Overcoming statistical bias to estimate genetic mating systems in open populations: a comparison of Bateman's principles between the sexes in a sex-role-reversed pipefish.

The genetic mating system is a key component of the sexual selection process, yet methods for the quantification of mating systems remain controversial. One approach involves metrics derived from Bateman's principles, which are based on variances in mating and reproductive success and the relationship between them. However, these measures are extremely difficult to measure for both sexes in open populations, because missing data can result in biased estimates. Here, we develop a novel approach for the estimation of mating system metrics based on Bateman's principles and apply it to a microsatellite-based parentage analysis of a natural population of the dusky pipefish, Syngnathus floridae. Our results show that both male and female dusky pipefish have significantly positive Bateman gradients. However, females exhibit larger values of the opportunity for sexual selection and the opportunity for selection compared to males. These differences translate into a maximum intensity of sexual selection (S'max) for females three times larger than that for males. Overall, this study identifies a critical source of bias that affects studies of mating systems in open populations, presents a novel method for overcoming this bias, and applies this method for the first time in a sex-role-reversed pipefish.