Why the Shaw-Mohler equation works and when it doesn't.

Fitness gain curves were introduced into the framework of the Shaw-Mohler equation, the foundation of sex allocation theory. I return to the Shaw-Mohler 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 are meant to describe reproductive success through male and female functions in hermaphrodites and have been inserted in place of male and female numbers in the Shaw-Mohler equation. In doing so, gain curves bypass consideration of the implicit mating process in the Shaw-Mohler argument and can lead to anomalies like unequal total male and female fitness in a population. If gain curves truly represent fitness gain, equality of total male and female fitness requires a constant sex allocation of equal resource investment into male and female functions. The blurring of input with fitness outcome has led to misinterpretation of what gain curves mean in reproductive ecology. They can describe a particular reproductive ecology, such as diminishing fitness returns on resource investment, but lack causal efficacy with respect to sex allocation.