294 Criticism of Hjipothesis of Linkage and Crossing Over 



The maximum number of cross-overs in double crossing over occurs 



between A on the one hand, and M and N on the other. The -number 



of cross-overs is no longer proportional to the distance aj)art of the 



factors. Y is twenty-four times the distance of B from A, but the 



cross-overs Ah and Ay are equal in number. G is twice as far from 



, „ . Ac 15-3 . . , ,. o 



A AS B IS, yet -.-, = -^r^ , i.e., is less than 2. 

 •' Ab 8-0 



Now these two systems of crossing over obviously cannot occur 



together in the same chromosome and the same nucleus. The gametes 



consequently owe their constitution to the operation of one or the other 



scheme (not to both). The observed ratios can only be adequately 



interpreted if we know the relative frequency of the divisions which 



occur ill each of these two systems. The American authors appear 



to have adopted the following point of view. If three pairs of factors 



are concerned, Bh, Ee, Nn, it is necessary, that all kinds of assortments 



should be obtained, that three types of behaviour should be possible to 



the chromo.somes, as represented in the following diagi-am. 



1. No cross-over 



2, Single cross- , 

 over 



3. Double cross-over 



By experiment, the eight types of gametes postulated are actually 

 found, as well as the numbers in ivhich they occur, and those individuals 

 whose constitution corresponds to the hypothetical double cross-over 

 are always fewer in number than those of any of the other classes. 



These three types of behaviour appear to be independent of each 

 other, as by hypothesis, they take place in different nuclei. I think 



