Evolutionarily stable sex ratios and sex allocations

The paternal fitness of a sexual individual is equated with the fitness of those eggs of its potential mates which it is able to fertilize. This property enables the total sexual fitness of individuals to be expressed in terms of female gamete contributions in separate equations for a cosex (an individual in a population composed of a single sexual class which combines male and female functions) and for parents in a dioecious population. The general equations are used in phenotypic models of selection which examine conditions maximizing the fitness advantage of one phenotype over another with a different sex ratio or allocation. As an example, it is shown that finite population size confers full stability on the sexual allocations in a cosexual population and on the sex ratio in a dioecious population.The use of fitness advantages provides the outcome of selection for all frequencies of contrasted phenotypes. It is therefore possible to redefine an ESS to allow for persistent variability in a population. A phenotype is an ESS in a population if, from any initial frequency, it is protected from loss by its fitness advantage. The conditions for a rare mutant to spread invariably coincide with those for its fixation only if an individual of any phenotype affects the fitness of other individuals of all phenotypes in identical ways.