Modifiers of mutation rate in selectively fluctuating environments

TL;DR

This paper models how mutation rates evolve in large populations under rapidly changing environments, deriving limit results and fixation probabilities for mutation rate modifiers in a two-locus setting.

Contribution

It introduces a mutation-selection model with a fluctuating environment and provides new limit results for allele frequency evolution under rapid environmental changes.

Findings

Derived general limit results for allele frequency distributions.

Computed fixation probabilities for higher mutation rates in a two-locus model.

Applied Fleming-Viot process to analyze mutation rate evolution.

Abstract

We study a mutation-selection model with a fluctuating environment. More precisely, individuals in a large population are assumed to have a modifier locus determining the mutation rate $u \in [0,\vartheta]$ at a second locus with types $v \in [0,1]$. In addition, the environment fluctuates, meaning that individual types change their fitness at some high rate. Fitness only depends on the type of the second locus. We obtain general limit results for the evolution of the allele frequency distribution for rapidly fluctuating environments. As an application, we make use of the resulting Fleming-Viot process and compute the fixation probabilities for higher mutation rates in the special case of two bi-allelic loci in the limit of small fitness differences at the second locus.