One- and two-locus population models with differential viability between sexes: parallels between haploid parental selection and genomic imprinting.

A model of genomic imprinting with complete inactivation of the imprinted allele is shown to be formally equivalent to the haploid model of parental selection. When single-locus dynamics are considered, an internal equilibrium is possible only if selection acts in the opposite directions in males and females. I study a two-locus version of the latter model, in which maternal and paternal effects are attributed to the single alleles at two different loci. A necessary condition for the allele frequency equilibria to remain on the linkage equilibrium surface is the multiplicative interaction between maternal and paternal fitness parameters. In this case the equilibrium dynamics are independent at both loci and results from the single-locus model apply. When fitness parameters are additive, analytic treatment was not possible but numerical simulations revealed that stable polymorphism characterized by association between loci is possible only in several special cases in which maternal and paternal fitness contributions are precisely balanced. As in the single-locus case, antagonistic selection in males and females is a necessary condition for the maintenance of polymorphism. I also show that the above two-locus results of the parental selection model are very sensitive to the inclusion of weak directional selection on the individual's own genotypes.