Evolutionary theory for modifiers of epistasis using a general symmetric model

Genetic interactions in fitness are studied by using modifier theory. The effects on fitness of two linked genes are perturbed by alleles at a third linked locus that controls the extent of epistasis in fitness between the first two. This epistasis is determined by a symmetric interaction matrix, and it is shown that a modifier allele that increases epistasis will invade when the linkage between the other two genes is sufficiently tight and these genes are in linkage disequilibrium. With linkage equilibrium among the major loci, increased or decreased epistasis may evolve depending on the allele frequencies at these loci.