Polyallelic mutational equilibria

Abstract

A new deterministic formulation is derived of the equilibrium between mutation and natural selection, which takes into account(a) the possibility of many allelic mutation states, (b) selection coefficients of the order of magnitude of the mutation rate and (c) the possibility of further mutation of already mutant alleles. The frequencies of classes of alleles 0, 1, 2, n mutant steps removed from the type allele are shown to form a Poisson distribution, with a mean and variance of the mutation rate divided by the coefficient of selection against each incremental mutational step.--This formulation is interpreted in terms of the expected frequencies of electromorphs, defined as classes of alleles characterized by common electrophoretic mobilities of their protein products. Electromorph frequencies are predicted to form stable unimodal distributions of relatively few phenotypic classes. Common electromorph frequencies found throughout the ranges of species with large population sizes are interpreted as being a uniquely electrophoretic phenomenon; band patterns on starch and acrylamide gels are phenotypes, not genotypes. It is predicted that individual electromorphs are highly heterogenous with regard to amino acid sequence.