Population models of genomic imprinting. I. Differential viability in the sexes and the analogy with genetic dominance

Many single-locus, two-allele selection models of genomic imprinting have b een shown to reduce formally to one-locus Mendelian models with a modified parameter for genetic dominance. One exception is the model where selection at the imprinted locus affects the sexes differently. We present two model s of maternal inactivation with differential viability in the sexes, one wi th complete inactivation, and the other with a partial penetrance for inact ivation. We show that, provided dominance relations at the imprintable locu s are the same in both sexes, a globally stable polymorphism exists for a r ange of viabilities that is independent of the penetrance of imprinting. Th e conditions for a polymorphism are the same as in previous models with dif ferential viability in the sexes but without imprinting and in a model of t he paternal X-inactivation system in marsupials. The model with incomplete inactivation is used to illustrate the analogy between imprinting and domin ance by comparing equilibrium bifurcation plots for fixed values of dominan ce and penetrance. We also derive a single expression for the dominance par ameter that leaves the frequency and stability of equilibria unchanged for all levels of inactivation. Although an imprinting model with sex differenc es does not formally reduce to a nonimprinting scheme, close theoretical pa rallels clearly exist.