Genomic Imprinting Leads to Less Selectively Maintained Polymorphism on X Chromosomes

Population-genetic models are developed to investigate the consequences of viability selection at a diallelic X-linked locus subject to genomic imprinting. Under complete paternal-X inactivation, a stable polymorphism is possible under the same conditions as for paternal-autosome inactivation with differential selection on males and females. A necessary but not sufficient condition is that there is sexual conflict, with selection acting in opposite directions in males and females. In contrast, models of complete maternal-X inactivation never admit a stable polymorphism and alleles will either be fixed or lost from the population. Models of complete paternal-X inactivation are more complex than corresponding models of maternal-X inactivation, as inactivation of paternally derived X chromosomes in females screens these chromosomes from selection for a generation. We also demonstrate that polymorphism is possible for incomplete X inactivation, but that the parameter conditions are more restrictive than for complete paternal-X inactivation. Finally, we investigate the effects of recurrent mutation in our models and show that deleterious alleles in mutation-selection balance at imprinted X-linked loci are at frequencies rather similar to those with corresponding selection pressures and mutation rates at unimprinted loci. Overall, our results add to the reasons for expecting less selectively maintained allelic variation on X chromosomes.