Epistatic selection opposed by immigration in multiple locus genetic systems

Abstract

AbstractA model of “complete” epistatis is considered in which all “plus” alleles must be present in an individual before the adaptive phenotype is expressed. The conditions under which the plus alleles and hence the adaptive phenotype can increase and reach a stable equilibrium in the presence of immigration of gametes carrying minus alleles are found. In haploids and diploids in which the plus alleles are recessive, frequencies of the plus alleles are the same at all loci, regardless of the linkage relationships. Tight linkage favors the existence of a locally stable polymorphic equilibrium, but the equilibrium with only minus alleles is locally stable unless there is very tight linkage or very strong selection. Thus, this kind of epistasis, which provides a simple model for a character that requires several components to be present at the same time, is very sensitive to even a small amount of immigration. Hence, the evolution of such characters is likely only in completely rather than partially isolated populations.