A general approach to genetic equilibria with an uneven sex ratio

It is shown that in a diploid population at a genetic equilibrium with an uneven sex ratio the distribution of all (inertial) autosomal genes is symmetric between the two sexes. If several allelic genes occur in the population then the sex ratios of the various genotypes uniquely determine the uneven population sex ratio. The equilibrium is unstable to invasion by new genes which are relatively more frequent among the less numerous sex. A new proof is given to the fact that if genotype sex ratios do not change then, following an invasion by a new allele, a new stable polymorphic equilibrium can only correspond to a sex ratio which is more even than the old one. Application of these general results to a model of offspring sex determination by parents' autosomal genes shows the equilibrium to be unstable to invasion by new genes which tend to increase the production of offspring of the minority sex, as proposed by Fisher. The relevance of the Shaw-Mohler formula in this context is shown to derive from its role in describing the dynamics of autosomal genes in general. In connection with a model for offspring sex determination by one parent, a new proof is given to the fact that, following an invasion by a new allele, a new stable polymorphic equilibrium can only correspond to a sex ratio which is more even than the old one.