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The mutation rate of a well adapted population is prone to reduction so as tohave a lower mutational load. We aim to understand the role of epistaticinteractions between the fitness affecting mutations in this process. Using amultitype branching process, the fixation probability of a single non-mutatoremerging in a large asexual mutator population is analytically calculated here.The mutator population undergoes deleterious mutations at constant, but at amuch higher rate than that of the non-mutator. We find that antagonisticepistasis lowers the chances of mutation rate reduction, while synergisticepistasis enhances it. Below a critical value of epistasis, the fixationprobability behaves non-monotonically with variation in mutation rate of thebackground population. Moreover, the variation of this critical value of theepistasis parameter with the strength of the mutator is discussed in theAppendix. For synergistic epistasis, when selection is varied, the fixationprobability reduces overall, with damped oscillations.

Role of epistasis on the fixation probability of a non-mutator in an adapted asexual population