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

Background/Question/Methods   Sex change in fishes and terrestrial plants has been discussed mostly based on the size advantage model - reproductive rate increases with body size for at least one sex and differently between the sexes. The ESS is first to mature as the sex with the slower increase and then to switch to the sex with the faster increase in reproductive rate with size. Past theoretical studies show that size-dependent sex change is the ESS when mortality differs between sexes, or growth rate differs between sexes, but the reproductive rate increases with size in the same manner between sexes. However, size-dependent sex changing terrestrial plants often show size-independent reproductive success, presumably due to limited pollen delivery by pollinators. 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 for terrestrial plants. We assume: (1) reproductive success is independent of size for both sexes; (2) mortality decreases with size in the same way for both sexes; (3) growth rates decrease at maturity, more for females than for males.

Results/Conclusions   We demonstrate that the ESS is in fact size-dependent sex expression: small individuals are vegetative, intermediate sized individuals are male, and large individuals are females. These results support earlier theoretical work that predicts that size-dependent mortality is important in size-dependent sex allocation even when mortality rate is independent of sex. This could explain why some empirical study results do not fit predictions of simpler models; perhaps size-dependent mortality and growth need to be accounted for in addition to reproductive rates. Results of elasticity analyses offer explanations of why we see sex ratios of populations in poor environments to be even more biased toward the first sex relative to high quality environments; it could be due to either slower growth or higher mortality risk in poor quality sites.