Fluctuations of fitness distributions and the rate of Muller's ratchet

TL;DR

This paper provides an analytical framework to understand the rate of Muller's ratchet by examining fitness fluctuations and their delayed effects on population dynamics, using a path integral approach.

Contribution

It introduces a novel analytical method to quantify Muller's ratchet rate considering delayed responses in fitness distributions.

Findings

Fluctuations in the fittest class propagate to lower fitness individuals.

Delayed restoring forces accelerate Muller's ratchet.

Derived an expression for the ratchet rate valid across various parameters.

Abstract

The accumulation of deleterious mutations is driven by rare fluctuations which lead to the loss of all mutation free individuals, a process known as Muller's ratchet. Even though Muller's ratchet is a paradigmatic process in population genetics, a quantitative understanding of its rate is still lacking. The difficulty lies in the nontrivial nature of fluctuations in the fitness distribution which control the rate of extinction of the fittest genotype. We address this problem using the simple but classic model of mutation selection balance with deleterious mutations all having the same effect on fitness. We show analytically how fluctuations among the fittest individuals propagate to individuals of lower fitness and have a dramatically amplified effects on the bulk of the population at a later time. If a reduction in the size of the fittest class reduces the mean fitness only after a delay, selection opposing this reduction is also delayed. This delayed restoring force speeds up Muller's ratchet. We show how the delayed response can be accounted for using a path integral formulation of the stochastic dynamics and provide an expression for the rate of the ratchet that is accurate across a broad range of parameters.