Epigenetically Inherited Mutation Rates Predicted to Maximize Adaptation Rates

Mutation rate plays an important role in adaptive evolution due to its effect on the rate of appearance of both beneficial and deleterious mutations and is therefore subject to second-order selection. The mutation rate varies between and within species and populations, increases under some stresses, and can be modified by mutator and anti-mutator alleles. It may also vary among genetically identical individuals: empirical evidence from bacteria suggests that the mutation rate can be affected by translation errors and expression noise in various proteins. Importantly, this non-genetic variation may be heritable via a transgenerational epigenetic mode of inheritance, giving rise to mutator phenotype switching that is independent from mutator alleles. Here we investigate mathematically how the rate of adaptive evolution on rugged, complex fitness landscapes is affected by the rate of mutation rate phenotype switching. Motivated by recent experimental results of mutation rate variation, we model an asexual population with two mutation rate phenotypes, non-mutator and mutator. An offspring may switch from its parental phenotype to the other phenotype. Thus, the mutation rate can be interpreted as a genetically inherited trait when the switching rate is low, as an epigenetically inherited trait when the switching rate is intermediate, or as a randomly determined trait when the switching rate is high. We find that intermediate switching rates maximize the rate of adaptation on rugged fitness landscapes. This is because an intermediate switching rate can maintain within the same individuals both a mutator phenotype and pre-existing mutations, a combination that facilitates the crossing of fitness valleys. Further, intermediate switching rates allow the population to quickly revert to a low mutation rate after adaptation is achieved, avoiding the accumulation of deleterious mutations linked to mutator alleles. Our results rationalize recently observed noise in the expression of proteins that affect the mutation rate and suggest that non-genetic inheritance of this phenotype may facilitate evolutionary adaptive processes.