

2-74 : 1

73-19

Expected 3654

1218

3-00:1

75-00

Again expectation has been fully realized in that the families in this table fall clearly into the two anticipated groups. The highest ratio in the second or heterozygous group is 4'79 : 1 and the lowest 1'97 : 1, and both these ratios are within the theoretical range of families of the size dealt with in these studies and having a chance distribution about the expected ratio 3:1. If the number of families tested were large enough, there should be in the second group twice as may families as in the first group. Of the 39 families here included the expected numbers in the two classes are 13 and 26 respectively instead of 8 and 31 as actually found. In numbers so small as these,

A second sowing from same lot of seeds that produced the preceding family.

Duplicate genes for capsule-form in Bursa' bursa-pastoris. 1 1 1

such a deviation would scarcely call for comment were it not for the rather remarkable circumstance that this deficiency in the number of homozygous dominants almost exactly balances a similar deficiency already reported (SmjLL 1911) in the recessives in the same family, a fact which will be considered more at length below.

The families recorded in the foregoing tables present a considerable range of variation in the percentages of dominants, and the question may arise whether the discontinuity is real, which is implied by their grouping into different sections of the tables accordingly as they are assumed to be theoretically referable to the ratio 3 : 1 on the one hand, or to 15 : 1 on the other; or whether the close agreement of each group, taken as a whole, with the theoretical ratio to which such group is referred, is simply an artefact produced by the association of families so balanced on either side of the expected ratio that their average must closely approximate that ratio. The perfectly continuous series of ratios, 1:1, 2:1, 3:1, 4:1, 5:1, 6:1, &c., may be divided into groups which will average very near to the Mendelian ratios, the first five members of the series having an average of 3:1, the next 20 terms, (from 6:1 to 25 : 1 inclusive) averaging 15*5 : 1, and so on. The dis- continuity in the ratios in my tables is perhaps sufficiently obvious on simple inspection, as there is no ratio between 4*79 : 1 and 10'3 : 1, that is, between 82'83 per cent dominants and 91*14 per cent domi- nants, but the exact significance of the interval can be easily grasped only when the data for the several families are re-tabulated in the form of variation-curves, as is done in fig. 5. Each little square in this figure represents a possible family of Bursa, the position being deter- mined by the percentage of individuals having the triangular type of capsule, as indicated by the schedule of percentages at the base of the figure. The two dotted lines running vertically through the figure represent the position of the two expected percentages, 75 and 93'75. The dark squares are the actual families produced and the radiating arrows represent the lines of descent. In order to separate the groups belonging to the higher ratios the expedient is adopted of decreasing the class-ranges regularly from left to right, each class having a range 0-124 less than the adjacent class to the left. The consequences of this changing class-range will be easily seen in the fact, for instance, that the class in which 75 per cent occurs, extends from 73'86 per cent to 76'34 per cent, a class-range of 2'48 per cent, while the class which contains 93'75 per cent is limited by 93'08 per cent and 94'32 per cent, thus having a range of only T24 per cent, - - exactly half as

112 Shull.

great. That this purely arbitrary method of compensating for the changing basis of comparison in the different ratios, results in no serious amount of distortion and that it is effective and therefore highly satisfactory, may be judged by the fact that all the curves show a' fairly normal distribution of the variates, and that the large groups, distributed about 75 per cent and 93*75 per cent respectively, in each case cover a range of six classes.

It should now be easy to interpret figure 5. On the base line the three Fi families are seen in the 100 per cent class indicating the dominance of the triangular type. From this group a single arrow rises to the F2 group of families, all of which approach the dotted line which marks the position of the 15 : 1 ratio. From this group of F2 families three arrows radiate to the three kinds of families which appear in the Fs, the one on the left approximating the line for the 3 : 1 ratio, the one on the right having only individuals with triangular capsules, and the middle group repeating essentially the ratios of the F2. Each of these three groups of F3 families bears a different relation to the F^, as seen from the arrows ascending from them to the group of families produced by selfing the dominant individuals in the Fs. The 3 : 1 group at the left has but two arrows, as only two kinds of F* families were derived from this group, while the middle group of the Fs, — the 15 : 1 group, - produced three groups of F4 families (shown in the upper series), which are seen to be located directly over the corresponding groups of Fs. Above these F4 groups are still other arrows indicating the relations each group bears to the Fs, this being an exact repetition of the relation between Fs and F4. The discontinuity of the several groups is most strikingly manifest, and can leave no possible doubt as to the fundamental correctness of the method of explanation here adopted.

This does not, however, exhaust the available tests of the hypothesis that there are two independent determiners for the triangular capsule. There still remains the possibility of showing that the extracted homo- zygotes are not all of the same genotypic constitution as the homozy- gotes used in the original crosses, though indistinguishable from them in external appearance. A reference to figure 4 will make the expected differences clear. Although the triangular capsules are all of the same phenotype, they represent five different genotypes which are symbolized in fig. 4 by the formulae CCDD, CCDd, CcDD, CCdd and ccDD and these five types may be expected to occur in the ratios 1:2:2:1:1. Only the first of them, CCDD, is genotypically identical with the original American biotype used in the crosses. In other words, only one in fifteen

Duplicate genes for capsule-form in Bursa bursa-pasloris.

113

Fig. 5.

Resume of ratios found in 142 families in the first five gen- erations following the cross between Bursa bursa-pastoris

and B. Heegeri. For details see text.

114 Shull.

of the bursa-pastoris plants of the F2 will give again the 15 : 1 ratio in the F2 from a new cross with Heegeri, though seven of them will continue to breed true, indefinitely, as long as they are selfed. Only by crossing can the differences among these seven be discovered.

As crossing the Bursas is a rather tedious process, and the results from selfing the hybrids during these five generations have so abundantly demonstrated the method of inheritance of the triangular capsule, I have made no attempt to analyze the extracted dominants, but a new cross made for another purpose has incidentally given proof of the central fact to be expected from such an analysis, namely, that the extracted dominants are not all identical with the original dominant parent in their hereditary behavior. As already indicated, the most satisfactory method of testing these various extracted dominants is to make new crosses between them and the recessive Heegeri. Certain crosses among the extracted dominants themselves would also yield very characteristic results, as, for instance, a cross between CCdd and ccDD, which would produce the original Fi genotype and yield 15 : 1 in the F2. When crossed with Heegeri the extracted dominants from the original F2 should all yield uniform Fi progenies of B. bursa-pastoris, of course, but among every seven extracted dominant plants from the F2 of the original cross,

1 (CCDD) should yield only 15 : 1 ratios in the new F2 families;

I should yield 15:1 in half of the new F2 families

/-v>n,7\ I and 3 : 1 ratios in the other half; and I (2 L>L>Ud) I

should yield only 3 : 1 ratios in the F2 of the new

2 \ and

. cross.

( (ccDD) j I

In crosses between B. Heegeri and extracted B. bursa-pastoris plants from the Fs and later generations of the original cross, the same distribution of dominant and recessive types as represented in the tabu- lation just given, would appear only when the extracted dominants used in the new crosses were themselves included in a family having a 15 : 1 ratio. In families of whatever generation, showing the 3 : 1 ratio, the extracted dominants could be of but one type in any given family; they must be either CCdd or ccDD and these in new crosses with Heegeri would yield only the monohybrid ratio 3:1.

In 1911 a cross was made between an extracted Bursa Heegeri simplex and an extracted B. bursa-pastoris heteris, the latter being

Duplicate genes for capsule-form in Bursa bursa-pastoris.

115

a member of family No. 09281, which is included above in Table IE, and is indicated in figure 5 with a star. With reference to the rosette- characters this cross was the reciprocal of the original cross, which had had the form B. bursa-pastoris simplex X Heegeri heteris, and the new cross was made for the purpose of clearing up some of the questions raised by the original cross with reference to the rosette-characters and not with the intention of further testing the inheritance of the capsule- determiners. As it turned out, this extracted dominant had but a single determiner for the triangular capsule. The first generation (No. 10394) was of the expected type, being entirely B. bursa-pastoris heteris. Four self-fertilizations were made among these Fi plants and yielded Fa families having the characteristics shown in the following table.

Table V.

Bursa Heegeri simplex (abc) X B. bursa-pastoris heteris (ABC) Fed. No. 09284 | Fed. No. 09281

Bursa bursa-pastoris heteris (AaBbO) Fed. No. 10394

Bursa-pastoris Series (€)

Heegeri Series (o)

o

§

SO

I

05

«

=0

o

.f

$

-4— ^3

d a <u a

E

S5j

c

s

'*!>

S5j

PH

1

1

**

§ "9

5

S oa

S

O

£l

11421

135

48

41

13

50

11

10

6

3-08 : 1

75-48

11422

131

31

46

17

48

16

20

4

2-56 : 1

71-88

11423

88

26

27

6

33

9

11

4

2-58 : 1

72-06

11424

109

42

35

14

34

14

12

3

3-17: 1

76-05

Total 463

147

149

50

165

50

53

17

2-84 : 1

73-95

Expected 461

154

154

51

154

51

51

17

3-00 : 1

75-00

Results from original cross:

Total 624

173

202

48

30

8

9

1

21-89: 1

95-63

Expected 577

192

192

64

39

13

13

4

15-00:1

93-75

In the last line of this table is inserted for comparison the summary of the results in the second generation from the original cross, reduced to the same number of individuals. The agreement between the ex-

116 Shull.

•

pected and the actual numbers in the F2 from the new crosses is much closer than in the original F2, largely due, I believe, to the fact that we have continued to learn how best to meet the cultural requirements of the plant. In the recent cultures nearly every individual could be classified, while in the earlier cultures the plants became diseased after growing long under unnatural conditions, and many died unclassified. Our present interest lies in the frequency of occurrence of the two kinds of capsules; the rosette -characters are given in the table only for the purpose of completing the parallel with the previously published results of the original F2. They serve, however, to demon- strate again the complete independence of the capsule-characters from the leaf-characters. It is seen that, with respect to the capsules in all four families of the new F2, the agreement with the monohybrid ratio is striking, whereas the original F2 showed in each family an approximation to the ratio 15 : 1.

Discussion.

We have seen that considerable departures from the expected ratios have appeared in many of the families, and yet, that in every test the essential features required by the assumption that there are two independent determiners for the triangular capsule have been strikingly manifest. I take it, therefore, that this hypothesis must be in a general way correct, although the deviations in the ratios have raised other questions which will need still further investigation for their definite solution.

The deviations from the expected ratios chanced in F2 and Fs to be all in the same direction, indicating in every family a deficiency in the number of individuals of the Heegeri type, and two hypotheses were suggested (SHULL 1911) as possibly accounting for this condition, namely,

(a) that B. Heegeri is a constitutionally weaker type and that in con- sequence there is a differential elimination of plants of this type; or

(b) that there is a selective mating in which the union of unlike gametes is favored.

