A Dynamic Model of Size‐Dependent Reproductive Effort in a Sequential Hermaphrodite: A Counterexample to Williams's Conjecture

Abstract

In 1966, G. C. Williams showed that for iteroparous organisms, the level of reproductive effort that maximizes fitness is that which balances the marginal gains through current reproduction against the marginal losses to expected future reproduction. When, over an organism's lifetime, the value of future reproduction declines relative to the value of current reproduction, the level of effort allocated to current reproduction should always increase with increasing age. Conversely, when the value of future reproduction increases relative to the value of current reproduction, the level of effort allocated to current reproduction should decrease or remain at zero. While this latter pattern occurs commonly in species that exhibit a delayed age at first reproduction, it may also occur following an initial period of reproduction in some sex-changing organisms that experience a dramatic increase in reproductive potential as they grow larger. Indeed, this schedule of reproductive effort is predicted by models of "early" sex change; however, these models may arrive at this result incidentally because they consider only two reproductive states: on and off. In order to examine the schedule of reproductive effort in greater detail in a system where the potential reproductive rate increases sharply, we adapt the logic and methods of time-dependent dynamic-programming models to develop a size-dependent model of reproductive effort for an example species that experiences a dramatic increase in reproductive potential at large sizes: the bluehead wrasse, Thalassoma bifasciatum. Our model shows that the optimal level of reproductive effort will decline with increasing size or age when increases to the residual reproductive value outpace the increases to current reproductive potential. This result confirms the logic of Williams's analysis of optimal life histories, while offering a realistic counterexample to his conjecture of ever-increasing allocation to current reproduction.