Genealogies and weak purifying selection

The assumption that selection alters the genealogical tree of a sample of alleles from a population relative to the neutral expectation underlies several "tests of neutrality." Two recent papers have studied the effect of purifying selection; their suggestive but incomplete results indicate that, in the single site case, the shape of a gene genealogy for a locus may differ only from the neutral expectation. We verify this finding for weak selection using the "ancestral selection graph." We consider a wider range of models, including both a four-allele single-site model and an infinite-sites model. Our results confirm the previous claim for the symmetric-mutation single site model. We emphasize, however, that a neutral-seeming genealogy is consistent with detectable effects of selection on the distribution of allele frequences within the sample. With selection operating, the information about a sample cannot be reduced to the genealogy. As a result, a distinction needs to be made between the selected sites themselves, for which the genealogy offers insufficient information, and linked neutral variation. This distinction seems to have been overlooked in previous papers, yet it has significant implications for the interpretation of data on DNA sequence variation. In particular, it predicts that under purifying selection, the frequency spectrum of neutral mutations will not reflect the skew toward rare polymorphisms at replacement sites even if there is no recombination between them. We caution, however, that the effect of weak selection on the genealogy is specific to the model; a (more realistic) model of multiple linked sites could lead to a more distorted genealogy than is observed for a single site.     

The age of nonsynonymous and synonymous mutations in animal mtDNA and implications for the mildly deleterious theory.

McDonald/Kreitman tests performed on animal mtDNA consistently reveal significant deviations from strict neutrality in the direction of an excess number of polymorphic nonsynonymous sites, which is consistent with purifying selection acting on nonsynonymous sites. We show that under models of recurrent neutral and deleterious mutations, the mean age of segregating neutral mutations is greater than the mean age of segregating selected mutations, even in the absence of recombination. We develop a test of the hypothesis that the mean age of segregating synonymous mutations equals the mean age of segregating nonsynonymous mutations in a sample of DNA sequences. The power of this age-of-mutation test and the power of the McDonald/Kreitman test are explored by computer simulations. We apply the new test to 25 previously published mitochondrial data sets and find weak evidence for selection against nonsynonymous mutations.     

Effect of selection on the topology of genealogical trees

Selection is one of the factors that most influence the shape of genealogical trees. Here we report results of simulations of the infinite-sites version of Moran's model of population genetics aiming at quantifying how the presence of selection affects the branching pattern (topology) of binary genealogical trees. In particular, we consider a scenario of purifying or negative selection in which all mutations are deleterious and each new mutation reduces the fitness of the individual by the same fraction. Analysis of five statistical measures of tree balance or symmetry borrowed from taxonomy indicates that the genealogical trees of samples of populations in which selection is actuating are in the average more asymmetric than neutral trees and that this effect is enhanced by increasing the sample size. However, a quantitative evaluation of the power of these balance measures to detect a tree topology significantly distinct from the neutral one indicates that they are not useful as tests of neutrality of mutations.     

Directional selection and the site-frequency spectrum.

In this article we explore statistical properties of the maximum-likelihood estimates (MLEs) of the selection and mutation parameters in a Poisson random field population genetics model of directional selection at DNA sites. We derive the asymptotic variances and covariance of the MLEs and explore the power of the likelihood ratio tests (LRT) of neutrality for varying levels of mutation and selection as well as the robustness of the LRT to deviations from the assumption of free recombination among sites. We also discuss the coverage of confidence intervals on the basis of two standard-likelihood methods. We find that the LRT has high power to detect deviations from neutrality and that the maximum-likelihood estimation performs very well when the ancestral states of all mutations in the sample are known. When the ancestral states are not known, the test has high power to detect deviations from neutrality for negative selection but not for positive selection. We also find that the LRT is not robust to deviations from the assumption of independence among sites.     

