The concept of the gain curve

Gain curves were introduced to explain how hermaphrodites could displace a dioecious population, and to account for sexual allocation in hermaphrodites. Terms for gamete production employed for the first purpose were transformed for the second into male and female gain curves that ostensibly defined fitness outcomes. These gain curves pose a conceptual challenge if they are specified separately because fitness at the population level cannot occur through one sex function independently of success through the other. If gain curves truly represent fitness outcomes, anomalies can arise, such as inequality of total male and female fitness in a population. Gain curves were originally used in a mathematical framework that treated the ostensible gain functions as inputs of male and female actors to a mating arena rather than as mating outcomes from that arena. I present a model of sex allocation that incorporates power functions to describe both gamete production and fitness gain in a manner that explicitly separates these two roles. In this formulation, the gamete production functions have the identical effect on optimal sex allocation originally attributed to gain curves while the true fitness gain curves lose nearly all effect on the optimum. Thus, despite the label, gain curves were implicitly describing inputs rather than outcomes. 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.