Evolution of sexual systems and sex allocation in plants when growth and reproduction overlap

The common sexual systems in seed plants are hermaphroditism, dioecy, and gynodioecy. Here we attempt to explain this pattern by extending the 'classical' resource allocation model for the evolution of sexual systems. First we derive the equilibrium frequencies of all sex morphs and the sex allocations of hermaphrodites as functions of the male and female gain exponents, under the classical assumption that allocation takes place instantaneously from a fixed pool of resources. This analysis reveals two implications of the model that are not widely appreciated: (i) individuals of one sex (males or females) with a decelerating gain function may coexist with hermaphrodites when the gain function for the other sex is accelerating; and (II) there are large regions of parameter space where the evolutionarily stable sexual system is subdioecy (a high frequency of one sex, with hermaphrodites whose allocation ratios are strongly biased toward the opposite sex function). Then we relax the unrealistic phenological assumption of the classical model and consider models where male allocation precedes female allocation, and where there are tradeoffs between growth and reproduction. When growth and reproduction overlap but there is no tradeoff between them, the predicted ESS sex allocations and sexual systems are identical to those of the classical model (for the same male and female gain exponents). But where there is a tradeoff, the ESS allocation ratios tend to be more female biased than in the classical model, and all three of the common sexual systems (but not androdioecy) can evolve where there is a saturating relation between investment in growth and realised growth.