The structure of allelic diversity in the presence of purifying selection

In the absence of selection, the structure of equilibrium allelic diversity is described by the elegant sampling formula of Ewens. This formula has helped to shape our expectations of empirical patterns of molecular variation. Along with coalescent theory, it provides statistical techniques for rejecting the null model of neutrality. However, we still do not fully understand the statistics of the allelic diversity expected in the presence of natural selection. Earlier work has described the effects of strongly deleterious mutations linked to many neutral sites, and allelic variation in models where offspring fitness is unrelated to parental fitness, but it has proven difficult to understand allelic diversity in the presence of purifying selection at many linked sites. Here, we study the population genetics of infinitely many perfectly linked sites, some neutral and some deleterious. Our approach is based on studying the lineage structure within each class of individuals of similar fitness in the deleterious mutation-selection balance. Consistent with previous observations, we find that for moderate and weak selection pressures, the patterns of allelic diversity cannot be described by a neutral model for any choice of the effective population site. We compute precisely how purifying selection at many linked sites distorts the patterns of allelic diversity, by developing expressions for the likelihood of any configuration of allelic types in a sample analogous to the Ewens sampling formula.     

The structured ancestral selection graph and the many-demes limit

We show that the unstructured ancestral selection graph applies to part of the history of a sample from a population structured by restricted migration among subpopulations, or demes. The result holds in the limit as the number of demes tends to infinity with proportionately weak selection, and we have also made the assumptions of island-type migration and that demes are equivalent in size. After an instantaneous sample-size adjustment, this structured ancestral selection graph converges to an unstructured ancestral selection graph with a mutation parameter that depends inversely on the migration rate. In contrast, the selection parameter for the population is independent of the migration rate and is identical to the selection parameter in an unstructured population. We show analytically that estimators of the migration rate, based on pairwise sequence differences, derived under the assumption of neutrality should perform equally well in the presence of weak selection. We also modify an algorithm for simulating genealogies conditional on the frequencies of two selected alleles in a sample. This permits efficient simulation of stronger selection than was previously possible. Using this new algorithm, we simulate gene genealogies under the many-demes ancestral selection graph and identify some situations in which migration has a strong effect on the time to the most recent common ancestor of the sample. We find that a similar effect also increases the sensitivity of the genealogy to selection.     

The relation between the neutrality index for mitochondrial genes and the distribution of mutational effects on fitness

We explore factors affecting patterns of polymorphism and divergence (as captured by the neutrality index) at mammalian mitochondrial loci. To do this, we develop a population genetic model that incorporates a fraction of neutral amino acid sites, mutational bias, and a probability distribution of selection coefficients against new nonsynonymous mutations. We confirm, by reanalyzing publicly available datasets, that the mitochondrial cyt-b gene shows a broad range of neutrality indices across mammalian taxa, and explore the biological factors that can explain this observation. We find that observed patterns of differences in the neutrality index, polymorphism, and divergence are not caused by differences in mutational bias. They can, however, be explained by a combination of a small fraction of neutral amino acid sites, weak selection acting on most amino acid mutations, and differences in effective population size among taxa.     

An investigation of the statistical power of neutrality tests based on comparative and population genetic data

In this report, we investigate the statistical power of several tests of selective neutrality based on patterns of genetic diversity within and between species. The goal is to compare tests based solely on population genetic data with tests using comparative data or a combination of comparative and population genetic data. We show that in the presence of repeated selective sweeps on relatively neutral background, tests based on the d(N)/d(S) ratios in comparative data almost always have more power to detect selection than tests based on population genetic data, even if the overall level of divergence is low. Tests based solely on the distribution of allele frequencies or the site frequency spectrum, such as the Ewens-Watterson test or Tajima's D, have less power in detecting both positive and negative selection because of the transient nature of positive selection and the weak signal left by negative selection. The Hudson-Kreitman-Aguadé test is the most powerful test for detecting positive selection among the population genetic tests investigated, whereas McDonald-Kreitman test typically has more power to detect negative selection. We discuss our findings in the light of the discordant results obtained in several recently published genomic scans.     

Gene genealogy and properties of test statistics of neutrality under population growth

We consider the Wright-Fisher model with exponential population growth and investigate effects of population growth on the shape of genealogy and the distributions of several test statistics of neutrality. In the limiting case as the population grows rapidly, the rapid-growth-limit genealogy is characterized. We obtained approximate expressions for expectations and variances of test statistics in the rapid-growth-limit genealogy and star genealogy. The distributions in the star genealogy are narrower than those in the cases of the simulated and rapid-growth-limit genealogies. The expectations and variances of the test statistics are monotone decreasing functions of the time length of the expansion, and the higher power of R(2) against population growth is suggested to be due to their smaller variances rather than to change of the expectations. We also investigated by simulation how quickly the distributions of test statistics approach those of the rapid-growth-limit genealogy.     

