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Evolution of the sex ratio and effective number under gynodioecy and androdioecy

We address the evolution of effective number of individuals under androdioecy and gynodioecy. We analyze dynamic models of autosomal modifiers of weak effect on sex expression. In our zygote control models, the sex expressed by a zygote depends on its own genotype, while in our maternal control models, it depends on the genotype of its maternal parent. Our analysis unifies full multi-dimensional local stability analysis with the Li-Price equation, which for all its heuristic appeal, describes evolutionary change over a single generation. We define a point in the neighborhood of a fixation state from which a single-generation step indicates the asymptotic behavior of the frequency of a modifier allele initiated at an arbitrary point near the fixation state. A concept of heritability appropriate for the evolutionary modification of sex emerges from the Li-Price framework. We incorporate our theoretical analysis into our previously-developed Bayesian inference framework to develop a new method for inferring the viability of gonochores (males or females) relative to hermaphrodites. Applying this approach to microsatellite data derived from natural populations of the gynodioecious plant Schiedea salicaria and the androdioecious killifish Kryptolebias marmoratus, we find that while female and hermaphrodite S. salicaria appear to have similar viabilities, male K. marmoratus appear to survive to reproductive age at less than half the rate of hermaphrodites.