284 CnticistH of HypofJiestin of Lhikwjc and Crossing Over 



Put in another way, any one of the capital letters A, B, C combines 

 with any one of the small letters d, e,f, and any one of the small letters 

 a, b, c combines with any one of the large letters D, E, F to form cross- 

 overs, but there are no corresponding non-cross-overs, if every chromosovie 

 has a constant behaviour. If however for every chromosome which 

 crosses over in this definite way, another similar chromosome in another 

 nucleus does not cross over at all, so that the ^ and % contributions 

 in this case simply separate from each other, then there would be 

 non-cross-overs present, AD, AE, AF\ etc. (along with others) corre- 

 sponding to the set of cross-overs given above. We should get, if both 

 types occur equally often, equal numbers of cross-overs and non-cross- 

 overs, e.g., 



AD ad aD Ad 



non-cross-overs cross-overs 



50% 50% 



If two, three, or four chromosomes remained uncrossed for each one 

 that crosses, the percentage of cross-overs would fall to 33 7^^, 25%, 

 20 7o. finfl ^" oil- In such a scheme it is obvious that the percentage 

 of cross-overs does not give any informatinn as to the relative position 

 of the factors in the chromosomes. This behaviour does not depend on 

 the selection of the middle point as the locus of the actual crossing 

 over. If the crossing over takes place at any one fixed point, a similar 

 conclusion is inevitable. Hence we may be sure that the authors of 

 the crossing over hypothesis had some other scheme than this in view. 



Now if the crossing over does not take place (if it takes place at 

 all) always at the middle part of the chromosome, or some other definite 

 point, let us suppose that it takes place according to the laws of chance 

 at any one point. With the same chromosomes as before, with six 

 factors each, there will obviously be five points at which crossing over 

 will take place, as in the following figures : 



A 



1. 



B 

 B 



2. 



3C 



