Gain curves and sex allocation: why the Shaw-Mohler equation works and when it doesn't

Abstract

Fitness gain curves were introduced into the framework of the Shaw-Mohler equation, the foundation of sex allocation theory. I return to this equation to consider how it embodies the rare-sex advantage underlying frequency-dependent selection on the sex ratio. The Shaw-Mohler formulation is based on the numbers of males and females randomly mating in a panmictic population. Gain curves were meant to describe reproductive success through male and female functions in hermaphrodites and were inserted in place of male and female numbers in the Shaw-Mohler equation. In doing so, gain curves bypass the implicit mating process in the Shaw-Mohler argument that creates frequency-dependent selection. Gain curves can then lead to anomalies like unequal total male and female fitness in a population. If gain curves truly represent fitness gain, they must have a population-level effect on both sexes, a basic necessity of sexual reproduction. The blurring of inputs with fitness outcome has lead to misinterpretation of what gain curves mean in reproductive ecology. They lack causal efficacy with respect to sex allocation. Because gain curves have been a staple of evolutionary ecology for decades, the implication is that much of our understanding of sexual allocation in hermaphrodites needs to be revisited. I outline some directions such an effort might take.