Response of polygenic traits under stabilising selection and mutation when loci have unequal effects

TL;DR

This paper derives analytical models for the genetic variance and short-term evolutionary dynamics of polygenic traits with unequal effects under stabilising selection and mutation, highlighting how effect size distribution influences adaptation speed.

Contribution

It provides new analytical expressions for genetic variance and models the short-term adaptation dynamics considering effect size heterogeneity.

Findings

Genetic variance remains stable when effects are small during adaptation.

Large-effect loci significantly influence variance change and adaptation speed.

Rapid adaptation occurs when many small-effect loci are involved.

Abstract

We consider an infinitely large population under stabilising selection and mutation in which the allelic effects determining a polygenic trait vary between loci. We obtain analytical expressions for the stationary genetic variance as a function of the distribution of effects, mutation rate and selection coefficient. We also study the dynamics of the allele frequencies, focussing on short-term evolution of the phenotypic mean as it approaches the optimum after an environmental change. We find that when most effects are small, the genetic variance does not change appreciably during adaptation, and the time until the phenotypic mean reaches the optimum is short if the number of loci is large. However, when most effects are large, the change of the variance during the adaptive process cannot be neglected. In this case, the short-term dynamics may be described by that of a single locus of large effect. Our results may be used to understand polygenic selection driving rapid adaptation.