Matrisibs, patrisibs, and the evolution of imprinting on autosomes and sex chromosomes

The conflict theory of genomic imprinting argues that parent-of-origin effects on allelic expression evolve as a consequence of conflict between maternally and paternally derived genomes. I derive explicit population-genetic models of this theory when individuals in a cohort with an arbitrary and variable number of sires and dams interact. I show that the evolution of imprinting is governed by the reciprocal of the harmonic mean number of fathers but the reciprocal of the arithmetic mean number of mothers per cohort. Thus, a few monandrous females in a polyandrous population decrease the strength of the genetic conflict and the opportunity for conflict-driven paternal imprinting. In contrast, in populations in which few males control large harems, rare males with small harems do not have such a disproportionate effect on genetic conflicts and maternal imprinting. Additionally, I demonstrate that under the conflict theory, selection for imprinted expression on paternally derived X chromosomes is much weaker than it is on maternally derived X chromosomes or autosomes.