On the optimal sex ratio.

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Abstract
The equilibrium structures for various multiallele sex-determining genetic models of panmictic populations with sex expression depending on the genotypes of either the zygote or a parent are described. Even-sex-ratio equilibrium surfaces can exist apart from equilibrium points having coincident male and female allelic frequency sets. The latter (symmetric) equilibrium states entail biased sex ratios. A stable symmetric equilibrium and an even-sex-ratio equilibrium segregating the same alleles cannot coexist. The tendency to evolve toward an even-sex ratio is embodied by the following optimality property: starting from an equilibrium having a biased sex ratio, mutant sex-determining alleles can accumulate only in the case in which in the augmented system all attainable equilibrium states have a sex ratio closer to 1 to 1.

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