No. 573] REDUPLICATION HYPOTHESIS 



545 



where »>1). (See Table I, Sturtevant, '14.) In fact, 

 as stated above, the fundamental scries always approxi- 

 mates the secondary (observed) series. 



There are two hypotheses as to the mechanics of re- 

 duplication series where more than two pairs of genes are 

 involved. The first was suggested by Bateson and Pun- 

 nett ('11), and consists in the assumption that when three 

 pairs are involved eight cells are formed by three succes- 

 sive divisions, each of which segregates one pair of genes. 

 The eight cells then represent the eight possible kinds of 

 gametes, and are supposed to reduplicate independently 

 until the proper proportions are reached. Bailey sup- 

 poses that if it be shown that two primary series do not 

 interact on each other this scheme will be more likely to be 

 correct than will Trow's, which I shall discuss next. It 

 seems to me. however, that this hypothesis begs the ques- 

 tion. It is derived entirely by working backwards from 

 the observed results ; it affords no basis for predictions ; 

 and it does not offer a simple mechanical explanation of 

 any of the observed results. For pragmatic reasons I 

 believe we should adopt it only as a last resort. 



Trow supposes that two cell divisions occur, segregating 

 two pairs of genes. The four resulting cells then go 

 through with their reduplication, which is a primary one. 

 "When this is finished there occur divisions which segre- 

 gate the other pair, and the other primary reduplication 

 is carried out. On Trow's general hypothesis, which I 

 have tried to show is the only one which can hold, it is 

 supposed that the second series of reduplications is 

 affected by both of the first two pairs of genes. C is re- 

 duplicating more if with B than if with b, less if with A 

 than if with a. This scheme of Trow's has one great 

 advantage in that it accounts for the fact that the class 

 which I have called AbC is always the smallest one. 

 Reference to Trow's calculations will show that this rela- 

 tion should always occur, and Table II shows that it does 

 occur. . On the octant scheme there is no explanation of 

 this relation — we simply have to assume that it does occur 

 somehow. 



