Role of epistasis on the fixation probability of a non-mutator in an adapted asexual population

TL;DR

This study analytically investigates how epistatic interactions influence the likelihood of a non-mutator fixing in an adapted asexual population, revealing that antagonistic and synergistic epistasis have opposite effects.

Contribution

It provides an analytical framework for understanding the impact of epistasis on mutation rate reduction in asexual populations, highlighting the non-monotonic behavior of fixation probability.

Findings

Antagonistic epistasis lowers fixation probability.

Synergistic epistasis increases fixation probability.

Fixation probability exhibits non-monotonic behavior below a critical epistasis value.

Abstract

The mutation rate of a well adapted population is prone to reduction so as to have a lower mutational load. We aim to understand the role of epistatic interactions between the fitness affecting mutations in this process. Using a multitype branching process, the fixation probability of a single non-mutator emerging in a large asexual mutator population is analytically calculated here. The mutator population undergoes deleterious mutations at constant, but at a much higher rate than that of the non-mutator. We find that antagonistic epistasis lowers the chances of mutation rate reduction, while synergistic epistasis enhances it. Below a critical value of epistasis, the fixation probability behaves non-monotonically with variation in mutation rate of the background population. Moreover, the variation of this critical value of the epistasis parameter with the strength of the mutator is discussed in the Appendix. For synergistic epistasis, when selection is varied, the fixation probability reduces overall, with damped oscillations.