Some consequences of selection by culling when there is superiority of heterozygotes.

N most of the existing theory of selection the genotypes present in a population I are assumed to have constant selective advantages or disadvantages in relation to each other. But a different case was considered by HALDANE (1 961 ) . He assumed that generations do not overlap and that in each generation a proportion C of the males and a proportion c of the females are removed from the population between birth and sexual maturity. If there is natural selection the removal is by death, while if there is artificial selection the removed individuals are those culled by the breeder. In both cases the mathematics is the same, so that for convenience we can say that there is selection by culling. HALDANE assumed, in conformity with what usually occurs in animal breeding situations, that C > c, so that there is more severe culling among males than among females. For simplicity, only the case in which two genes, A and a, were present was considered. It was assumed that there were at least two distinguishable phenotypes among the three genotypes. A way in ‘which this selection scheme differs from that usually considered is that the adaptive value of a given genotype is no longer necessarily constant, but may change with the frequency of a gene. For in any generation the worst individuals are culled, and this results in reducing the frequency of the most inferior genotype. It is then possible, after a certain number of generations, for some individuals of another genotype to be culled, although originally all such individuals were allowed to breed. The problem: HALDANE considered cases in which one of the two genes is dominant or partially dominant to the other. We shall consider a case of overdominance in which the genotypic values of AA, Aa and aa individuals are yll, y12 and y Z 2 respectively, where yna < yll < y12. In every generation some of the individuals having the lowest genotypic values are culled. Following HALDANE’S notation, we say that the females in the nth generation produce the gametic array p,A + (1 -pm) a while the males of that generation produce the gametic array g,A + (1 g , ) a. Then if the survivors mate at random the genotypic array at birth in the next generation is p+AA + (pn + 4, 2p,q,)Aa + (1 p , ) ( 1 g,)aa . There can then be five possible stages in the process of selection. These are: (a) only aa’s are culled; ( b ) only ua’s are culled from the females, but all aa’s