Average time until fixation of mutants with compensatory fitness interaction

Abstract

We consider two loci (or DNA sites) in which mutation occurs from the wild-type allele A1 (resp. B1) to a mutant allele A2 (resp. B2) in the first (resp. second) locus. Gene combinations or haplotypes with a single mutation, A1B2 or A2B1, are deleterious. The double mutant, however, does not have the harmful effect of the single mutations. This model is a two- locus two-allele model with compensatory fitness interaction. With this model and a finite population, the average time until fixation of the double mutant, A2B2, starting from the state in which the population consists exclusively of A1B1, is calculated. We show that linkage between the loci is an important factor in the average time until fixation and that compensatory fitness interaction can be a mechanism for molecular evolution when linkage between the loci is not weak. Deleterious mutation can accelerate the speed of fixation of a double mutant. An interpretation of this phenomenon is presented.