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

Abstract

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 γ = N λ/( Ns · log( N λ)) as most important for the speed of accumulation of deleterious mutations. Here N is population size, s is the selection coefficient and λ 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 λ with exponent γ if γ ≥ 0.5. For γ Introduction Muller's ratchet is a mechanism that has been suggested as an explanation for the evolution of sex [13]. The idea is simple; in an asexually reproducing population chromosomes are passed down as indivisible blocks and so the number of deleterious mutations accumulated along any ancestral line in the population can only increase.