Selection on amino acid substitutions in Arabidopsis

Studies of nucleotide diversity have found an excess of low-frequency amino acid polymorphisms segregating in Arabidopsis thaliana, suggesting a predominance of weak purifying selection acting on amino acid polymorphism in this inbreeding species. Here, we investigate levels of diversity and divergence at synonymous and nonsynonymous sites in 6 circumpolar populations of the outbreeding Arabidopsis lyrata and compare these results with A. thaliana, to test for differences in mutation and selection parameters across genes, populations, and species. We find that A. lyrata shows an excess of low-frequency nonsynonymous polymorphisms both within populations and species wide, consistent with weak purifying selection similar to the patterns observed in A. thaliana. Furthermore, nonsynonymous polymorphisms tend to be more restricted in their population distribution in A. lyrata, consistent with purifying selection preventing their geographic spread. Highly expressed genes show a reduced ratio of amino acid to synonymous change for both polymorphism and fixed differences, suggesting a general pattern of stronger purifying selection on high-expression proteins.     

Comparing phylogeny and the predicted pathogenicity of protein variations reveals equal purifying selection across the global human mtDNA diversity

We used detailed phylogenetic trees for human mtDNA, combined with pathogenicity predictions for each amino acid change, to evaluate selection on mtDNA-encoded protein variants. Protein variants with high pathogenicity scores were significantly rarer in the older branches of the tree. Variants that have formed and survived multiple times in the human phylogenetics tree had significantly lower pathogenicity scores than those that only appear once in the tree. We compared the distribution of pathogenicity scores observed on the human phylogenetic tree to the distribution of all possible protein variations to define a measure of the effect of selection on these protein variations. The measured effect of selection increased exponentially with increasing pathogenicity score. We found no measurable difference in this measure of purifying selection in mtDNA across the global population, represented by the macrohaplogroups L, M, and N. We provide a list of all possible single amino acid variations for the human mtDNA-encoded proteins with their predicted pathogenicity scores and our measured selection effect as a tool for assessing novel protein variations that are often reported in patients with mitochondrial disease of unknown origin or for assessing somatic mutations acquired through aging or detected in tumors.     

A weak effect of background selection on trinucleotide microsatellites in maize

Artificial selection during the domestication of maize is thought to have been predominantly positive and to have had little effect on the surrounding neutral diversity because linkage disequilibrium breaks down rapidly when physical distance increases. However, the degree to which indirect selection has shaped neutral diversity in the maize genome during domestication remains unclear. In this study, we investigate the relationship between local recombination rate and neutral polymorphism in maize and in teosinte using both sequence and microsatellite data. To quantify diversity, we estimate 3 parameters expected to differentially reflect the effects of indirect selection and mutation. We find no general correlation between diversity and recombination, indicating that indirect selection has had no genome-wide impact on maize diversity. However, we detect a weak correlation between heterozygosity and recombination for trinucleotide microsatellites deviating from the stepwise mutation model and located within genes (rho = 0.32, P < 0.03). This result can be explained by a background selection hypothesis. The fact that the same correlation is not confirmed for nucleotide diversity suggests that the strength of purifying selection at or near this class of microsatellites is higher than for nucleotide mutations.     

Fitness effects of derived deleterious mutations in four closely related wild tomato species with spatial structure

A key issue in evolutionary biology is an improved understanding of the genetic mechanisms by which species adapt to various environments. Using DNA sequence data, it is possible to quantify the number of adaptive and deleterious mutations, and the distribution of fitness effects of new mutations (its mean and variance) by simultaneously taking into account the demography of a given species. We investigated how selection functions at eight housekeeping genes of four closely related, outcrossing species of wild tomatoes that are native to diverse environments in western South America (Solanum arcanum, S. chilense, S. habrochaites and S. peruvianum). We found little evidence for adaptive mutations but pervasive evidence for strong purifying selection in coding regions of the four species. In contrast, the strength of purifying selection seems to vary among the four species in non-coding (NC) regions (introns). Using F(ST)-based measures of fixation in subdivided populations, we suggest that weak purifying selection has affected the NC regions of S. habrochaites, S. chilense and S. peruvianum. In contrast, NC regions in S. arcanum show a distribution of fitness effects with mutations being either nearly neutral or very strongly deleterious. These results suggest that closely related species with similar genetic backgrounds but experiencing contrasting environments differ in the variance of deleterious fitness effects.     