In the F4 and F5, however, the Heegeri plants have been in excess of expectation about as frequently as they have been deficient. This result might seem to dispose of the first of the two hypotheses, - - the one which I thought the more probable, — for if the Heegeri type were much weaker at an early stage of its development, than the bursa- postoris type, we might expect that there would always be a deficiency in the number of Heegeri plants reaching maturity. This would be an

Duplicate genes for capsule-form in Bursa bursa-pastoris. 117

obviously correct inference were it not for the fact, already mentioned, that our cultural treatment of Bursa has become much more successful. Elimination after germination has been almost completely conquered; at any rate it has been reduced until it has become a nearly negligible factor. The fact that these later generations have given a nearly normal distribution of the ratios may consequently be taken as strongly supporting the hypothesis that the deficiency of Heegeri plants in the earlier cultures was due to selective elimination. The cause for the elimination was probably not, however, as was assumed, the constitu- tional weakness of the Heegeri type, but only its longer period of vege- tative development. There has been in general an excess of the bursa- pastoris type among the plants first coming to bloom and a corresponding excess of Heegeri among the plants last to bloom. This relation will l>e considered more in detail on another occasion. It need only be pointed out here that if cultures which have stood for a long time in the greenhouse become unhealthy from the attacks of insects or fungous pests, or from the cumulative effects of any unfavorable conditions of the environment, the more slowly developing plants will suffer most; and if many die from such causes without having fruited, there would result just the differential elimination necessary to explain the deficiency of Heegeri plants in the injured families.

While at first sight this seems to be an adequate explanation 'of the deficient ratios, there are indications that this may not be the whole story. The elimination of a disproportionate number of Heegeri plants should have no influence on the composition of the bursa-pastoris portion of the same family. In the case of a monohybrid family this would mean that one-third of the bursa-pastoris plants would be homozygous and two-thirds heterozygous, regardless of the deficiency in the number of recessives present. The only monohybrid family (No. (59284) in the Fs from the original cross, consisted of 42 bursa-pastoris and 9 Heegeri or 4'67 : 1. An attempt to test the constitution of all the bursa-pastoris individuals in this family by selfing them, was successful in the case of 39 of them, and these 39 were shown by their progenies (Table IV) to have consisted of 8 homozygotes and 31 heterozygotes, instead of the 13 homozygotes and 26 heterozygotes that were to be expected. It is thus seen that this F3 family (No. 09284) really presented a ratio approximately 1:4:1 instead of 1:2:1.

The fact that the deficiency in the recessive class is ^balanced by a similar deficiency in the number of homozygous dominants may be merely a coincidence, of course, this possibility being rendered

118 Shull.

the more probable owing to the small size of the family. If not a mere coincidence, the ratio 1:4:1 suggests the possible correctness of my second original hypothesis, namely, that there may have been here a case of differential mating in which the union of unlike gametes was favored. If this were correct, the evidence from this one family would indicate that a sperm carrying the bursa-pastoris character is twice as likely to fertilize an egg lacking that character, as an egg having it, and vice versa, that sperms bearing only the Hecgeri determiners will fertilize twice as many bursa-pastoris eggs as Heegeri eggs. There is one serious obstacle in the way of this expla- nation of the ratio 1:4:1; among the numerous hybrid families in F2 there were a number of families in which the excess of Heegeri individuals beyond the expected 25 per cent was quite as striking as was their deficiency in the families of the second and third generations. An attempt is being made to analyze the dominant groups of some of these families in order to determine whether in those cases in which there was an excess of Heegeri, there was also a corresponding excess of homozygous dominants.

The same fact also stands in the way of another possible inter- pretation of the 1:4:1 ratio: If the heterozygous class were always in excess of expectation, it might be assumed to be due to the physio- logical superiority of the heterozygous individuals over the homozygous, owing to the stimulating effect of heterozygosis. - - a phenomenon now generally recognized. The homozygotes, being weaker, would be elimi- nated in greater measure than the stronger heterozygotes, and it would not be strange that an elimination on this basis should be about equal in both positive and negative homozygotes. Also against such a hypoth- esis, however, is the fact that Bursa is normally self-fertilizing, and that the hybrids are consequently not as a rule markedly superior to the pure types; it is difficult to conceive of their elimination to the extent required by the ratio 1:4:1.

There remains a fourth possibility, namely, that there is some degree of "linkage" of determiners, resulting in partial "coupling" in some families, balanced by a corresponding "repulsion" in other families. All of these hypotheses need further experimental study, and further dis- cussion of them will be postponed until more data is at hand.

The phenomenon of plurality of genes having a similar function, i.e., independently producing the same character, is called by LANG- (1911) "polymery" and by PLATE (1913) "homomery". JOHANNSEN (1913) suggests that both these terms be retained, the former for the

Duplicate genes for capsule-form in Bursa bursa-pastoris. ]19

phenomenon in general, the latter for those cases in which there is complete dominance and no cumulative effect produced by the presence of several genes for the character in question, as compared with the presence of but one. To the genes themselves which independently produce the same or similar effects, LANG applies the name "genomeres". The demonstration of the phenomenon, or rather the phenomena, which have suggested these new words, marks an important advance in genetic progress, because it has led to a fairly well grounded Mendelian interpretation of inheritable quantitative characters, which have often been cited as offering fundamental exceptions to the Mendelian principles. There is some danger, however, that this assignment of names will give a wrong impression as to the nature and unity of the phenomena for which they have been suggested. The fact must never be lost sight of that the real nature of the genes is purely inferential, since we can know nothing of them except through the morphological or physiological effects which they produce. Two determiners producing or affecting a given character may be identical, slightly different, or profoundly different, from each other, and the question is likely to arise over and over again as to whether any given character represents a case of polymery or not. Thus, we may assume, merely as an illustration, that a plant has its number of internodes determined by a Mendelian gene N and the length of the internodes by another independent determiner L. Are these to be considered "genomeres" in the sense of LANG? One can scarcely think so, and yet these two elements make up the height of the plant in question, and plant -height is one of the characters for the expla- nation of whose hereditary behavior polymery has been assumed1)! Or are we to speak of "polymery" only when the effects of the

*) The reader is also urged to read the valuable paper by HAGEDOOKN (1914) which appeared after the present paper was in press. No change has been made in the present paper except the inclusion of HAGEDOOEN'S paper in the references, and the addition of this footnote. It will be seen that my views and HAGEDOOEN'S are in complete harmony; on a number of points there is a close parallel between his discussion of plural determiners and mine. There are several points, however, in which I do not fully agree with him. I see no good reason, for instance, for abandoning the use of the expression "unit-characters", nor for giving up the system of symbols for the genes, which suggests, whenever it can be conveniently done, some characteristic reaction in which the gene in question takes a critical part. The abandonment of this method tends to make the results of genetic research more inaccessible. With proper emphasis upon the real relation between the determiners and the unit-characters, the suggestive symbol can lead to no more serious misapprehension than that which results from the use of any symbol whatever.

120 Shull.

individual genes have not been identified? To avoid confusion from this inability to decide whether in any case we are dealing with poly- mery or not, I will distinguish in what follows, between "duplicate" determiners and "plural" determiners for any given character. These two terms must still be understood as making absolutely no assumption regarding the nature or identity of the genes themselves. By "dupli- cate" determiners I understand those which, when separated from each other, produce characters so like that they can not be distinguished from one another; e. g., if P and R are duplicate determiners and XX the residual genotypic "nucleus", then XXPPrr will be indistinguishable from XXppBR and from XXPpEr. By "plural" determiners I shall indicate two or more genes which independently produce a given character, or which, modify it in any way whatever, which does not de- stroy its identity. "Plural" determiners thus also include "duplicate" determiners, of course. In this sense the above mentioned hypothetical genes, N and L, for the internode-number and internode-length, respec- tively, are "plural" genes for plant-height, though by no means "duplicate" genes. This distinction has not been clearly made by writers who have discussed the Mendelian inheritance of quantitative characters, and as such discussions have invariably taken as their point of departure, cases in which duplicate determiners have been demon- strated, there has always been a more or less obvious implication, if not a direct statement, that in the inheritance of these various quanti- tative characters, duplicate determiners are involved.

The consequences which result from the existence of duplicate determiners for single characters, have been so well discussed by NILSSON-EHLE (1908, 1909, 1911), EAST (1910, 1912), LANG (1910, 1911), EMERSON and EAST (1913) and others, that it may suffice to indicate here the characters for which duplicate determiners, or at least plural determiners>>/have been demonstrated (in full-faced type), and those incompletely analyzed characters for which, as a sequel to the discovery of duplicate determiners, a plurality of Mendelian genes has been assumed to exist. The following list is believed to be fairly com- plete for the cases in which relevant data are given, or definitely re- ferred to. In some of the more enthusiastic statements regarding the importance of plural Mendelian genes, suggestions of their applicability to other cases have been made, as, e. g., in EAST'S interpretation (1912) of hybridization phenomena in Oenothera, but such cases are not here included.

ADD: which according to present evidence appear to b© duplicate,

Duplicate genes for capsule-form in Bursa bursa-pastoris. ^ 121

Plants.

Avena saliva (oats) : —

Black color of glumes (Nilsson-Ehle 1908, 1909)

Presence of a ligula »

. ,, (Nilsson-Ehle 1909)

Paniculate inflorescence

Hairiness of glumes (Nilsson-Ehle 1908, von Tschermak 1911)

Length of glumes

Number of flowers per spikelet

Weight of grains

(Nilsson-Ehle 1908)

Height of stem Width of leaves Vegetative period,

i.e., time of ripening (Nilsson-Ehle 1908, 1911b) Beta vulgaris (beet) : — Length of root

Form of root ( .„ .

(Kaianus Yellow root -color

Red root -color Brassica napus (Swedish turnip):—

Red root-color (Kajanus 1912b)x) Brassica rapa (turnip): —

Length of root (Kajanus 1912b)1) Bursa bursa-pastoris (shepherds purse): —

Triangular form of capsule (Shull 1911a, 1914)

go r damn eativuro (barley ):-

Abortion cf craine ("Sch&rti^keit" ) (johanneen 1913).

Linum crepitans

Linum usitatissimum (flax): —

Length of seeds (Tammes 1911, 1913, Johannsen 1913)

Length of petals

Width of petals /m

(Tammes 1911, 1913) Color of flowers

Dehiscence of capsules

r) KAJANTTS presented much data from the F2 families in support of the view

that each of these characters is in certain cases independently produced by two or more

Mendelian genes. In a later study, however, (KAJANUS 1913) he entirely abandons this interpretation.

