MODIFIERS OF MUTATION-SELECTION BALANCE - GENERAL-APPROACH AND THE EVOLUTION OF MUTATION-RATES

A general approach is developed to estimate secondary selection at a m odifier locus that influences some feature of a population under mutat ion-selection balance. The approach is based on the assumption that th e properties of all available genotypes at this locus are similar. The n mutation-selection balance and weak associations between genotype di stributions 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 featur es 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 modif ier locus are almost invariant. Selection at the modifier locus can be estimated by calculating quasiequilibrium values of these association s. This approach is developed for the situation where distributions of the number of mutations per genome within the individuals with a give n modifier genotype are close to Gaussian. The results are used to stu dy the evolution of the mutation rate. Because beneficial mutations ar e ignored, secondary selection at the modifier locus always diminishes the mutation rate. The coefficient of selection against an allele whi ch increases the mutation rate by v is approximately v delta(2)/[U(2-r ho)] = v ($) over cap s, where U is the genomic deleterious mutation r ate, delta is the selection differential of the number of mutations pe r individual in units of the standard deviation of the distribution of this number in the population, rho is the ratio of variances of the n umber of mutations after and before selection, and ($) over cap s is t he selection coefficient against a mutant allele in the quasiequilibri um population. However, the decline of the mutation rate can be counte rbalanced by the cost of fidelity, which can lead to an evolutionary e quilibrium mutation rate.