The evolution of genomic imprinting: two modifier-locus models.

We present two autosomal two-locus models in which the primary locus, A, may be imprinted according to the alleles present at the second, modifier locus, M. In the first model, the modifier is cis-acting, which assumes that imprinting occurs late in gametogenesis: whether or not A is imprinted depends only on the M allele in the (unfertilized) egg. We examine three cases in which polymorphism at A is maintained by a mutation-selection balance or heterozygote advantage. We show that a newly arising modifier allele without direct fitness effects can increase at a rate only of the order of the mutation rate at the A locus. This result mirrors that found in two-locus models of the evolution of dominance modifiers. Modifiers that also alter fitnesses, however, may spread quickly. In the second model, a monomorphic primary locus, A, is imprinted according to the mother's genotype at the second, diallelic modifier locus, M. The model is therefore trans-acting, which assumes imprinting occurs early in gametogenesis: whether or not A is imprinted depends on both of the mother's M genes. We show that a newly arising modifier will increase in frequency via selection if either imprinting is advantageous and the modifier increases the proportion of imprinted gametes or imprinting is disadvantageous and the proportion is decreased. Both of these factors-the selective effect of imprinting and the proportion of gametes imprinted-affect the rate of modifier evolution. Selectively maintained polymorphism at the modifier locus is unlikely unless the alleles interact in a nonadditive fashion.