Induktive Abstainmungs- und Vererbungslehre. XH. 9

120 Shull.

individual genes have not been identified? To avoid confusion from this inability to decide whether in any case we are dealing with poly- niery or not, I will distinguish in what follows, between "duplicate" determiners and "plural" determiners for any given character. These two terms must still be understood as making absolutely no assumption regarding the nature or identit}r of the genes themselves. By "dupli- cate" determiners I understand those which, when separated from each other, produce characters so like that they can not be distinguished from one another; e. g., if P and R are duplicate determiners and XX the residual genotypic "nucleus", then XXPPrr will be indistinguishable from XXppER and from XXPpEr. By "plural" determiners I shall indicate two or more genes which independently produce a given character, or which, modify it in any way whatever, which does not de- stroy its identity. "Plural" determiners thus also include "duplicate" determiners, of course. In this sense the above mentioned hypothetical genes, N and L, for the internode-number and internode-length, respec- tively, are "plural" genes for plant -height, though by no means "duplicate" genes. This distinction has not been clearly made by writers who have discussed the Mendelian inheritance of quantitative characters, and as such discussions have invariably taken as their point of departure, cases in which duplicate determiners have been demon- strated, there has always been a more or less obvious implication, if not a direct statement, that in the inheritance of these various quanti- tative characters, duplicate determiners are involved.

The consequences which result from the existence of duplicate

lur wiucn uupiiuatt; utJteriiiiiiers, or at least plural determinersVhave been demonstrated (in full-faced type), and those incompletely analyzed characters for which, as a sequel to the discovery of duplicate determiners, a plurality of Mendelian genes has been assumed to exist. The following list is believed to be fairly com- plete for the cases in which relevant data are given, or definitely re- ferred to. In some of the more enthusiastic statements regarding the importance of plural Mendelian genes, suggestions of their applicability to other cases have been made, as, e. g., in EAST'S interpretation (1912) of hybridization phenomena in Oenothera, but such cases are not here included.

ADD: which according to present evidence be duplicate.

Duplicate genes for capsule-form in Bursa bursa-pastoris. _ 121

Plants.

Avena sativa (oats) :—

Black color of glumes (Nilsson-Ehle 1908, 1909)

Presence of a ligula }

. ,, (Nilsson-Ehle 1909)

Paniculate inflorescence J v

Hairiness of glumes (Nilsson-Ehle 1908, von Tschermak 1911)

Length of glumes

Number of flowers per spikelet

Weight of grains

(Nilsson-Ehle 1908)

Height of stem Width of leaves Vegetative period,

i.e., time of ripening (Nilsson-Ehle 1908, 1911b) Beta vulgaris (beet): — Length of root

Form of root , .„ .

(Kaianus 1912 a)1) Yellow root -color

Red root -color Brassica napus (Swedish turnip): —

Red root-color (Kajanus 1912b)1) Brassica rapa (turnip):—

Length of root (Kajanus 1912^*) Bursa bursa-pastoris (shepherds purse):—

Triangular form of capsule (Shull 1911a, 1914) Cucurbita Pepo (gourd): —

Size of fruit > ,„

, (Emerson 1910)

Shape of fruit I

Linum angustifolium

Linum crepitans

Linum usitatissimum (flax): —

Length of seeds (Tammes 1911, 1913, Johannsen 1913)

Length of petals

Width of petals ,m 1nin In10,

« , . „ \ (Tammes 1911, 1913)

Color of flowers

Dehiscence of capsules

1) KAJANUS presented much data from the F2 families in support of the view that each of these characters is in certain cases independently produced by two or more Mendelian genes. In a later study, however, (KAJANUS 1913) he entirely abandons this interpretation.

Induktive Abstammungs- und Vererbungslehre. XII. 9

122 Shull.

Nicotiana Tabacum (tobacco)1): —

Number of leaves ^ (Hayes 1912, Hayes, East and Height of stem j Be in hart 1913)

Length of leaf i

Breadth of leaf (Hayes, East and Beinhart 1913) Area of leaf

Oenothera (Evening primrose):—

Red veins of leaves (Heribert-Nilsson 1913)2) Phaseolus vulgaris (bean): —

Length of seeds ,

^.v:, , i (Emerson 1910, Johannsen 1913)

Width of seeds J

Thickness of seeds ^

^ . , , , \ (Emerson 1910)

Weight of seeds /

Pisum sativum (pea):—

Time of flowering3) (von Tschermak 1911, 1912) Stizolobium (Lyon beans, velvet beans):—

Size of pods j

Size of seeds I (data of Belling) (Emerson and East 1913)

Time of flowering | Triticum vulgare (wheat) : —

Red grain-color

Length of internodes, (Nilsson-Ehle 1908, 1909, 1911 a)

i.e., density of heads | Beardlessness (Nilsson-Ehle 1908)

Glume-color ^

(Nilsson-Ehle 1909) Height of stem J

Resistance to yellow rust

(Puctini'a glumarum (Nilsson-Ehle 1908, 1911a)

1) GOODSPEED (1912, 1913) has demonstrated a notable increase in variability of flower-size in the F2 of certain tobacco-hybrids, but refuses to ascribe this greater variability to Mendelian segregation.

2) HERIBERT-NILSSON assumes that practically all the genetic phenomena of Oeno- thera may be explained on the basis of plural Mendelian determiners, but gives no relevant data except for the red nerves of one of his mutant forms. To one who is familiar with the genetic phenomena in Oenothera his conclusions in this regard must appear premature.

8) KEEBLE and PELLEW (1910) have also interpreted the inheritance of time of flowering as well as height of plants of Pisum on the basis of several Mendelian deter- miners affected by partial coupling, but assign definitely diverse functions to these several determiners.

Duplicate genes for capsule-form in Bursa bursa-pastoris. _ 123

Resistance to cold,

i. e. wintering-capacity (Nilsson-Ehle 1908, 1911 b) Vegetative period,

i. e. time of ripening (Nilsson-Ehle 1911b) Zea Mays (maize):—

Yellow endosperms (East 1910, East and Hayes 1911)

Blue aleurone (East and Hayes 1911, East 1912)

Red pericarp (East and Hayes 1911, Emerson and East 1913)

Dent vs. flint endosperms (East and Hayes 1911)

Size of grains (Emerson 1910)

Breadth of grains (Emerson and East 1913)

Weight of grains (East 1911, Emerson and East 1913)

Number of rows on the ear (East 1910, 1911, Shull1) 1910, 1911b,

East and Hayes 1911, Emerson and East 1913) Length of ears (East and Hayes 1911, East 1911, Emerson

and East 1913)

Diameter of ears (Emerson and East 1913) Height of stalks (Emerson 1910, 1911, East and Hayes 1911,

Emerson and East 1913) Nuinber of stalks Total length of stalks Number of nodes per stalk Length of internodes Vegetative period, i. e. time of

flowering or ripening

Animals.

Anas (duck):—

Body-weight (Phillips 1912) Oallus (domestic fowl): —

Fecundity (Pearl 1912) Homo sapiens (man): —

Skin-color (Davenport 1910, 1914, Lang 1911) Lepus (rabbit): —

Ear-length (data of Castle) (Lang 1910, Walter 1913)

Size of body (data of Mac Do well) (East 1912)

*) I did not interpret the increased F2 variability in the number of rows as due to the segregation of plural determiners for row-number, but as the result of segregation of Mendelian characters iiigeneral, resulting in different degrees of heterozygosis and consequently in different degrees of heterozygotic stimulation. See text.

124 Shull.

J\fus musculus (mouse): —

Piebald coat-color (Cuenot 1907, Lang 1911) Mus rattus (rat): —

Hooded coat-pattern (data of Castle) (East 1912, Johannsen 1913, Hagedoorn 1914).

Until the plural determiners for any characteristic have been iso- lated in different individuals, the actual similarity or difference of the characters they produce and the method of their inheritance can not be demonstrated. For all cases in which such analysis has not been made the existence of plural Mendelian determiners must be purely hypothetical; nevertheless, in the absence of other adequate interpreta- tions for the phenomena recorded by these investigators, the existence of plural Mendelian determiners should be accepted as a plausible work- ing hypothesis.

Granting the existence of such plural determiners, what is the likelihood that any of them are also duplicate determiners? There is no reason to suppose that a larger proportion of the independently in- heritable factors of size, form, etc., are really duplicate, than of those more easily analyzed characters whose Mendelian inheritance has now been fully demonstrated. How many thousands of characters of various kinds have been proved to follow the Mendelian method of inheritance, I do not know, but certainly the four cases of fully demonstrated dupli- cation of determiners represent an insignificant proportion of these, and would, therefore, by themselves form an extremely slender basis on which to rest the thesis that quantitative characters are generally Mendelian in inheritance. It is only because such general features as size and form and such physiological relations as length of vegetative period and resistance to disease or to cold, may rest upon many quali- tatively as well as quantitatively different elements, each of which may be controlled, conceivably, by one or more Mendelian determiners, that the hypothesis of the Mendelian inheritance of these features becomes adequate. It ought to be emphasized, therefore, (1) that although, historically, the Mendelian interpretation of the inheritance of size- differences and of complex physiological capacities and activities has been developed as a result of the discovery of duplicate determiners, it need not have awaited that discovery, and (2) that this historical connection must not be taken to indicate that the elements which make up these complex characteristics, or the genes which produce or control them, are in any case of duplicate nature, - - although, on the other

Duplicate genes for capsule-form in Bursa bursa-pastoris. 125

hand, the possibility that they are sometimes duplicate (shall we say once in a thousand times?), is not to be overlooked.

The theoretical and practical importance of the conclusions drawn from these studies on quantitative characters makes it essential that the evidence be made as impregnable as possible. The extreme diffi- culties to be overcome in the attainment of a fairly complete and de- cisive demonstration of the manner of inheritance of such characters are a challenge for a great deal of intensive work on some single, easily handled quantitative character, with perfectly controlled individual anal- ysis through as many generations as may be required. In anticipation of such future work, and without calling into question the correctness of the conclusions arrived at by any of the investigators whose work has been included in the above list, it may not be out of place to point out several weaknesses in the evidence upon which the conclusions have been based, in order that future work along these lines may be strengthened.

For a considerable portion of the characters listed in the above table the only evidence yet available that Mendelian segregation has taken place, is the greater variability of the F2 compared with the parent strains and their Fi hybrids. Sometimes there 'is added a small amount of evidence that the Fs families are significantly differentiated. CASTLE (1912) maintains that other explanations of this increased varia- bility in the F2 are possible. This ought to be granted, but the rather vague hypothesis actually offered by CASTLE as an alternative seems far less plausible than the hypothesis of segregation of plural Mendelian determiners.

