EVOLUTION, VARIATION AND HEREDITY 471 



sisting of at any rate 100, 75, and 60 factors, and one small group is 

 intimately associated with sex inheritance and depends upon the 

 presence of a certain small " sex chromosome." Furthermore, up 

 to the present no species has been found in which the number of 

 linked groups exceeds the number of chromosomes. When this is 

 taken into consideration, therefore, we find that the second law 

 should read that groups of characters tend to keep together this is 

 linkage but that the pairs of groups may be assorted independently. 

 Thus the explanation of Mendel's apparently contradictory result is 

 that he happened to choose factors that belonged to separate groups. 

 The linkage of these large groups is not absolute, and while on 

 the whole the members of one group tend to keep together, yet in a 

 certain percentage of cases in some of the crosses it is clear that a 

 small group from each one of a pair of large groups interchanges. 

 This can be represented diagrammatically as follows : suppose 

 the allelomorphic factors of the original large linked group to be 

 represented by letters : 



A, B, C, D, E, F, G, H, I, J, K, L, 



a, b, c, d, e, f, g, h, i, j, k, 1, 



Then in a certain percentage we shall find that in the formation of 

 the germ cell, equivalent groups from each have interchanged (as 

 evidenced by the appearance of the corresponding factors in the 

 zygote) thus : 



a, b, c, d, E, F, G, H, I, J, K, L, 

 A, B, C, D, e, f, g, h, i, j, k, 1, 



As a rule, the percentage that do this is small, though sometimes 

 it may reach as high as 33 per cent. ; in such cases we say that the 

 two groups at the beginning were loosely linked. It should be borne 

 in mind, however, that the exchange takes place between allelo- 

 morphic factors in homologous large groups the exchange is not 

 haphazard, but exact ; and also that the percentage of cases in which 

 it occurs is definite in all crosses for the same group of factors. This 

 phenomenon is termed " crossing over," and is, as it were, an 

 addendum to the law of linkage, which can be correspondingly 

 modified to state that while groups tend to remain linked in in- 

 heritance, yet in some cases a definite amount of crossing over may 

 occur. Without entering into a discussion of the subject, it may be 

 noted in passing that there is a possibility of such an exchange 

 taking place during the synapsis stage of maturation when the two 

 halves of a bivalent chromosome may be twisted around one another 

 to a greater or less extent. 



When the numerical results of a series of matings in which 



