Mutation-selection balance at a modifier-of-imprinting locus

We propose a pair of population genetic models for a modifier-of-imprinting locus for which different genotypes imprint different proportions of an imprintable target locus in their gametes. The two models examine the situations in which imprinting is advantageous, and we discuss three cases for which the modifier is respectively partially dominant, dominant, or recessive. The models predict the stable equilibrium frequencies of the mutant modifier and functionally diploid individuals in a large population in terms of up to four parameters: the mutation rate at the modifier locus, nu; the selection coefficient against the disadvantageous phenotype, sigma; the proportion of unimprinted eggs produced by homozygotes for the mutant modifier, theta, and, in the partially dominant models, the dominance parameter, kappa. The equilibrium frequency of the mutant phenotypes is shown to be approximately twice that of standard Mendelian models: 2 nu/sigma or 4nu/sigma when the modifier is recessive or dominant, respectively. Mathematical equivalences between these and nonimprinting models are noted.