Already in 1906, JOHANNSEN gave, by a comparison of coeffi- cients of variation, a full demonstration of the fact that the variability of the Fi in regard to several quantitative characters was of the same order as that of the parents. He also expressed the view, based upon some preliminary experiments in the greenhouse, that segregations of size-characters were represented in the second generation hybrids from his "pure-line" beans. The author (SKULL 1910) was perhaps the first to actually bring an F2 coefficient of variability into comparison with the coefficients of variability of the parent strains and of their Fi hy- brids, thus giving adequate mathematical proof of the increased varia- bility of an apparently continuous quantitative character in the F2.

This greater variability was definitely referred, in my paper, to the segregation of numerous hypothetical Mendelian determiners; but these were not assumed to be plural determiners for the particular character then being studied, namely, the number of rows of grains on

126 Shull.

the ears of maize, but for all the characters, internal as well as exter- nal, by which the parents had been differentiated. My investigations on the effect of cross and self-fertilization in maize, had led me as early as 1907 to the conclusion that the decreased vigor which appears when a normally cross-bred plant is selfed, is a counterpart of the increased vigor long known to result when species or varieties not too remotely related to each other are hybridized (SHULL 1908). In other words, hybridity itself, - - the union of unlike elements, the state of being heterozygous, — has, according to my view, a stimulating effect upon the physiological activities of the organism, which effect disappears as rapidly as continuous breeding reduces the progenies to homozygous types. There can be little doubt of the general validity of my conclu- sions in this regard, completely supported as the have been by my own continued work (SHULL 1909 a, 1910, 1911a) and by the splendid researches of EAST (1909, 1911), EAST and HAYES (1912) and others. Here again as in the case of plural determiners, there is some danger of misconception due to the fact that all discussions of the stimulus of hybridity have taken as their starting point, for the sake of simplicity, the typical Mendelian distribution of the germinal sub- stances. The essential features of the hypothesis may be stated in more general terms, as follows: The physiological vigor of an organism, as manifested in its rapidity of growth, its height and general robust- ness, is positively correlated with the degree of dissimilarity in the gametes by whose union the organism has been formed; In other words, the resultant heterogeneity and lack of balance produced by such differences in the reacting and interacting elements of the germ-cells act as a stimulus to increased cell-division, growth, &c. The more numerous the differences between the uniting gametes, — at least with- in certain limits, — the greater, on the whole, is the amount of stimu- lation. These differences need not be Mendelian in their inheritance, although in most organisms they probably are Mendelian to a prevailing extent. It is not improbable that the same phenomenon is manifested also in some cases as a result of interaction between the Mendelian genes (and the non- Mendelian genes, if such be present) of the male nucleus, and the elements of the egg-cytoplasm which it enters in the process of fertilization, as emphasized by A. F. SHULL (1912), but it seems unlikely that an initial stimulation of this kind can account for any large part of the increased vigor which is maintained throughout all subsequent development; if the continued stimulation which is mani- fested by hundreds or even thousands of clonal generations, be attributable

Duplicate genes for capsule form in Bursa bursa-pastoris. 127

in more than very slight degree to the fact that the sperm-nucleus was. introduced into a new cytoplasmic environment, the permanence of that cytoplasmic environment and its freedom from modification by the nuclear elements which are so intimately associated with it, are more complete than is generally believed.

This stimulation or increased metabolic activity due to the dif- ferences in uniting gametes, is a purely physiological phenomenon and is of very widespread occurrence, but need not be universally mani- fest because, when differences between the gametes become too numerous or too great, sterility or even complete incompatability may result, and in any particular case the expected stimulation may be more than counterbalanced by the specific action of some depressing or in- hibiting factor or combination of factors. To avoid the implication that all the genotypic differences which stimulate cell-division, growth, and other physiological activities of an organism, are Mendelian in their inheritance, and also to gain in brevity of expression, I suggest that instead of the phrases, "stimulus of heterozygosis", "heterozygotic stimulation", "the stimulating effects of hybridity", "stimulation due to differences in uniting gametes", etc. which have been used by myself and others, the word "heterosis" be adopted1). The corresponding ad- jective "heterotic" may also be useful in such expressions as "heterotic effects", or "heterotic stimulation", - - the latter expression being synonymous with "heterosis".

Returning now to the bearing of this phenomenon on the increased variability of the F2 as compared with pure types and their Fi-hybrids: In the pure types there is no "heterosis" or stimulating effect of hetero- zygosis and in the Fi where this stimulation is at its maximum, it is the same in all the individuals and consequently can have only an indirect effect (if any) upon variability2). In the F2 on the other hand,

x) The word "heterozygosis" has been occasionally used for this "stimulus of hybridity", but it should not be considered available for such restricted usage even by those who hold that all inheritance is essentially Mendelian, for the reason that, as used by its originator, Dr. SPII.LMAN, and also as rather generally used in genetic literature, the word "heterozygosis" signifies only the state of being heterozygous.

2) It is conceivable that a vigorous plant may be less susceptible than a weak one to certain variations in the environment, and if this be time in any case, the varia- bility (fluctuation) will be indirectly decreased in that case by heterosis. On the other hand, there is at least one simple way in which variability can be indirectly increased by heterosis, especially in regardwfc to repeated organs. A highly heterotic plant, for instance, because of its unusual vigor may develop branches from buds which in a weaker plant would remain dormant. The foliar or floral organs borne by such

128 Shull.

the segregation of Mendelian characters produces some pure homo- zygotes and some individuals which have as many heterozygous elements as there were in the Fi individuals, i. e. there are some un- stimulated individuals and some which are highly stimulated, as well as individuals having all intermediate degrees of stimulation. The phenomenon of heterosis alone, therefore, in so far as it arises from Mendelian differences, will cause an increased variability in size-relations in the F2 as compared with the Pi and the Fi generations.

Furthermore, those F2 individuals which owe their differences of size and form to their different degrees of heterosis, will yield Fs families also showing different average heights or different average sizes of any organ which may be under consideration, because such families will possess different average degrees of stimulation. Such F3 families thus exhibit apparent differentiation in size-characters wholly aside from the existence and segregation of specific size-determiners. That some of these differ- entiating genes whose heterozygous condition stimulates to greater physiological vigor are specific modifiers of size, form or function of the organism, or of one or more of its parts, is extremely probable, / — ^ut this fact can be demonstrated beyond question only by comparison among extracted homozygous types.

In most of the work on increased F2 variability, the facts here stressed seem to have been left entirely out of account, namely, that every criterion given for the segregation of continuously variable size- characters, is also produced, to a certain extent at least, by heterosis from Mendelian determiners which, in their homozygous condition, are not necessarily productive of size-differences. Only in one instance have I found any mention of these particular effects of heterosis, HAYES, EAST and BEINHAKT (1913, p. 55) having recently assigned them as a reason why "the coefficient of variability is not a very safe criterion by which to judge when dealing with a character such as area of leaves."

That the occurrence of heterosis increases the difficulty of genetic analysis of size-characters in another way, namely, by throwing the stimulated individuals into size-classes in which they would not belong if not thus stimulated, has been recognized by several investigators, particularly by EAST and HAYES (1911), HAYES (1912) and EMERSON and EAST (1913) and these authors have for this reason laid stress on certain cases in which the Fi hybrids do not exceed the average of

branches may differ from those on the branches which usually develop. The increased variability in flower-size in GOODSPEED'S (1912, 1913) F1 Nicotiana-liybrids may perhaps be accounted for in this way.

Duplicate genes for capsule-form in Bursa bursa-pastoris. 129

the two parents in respect to the particular character under consider- ation, on the assumption (in some cases specifically stated) that such a character is not affected by heterosis. The intermediacy of a char- acter in the Fi does not prove, however, that heterosis has no effect upon this particular character, especially when the parent stocks are complex hybrid material like maize. In such material, the size any organ whould have if all the determiners possessed by the given indi- vidual were homozygous, is unknown, and consequently there is no secure basis on which to predict the purely genetic (unstimulated) con- dition of such a character in the Ft, from its stimulated condition in the parents. For example, because the length of ears in the Fi from a cross between Tom Thumb pop-corn and Black Mexican sweet-corn is intermediate between the ear -lengths of the parents, EAST and HAYES (1911 p. 124) say that "ear-length does not show the increased vigor due to heterozygosis that is seen in the heights of plants." The two parents were in this case grown from commercial seed and were both undoubtedly in a complex condition. These authors may have intended to say merely, that the effect of heterosis is not as obvious in ear-lengths as in height of stems, for EMEESON and EAST (1913, p. 40) in discussing the same cross state that ear-length in maize "is not affected by heterozygosis to as great a degree as height, although some effect may be traced" *). In my crosses among nearly homo- zygous strains of maize, there were always a great increase in ear- length in the FI, and decreasing ear-length in subsequent generations, showing that, at least in some cases, ear-length is markedly subject to increase by heterosis.

An increased F2 variability following an intermediate average value in Fi might result from the bringing together of as few as two Mendelian genes affecting different elements in the given character, the one acting in a positive direction, the other in a negative direction, and the dominance or lack of dominance would be immaterial, so long as the effects of the genes in question were slight compared with the fluctuations of the same character. Thus, if a plant possessing a partial inhibitor or reducer of internode-number be crossed with another plant having a stimulator for internode-length, all the other genes being the same in the two cases, the height of the Fi plants would be inter- mediate between the heights of the parents, with variability due alone to fluctuation, as it is in the homozygous parents. The F» would show

1) Italics are mine.

130 Shull.

increased variability and this increase would appear greater if the two differentiating genes were dominant, than if dominance were absent. This being the case, the point may be emphasized that the mere demon- stration of an increased variability in F2 does not by itself prove either that several genes of similar nature are involved, that their dominance is lacking, or that all the inheritable size-differences between the Pi individuals are Mendelian, though it does render probable the one essential point, namely, that a Mendelian segregation of some sort has taken place. The latter conclusion is all that has been specif- ically maintained in many cases in which an increased variability has been found in the F2 and the matter is emphasized here only because the impression might be gained that every demonstration of increased variability in F2 supports the several assumptions which have been made in the development of the Mendelian explanation of inheritable quantitative differences.

Attention may be called also to a purely technical manner in which F2 variability coefficients may be increased. In a number of characters in respect to which the F2 families of maize (EAST and HAYES 1911) have been reported more variable than the Fi , the data for the parents and the F2 generation are in each case derived from the progeny of a single mother-plant, while the data for the F2 are given for the com- bined progenies of 2 — 5 plants. There is no proof given in these cases that the parents and their Fi hybrids were not as heterogeneous as the F2. As the parents were certainly not homozygous some segregation must have taken place in the Fi as well as in the F2, so that an Fi progeny grown from a number of ears corresponding with the number used for the F2 should have shown a larger Fi variability than is re- ported. Consequently in these cases a proper comparison can not be made between the variability of the several generations. It is a pleasure to note, however, that most of HAYES'S data for tobacco (HAYES 1912) and all of EMERSON and EAST'S (1913) excellently handled data for maize, have been derived from strictly individual analyses, and as the results in these cases are not materially different from those reported earlier by EAST and HAYES, it is obvious that the general results of the latter investigators, although in part due to unequal treatment of the several generations, will not on this account need a revision. In supporting the thesis, that near-homozygous types have appeared in the F2, by a comparison of F3 coefficients of variability with the Pi and Fi coefficients, it is likewise important that the several generations to be compared be given like treatment. There should be as many tests of

Duplicate genes for capsule-form in Bursa bursa-pastoris. 131

variability in the parental, Fi, and F2, generations, as in the F3, if the range of the coefficients of variation in the different F3 families is to be properly evaluated.

