The Equilibrium Allele Frequency Distribution for a Population with Reproductive Skew

Abstract

We study the population genetics of two neutral alleles under reversible mutation in a model that features a skewed offspring distribution, called the Λ-Fleming-Viot process. We describe the shape of the equilibrium allele frequency distribution as a function of the model parameters. We show that the mutation rates can be uniquely identified from this equilibrium distribution, but the form of the offspring distribution cannot itself always be so identified. We introduce an estimator for the mutation rate that is consistent, independent of the form of reproductive skew. We also introduce a two-allele infinite-sites version of the Λ-Fleming-Viot process, and we use it to study how reproductive skew influences standing genetic diversity in a population. We derive asymptotic formulas for the expected number of segregating sites as a function of sample size and offspring distribution. We find that the Wright-Fisher model minimizes the equilibrium genetic diversity, for a given mutation rate and variance effective population size, compared to all other Λ-processes.