A Bayesian model for assessing the frequency of multiple mating in nature

Many breeding systems have multiple mating, in which males or females mate with multiple partners. With the advent of molecular markers, it is now possible to detect multiple mating in nature. However, no model yet exists to effectively assess the frequency of multiple mating (f(mm))-the proportion of broods with at least two males (or females) genetically contributing-from limited genetic data. We present a single-sex model based on Bayes' rule that incorporates the numbers of loci, alleles, offspring, and genetic parents. Two genetic criteria for calculating f(mm) are considered: the proportion of broods with three or more paternal (or maternal) alleles at any one locus and the total number of haplotypes observed in each brood. The former criterion provides the most precise estimates of f(mm). The model enables the calculation of confidence intervals and allows mutations (or typing errors) to be incorporated into the calculation. Failure to account for mutations can result in overestimates of f(mm). The model can also utilize other biological data, such as behavioral observations during mating, thereby increasing the accuracy of the calculation as compared to previous models. For example, when two sires contribute equally to multiply mated broods, only three loci with five equally common alleles are required to provide estimates of fmm with high precision. We demonstrate the model with an example addressing the frequency of multiple paternity in small versus large clutches of the endangered Kemp's Ridley sea turtle (Lepidochelys kempi) and show that females that lay large clutches are more likely to have multiply mated.