In thus pointing out some limitations in the legitimate interpreta- tion of increased Fa variability and size-differentiations in Fs, it is hoped that the reader will not mistake my attitude. I believe that all of these points can be taken into account without reversing the funda- mental conclusions that plural Mendelian factors exist, which may affect in an apparently continuous manner the various quantitative characters and complex physiological activities of plants and animals, and that Mendelian segregations offer at present the most plausible interpretation of most of the phenomena encountered in the inheritance of these characters.

Attempts to decide how many differentiating genes affect a certain quantitative character in a given cross, have been, up to the present time, premature. HAYES'S (1912) conclusion that if the number of F2 individuals is large enough, the F2 range will equal the combined ranges of the parents and the Fi hybrids, is not a legitimate conclusion from the evidence he presents, but only a logical necessity for the hypothesis he holds, namely, that the size-differences with which he is working are wholly the product of plural Mendelian determiners. It is well known that the empirical range of a continuous variation increases with the increase in the number of variates. The total combined range of variation in number of leaves on the paternal strains and on the Fi of HAYES'S <'Sumatra"-"Broadleaf" tobacco-cross extended from 16 to 31, thus in- cluding 16 classes, and that of the F2 from 17 to 35, or 18 classes, but the combined number of individuals included in the Pi and Fi were only 683, while the total number in the F2 families was 6340, besides which, the former were grown on good soil, heavily fertilized. HAYES shows that there is only slight modification of leaf-number on different soils, and although he gives no evidence as to the relative variability Mm the different soils, this also is probably but little affected, so that too much stress must not be laid on the different conditions under which the several generations were grown; but the extent to which the combined ranges of PI and Fi would have been stretched if ten times as many individuals had been available in those generations, remains a question, and leaves the conclusion as to the identity of range be- tween the F2 and Pi -f- Fi incompletely supported.

This extension of the F-_. range of variation to include the two Pi ranges is the basis upon which estimates of the number of plural

132 Shull.

determiners involved in any given cross have been based. NILSSON- EHLE (1911) has described a case in which the range of variation in the length of heads of wheat in the F2 considerably exceeded the com- bined ranges of the two parents. HAYES (1912) has found a similar case in the number of leaves in tobacco, and EMEESON and EAST (1913) have seen the same phenomenon in the length of internode and total length of stalks in maize. It seems probable that such transgressive variation may be the rule rather than the exception when very complex characters are investigated; for it is hardly to be expected that a large number of plural determiners, affecting such a character, shall all act in the same direction, or that the parent having the highest development of the given character shall generally contain all the genes which the other chosen parent possesses. Whenever such transgressive' variability is producible by the genotypic recombinations of parental characters, the frequency with which F;> individuals simulate either parent, gives no clue to the total number of plural determiners which have been brought together, with respect to any character under consideration. The difficulty of making an estimate of the number of genes which affect the same character will be more fully appreciated when it is kept clearly in mind that these plural determiners need not be duplicate, and that consequently there is no reason for assuming that the in- fluence of the several determiners is quantitatively equal.

Qualitative and quantitative differences in the effects individually produced by the several plural factors for a character will assist in interpreting certain phenomena for which less simple hypotheses have been offered. The now celebrated hooded rats may serve to illustrate: Because the hooded -pattern reappears in all crosses as a Mendelian recessive to the self-colored pelages, in the simple monohybrid proportion, it is accepted by CASTLE (1912) as a case in which a single de- terminer is involved. Selection of high and low extremes of this pattern during a series of generations has resulted in increasing the size of the pattern in the one series and in diminishing it in the other, just as CUENOT (1907) found to be true in regard to the piebald- pattern of mice. When hooded rats from either the plus or the minus selected series are crossed with self-colored rats the hooded -pattern still acts in each case as a simple monohybrid recessive, though the ex- tracted pattern is somewhat larger when an individual of the plus series has been used in the cross, and somewhat smaller when the hooded parent was taken from the minus series. CASTLE concludes, therefore, that selection does not simply sort out variations already

Duplicate genes for capsule-form in Bursa bursa-pastoris. _ ]33

existing, but is a "creative force", which, by modifying unit-characters, produces something otherwise unattainable. Leaving aside the faulty logic which requires that something can be selected that is not first presented for selection, the best explanation of the case appears to be that this hooded color-pattern is really a complex character instead of a simple one, the genotypic basis of which consists of one gene having a large and fundamental effect in determining the general nature of the hooded-pattern, and a number of other independently inheritable factors which act as slight plus- and minus-modifiers of the action of this fundamental gene. As these modifiers are not in any sense duplicates of the fundamental pattern-factor itself, we are not driven, as CASTLE says we are, as "the only logical escape" from the dilemma presented by the invariable occurrence of a monohybrid ratio, "to assume further that the assumed multiple units are all coupled."

Another case in point concerns the inheritance of heights in maize (EMEESON 1911). In two of EMERSON'S hybrid families there was a sharp segregation into tall and dwarf plants, apparently due to the presence and absence of a single Mendelian determiner, while in other maize- crosses the F2 presents a continuous series of height-differences which suggest the presence of several independent determiners af- fecting the height. EMERSON accepts CASTLE'S "only logical escape" and assumes that in the apparently monohybrid families there was prob- ably "a coupling of the several height characters." As EMERSON him- self says, he is led to this construction by the consideration that "it would seem more reasonable to suppose that similar differences in height are due to a similar number of height characters." Here again lurks the idea that these plural genes for height are duplicate genes. To me it seems more reasonable to suppose that the height-modifiers are generally not duplicate, and that consequently it is not illogical to expect that some of them will produce much larger height-differences than others. The possibility of coupled height-differences is not denied, of course, for it is not improbable that coupling occurs among the genes for quantitative differences as frequently as among those of fully analyzable Mendelian characters, but coupling should not be assumed in any case so long as a simpler interpretation is available.

In connection with studies of plural determiners, HAYES (1912, p. 22) and TAMMES (1913) have used the biometric coefficients of cor- relation as indicative of the genotypic relations among the several quantitative characters, but such correlations are so nearly universal and are due to such a conglomeration of different causes that their use as

134 Skull.

a measure of genotypic constitution is apt to lead to quite factitious conclusions; consequently, such use of the correlation table should be most guarded and genetic inferences should be drawn from it with the utmost reserve. If two different size - characters , such as number of leaves and total area of leaves, show increased variability in the F2, this increase in each case may be interpreted logically as the result of segregations among plural Mendelian determiners which affect these characters, but a low statistical correlation between such characters does not necessarily indicate that the series of determiners which affect the one character is in large measure distinct from the set of genes which modify the other character. Both may owe their greater F2 variability to exactly the same 'set of segregating genes, the low corre- lation being due to the fact that the independent fluctuation of the two characters is much greater than the modifications produced by each of the several hereditary factors which affect them. Such independent fluctuations are readily comprehensible when it is remembered that the number of leaves and the area of each leaf are determined at different times, and conceivable under the influence of very different elements of the environment.

Neither does a high coefficient of correlation between the quanti- tative variations of two characters prove that any of the Mendelian genes which affect those characters are coupled, as assumed by TAMMES (1913). She found by careful measurements of length and breadth of seeds, and length and breadth of petals, and by estimations of the in- tensity of pigmentation of the petals, in her F2 Linum-hybrids , that all of these characters are positively correlated; the larger the petals borne by one of these F2 hybrids, on the whole, the deeper blue is the color of its flowers, and the larger its seeds. All of these charac- ters exhibit increased variability in the F2, thus indicating that they are probably controlled or affected by segregating Mendelian determiners (TAMMES 1911). The obvious basis for the inference that genetic coup- ling exists among some of the plural factors which affect these charac- ters in flax, is the assumption that they are specific determiners for the particular quantitative character under investigation, and therefore essentially duplicate. I believe I have made it sufficiently clear by the foregoing discussion that nothing in the observed facts warrants such an assumption. Such correlations are readily understood if we keep in mind the fact that the various unit- characters are always compound, - the result of the combined action of a gene and the rest of the geno- type, under limiting conditions supplied by both the internal and the

Duplicate genes for capsule-form in Bursa bursa-pastoris. ____ 135

external environment. This "rest of the genotype" may be the deter- mining factor in producing the correlations. It is probable that the correlations found by TAMMES represent in large measure, if not wholly, the phenomenon long known as physiological correlation, and recently designated by BALLS (1911) "autogenous fluctuation". An individual is not a mosaic of independent parts, but a unit made up of members and characteristics which are often independent from each other in inheritance, but which are largely dependent upon each other in devel- opment. If the correlation of these characters is not simply due to their somatic interdependence it is much more plausible to assume that some of the plural determiners which affect one of these characters are also among the plural determiners which modify one or more of the other characters, and that all of these determiners are inherited independently according to the simple Mendelian method, than to assume that there is a complex coupling of some sort, resulting in gametic series such as 3 : 1 : 1 : 3, 7:1:1:7, &c., instead of the usual 1:1:1:1. When we begin to speculate regarding the genotypic basis for the plural determiners, it is of the greatest importance that the rela- tively rare phenomenon of duplication of determiners be not confused with the nearly universal occurrence of non- duplicate plural determiners. There is nothing special in the history or the genotypic interpretation of the latter, their peculiarity in affecting the same organ or other character of an organism, is purely an incident of somatic physiology,

- a "physiological correlation", - - and therefore, any discussion of the genotypic basis of such complex characters must be simply a con- sideration of the material basis for the Mendelian behavior in general,

- a subject whose adequate discussion can not be undertaken here. The actual duplication of Mendelian unit-characters, on the other hand, deserves some special consideration because in these there is some likelihood that the cause for the duplication may involve, at least in some cases, a series of special genotypic phenomena.

