Stepwise mutation model and distribution of allelic frequencies in a finite population

Abstract

A mathematical theory is developed that enables us to derive a formula for the equilibrium distribution of allelic frequencies in a finite population when selectively neutral alleles are produced in stepwise fashion (stepwise mutation model). It is shown that the stepwise mutation model has a remarkable property that distinguishes it from the conventional infinite allele model (Kimura-Crow model): as the population size increases indefinitely while the product of the effective population size and the mutation rate is kept at a fixed value, the mean number of different alleles contained in the population rapidly reaches a plateau which is not much larger than the effective number of alleles (reciprocal of homozygosity).