# Fixation probability of a nonmutator in a large population of asexual mutators

## TL;DR

This paper calculates the fixation probability of a nonmutator in a large asexual mutator population, revealing complex dependencies on mutation rates and the influence of beneficial mutations, using a multitype branching process.

## Contribution

It introduces a model to compute fixation probabilities of nonmutators considering mutation effects and beneficial mutations, providing new insights into mutation rate evolution.

## Key findings

- Fixation probability is nonmonotonic with mutator mutation rate.
- Beneficial mutations increase nonmutator fixation probability.
- Fixation probability decreases exponentially at high mutation rates.

## Abstract

In an adapted population of mutators in which most mutations are deleterious, a nonmutator that lowers the mutation rate is under indirect selection and can sweep to fixation. Using a multitype branching process, we calculate the fixation probability of a rare nonmutator in a large population of asexual mutators. We show that when beneficial mutations are absent, the fixation probability is a nonmonotonic function of the mutation rate of the mutator: it first increases sublinearly and then decreases exponentially. We also find that beneficial mutations can enhance the fixation probability of a nonmutator. Our analysis is relevant to an understanding of recent experiments in which a reduction in the mutation rates has been observed.