  We study the evolutionary dynamics of an asexual population of nonmutators
and mutators on a class of epistatic fitness landscapes. We consider the
situation in which all mutations are deleterious and mutators are produced from
nonmutators continually at a constant rate. We find that in an infinitely large
population, a minimum nonmutator-to-mutator conversion rate is required to fix
the mutators but an arbitrarily small conversion rate results in the fixation
of mutators in a finite population. We calculate analytical expressions for the
mutator fraction at mutation-selection balance and fixation time for mutators
in a finite population when mutational effects are weaker (regime I) and
stronger (regime II) than the selective effects. Our main result is that in
regime I, the mutator fraction and the fixation time are independent of
epistasis but in regime II, mutators are rarer and take longer to fix when the
decrease in fitness with the number of deleterious mutations occurs at an
accelerating rate (synergistic epistasis) than at a diminishing rate
(antagonistic epistasis). Our analytical results are compared with numerics and
their implications are discussed.
