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Although mutations drive the evolutionary process, the rates at which themutations occur are themselves subject to evolutionary forces. Our purpose hereis to understand the role of selection and random genetic drift in theevolution of mutation rates, and we address this question in asexualpopulations at mutation-selection equilibrium neglecting selective sweeps.Using a multitype branching process, we calculate the fixation probability of arare nonmutator in a large asexual population of mutators, and find that anonmutator is more likely to fix when the deleterious mutation rate of themutator population is high. Compensatory mutations in the mutator populationare found to decrease the fixation probability of a nonmutator when theselection coefficient is large. But, surprisingly, the fixation probabilitychanges nonmonotonically with increasing compensatory mutation rate when theselection is mild. Using these results for the fixation probability and adrift-barrier argument, we find a novel relationship between the mutation ratesand the population size. We also discuss the time to fix the nonmutator in anadapted population of asexual mutators, and compare our results withexperiments.

Fixation probability of rare nonmutator and evolution of mutation rates