THE STATliS OF VAIUABILITY 



ancestors, to being entirely free in the homozygous descendants. 

 Crossing two unlike homozygotes among these descendants 

 [AA X aa) will restore the ancestral condition: the variability will 

 once more be entirely potential. Variability is thus set free by 

 segregation, and locked up by crossing unhke types. 



An inbreeding population consists completely of homozygotes, 

 apart from the effects of mutation; but a crossbreeding population 

 caimot consist only of heterozygotes, except in the special case 

 where the gene happens itself to determine the breeding system. A 

 gene such as that controlling incompatibility in cherries must 

 always be in a heterozygous condition, because individual gametes 

 alike in respect of it cannot be brought together. But a gene without 

 this effect on the breeding system is in a different case. Maximum 

 outbreeding in a large population can do no more than maintain 

 such a gene in the states and frequencies given by random mating. 

 With random mating, where the relative frequencies of the two 

 allelomorphs {A and a) are u and v, the frequencies of individuals 

 of the types AA, Aa and aa will clearly be : 



AA u" : Aa 2uv : aa v" 



and the maximum proportion of heterozygotes will be 0-5, 

 achieved when u = v. With more than two allelomorphs the 

 proportion of heterozygotes may be higher. 



Now, potential variability in respect of a single gene can be 

 carried only by heterozygotes. A crossbreeding population will- 

 therefore have some of its variability free and some potential. 

 With two allelomorphs of equal frequencies, half the population 

 will be Aa and half the variability must consequently be potential. 

 Segregation will release half this potential variability in each 

 generation, but at the same time inter-crossing of .4^4 and aa will 

 be returning half the free variability to the potential state. These 

 two processes thus balance one another, and the proportion of free 

 to potential variability will remain constant. Nevertheless, because 

 of the continual interchange of variability between the free and 

 potential states, the situation cannot be a fixed one. There is, in fact, 

 a. flow of variability: any particular variant, although present in the 

 same proportions in different generations, appears in different 

 families or lineages. The population may be, in a certain sense, 



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