The opportunity to be misled in studies of sexual selection

It is a challenge to measure sexual selection because both stochastic events (chance) and deterministic factors (selection) generate variation in individuals' reproductive success. Most researchers realize that random events ('noise') make it difficult to detect a relationship between a trait and mating success (i.e. the presence of sexual selection). There is, however, less appreciation of the dangers that arise if stochastic events vary systematically. Systematic variation makes variance-based approaches to measuring the role of selection problematic. This is why measuring the opportunity for sexual selection (I(s) and I(mates)) is so vulnerable to misinterpretation. Although I(s) does not measure actual sexual selection (because it includes stochastic variation in mating/fertilization success) it is often implicitly assumed that it will be correlated with the actual strength of sexual selection. The hidden assumption is that random noise is randomly distributed across populations, species or the sexes. Here we present a simple numerical example showing why this practice is worrisome. Specifically, we show that chance variation in mating success is higher when there are fewer potential mates per individual of the focal sex [i.e. when the operational sex ratio (OSR), is more biased]. This will lead to the OSR covarying with I(s) even when the strength of sexual selection is unaffected by the OSR. This can generate false confidence in identifying factors that determine variation in the strength of sexual selection. We emphasize that in nature, even when sexual selection is strong, chance variation in mating success is still inevitable because the number of mates per individual is a discrete number. We hope that our worked example will clarify a recent debate about how best to measure sexual selection.