Size-dependent sex change can be the ESS without any size advantage of reproduction when mortality is size-dependent

Almost all models of sex change evolution assume that reproductive rate increases with body size. However, size-dependent sex changing plants often show size-independent reproductive success, presumably due to pollen limitation. Can the observed size-dependent sex change pattern be the ESS in this case? To answer this question, we analyze a game model of size-dependent sex expression in plants. We assume: (1) reproductive rate is perfectly independent of size; (2) mortality decreases with size in the same way for both sexes; (3) growth rates decrease at maturity, more for females than males. We show that the ESS is size-dependent sex expression: small individuals are vegetative, intermediate individuals are male, and large individuals are female. These results demonstrate that mortality is important in size-dependent sex allocation even when mortality rate is independent of sex. They also offer an explanation of why we see populations in poor environments to have sex ratios more biased toward the first sex relative to high quality environments.