The fixation probability of rare mutators in finite asexual populations

TL;DR

This study combines simulation and analytical methods to understand the fixation probability of rare mutator alleles in finite asexual populations, considering mutation rates, genetic drift, and mutational load, with implications for evolutionary dynamics.

Contribution

It introduces a diffusion-based approximation for mutator fixation probability that accounts for multiple factors, providing new insights into conditions favoring mutator evolution.

Findings

Fixation probability is mainly influenced by genetic drift and mutational load.

Effect of competition with wild-type mutations is generally small for strong-effect mutators.

Results align semi-quantitatively with laboratory evolution experiments.

Abstract

A mutator is an allele that increases the mutation rate throughout the genome by disrupting some aspect of DNA replication or repair. Mutators that increase the mutation rate by the order of 100 fold have been observed to spontaneously emerge and achieve high frequencies in natural populations and in long-term laboratory evolution experiments with \textit{E. coli}. In principle, the fixation of mutator alleles is limited by (i) competition with mutations in wild-type backgrounds, (ii) additional deleterious mutational load, and (iii) random genetic drift. Using a multiple locus model and employing both simulation and analytic methods, we investigate the effects of these three factors on the fixation probability $P_{fix}$ of an initially rare mutator as a function of population size $N$, beneficial and deleterious mutation rates, and the strength of mutations $s$. Our diffusion based approximation for $P_{fix}$ successfully captures effects (ii) and (iii) when selection is fast compared to mutation ($\mu/s \ll 1$). This enables us to predict the conditions under which mutators will be evolutionarily favored. Surprisingly, our simulations show that effect (i) is typically small for strong-effect mutators. Our results agree semi-quantitatively with existing laboratory evolution experiments and suggest future experimental directions.