Statistical power to detect multiple paternity in populations of highly fertile species: how many females and how many offspring should be sampled?

Abstract

One of the central issues of behavioral ecology focuses on the probability of detecting multiple paternity in a scenario of polygamy. The main problem for this kind of analysis arises in species with large number of offspring in the same litter and large population sizes in which only a small fraction of progeny and females can be analyzed. Here, we present a method to estimate the statistical power to detect multiple paternity for these species. Since calculations involved handling of very large numbers, Ramanujan's approximation to factorials was used to make them possible in the R software. We exemplified this method using features observed in crabs; (i) females carry thousands or millions of embryos per brood, (ii) typically less than 50% of females show multiple paternity, and (iii) high contribution of a single male (>90%) in a brood. Genetic parental analysis assumes the use of loci that allow maximal discrimination among individuals. The results showed that the number of females sampled is an important point to be considered to detect multiple paternity with high statistical power. Comparisons of different numbers of sampled females and embryos showed that 20 larvae from 50 females present satisfactory statistical power even when all males except the main contributor sired a modest number of embryos and only a small proportion of females showed embryos sired by more than one male. The proposed method can improve the sampling design in order to reach sufficient levels of statistical power when testing for multiple paternity in species with high fecundity, a common characteristic in both terrestrial and aquatic environments. Significance statement To detect multiple paternity in highly fertile species, researchers commonly use the probability of detecting multiple mating (PrDM). Although the PrDM is a powerful tool to detect multiple paternity in a litter/brood/clutch, this analysis neglects the estimation of the statistical power at the population level. Here, we developed an analytical method to assess the statistical power to detect multiple paternity considering brood size and the number of females sampled in a population. The model tested with 1,000,000 of embryos per brood (as in marine crabs), different numbers of embryos per brood, and different numbers of females analyzed reached values of statistical power greater than 99% when the first male sired 90% of the progeny and 50% of females had multiple paternity. This analysis showed the importance of focusing on the experimental unit in the experimental design in studies where multiple paternity is being tested.