Selection and mutation at an X-linked locus

The most general mutation-selection model with discrete non-overlapping generations is formulated for a multiallelic X-linked locus. The difference equations for the gene frequencies, though dependent on the female genotypic proportions, are shown to have a simple form. If mating is random and the rates at which various unions produce females may be expressed as products of factors depending on the male and female parental genotypes, then the female zygotic frequencies are proved to be generalized Hardy-Weinberg proportions with respect to the male and female gametic frequencies. As the main application of the formalism, assuming only that mutation is much weaker than selection, the total frequencies of mutant alleles in males and females at equilibrium are related to the mutation rates and mean selection coefficients in the two sexes.