Loss of least-loaded class in asexual populations due to drift and epistasis

TL;DR

This paper analyzes how deleterious mutations accumulate in asexual populations, showing that synergistic epistasis can halt this process, with explicit formulas for the rate of mutation accumulation.

Contribution

It provides analytical expressions for the rate of Muller's ratchet in populations with and without epistasis, highlighting the impact of synergistic interactions.

Findings

Without epistasis, the ratchet speed depends on population size and selection.

Synergistic epistasis rapidly slows or halts the ratchet.

Analytical results match numerical simulations.

Abstract

We consider the dynamics of a non-recombining haploid population of finite size which accumulates deleterious mutations irreversibly. This ratchet like process occurs at a finite speed in the absence of epistasis, but it has been suggested that synergistic epistasis can halt the ratchet. Using a diffusion theory, we find explicit analytical expressions for the typical time between successive clicks of the ratchet for both non-epistatic and epistatic fitness functions. Our calculations show that the inter-click time is of a scaling form which in the absence of epistasis gives a speed that is determined by size of the least-loaded class and the selection coefficient. With synergistic interactions, the ratchet speed is found to approach zero rapidly for arbitrary epistasis. Our analytical results are in good agreement with the numerical simulations.