Theoretical sex ratios of dioecious and gynodioecious angiosperms

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The following parameters affecting the frequency of male and female plants in sexually dimorphic Angiosperms are defined: relative fecundity (as seed parent), F, differential survival, S, and gamete success, G, all as male/female quotients, and the probability of fertilisation of ovules on female plants, in terms of the number of pollinator visits to the flowers, x. Four different modes of inheritance of gynodioecy and dioecy are examined: The equilibrium frequencies of females and (for three models) the rates of change in female frequency per generation at non-equilibrium frequencies are expressed in terms of the controlling parameters. The conditions necessary for sexual dimorphism and the changes in frequencies of the sex genotypes as the number of pollinator visits increase and the relative seed fecundity decreases towards zero (dioecy) are derived for each model. Differential survival of the sexes (and differential gamete success in the heterozygous male model) cause an increase at equilibrium in the sex surviving more frequently or the sex derived from the more successful gamete. In a dioecious population, the ratio of the sexes is equal to their relative survival or their relative gamete success. Populations at non-equilibrium frequencies return more rapidly to equilibrium with the heterozygous male model than with the heterozygous female and cytoplasmic models. In the extreme case when females are lost from a population, with the heterozygous female and cytoplasmic models extinction or loss of sexual dimorphism occurs, but with the heterozygous male and dual male models sexual dimorphism is regenerated. The ability of systems with heterozygous males to regenerate dimorphism may explain the prevalence of such systems in both gynodioecious and dioecious populations.