Purifying Selection, Drift, and Reversible Mutation with Arbitrarily High Mutation Rates

Abstract

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 =...

Methylome evolution in plants

“…More popularized classic population genetics models that assume irreversible mutations (see also Wright [121]) on infinitely many sites [125], as is often the case for genomic data, are not suitable in the context of epimutations because of their reversibility and relatively high asymmetric rates. Recently, Charlesworth and Jain [123] derived analytical results based on the work of Wright [121], which incorporate many of the key features of epimutations (Box 1). Their formulas can be directly applied to WGBS-seq data that describe single methylation polymorphisms (SMPs) or DMRs to make inferences about the evolutionary role of epimutations and selection in shaping methylome diversity patterns in natural populations.

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“…These counts define discrete epiallelic classes (number of unmethylated alleles). b The observed frequencies of each epiallelic class is determined, in this case, from genic CG sites of 92 A. thaliana worldwide natural accessions ( red bars ), along with the maximum likelihood estimate based on the theoretical result of Charlesworth and Jain [123] ( pink bars ). The theoretical model (see Box 1) provides an accurate fit to the observed genic CG methylation diversity patterns, suggesting that CG epimutations are a major factor in shaping methylome diversity in natural populations of A. thaliana over evolutionary timescales …”

Mutation Rate Variation is a Primary Determinant of the Distribution of Allele Frequencies in Humans

“…6,65,77] rely on the infinite-sites model, which is evidently not a valid assumption for large samples. Adjusting demographic inference schemes to include the effects of recurrent mutations on the SFS (for examples of recent efforts towards this goal, see [78–82]) has the potential to significantly improve inference accuracy.…”

Rate, spectrum, and evolutionary dynamics of spontaneous epimutations

“…In light of our estimates of forward-backward epimutation rates, future work should examine the effect of selection in more complex population genetic models that account for finite population sizes, migration, and drift such as those proposed by Charlesworth and Jain (13). Recently, Wang and Fan (14) devised a neutrality test based on single methylation polymorphism data using a modified version of Tajima's D. We caution that care needs to be taken when supplying epimutation rates to this or similar tests.…”

“…In the model plant Arabidopsis thaliana, spontaneous methylation changes at CG dinucleotides accumulate in a rapid but nonlinear fashion over generations (2,3,10), thus pointing to high forward-backward epimutation rates (11). Precise estimates of these rates are necessary to be able to quantify the long-term dynamics of epigenetic variation under laboratory or natural conditions, and to understand the molecular mechanisms that drive methylome evolution (12)(13)(14). Here we combine theoretical modeling with high-resolution methylome analysis of multiple independent A. thaliana mutation accumulation (MA) lines (15), including measurements of methylation changes in continuous generations, to obtain robust estimates of forward and backward epimutation rates.…”