The fixation probability of rare mutators in finite asexual populations

A mutator is an allele that increases the mutation rate throughout the genome by disrupting some aspect of DNA replication or repair. Mutators that increase the mutation rate by the order of 100-fold have been observed to spontaneously emerge and achieve high frequencies in natural populations and in longterm laboratory evolution experiments with Escherichia coli. In principle, the fixation of mutator alleles is limited by (i) competition with mutations in wild-type backgrounds, (ii) additional deleterious mutational load, and (iii) random genetic drift. Using a multiple-locus model and employing both simulation and analytic methods, we investigate the effects of these three factors on the fixation probability P_fix of an initially rare mutator as a function of population size N, beneficial and deleterious mutation rates, and the strength of mutations s. Our diffusion-based approximation for P_fix successfully captures effects ii and iii when selection is fast compared to mutation (μ/s ≪1). This enables us to predict the conditions under which mutators will be evolutionarily favored. Surprisingly, our simulations show that effect i is typically small for strong-effect mutators. Our results agree semiquantitatively with existing laboratory evolution experiments and suggest future experimental directions.