When can fitness epistasis be ignored in a polygenic trait at equilibrium?

TL;DR

This paper analyzes when fitness epistasis can be ignored in modeling allele frequencies of polygenic traits at equilibrium, providing conditions under which epistasis impacts frequency distributions but not phenotypic measures.

Contribution

It offers an analytical framework to determine parameter regimes where fitness epistasis influences allele frequencies but not phenotypic quantities in polygenic traits.

Findings

Identifies parameter regimes where epistasis affects allele frequency distribution.

Shows phenotypic measures are well captured even when epistasis is ignored.

Finds a threshold effect size distinguishing unimodal and bimodal allele frequency distributions.

Abstract

Although many phenotypic traits are determined by a large number of genetic variants, the behavior of allele frequencies in a polygenic trait is not completely understood. The problem is especially challenging when the quantitative trait of interest is under epistatic selection as the allele frequency at a locus is affected by those at other loci. Here, we consider a panmictic, diploid finite population evolving under stabilizing selection and symmetric mutations when the population is in linkage equilibrium. In the stationary state, using a diffusion theory, we calculate the marginal distribution of allele frequency, and find parameter regimes where fitness epistasis can not be ignored for an accurate description of the frequency distribution. For such parameters, the mean deviation in the phenotypic optimum and genic variance are, however, found to be well captured even when epistatic interactions are neglected. Thus, while the presence of epistasis may not be evident in phenotypic quantities, it can strongly affect the allele frequency distribution.We also find that the allele frequency distribution at a locus is unimodal if its effect size is below a threshold effect and bimodal otherwise; these results are the stochastic analog of the deterministic ones where the stable allele frequency becomes bistable when the effect size exceeds a threshold. Our analytical results are verified against Monte Carlo simulations and numerical integration of a Langevin equation.