How often does the ratchet click? Facts, heuristics, asymptotics

TL;DR

This paper investigates the rate at which deleterious mutations accumulate in asexual populations due to Muller's ratchet, identifying key parameters and providing diffusion approximations supported by simulations.

Contribution

It introduces discrete and continuous models of Muller's ratchet, highlighting the importance of the parameter gamma and deriving diffusion approximations for different regimes.

Findings

Deleterious mutations accumulate following a power law when gamma > 0.5.

Mutations do not accumulate when gamma < 0.5.

Diffusion approximations align with previous analyses and are validated by simulations.

Abstract

The evolutionary force of recombination is lacking in asexually reproducing populations. As a consequence, the population can suffer an irreversible accumulation of deleterious mutations, a phenomenon known as Muller's ratchet. We formulate discrete and continuous time versions of Muller's ratchet. Inspired by Haigh's (1978) analysis of a dynamical system which arises in the limit of large populations, we identify the parameter gamma = N*lambda/(Ns*log(N*lambda)) as most important for the speed of accumulation of deleterious mutations. Here N is population size, s is the selection coefficient and lambda is the deleterious mutation rate. For large parts of the parameter range, measuring time in units of size N, deleterious mutations accumulate according to a power law in N*lambda with exponent gamma if gamma>0.5. For gamma<0.5 mutations cannot accumulate. We obtain diffusion approximations for three different parameter regimes, depending on the speed of the ratchet. Our approximations shed new light on analyses of Stephan et al. (1993) and Gordo & Charlesworth (2000). The heuristics leading to the approximations are supported by simulations.