A novel application of Approximate Bayesian Computation for detecting male reproductive advantages due to mating order

Abstract

Studies of the effects of mating order on fertilization success, classically analyzed as the proportional paternity of the second male, have advanced our understanding of the relative influences of postcopulatory male–male competition and female choice on sexual selection. However, results from these studies are often difficult to analyze because (1) distributions of offspring per dam rarely follow a normal distribution and (2) proportional paternities are never normally distributed. Previous studies partially account for these limitations by using nonparametric statistics. However, behavioral studies are often plagued by relatively small sample sizes and require a more powerful analytical approach. Here, we develop a new analytical framework for studying fertilization bias. Our Approximate Bayesian Computational (ABC) model overcomes many of the limitations of currently employed methods. We apply our model to analyze the effects of male mating order on paternity success in the brown anole lizard, Anolis sagrei. Using our ABC simulation, we find a marked first-male advantage: first males sired approximately 80 % of the offspring in our study. Next, based on re-analysis of four previously published datasets, we show that traditional statistical methods often over- or underestimate biases related to mating order. Moreover, by comparing our model to more traditional statistical tests, we show that the ABC method is robust to relatively small samples sizes and should therefore be useful for studying mating-order effects in a variety of systems. Our model is implemented as an R package, ABCp2, and is freely available for use.