The nature of gain curves.

Gain curves have been a staple of sex allocation theory for decades. They represent patterns in which fitness is obtained from resource investments in reproductive functions. The monotonic forms that have been used for gain curves can represent fitness accrual by individuals, but only on the assumption that sufficient mates are always available to allow the stipulated monotonic pattern of reproductive success to occur. However, sexual populations do not have external banks of mating opportunities that lie outside the dynamics of the population (such opportunities would, by definition, be part of the population). Thus, the reproductive behaviour of whole populations cannot be simple scaled-up versions of individual gain curves. As sex allocation evolves within a breeding population, frequency-dependent selection creates a shifting advantage for the rarer sex. Individual gain curves cannot then remain stable possibilities at the population level. Evolutionary models based on fixed gain curves can predict evolutionary outcomes with unequal total fitness for male and for female function, an outcome that the biology of syngamy does not allow. Such biologically impossible outcomes are easily demonstrated. Gain curves have also been widely used as a framework for interpretation of interspecific empirical patterns, such as low male allocation in monogamously mating hermaphroditic animals or self-pollinating plants, and higher male allocation in wind-pollinated than in animal-pollinated plants. However, if gain curves incorrectly characterize whole populations or species, interspecific differences in gain curves cannot explain these patterns. Even if they superficially appear to predict the empirical pattern, other processes must be operating. The selective effects of local mating competition and sex-specific dispersal patterns have long been known. They are likely replacements for gain curves as explanations of many broad interspecific patterns, but the predominance of gain-curve explanations has distracted attention from these alternatives. A revision of our understanding of gain curves seems needed.