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Title: The Population Genetics of dN/dS}
Article:
Abstract:
Evolutionary pressures on proteins are often quantified by the ratio of substitution rates at non-synonymous and synonymous sites. The dN/dS ratio was originally developed for application to distantly diverged sequences, the differences among which represent substitutions that have fixed along independent lineages. Nevertheless, the dN/dS measure is often applied to sequences sampled from a single population, the differences among which represent segregating polymorphisms. Here, we study the expected dN/dS ratio for samples drawn from a single population under selection, and we find that in this context, dN/dS is relatively insensitive to the selection coefficient. Moreover, the hallmark signature of positive selection over divergent lineages, dN/dS>1, is violated within a population. For population samples, the relationship between selection and dN/dS does not follow a monotonic function, and so it may be impossible to infer selection pressures from dN/dS. These results have significant implications for the interpretation of dN/dS measurements among population-genetic samples.
Introduction:
The identification of genetic loci undergoing adaptation is a central project of evolutionary biology. With the advent of sequencing technologies, a variety of statistical tests have been developed to quantify selection pressures acting on protein-coding regions. Among these, the dN/dS ratio is one of the most widely used, owing in part to its simplicity and robustness. This measure quantifies selection pressures by comparing the rate of substitutions at silent sites( dS), which are presumed neutral, to the rate of substitutions at non-silent sites( dN), which possibly experience selection. The ratio dN/dS is expected to exceed unity only if natural selection promotes changes in the protein sequence; whereas a ratio less than unity is expected only if natural selection suppresses protein changes[1],[2]. This intuitive interpretation of dN/dS is supported by theoretical work on the relationship between the dN/dS statistic and the underlying selection pressure in a Wright-Fisher model[3]. The dN/dS ratio was originally developed for the analysis of genetic sequences from divergent species[1],[4],[5], the differences amoung which represent fixation events along independent lineages. Theoretical work on the relationship between dN/dS and selection likewise assumes that sequences are sampled from independent, divergent species[3], as do computer packages used to estimate dN/dS from data[6],[7]. Nonetheless, the dN/dS ratio test is frequently applied to data that may represent samples from a single population, particularly in the case of microbes( e. g.[3],[8]–[18]). In such cases, the differences between sequences do not represent fixation events along independent lineages, but rather polymorphisms segregating in a single population. It is important, therefore, to understand the relationship between selection pressures and the dN/dS statistic for samples from a single population. Here we analyze the population genetics of dN/dS. We find that the relationship between the selection pressure and dN/dS is qualitatively different for samples drawn from a single population compared to sampled from divergent lineages. As a result, standard tests for selection based on dN/dS are extremely sensitive to violation of the assumption of divergent lineages. We show that the expected dN/dS ratio within a population is relatively insensitive to selection pressure—a result which helps to explain a body of empirical observations about microbial populations. Moreover, we show that the hallmark signature of positive selection across divergent lineages, dN/dS>1, does not hold within population: strong positive selection is expected to produce dN/dS<1 among population samples. As a result, when applied to intra-specific samples, the standard interpretation of dN/dS is unjustified and may lead to surprising conclusions. This point is illustrated by two recent studies that report dN/dS ratios near 1 among strains of Salmonella enetrica serovar Typhi[17],[18], and conclude that genetic drift dominates the bacterium's evolution. This conclusion is surprising in light of the large population size of the bacterium( estimated to be on the order of 105) and strong selective advantages of antibiotic-resistance mutations[17]. However, our analysis shows that dN/dS values obtained from closely related isolates may be near 1 under both strong positive selection or moderate negative selection, and so parts of the Salmonella Typhi genome may well be evolving under considerable selection pressure. Our presentation begins with a review of the theory underlying the interpretation of dN/dS across divergent lineages. We then develop the appropriate theory for studying selection and dN/dS within a single population. We compare our theoretical expectations to Monte Carlo simulations based on the Wright-Fisher model. We conclude with a discussion of practical implications.