It may prepare sufficiently for what follows to indicate briefly my attitude toward the question of the material basis of Mendelian characters. The following three propositions may serve this purpose: (1) The observed behavior of the chromosomes is such that if different chromosomes have permanently different functions, these functions must be distributed among the offspring exactly as Mendelian unit-characters are distributed; (2) It is not necessary to assume that the visible chromosomes are the only elements of the cell which partake of the same method of distribution during the processes of reduction, fertil-

136 Shull.

ization and cell-division; (3) If the distribution of the chromosomes is the determining cause of the distribution of the unit-characters, it is immaterial for most of the known phenomena of heredity, whether these genes are whole chromosomes parts of chromosomes, or physical or energic differences in the chromosomes or their parts. With the under- standing that the chromosomes simply represent a type of behavior which Mendelian genes probably also exhibit, they may be substituted with some degree of reserve for the Mendelian determiners, in picturing to ourselves the probable relations and movements of such determiners.

Without abandoning any of these propositions, except for an im- mediate didactic purpose, I shall frankly assume in the following dis- cussion of the genotypic and evolutionary significance of duplicate determiners, that the genes are definitely associated with the chromo- somes.

If any Mendelian character be inherited as a single unit, its heredity may be explained by assuming that the gene A for that partic- ular character occurs in only one pair of (homologous) chromosomes (1,1, Fig. 6) in the one parent (the positive homozygote), and that it is absent from all the chromosomes of the other parent (the negative homozygote). In order that another character may be independently inherited in the same manner, its determiner, B, must occur in a differ- ent pair of chromosomes (2,2) either of the same parent that contained A or in the other parent, but must be absent from all other chromo- somes of the two chosen parents. In the same manner, as many in- dependently inherited determiners, A, B, C, D, E, etc., can be accounted for as there are haploid chromosomes. All the phenomena of duplicate determiners will be fully accounted for, then, by assuming that B = A, that C=B=A, that D = C=B=A, etc., the total number of independently inheritable duplicate determiners being likewise limited by the number of haploid chromosomes.

When we try to picture to ourselves how duplicate determiners have originated, several possibilities at once present . themselves. In the first place such duplication of determiners may be either a primi- tive or a derivative condition. EMERSON (1911) has suggested that many fundamental characteristics of any biotype may be "represented" *)

*) It will be understood, of course, that this convenient mode of expression is purely figurative. The true relation between the genes and the characters toward whose development they make essential contributions, has been indicated with sufficient ac- curacy elsewhere in this paper that no misconception will arise from the adoption here of this more figurative phraseology.

Duplicate genes for capsule-form in Bursa bursa-pastoris. 137

in duplicate in every chromosome. If this be true, such a repetition of genes producing independently the same character is almost certainly a primitive condition, and the evolutionary progress from such a condi- tion to that in which the duplicately represented character finally has no representative in any chromosome and therefore disappears from the soma, is plausibly traceable through a continuous series in which the duplicate genes have disappeared from one chromosome pair after another. Such a descending series must be due in part to retrogressive mutation, - to the loss of one or more factors, - - but may be due also in part to rearrangement of determiners in some such manner as described below in connection with derivative, duplication.

EMERSON and EAST (1913) point out, on the other hand, that "if in any line of descent a factor X should become located in different chromosomes, or in any other way be so affected as not to be allelo- morphic to itself in all combinations," a duplication of determiners will result. In this case the duplication would be a derivative condition, the dihybrid being derived from the monohybrid, the trihybrid from the dihybrid, and so on. A derivative duplication of determiners might also result from repeated progressive mutations. For example, we may think of the appearance of a new character as a result of some chemical transformation, such as isomerization or polymerization, which takes place in a chromosome; the nature of such a chemical change must be determined by the antecedent chemical constitution of this chromosome; then if we assume with EMERSON that the several chromosomes may have fundamentally similar constitutions, it is not illogical to believe that the same sort of transformation may occur independently in different chro- mosomes.

All of these methods may have been operative in different cases in producing duplication of determiners, but the assumption of a physical rearrangement of elements already existing appears to me to offer the fewest difficulties and therefore to have been in all probability one of the most potent sources of duplicate determiners. An important question to be considered then is how a factor may come to be located in different (i. e. non-homologous) chromosomes.

There are at least two very simple ways in which such a result could conceivably come about. The normal Mendelian behavior may be supposed to result from the invariable meeting of homologous chromo- somes at the time of fertilization and their invariable separation into different germ-cells during gametogenesis, but the invariability of neither of these processes is a logical necessity. If two chromosomes should

Induktive Abstammungs- und Vererbungslehre. XII. 10

138

Shall.

change places, each uniting with the homolog of the other, as illustrated diagrammatically in fig. 6, the result would be exactly the same as if two determiners of the same type had originated independently in these two pairs of chromosomes, for now two chromosomes (3 and 4, fig. 6), each bearing the gene C, could enter into a single germ-cell, while into the sister germ-cell would pass two chromosomes in which the same determiner is absent. This same chromosome might carry other determiners in a coupled system with C, all acting together as a single unit, but it matters not in such a case how complicated the par- ticular chromosome is, - - oversow large a portion of the organic it operates, or in how many diff,< -nt physiological and morphological .fea- tures it produces characteristic v^-ible

i XA b c i i Xa fie j ; Xa b c • j xa be i or invisible effects, — the duplicate de- terminer would represent exactly the same coupled system and play exactly the same role, because, although located in a new position this chromosome would really be the same organ and not a new and independently originated duplicate of it.

There is another readily conceiv- able method of rearrangement of genes by which a duplication of determiners would be brought about. While it is now known that chromosomes do not invariably unite to form a continuous spireme, the work of numerous cytol- ogists has made it probable that this is the usual procedure. At one stage in cell-division the chromosomes are united into an apparently continuous strand, and at another stage the strand segments preparatory to the formation of the daughter chromosomes. If the determiner C happened to be located in the extreme end of one chromosome (3,3, fig. 7), it seems a very reasonable assumption that the break in the strand which forms the new chromosomes might once occur on the opposite side of this determiner, so that instead of lying in the chromosome in which it had been originally located (3), it would become a part of the reverse end of the adjacent chromosome (4). The same result might come about

Fig. 6. Hypothetical duplication of a determiner by the displacement of a chromosome. X represents the unhy- pothesized residual constitution of the chromosome; A, B, C, are hypothetical Mendelian genes; a, b, c, simply call attention to the absence of the genes rep- resented by the corresponding capitals.

Duplicate genes for capsule-form in Bursa bursa-pastoris. 139

through a rearrangement of substances in the region of the break between two chromosomes, - - resulting in a sort of "longitudinal cross- over". This would now serve to locate the determiner C in two differ- ent pairs of chromosomes, so that here again as in the preceding case, two chromosomes containing the same gene, C,C, could be included in a single germ-cell, leaving a corresponding germ-cell with only c,e chromo- somes. The one important difference between the two methods of duplication illustrated by figures 6 and 7 relates to the coupling of det^ miners, for by the method illustrated in figure 6, in which a whole chr* ^osome is displaced, a mechanism is provided which would preserve any oupling which had existed through the association of several genes in • "i same chromosome. The method illustrated in figure 7 would favor the breaking of such , 2 3 4

a c< ipled system. Some situation may arise in which this difference may give a clue to the method by which duplication has arisen.

Both of these methods of origin of duplicate deter- miners from single ones seem very plausible. If the chro-

X A

bc\ \X a B c | X a b C

X a

b c

'X A

b c I ' X a B c '• < X a b c 1

:c

i

X

^ b :

1 L

\X A

b c \ X a B c X a b JC

—

X a

b c

Fig. 7. Hypothetical duplication of a determiner

by a longitudinal transfer of a gene from one

chromosome to an adjacent one. Significance of

symbols the same as in fig. 6.

mosomes are the bearers of the Mendelian genes, the relative rarity of duplication leads necessarily to the inference that, in the first place, homologous chromosomes are very fixed in the relations in which they pair during fertilization, and in the second place, that division of the spireme to form the daughter chromosomes is also very fixed in position. Upon this fixity of relations, both in the formation of the chromosomes and in their subsequent movements must depend, then, the very general occurrence of normal Mendelian inheritance.

It is of great interest and importance in relation to the duplica- tion of determiners for the triangular capsule in Bursa, to note that either of the two methods just described, or any other process by which a Mendelian gene is carried out of its previous relative position, would result not only in the duplication of this determiner, but, if this gene had not been previously duplicated, the rearrangement would at the same time make possible the production of an individual from which the character is missing, for whose production this gene is an essential

10*

140 Shull.

element, because, as we have already seen, when two chromosomes, each possessing the determiner C, pass into the same germ-cell, the sister germ-cell receives their two homologs from which C is absent. Then by the union of two germ-cells of the latter type an individual will be produced in which the gene C is omitted, and whose soma can not ex- hibit, therefore, the characteristic reaction in which C plays an essential role. Here then is an easy explanation of the origin of recessive mutants without the actual destruction or loss of determiners. Applied to the specific case of Bursa, the very same operation which doubled the de- terminer for the triangular capsule in Bursa bursa-pastoris, may have given rise also to Bursa Heegeri.

Of the four cases of duplicate determiners thus far demonstrated, namely, the presence of a ligula in oats, red pericarp-color in wheat, yellow endosperm -color in maize, and the triangular capsule in Bursa, two are color- characters, and two are structural characters. The color-characters do not suggest in any clear way their probable method of origin; the phenomena they present may be primary or secondary; they are about equally well explained on the basis of any of the above described schemes. The simplicity of such a char- acter makes it about as easy to imagine that the duplication is due to repeated mutations as to a rearrangement of the genes. In the two structural characters, however, I believe it to be clearly indi- cated that for the ligula of Avena the duplication of determiners is a primitive condition, and that for the triangular capsule in Bursa it is a derivative condition. Comparative morphology offers the first evidence in favor of this fundamental difference between these two cases, for the ligula is almost universally present in the grasses and so must have been present in the ancestors of Avena, while a triangular capsule is formed, so far as I am aware, in no Crucifer other than Bursa, and therefore this form of capsule was probably absent in the ancestors of this genus. A further indication that the duplication in the case of the ligula was the primitive condition is given by the large number of duplicate genes whose existence has been made probable, four having been indicated in one cross, though only two have been adequately demonstrated. The crucial test of the hypothesis is a cross between the liguleless oat, "Jaune geant a grappes", or one of its recessive derivatives, with an undoubted wild oat. Owing to the large number of duplicate determiners for the ligula likely to be found in such a cross, it must be carried out on an unusually large scale; indeed, completely decisive analysis may prove to be impossible, owing to the

Duplicate genes for capsule-form in Bursa bursa-pastoris. 141

limited number of seeds produced by each individual. The fact that one of the two fully demonstrated duplicate determiners for the ligula in oats was associated with a particular form of panicle may mean that the two duplicate genes were brought to light by independent mutations resulting in the loss of the ligula-gene from two different chromosomes which had other differences which affected the form of the inflorescence. It must not be inferred, however, that because a character is primitive, it is necessarily, or even generally, represented by duplicate determiners in the germ-cells. The ligula in maize serves to strongly impress this statement, for EMERSON (1912) finds that in each of several independent stocks of maize there is only one pair of genes present for the ligula.

