Population-genetic models of sex-limited genomic imprinting

Genomic imprinting is a form of epigenetic modification involving parent-of-origin-dependent gene expression, usually the inactivation of one gene copy in some tissues, at least, for some part of the diploid life cycle. Occurring at a number of loci in mammals and flowering plants, this mode of non-Mendelian expression can be viewed more generally as parentally-specific differential gene expression. The effects of natural selection on genetic variation at imprinted loci have previously been examined in a several population-genetic models. Here we expand the existing one-locus, two-allele population-genetic models of viability selection with genomic imprinting to include sex-limited imprinting, i.e., imprinted expression occurring only in one sex, and differential viability between the sexes. We first consider models of complete inactivation of either parental allele and these models are subsequently generalized to incorporate differential expression. Stable polymorphic equilibrium was possible without heterozygote advantage as observed in some prior models of imprinting in both sexes. In contrast to these latter models, in the sex-limited case it was critical whether the paternally inherited or maternally inherited allele was inactivated. The parental origin of inactivated alleles had a different impact on how the population responded to the different selection pressures between the sexes. Under the same fitness parameters, imprinting in the other sex altered the number of possible equilibrium states and their stability. When the parental origin of imprinted alleles and the sex in which they are inactive differ, an allele cannot be inactivated in consecutive generations. The system dynamics became more complex with more equilibrium points emerging. Our results show that selection can interact with epigenetic factors to maintain genetic variation in previously unanticipated ways.