248 



THE AMERICAN NATURALIST 



[Vol. LII 



ratios of crossing over when diverse pairs are compared ; 

 the cross-over ratio between A-a and B-b would be dif- 

 ferent from that between A-a and C-c, and so on. It is 

 this theory that I propose to examine. I do not under- 

 stand that Goldschmidt commits himself to any form of 

 this theory, or to any theory that is exclusively of this 

 type, so that this discussion is not presented as a com- 

 mentary on his views, but on this type of theory for its 

 own sake. Is it possible to explain the observed ratios of 

 crossing over by any theory of this type? 



To grasp the matter clearly, it will help to have an 

 example before us. Let the following twelve groups of 

 letters represent twelve pairs of chromosomes in twelve 

 cells, each chromosome bearing two factors, which we 

 will call A-B and a-b. The upper two letters in each 

 pair show a single chromosome containing the factors 

 A-B, the lower two the mated chromosome containing the 

 factors a-b. 



AB AB AB AB AB AB AB AB AB AB AB AB 

 ' ab ab a b ab ab ab ab ab ab ab ab ab 



Now suppose that the forces holding A and a to their 

 chromosomes are such that A and a exchange in one 

 fourth of all cases, while B and b exchange in one third of 

 all cases. That is, A and a exchange places in every 

 fourth chromosome pair, B and b exchange places in every 

 third pair. The letters that are thus to exchange with 

 their mates are italicized in the pairs indicated above. 

 The exchanges will evidently give the following result : 

 TT AB AB Ab aB AB Ab AB aB Ab AB AB ab 

 AL ab ab aB Ab ab aB ab Ab aB ab ab AB 

 + + + + + 



By a cross-over is meant the fact that two factors of 

 diverse pairs, as A and B, which in the germ cells that 

 formed the parent were following the same chromosome 

 (as in I, above), are found in the germ cells from those 

 parents (II, above) to be following diverse chromosomes 

 (as in the third pair of II, above) ; while conversely the 

 two factors A and b, which were following diverse 



