Modifiers of mutation-selection balance: general approach and the evolution of mutation rates

Abstract

SummaryA general approach is developed to estimate secondary selection at a modifier locus that influences some feature of a population under mutation-selection balance. The approach is based on the assumption that the properties of all available genotypes at this locus are similar. Then mutation-selection balance and weak associations between genotype distributions at selectable loci and the modifier locus are established rapidly. In contrast, changes of frequencies of the modifier genotypes are slow, and lead to only slow and small changes of the other features of the population. Thus, while these changes occur, the population remains in a state of quasi-equilibrium, where the mutation-selection balance and the associations between the selectable loci and the modifier locus are almost invariant. Selection at the modifier locus can be estimated by calculating quasiequilibrium values of these associations. This approach is developed for the situation where distributions of the number of mutations per genome within the individuals with a given modifier genotype are close to Gaussian. The results are used to study the evolution of the mutation rate. Because beneficial mutations are ignored, secondary selection at the modifier locus always diminishes the mutation rate. The coefficient of selection against an allele which increases the mutation rate by υ is approximately υδ2/[U(2−ρ)] = υŝ, where υ is the genomic deleterious mutation rate, δ is the selection differential of the number of mutations per individual in units of the standard deviation of the distribution of this number in the population, ρ is the ratio of variances of the number of mutations after and before selection, and ŝ is the selection coefficient against a mutant allele in the quasiequilibrium population. However, the decline of the mutation rate can be counterbalanced by the cost of fidelity, which can lead to an evolutionary equilibrium mutation rate.