The very complexity of the capsule- character of Bursa, is, to my mind, against the origin of its duplicate determiners by independent mutations, for not only are there differences in form, size and pigmen- tation, but the entire structural mechanism which provides for the freeing of the mature seeds by the falling off of the valve, including a thickening of the interior epidermis and a definite articulation at the margin of the dissepiment, remain together as a single characteristic or unit-character, whether produced by either of the duplicate genes, C or D, or by both. In my most recent crop of Bursa there were several individuals which showed some modifications of the Heegeri capsule - character, of such a nature as to suggest that the bursa-pastoris capsule -character may be in reality produced by a coupled system of determiners instead of a single determiner. This matter is not yet ready for report but it is under investigation. It is mentioned here only because of the im- portant bearing such coupling of characters would have upon the problem of the method by which the duplication of determiners for the triangular capsule may have been brought about. If the triangular capsule should be found to represent a complex coupled system of determiners acting together as a single unit, the possibility of its duplication by indepen- dent mutations or by longitudinal "crossing-over" between adjacent chromosomes would be nearly incomprehensible.

It may be possible to get some further experimental evidence that duplication of the capsule-character in Bursa is a comparatively recent derivative condition, in a manner parallel to that suggested above for testing the primitive nature of duplication for the ligula-character in Avena, namely, by means of crosses between Bursa Heegeri and the oldest races of B. bursa-pastoris which can be found; for if my hypoth- esis is correct, such crosses would probably result in 3 : 1 ratios in F2. I am now seeking evidence along this line by new crosses with B. bursa-

Shull.

pastoris from different regions, and hope to be able at a later date to give further data bearing upon this question.

As we have already seen, the simple shifting of a chromosome carrying the determiner for the triangular capsule into a new position with reference to the other chromosomes probably gave rise to the recessive mutant B. Heegeri, a result which has been generally referred heretofore to the "loss" or "destruction" of a determiner. It is an attractive hypoth- esis that such shifting of determiners may account for the occurrence of recessive mutants generally, as well as to some dominant mutants, but it is a hypothesis which I believe incapable of more than a very limited application, for the simple reason that retrogressive mutation is a rel- atively frequent phenomenon, while duplication of determiners is, so far as present evidence indicates, a relatively infrequent one. If both phenomena were due generally to the same cause they should appear with similar frequency. The suggestion of EMERSON and EAST (1913, p. 13) that it is "quite within the range of possibility that some of DE VEIES'S Oenothera mutants have originated" from the union of germ- cells having duplicate Mendelian determiners for the parental charac- teristics, none of these duplicate genes happening to occupy homologous positions in both germ-cells, can not be accepted by any one familiar at first hand with the genetic phenomena in the genus Oenothera, A consequence of such an interpretation would be that plants should often be found whose progeny produced by self-fertilization would consist of 75 per cent of the parent- type and 25 per cent of the particular mutant -type. From hundreds of such self-fertilizations which have been made among the "mutating Oenotheras", with strictly individual analysis, no such result has been secured. The total number of mutants of all types has rarely exceeded 5 — 7 per cent. Attempts to interpret the genetic behavior of the Oenotheras on a Mendelian basis or to apply experiences with Oenotheras to other groups in which Mendelian inheritance has been demonstrated, is still premature. A great deal of purely inductive work on this genus will be required before it can be safely articulated genetically with other groups.

The data presented in the present paper removes the duplication of genes of the triangular capsule in Bursa from the status of a mere interpretation to one of complete demonstration. Although this has required considerable labor, it has been accomplished with ease compared with the work which will be necessary to demonstrate the truth or falsity of the proposition that plural Mendelian determiners adequately explain any case of a) the inheritance of apparently continuous quan-

Duplicate genes for capsule-form in Bursa bursa-pastoris^^ 143

titative differences, b) the inheritance of apparently blended characters, c) the apparent modification of a unit- character by means of selection, or d) the origin of an apparent recessive mutant. For each of these propositions there are certain simple corollaries whose demonstration will give a better basis than is now available for judging of the probable correctness of this method of interpretation. It may be useful to point out several of these corollaries as constituting hopeful points of attack. No attempt is made to be exhaustive and other criteria will readily present themselves.

a) For continuous characters, if the hypothesis be true, it should be demonstrable that the F2 is not only more variable than the Pi and Fi, as is now well established in a large number of cases, but also that it does actually include the two parental conditions in respect to the particular quantitative character under consideration, when suffi- ciently large numbers are grown. This must be shown to be a general rule, for occasional instances of this sort can come about by the same fortuitous circumstances that produce striking transgressive variations in other special cases. In F3 there should be not only a range of variation-coefficients extending from the value of the Pi and Fi coefficients to the F2 coefficients; it ought to be demonstrated also that the individuals taken from the extreme classes of the F2 and later generations yield progenies which tend to have lower variation coefficients and less va- riation among the coefficients themselves, than individuals taken from the middle classes of the same generation. Extensive comparisons between progenies from extreme minus-variants and extreme plus-variants of any given generation should give evidence as to the extent to which heterosis is distorting the effects of the hypothetical size-determining genes.

b) According to hypothesis, blended characters are only a special case of a), in which the number of determiners is supposed to be large compared with the number of offspring available. If the small number of available offspring is due to limitations in the breeding capacities of the individual organism, as is the case in all higher animals, the dem- onstration will be rendered the more difficult. Indeed, it may be that with such material it will be possible to show only that, as far as they go, the empirical results are in harmony with those in other cases which are capable of more complete analysis.

c) For apparently modifiable unit-characters, the crucial test of the hypothesis should be the reversibility of the process. If selection is a "creative force", the selection to one extreme should raise no barrier to the attainment of the opposite extreme without the introduction of

144 Shull.

new genotypic elements by out-crossing. If, on the other hand, the observed progress in the intensification or elimination of any unit- character under selection, be due to segregation of plural Mendelian determiners, it should be impossible by a reversal of selection, without out-crossing, to completely reach the one extreme after having attained a definite advance in the direction of the opposite extreme. The degree to which such a reversal may prove effective in any case will certainly be illuminating.

d) To make it probable that a supposed recessive mutant has re- sulted from the complete lack of homology of all duplicate Mendelian determiners for the dominant parental character in the one parent, with any of the duplicate genes of the same character in the other parent, it is only necessary to self-fertilize a sufficiently large number of individuals of the dominant type among the progeny in which the new form appeared, and so to demonstrate that some of them yield monohybrid ratios, some dihybrid ratios, and so on. If the immediate progeny in which the recessive mutant (?) made its appearance is not available for such a test, it may be necessary or advisable to cross with one another, a large number of individuals belonging to the stock in which the new form made its appearance. If the hypothesis has any considerable degree of probability, some combination should be found by this process, in which the mutant (?) form is repeated. Then this progeny in which the new mutant occurs, should be analyzed by an adequate number of self-fertili- zations among the dominant individuals, as already indicated. The crossing of the new type extensively with individuals of the parent-type, — the latter being taken from as many independent sources as possible, - might discover a duplication of Mendelian determiners, but failure to find them by this process would not absolutely disprove the hypothesis, because no two duplicate determiners might happen to occur together in any single individual, in which case all crosses with the recessive type would give monohybrid ratios.

It is thus seen that the discovery of duplicate determiners, not only because of their own direct implications, but also by calling at- tention to the widespread existence of plural determiners, has tapped a rich mine of new and important genetic problems. The discovery that a given characteristic is probably determined by plural genes should be the beginning and not the end of investigations dealing with this characteristic. The chief value of the hypothesis at present must be determined by the extent to which it is made a working hypothesis.

Duplicate genes for capsule-form in Bursa bursa-pastori»r- — . 145

Summary.

The triangular form of capsule, characteristic of Bursa bursa-pastoris, is produced by either of two independently inheritable Mendelian de- terminers, C and D. When both of these are absent B. Heegeri appears, having a small top-shaped capsule. The following facts have been dem- onstrated in support of this conclusion:

1. All individuals of the Fi families formed by crossing certain American biotypes of B. bursa-pastoris with B. Heegeri, have triangular capsules.

2. In all F2 families there is an approximation to the ratio 15 : 1 between plants having triangular capsules and those having top-shaped capsules.

3. When F2 plants having triangular capsules are srelf-fertilized, three kinds of families are produced: namely, a) those in which all of the individuals have triangular capsules ; b) those in which the individuals having the two kinds of capsules, bursa-pastoris and Heegeri, occur in the ratio 15 : 1; and c) those in which the two kinds of plants appear in the ratio 3:1.

4. In the Fi the results differ according to the type of Fs family to which the parents belonged: a) The members of those Fs families which contained only plants with triangular capsules, when self-fertilized, produce only triangular capsules again, i. e., they breed true to the B. bursa-pastoris character; b) when the parents are triangular-capsuled plants from an Fa family in which a 15 : 1 ratio occurred, the F4 families fall into the same three groups as the Fs families described above under 3.; c) from the dominant individuals of an Fs family in which a 3 : 1 ratio occurred only two kinds of F± families arise, namely, (i) with triangular capsules only, (ii) with the two kinds of capsules in the ratio 3:1.

5. Extracted dominants in the F2 and later generations have not all the same genotype as the original bursa-pastoris individuals used in the crosses, though indistinguishable from them by inspection. A cross between one of these extracted dominants and Heegeri has yielded several F2 families all of which gave a ratio 3 : 1 instead of 15:1 as found in the original F2 families.

The deviations from the expected ratios were not as great as those in the families reported in previous papers, and about as many families have shown an excess of Heegeri as of bursa-pastoris, probably due to the development of a more successful technique in handling the cultures.

146 Shull.

This indicates that the deficiency in the Heegeri individuals, previously- reported, was probably due, in large part at least, to selective elimination.

In one family there was an equal deficiency in the proportion of recessives and of homozygous dominants, so that the ratio DD : DR : RR was about 1:4:1 instead of 1:2:1. Several possible interpretations of this result are considered: namely, a) that it is a purely chance result; b) that a selective fertilization has favored the union of unlike gametes; c) that selective elimination has affected positive and negative homozygotes equally because they lack the vigor produced by hetero- zygosis; and d) that some form of gametic coupling occurs between the two genes C and D. Of these hypotheses a) and d) appear most promising.

The discovery by NILSSON-EHLE and EAST that the same character may be produced by any one of several independently inheritable de- terminers, marks an important advance in genetic progress because it has led to a well grounded Mendelian interpretation of inheritable quan- titative differences. Determiners which independently produce such equivalent results, I have called "duplicate" genes.

