Dynamics of mutators of arbitrary dominance in humans

Recent findings in humans and other species have revealed the presence of "mutator" alleles that increase germline mutation rate across the genome. Such mutators are expected to be selected against because of the additional deleterious alleles that they generate, to a degree that will depend on how much they increase the mutation rate in heterozygotes and homozygotes. To describe their dynamics, we develop a population genetic model of mutation rate modifiers with arbitrary dominance coefficients, in which fitness effects stem from additional germline mutations. We then use it to interpret findings for the seven human mutators identified to date. For six of the seven known mutators, the observed frequencies are well fit by the model and thus consistent with purifying selection arising solely due to their effects on germline mutation rates, although also consistent with a wide range of parameters; in two, the observed frequencies are readily explained by purely recessive fitness effects. The exception is a variant in MUTYH, which is more common than predicted under plausible parameters, for reasons that remain unclear. We also use the model to explore what types of mutators are most likely to be discovered in parents, based on identifying offspring with unexpectedly high numbers of de novo mutations. Although the two first mutators identified by this approach seem to be recessive, our modeling suggests that, for the same effect size, semi-dominant mutators are much more likely to be detected. These findings therefore imply that there are many more modifier sites with recessive effects than semi-dominant ones. More generally, our model provides a framework for interpreting properties of mutators in humans and other species and for learning about the genetic architecture of germline mutation rate variation.