The accumulation of deleterious genes in a population—Muller's Ratchet

Abstract

A quantitative study of the operation of Muller's Ratchet for the accumulation of deleterious genes in an asexually reproducing population is made. For a population of size N, in which deleterious mutations occur at rate λ/genome/ generation, and the relative fitness of an individual with k mutants is (1 − s) k , the most important parameter is n 0 = Ne −θ, where θ = λ s . If n 0 is large (⩾25), deleterious mutations will accumulate very slowly, and independently of each other; if n 0 is small (<1), the rate of accumulation of deleterious mutations will be greater than a natural population could plausibly bear; an estimate of the speed of the Ratchet for intermediate values of n 0 is made. It is pointed out that the frequency distribution for the numbers of individuals carrying k mutants will retain its shape, but will move bodily to the right at the same average speed as the Ratchet. When favourable mutations also occur, the frequency distributions can move right of left; an estimate of the probability that any particular step is right or left is made, and it is shown that, for a given net rate of arrisal of deleterious mutations, the greater the rate of beneficial mutation, the greater the chance that beneficial mutations will accumulate.