Recombination, balancing selection and phylogenies in MHC and self-incompatibility genes.

Using a coalescent model of multiallelic balancing selection with recombination, the genealogical process as a function of recombinational distance from a site under selection is investigated. We find that the shape of the phylogenetic tree is independent of the distance to the site under selection. Only the timescale changes from the value predicted by Takahata's allelic genealogy at the site under selection, converging with increasing recombination to the timescale of the neutral coalescent. However, if nucleotide sequences are simulated over a recombining region containing a site under balancing selection, a phylogenetic tree constructed while ignoring such recombination is strongly affected. This is true even for small rates of recombination. Published studies of multiallelic balancing selection, i.e., the major histocompatibility complex (MHC) of vertebrates, gametophytic and sporophytic self-incompatibility of plants, and incompatibility of fungi, all observe allelic genealogies with unexpected shapes. We conclude that small absolute levels of recombination are compatible with these observed distortions of the shape of the allelic genealogy, suggesting a possible cause of these observations. Furthermore, we illustrate that the variance in the coalescent with recombination process makes it difficult to locate sites under selection and to estimate the selection coefficient from levels of variability.     

The stationary distribution of allele frequencies when selection acts at unlinked loci

We consider population genetics models where selection acts at a set of unlinked loci. It is known that if the fitness of an individual is multiplicative across loci, then these loci are independent. We consider general selection models, but assume parent-independent mutation at each locus. For such a model, the joint stationary distribution of allele frequencies is proportional to the stationary distribution under neutrality multiplied by a known function of the mean fitness of the population. We further show how knowledge of this stationary distribution enables direct simulation of the genealogy of a sample at a single-locus. For a specific selection model appropriate for complex disease genes, we use simulation to determine what features of the genealogy differ between our general selection model and a multiplicative model.     

Dynamic mutation-selection balance as an evolutionary attractor

The vast majority of mutations are deleterious and are eliminated by purifying selection. Yet in finite asexual populations, purifying selection cannot completely prevent the accumulation of deleterious mutations due to Muller's ratchet: once lost by stochastic drift, the most-fit class of genotypes is lost forever. If deleterious mutations are weakly selected, Muller's ratchet can lead to a rapid degradation of population fitness. Evidently, the long-term stability of an asexual population requires an influx of beneficial mutations that continuously compensate for the accumulation of the weakly deleterious ones. Hence any stable evolutionary state of a population in a static environment must involve a dynamic mutation-selection balance, where accumulation of deleterious mutations is on average offset by the influx of beneficial mutations. We argue that such a state can exist for any population size N and mutation rate U and calculate the fraction of beneficial mutations, ε, that maintains the balanced state. We find that a surprisingly low ε suffices to achieve stability, even in small populations in the face of high mutation rates and weak selection, maintaining a well-adapted population in spite of Muller's ratchet. This may explain the maintenance of mitochondria and other asexual genomes.     

Population genetics of polymorphism and divergence for diploid selection models with arbitrary dominance

We develop a Poisson random-field model of polymorphism and divergence that allows arbitrary dominance relations in a diploid context. This model provides a maximum-likelihood framework for estimating both selection and dominance parameters of new mutations using information on the frequency spectrum of sequence polymorphisms. This is the first DNA sequence-based estimator of the dominance parameter. Our model also leads to a likelihood-ratio test for distinguishing nongenic from genic selection; simulations indicate that this test is quite powerful when a large number of segregating sites are available. We also use simulations to explore the bias in selection parameter estimates caused by unacknowledged dominance relations. When inference is based on the frequency spectrum of polymorphisms, genic selection estimates of the selection parameter can be very strongly biased even for minor deviations from the genic selection model. Surprisingly, however, when inference is based on polymorphism and divergence (McDonald-Kreitman) data, genic selection estimates of the selection parameter are nearly unbiased, even for completely dominant or recessive mutations. Further, we find that weak overdominant selection can increase, rather than decrease, the substitution rate relative to levels of polymorphism. This nonintuitive result has major implications for the interpretation of several popular tests of neutrality.     

