The equilibrium allele frequency distribution for a population with reproductive skew

TL;DR

This paper investigates how reproductive skew affects the equilibrium allele frequency distribution and genetic diversity in populations, revealing unique mutation rate identification and the minimal diversity under Wright-Fisher dynamics.

Contribution

It introduces an analysis of allele frequencies under bb-processes with reproductive skew and compares genetic diversity across models, including an infinite-sites version.

Findings

Mutation rates can be uniquely identified from equilibrium distributions.

Reproductive skew influences the shape of allele frequency distributions.

Wright-Fisher minimizes genetic diversity for given parameters.

Abstract

We study the population genetics of two neutral alleles under reversible mutation in the \Lambda-processes, a population model that features a skewed offspring distribution. 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 the equilibrium distribution, but that the form of the offspring distribution itself cannot be uniquely identified. We also introduce an infinite-sites version of the \Lambda-process, and we use it to study how reproductive skew influences standing genetic diversity in a population. We derive asymptotic formulae for the expected number of segregating sizes as a function of sample size. 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 \Lambda-processes.