Theoretical Analysis of Electrophoretically Detectable Polymorphisms: Models of Very Slightly Deleterious Mutations

Abstract

The nature of mutation-selection balance was investigated using models of mutation which assume stepwise production of new alleles in the allele space occupied by one or two type genes and multiple slightly deleterious mutations. The distribution of allelic frequencies and the effective number of alleles at equilibrium were obtained based on deterministic treatments. It was shown that they depend on the ratio between the selection coefficient and the mutation rate (s/v). When this ratio is large, the frequencies of the deleterious alleles become too low to form polymorphism; however, when the ratio is small, such a mutation-selection balance becomes important as a cause of polymorphism. In addition to analytical treatments, extensive Monte Carlo experiments were per. formed to investigate the stochastic effect due to small population size. When the effective population size (N_e) is small so that both N_e ^v and N_e ^s are small, the allele distribution is indistinguishable from the neutral case, while it approaches the deterministic equilibrium as N_e gets larger. The bearing of the present models on observations regarding protein polymorphisms was discussed.