Heritable epigenetic variation facilitates long-term maintenance of epigenetic and genetic variation.

How genetic and phenotypic variation are maintained has long been one of the fundamental questions in population and quantitative genetics. A variety of factors have been implicated to explain the maintenance of genetic variation in some contexts (e.g. balancing selection), but the potential role of epigenetic regulation to influence population dynamics has been understudied. It is well recognized that epigenetic regulation, including histone methylation, small RNA expression, and DNA methylation, helps to define differences between cell types and facilitate phenotypic plasticity. In recent years, empirical studies have shown the potential for epigenetic regulation to also be heritable for at least a few generations without selection, raising the possibility that differences in epigenetic regulation can act alongside genetic variation to shape evolutionary trajectories. Heritable differences in epigenetic regulation that arise spontaneously are termed "epimutations." Epimutations differ from genetic mutations in 2 key ways-they occur at a higher rate and the loci at which they occur often revert back to their original state within a few generations. Here, we present an extension of the standard population genetic model with selection to incorporate epigenetic variation arising via epimutation. Our model assumes a diploid, sexually reproducing population with random mating. In addition to spontaneous genetic mutation, we included parameters for spontaneous epimutation and back-epimutation, allowing for 4 potential epialleles at a single locus (2 genetic alleles, each with 2 epigenetic states), each of which affect fitness. We then analyzed the conditions under which stable epialleles were maintained. Our results show that highly reversible epialleles can be maintained in long-term equilibrium under neutral conditions in a manner that depends on the epimutation and back-epimutation rates, which we term epimutation-back-epimutation equilibrium. On the other hand, epialleles that compensate for deleterious mutations cause deviations from the expectations of mutation-selection balance by a simple factor that depends on the epimutation and back-epimutation rates. We also numerically analyze several sets of fitness parameters for which large deviations from mutation-selection balance occur. Together, these results demonstrate that transient epigenetic regulation may be an important factor in the maintenance of both epigenetic and genetic variation in populations.