Some species exhibit very high levels of DNA sequence variability; there is also evidence for the existence of heritable epigenetic variants that experience state changes at a much higher rate than sequence variants. In both cases, the resulting high diversity levels within a population (hyperdiversity) mean that standard population genetics methods are not trustworthy. We analyze a population genetics model that incorporates purifying selection, reversible mutations, and genetic drift, assuming a stationary population size. We derive analytical results for both population parameters and sample statistics and discuss their implications for studies of natural genetic and epigenetic variation. In particular, we find that (1) many more intermediate-frequency variants are expected than under standard models, even with moderately strong purifying selection, and (2) rates of evolution under purifying selection may be close to, or even exceed, neutral rates. These findings are related to empirical studies of sequence and epigenetic variation.T HE infinite sites model, originally proposed by Fisher (1922Fisher ( , 1930 and developed in detail by Kimura (1971), has been the workhorse of molecular population genetics for four decades. Its core assumption is that any nucleotide site segregates for at most two variants and that the mutation rate scaled by effective population size (N e ) is so low that new mutations arise only at sites that are fixed within the population (see also Charlesworth and Charlesworth 2010, p. 207). This assumption facilitates calculations of the theoretical values of some key observable quantities, such as the expected level of pairwise nucleotide site diversity or the expected number of segregating sites in a sample (Kimura 1971;Watterson 1975;Ewens 2004). In the framework of coalescent theory, this implies a linear relation between the genealogical distance between two sequences and the neutral sequence divergence between them, greatly simplifying methods of inference and statistical testing (Hudson 1990;Wakeley 2008).There has recently been some discussion of how to go beyond the infinite sites assumption of a low scaled mutation rate, which breaks down for species with very large effective population sizes, including some species of virus and bacteria, and even eukaryotes such as the sea squirt and outbreeding nematode worms, resulting in "hyperdiversity" of DNA sequence variability within a population . It is important to note, however, that this problem can arise even when the scaled mutation rate is relatively low, since then the proportion of neutral nucleotide sites that are currently segregating in a population (which depends on the scaled mutation rate) can be substantial when the population size is sufficiently large. For example, with a neutral mutation rate of u per site in a population of N breeding adults, the expected fraction of sites that are segregating in a randomly mating population is f s = u [ln(2N) + 0.6775], where u = 4N e u (Ewens 2004, p. 298). Thus, with u =...