The effect of selection on genealogies

The coalescent process can describe the effects of selection at linked loci only if selection is so strong that genotype frequencies evolve deterministically. Here, we develop methods proposed by Kaplan, Darden, and Hudson to find the effects of weak selection. We show that the overall effect is given by an extension to Price's equation: the change in properties such as moments of coalescence times is equal to the covariance between those properties and the fitness of the sample of genes. The distribution of coalescence times differs substantially between allelic classes, even in the absence of selection. However, the average coalescence time between randomly chosen genes is insensitive to the current allele frequency and is affected significantly by purifying selection only if deleterious mutations are common and selection is strong (i.e., the product of population size and selection coefficient, Ns>3). Balancing selection increases mean coalescence times, but the effect becomes large only when mutation rates between allelic classes are low and when selection is extremely strong. Our analysis supports previous simulations that show that selection has surprisingly little effect on genealogies. Moreover, small fluctuations in allele frequency due to random drift can greatly reduce any such effects. This will make it difficult to detect the action of selection from neutral variation alone.     

Power of neutrality tests to detect bottlenecks and hitchhiking

The power of several neutrality tests to reject a simple bottleneck model is examined in a coalescent framework. Several tests are considered including some relying on the frequency spectrum of mutations and some reflecting the linkage disequilibrium structure of the data. We evaluate the effect of the age and of the strength of the bottleneck, and their interaction. We contrast two qualitatively different bottleneck effects depending on their strength. In genealogical terms, during severe bottlenecks, all lineages coalesce leading to a star-like gene genealogy of the sample. Some time after the bottleneck, once new mutations have arisen, they tend to show an excess of rare variants and a slight excess of haplotypes. On the contrary, more moderate bottlenecks allow several lineages to survive the demographic crash, leading to a balanced genealogy with long internal branches. Soon after the event, data tend to show an excess of intermediate frequency variants and a deficit of haplotypes. We show that for moderate sequencing efforts, severe bottlenecks can be detected only after an intermediate time period has allowed for mutations to occur, preferably by frequency spectrum statistics. Moderate bottlenecks can be more easily detected for more recent events, especially using haplotype statistics. Finally, for a single locus, the bottleneck results closely approximate those of a simple hitchhiking model. The main difference concerns the frequency distribution of mutations and haplotypes after moderate perturbations. Hitchhiking increases the number of rare ancestral mutations and leads to a more predominant major haplotype class. Thus, despite a number of common features between the two processes, hitchhiking cannot be strictly modeled by bottlenecks.     

Evidence for a slightly deleterious effect of intron polymorphisms at the EF1alpha gene in the deep-sea hydrothermal vent bivalve Bathymodiolus

A multilocus analysis was initiated in order to infer the general effect of demography and the indirect effect of positive selection on some chromosome segments in Bathymodiolus. Mussels of the genus Bathymodiolus inhabit the very hostile, fragmented and variable environment of deep-sea hydrothermal vents which is thought to cause recurrent population bottlenecks via extinction/colonisation processes and adaptation to new environmental conditions. In the course of this work we discovered that the assumption of neutrality of non-coding polymorphisms usually made in genome scan experiments was likely to be violated at one of the loci we analysed. The direct effect of slight purifying selection on non-coding polymorphisms shares many resemblances with the indirect effect of positive selection through genetic hitchhiking. Combining polymorphism with divergence data for several closely related species allowed us to obtain different expectations for the direct effect of negative selection and the indirect effect of positive selection. We observed a strong excess of rare non-coding polymorphisms at the second intron of the EF1alpha gene in the two species Bathymodiolus azoricus and Bathymodiolus thermophilus, while two other loci, the mitochondrial COI gene and an intron of the Lysozyme gene, did not exhibit such a deviation. In addition, the divergence rate of the EF1alpha intron was estimated to be unexpectedly low when calibrated using the closure of the Panama Isthmus that interrupted gene flow between the two species. The polymorphism to divergence ratio was similar to the one observed for the other two loci, in accordance to the hypothesis of purifying selection. We conclude that slight purifying selection is likely to act on polymorphic intronic mutations of the EF1alpha second intron and discuss the possible relationship with the specific biology of Bathymodiolus mussels.