A sharp distinction must be maintained between "duplicate1' determiners and "plural" determiners, the latter including all determiners, of whatever nature, which produce a given characteristic or which modify it in any way that does not destroy its identity. Inheritable quantita- tive characters are probably the product of plural determiners, but not to any considerable extent of duplicate determiners, and the develop- ment of an adequate Mendelian interpretation of the inheritance of such characteristics need not have awaited the discovery of duplicate determiners.

For only four characters is the evidence of duplicate genes to be deemed adequate: namely, for the presence of a ligula in oats, red pericarp-color in wheat, yellow endosperm-color in maize, and the tri- angular capsule-form in Bursa. For many other characters the existence of plural determiners has been rendered probable, but there are weaknesses in the evidence, and apparently fallacious inferences have been drawn in a number of cases, owing to the failure to distinguish between plural and duplicate determiners.

For many characters the only evidence of plural Mendelian size- determiners is an increased variability in Fi as compared with the Pi and Fi generations. It is here shown: a) that the stimulating effect of hybridity, for which the name "heterosis" is adopted, produces increased variability in quantitative characters in the F2 and a pseudo-segregation in Fa, independently of the existence of specific determiners for size; b) that the demonstration of an increased variability in F2 does not by

Duplicate genes for capsule-form in Bursa bursa-pastori&^^___^ 147

itself prove that several genes of similar nature are involved, that dominance is lacking, or that all inheritable quantitative differences between the parents of the particular cross are Mendelian; and c) that unequal treatment of the several generations may produce a purely fac- titious increase in the range and coefficients of variability of the Fa.

Attempts to determine how many plural determiners for any quan- titative character are involved in a particular cross are as yet premature. Such attempts are based on the unproven hypothesis that the range of variability in Fa equals the combined ranges of the Pi and Fi genera- tions and the unwarranted assumption that the different plural deter- miners are essentially equal in effect.

Qualitative and quantitative inequality of plural determiners give a simple explanation of CASTLE'S results with hooded rats, and EMERSON'S recessive dwarf maize-segregates, without resort to coupling of the genes.

Low coefficients of correlation do not indicate a high degree of genotypic independence of characters, nor does a high correlation indicate gametic coupling. Such differences in the degree of correlation are produced by so many different causes that genetic inferences from them should be most carefully guarded.

The duplication of determiners for the ligula of oats is probably a primitive condition, and that for the triangular capsule of Bursa a derivative condition.

If the genes are functions of the chromosomes, the simple exchange of relative positions by two chromosomes would give rise at the same time to the duplication of the determiner for the triangular capsule in B. bursa-pastoris and the origin of the recessive mutant, B. Heegeri, without a progressive mutation on the one hand, or the loss of a de- terminer on the other hand. A longitudinal transfer of the capsule- determiner from one chromosome to another adjacent chromosome would have a like result.

The occurrence of recessive mutants is apparently much more frequent than the duplication of determiners; consequently, no con- siderable portion of such mutations can have originated by the method here made probable for B. Heegeri. The author can not agree with those who would explain the Oenothera mutants as due to the segregation of duplicate or plural Mendelian determiners.

For the present the hypothesis that plural Mendelian genes ad- equately account for the inheritance of complex quantitative and physio- logical characters is valuable only to the extent that it is made a working hypothesis.

148 Shull.

Literature cited.

BALLS, W. L., 1911: The inheritance of measurable characters in hybrids between reputed species of cotton. Compt. rend. IVe Conf. Internat. de Genetique, Paris, pp. 429 — 440.

CASTLE, W. E., 1912: The inconstancy of unit-characters. Amer. Nat. 46: 352—362.

CUENOT, L., 1907: Recherches sur 1'hybridation. Proc. 7th. Internat. Cong. Zool. 1907, pp. 99—110. Boston, 1912.

DAVENPORT, G. C., and C. B., 1910: Heredity of skin-pigmentation in man. Amer. Nat. 44: 641—672, 705—728.

- 1913: Heredity of skin color in Negro-white crosses. Carnegie Institution of Washington, Publ. No. 188, pp. 106.

EAST, E. M., 1909: The distinction between development and heredity in inbreeding. Amer. Nat. 43: 173—181.

- 1910: A Mendelian interpretation of variation that is apparently continuous. Amer.

Nat. 44: 65—82.

- 1911: The genotype hypothesis and hybridization. Amer. Nat. 45: 160 — 174.

- 1912: The Mendelian notation as a description of physiological facts. Amer. Nat.

46: 633—655.

EAST, E. M., and HAYES, H. K., 1911: Inheritance in maize. Conn. Agr. Exp. Sta. Bull. 167, pp. 142.

- 1912: Heterozygosis in evolution and in plant breeding. U. S. Bureau of Plant Ind. Bull. 243, pp. 58.

EMERSON, R. A., 1910: The inheritance of sizes and shapes in plants. Amer. Nat. 44: 739—746.

- 1911: Genetic correlation and spurious allelomorphism in maize. Ann. Rep. Nebraska

Agr. Exp. Sta. 24: 59—90.

- 1912: The inheritance of the ligule and auricles of corn leaves. Ann. Rep. Nebraska

Agr. Exp. Sta. 25: 81—88. EMERSON, R. A., and EAST, E. M., 1913: The inheritance of quantitative characters in

maize. Agr. Exp. Sta. of Nebraska, Research Bull. 2, pp. 120. GOODSPEED, T. H., 1912: Quantitative studies of inheritance in Nicotiana hybrids. Univ.

of Calif. Pub., Botany 5: 87—168.

- 1913: Quantitative studies of inheritance in Nicotiana hybrids II. Univ. of Calif.

Pub., Botany 5: 169—188. HAGEDOORN, A. L., and Mrs. A. C., 1914: Studies on variation and selection. Zeitschr.

f. ind. Abstamm.- u. Vererb. 11: 145—183. HAYES, H. K., 1912: Correlation and inheritance in Nicotiana Tabacum. Conn. Agr.

Exp. Sta. Bull. 171, pp. 45.

HAYES, H. K., EAST, E. M., and BEINHART, E. G., 1913: Tabacco breeding in Connect- icut. Conn. Agr. Exp. Sta. Bull. 176, pp. 68. JOHANNSEN, W., 1906: Does hybridization increase fluctuating variability? Rep. 3rd.

Conf. Genetics. London, pp. 98 — 112. ^- 1913: Elemente der exakten Erblichkeitslehre. 2. Auflage, pp. XI -j- 723. (See

p. 560 et seq.) KAJANUS, B., 1912a: Genetische Studien an Beta. Zeitschr. f. ind. Abstamm.- u. Vererb.

6: 137-179. — 1912b: Genetische Studien an Brassica. Zeitschr. f. ind. Abst.- u. Vererb. 6: 217—237.

Duplicate genes for capsule-form in Bursa bursa-pastoris~ 149

K. A JANUS, B., 1913: Uber die Veierbungsweise gewisser Merkmale der Beta- und Brassica-

Ruben. Zeitschr. f. Pflanzenziichtung 1: 125—186, 419—463. KEEBLE, F., and PELLEW, Miss C., 1910: The mode of inheritance of stature and of

time of flowering in peas (Pisum sativuni). Jour. Genetics 1: 47 — 56. LANG, A., 1910: Die Erblichkeitsverhaltnisse der Ohrenlange der Kaninchen nach Castle

und das Problem der intermediaren Vererbung und Bildung konstanter Bastard-

rassen. Zeitschr. f. ind. Abstamm.- u. Vererb. 4: 1 — 23.

- 1911: Fortgesetzte Vererbungsstudien. Zeitschr. f. ind. Abstamm.- u. Vererb. 5:

97 — 138. See U. Die Hautfarbe der Mulatten und die Hypothese der Polymeric, pp. 111—127.

NILSSON-EHLE, H., 1908: Einige Ergebnisse von Kreuzungen bei Hafer und Weizen. Botaniska Notiser, pp. 257 — 294.

- 1909: Kreuzungsuntersuchungen an Hafer und Weizen. Lunds Universitets Arsskrift,

N. F. Afd. 2, Bd. 5, Nr. 2, pp. 122.

- 1911 a: Kreuzungsuntersuchungen an Hafer und Weizen II. Lunds Universitets

Arsskrift, N. F. Afd. 2, Bd. 7, Nr. 6, pp. 83.

- 1911 b: Mendelisme et Acclimatation. Compt. rend. IVe., Conf. Intern, de Genetique,

Paris, pp. 136—157. PEARL, R., 1912: The Mendelian inheritance of fecundity in the domestic fowl. Amer.

Nat. 46: 697—711.

PHILLIPS, J. C., 1912: Size inheritance in ducks. Jour. Exp. Zool. 12: 369 — 380. PLATE, L., 1913: Vererbungslehre. Mit besonderer Beriicksichtigung der Menschen, fur

Studierende, Arzte und Ziichter. pp. 519, Leipzig. See p. 155. SHULL, A. F., 1912: The influence of inbreeding on vigor in Hydatina senta. Biol.

Bull. 24: 1 — 13. SHULL, G. H., 1907: Results of crossing Bursa hursa-pastoris and Bursa Heeyeri.

Proc. 7th Internal. Cong. Zool. 1907, Boston 1912. Advance reprint in 1910, 6 pp.

- 1908: The composition of a field of maize. Ann. Rep. Amer. Breeders' Association,

4: 296—301.

- 1909a: A pure-line method in corn-breeding. Ann. Rep. Amer. Breeders' Association,

5: 51—59.

- 1909b: Bursa bursa-pasioris and Bursa Heegeri: biotypes and hybrids. Carnegie

Institution of Washington. Publ. No. 112, pp. 57.

- 1910: Hybridization methods in corn breeding. Amer. Breeders' Mag. 1: 98 — 107.

- 1911 a: The genotypes of maize. Amer. Nat. 45: 234 — 252.

- 1911 b: Defective inheritance-ratios in Bursa hybrids. Verb d. naturf. Verein. Briinn,

49: 157—168.

VON TSCHEEMAK, E., 1911: Uber die Vererbung der Bliitezeit bei Erbsen. Verh. d. naturf. Verein. Brunn, 49: 169—191.

- 1912: Bastardierungsversuche an Levkojen, Erbsen und Bohnen, mit Riicksicht auf

die Faktorenlehre. Zeitschr. f. ind. Abstamm.- u. Vererb. 6: 81 — 234. TAMMES, T., 1911: Das Verhalten fluktuierend variierender Merkmale bei der Bastardie- rung. Recueil d. Trav. bot. Neerlandais 8: 201—288.

- 1913: Einige Korrelationserscheinungen bei Bastarden. Recueil d. Trav. bot. Neer-

landais 10: 69—84.

WALTER, H. E., 1913: Genetics. An introduction to the study of heredity, pp. 272 New York, Macmillan Co. See pp. 183 — 196.

U.C. BERKELEY LIBRARIES

University of California Richmond, CA 94804-4698

DUE AS STAMPED BELOW