Rise and fall of asexual mutators in adapted populations
Ananthu James, Kavita Jain
Subjects: Populations and Evolution (q-bio.PE)

In an adapted population in which most mutations are deleterious, the mutation rates are expected to be low. Indeed, in recent experiments on adapted populations of asexual mutators, beneficial mutations that lower the mutation rates have been observed to get fixed. Using a multitype branching process and a deterministic argument, we calculate the time to fix the wildtype mutation rate in an asexual population of mutators, and find it to be a ${\tt U}$-shaped function of the population size. In contrast, the fixation time for mutators is known to increase with population size. On comparing these two time scales, we find that a critical population size exists below which the mutators prevail, while the mutation rate remains low in larger populations. We also discuss how our analytical results compare with the experiments.