Sex Determination in a Symmetrical Autosomal Multi-locus Model

A model of determination of sex by an individual′s genotype at n loci is discussed. The parameters that determine the probability that an individual is male (or female) depend only on the loci at which the individual is heterozygous, extending the two-gene theory of Feldman et al. (1991, Genetics129, 297-312). The analysis uses a set indexation technique that allows a compact expression of the recombination process, and a transformation of the chromosome frequencies that induces a natural subgroup structure on hyperplanes in the frequency simplex. It is shown that the polymorphic equilibria correspond to these subgroups. Conditions are determined under which equilibria that exhibit the even sex ratio are stable. How recombination affects the stability of other equilibria, including those with linkage disequilibrium, are also explored.