Discussion:
The dN/dS ratio remains one of the most popular and reliable measures of evolutionary pressures on protein-coding regions. Much of its popularity stems from the simple, intuitive interpretation of dN/dS<1 as negative selection, dN/dS = 1 as neutrality, and dN/dS>1 as positive selection. However, this simple interpretation requires that the sequences being compared represent stereotypical samples from divergent populations—an assumption that is also implicit in the methods that estimate dN/dS by maximum likelihood[7]. As we have demonstrated here, the relationship between selection pressure and dN/dS for samples within a population is radically different than the relationship for samples from divergent populations. In particular, within a population dN/dS does not increase monotonically with γ, dN/dS is less sensitive to changes in γ, and dN/dS<1 can occur under both negative and positive selection. Recently, Rocha et al. have investigated the relationship between divergence time and dN/dS[44]. Those authors considered an infinite-sites model under negative selection, and they presented an expression for the expected dN/dS ratio in an infinite population. By contrast, we have derived an analytic relationship between the selection pressure and dN/dS at a site under the Wright-Fisher model of a finite population, for both negative and positive selection. The fact that polymorphisms within a population differ from divergences between species is well understood by population geneticists[23],[45]. However, this important fact is often neglected in many applications of dN/dS to population data. In fact, one recent study explicitly suggests that dN/dS within a population should be used as a surrogate for dN/dS across divergent species[46]. Moreover, the standard infinite-site analysis of neutral and selected segregating polymorphisms( e. g.[23],[47]) would suggest that the ratio approaches 2 as γ gets large, whereas in fact the dN/dS ratio within a population approaches zero for strong positive selection( Equation 5). This discrepancy arises because the infinite-site analysis considers only the mean time that an allele spends in each frequency class while segregrating. By contrast, the single-site analysis( Equation 4) accounts for for the increased amount of time that a site spends in the monomorphic state as γ gets large. Our analysis of selection and dN/dS has assumed independence of sites or, equivalently, free recombination between sites. This assumption is unrealistic in many practical settings. However, the same assumption has been made in prior analytic work on dN/dS[3], and the assumption is expected to be more accurate for small mutation rates, or for weak selection pressures. Outside of this parameter regime, the effects of linkage on dN/dS are difficult to analyze, and they form an important topic for further study. We have focused our analysis on Yang's particular formulation of selection, which stipulates that all mutations experience the same selection coefficient compared to the resident type[3],[4],[36],[40]. Alternative formulations of selection( e. g. those that assume a constant fitness for each allele) can produce different relationships between γ and dN/dS over long time-scales[3]. Our results here, however, do not arise because we have considered a different selective model than Nielsen and Yang[3]; we are studying the same model, but considering samples from a single population instead of divergent populations. Complications associated with interpreting dN/dS for population samples do not arise in many practical applications of dN/dS—i. e. those involving comparisons among divergent species. However, as sequence data are increasingly available, there is a temptation to apply computer packages such as PAML to intraspecific data—as has been done in many cases already( e. g.[3],[8]–[18]). Published estimates of dN/dS based on samples from a single population are common for microbes and viruses. Inferences about natural selection drawn from such analyses should be interpreted with caution. Many empirical studies of genes evolving under negative selection have found quizzical results, which our analysis helps to clarify: dN/dS values for such genes are typically closer to 1 when comparing intra-specific samples as opposed to inter-specific samples. This observation holds for bacterial data[11],[12],[14],[16],[18], for viral samples isolated from a single host versus viral samples isolated from different hosts[13], for closely related viral samples versus distantly diverged samples[48], and for conspecific versus interspecific mammalian sequences[49],[50]. A variety of factors have been suggested to explain the elevation of dN/dS within a population under negative selection[49]: balancing selection, variable population sizes, variable mutation rates, relaxed selective constraint within certain lineages[51],[52], statistical artifacts[53], or the prevalence of slightly deleterious mutations[13],[48],[49],[54],[55]. Our analysis clarifies these systematic empirical observations: elevated dN/dS values among conspecifics is expected under a model of continual negative selection, in which all protein-coding mutations experience the same selective constraint at all times( Figure 1). It is important to note that this explanation does not require us to assume a separate class of weakly deleterious mutations[13],[48],[49] or time-varying selective regimes[56]. Our results also have implications for inferences of positive selection based on dN/dS among conspecific samples. Even when samples come from independently evolving populations, the power of the dN/dS statistic to detect positive selection is low when the majority of sites in the protein evolve under purifying selection[28],[57],[58]. Our results indicate that the power of the dN/dS statistic to detect positive selection is further reduced when samples come from a single population( see Table 1). This lack of power has indeed been observed—and, in some cases, interpreted as a lack of selection—in studies of intrapatient HIV evolution[8],[9],[59] and genetic variation in Salmonella Typhi[17],[18]. For higher eukaryotes, the distinction between multiple independent populations versus a single population is usually clearcut: samples from different species represent independent populations, whereas conspecific samples should be treated as arising from a single population( unless they are sampled from regions that have been reproductively isolated for more than generations). For microbes and viruses, however, the distinction may be more opaque. The central issue is whether or not the sequences being compared represent competing genotypes in the sense of a Wright-Fisher population model. In the case of the human influenza A virus, for example, contemporaneous samples should probably be considered as arising from a single population, because the global population of influenza A strains is known to be well-mixed and genotypes are known to compete for available hosts[60]. When comparing non-contemporaneous samples, however, it is less clear whether the samples should be treated as arising from a single population or independent populations. In some sense, an influenza virus sample from the year 1968 is independent of a sample from year 2000. We might therefore expect that positive selection on influenza's HA locus would produce ω>1 when comparing non-contemporaneous samples( independent populations), but ω≈1 when comparing nearly contemporaneous samples( single population). This type of pattern has indeed been reported[56], but it was interpreted as a signature of time-varying selection pressures on the HA protein. In fact, this kind of pattern would be expected under continual positive selection, given our analysis of dN/dS over short versus long time-scales. As the discussion above suggests, it may be difficult to determine the appropriate time-scale associated with a dataset of sampled microbial sequences, particularly for a virus sampled at different timepoints. In fact, there may not be a single time-scale that applies to the entire dataset. In such cases, the relationship between the observed dN/dS ratios and the underlying selection coefficients will be described by some( unknown) mixture of Equation( 2) and Equation( 5). In such cases our central conclusion still holds: the relationship between selection and dN/dS is not necessarily a simple monotonic function, and it may be impossible to infer the selection pressure from the dN/dS measurement.
Since the time of Darwin , biologists have worked to identify instances of evolutionary adaptation . At the molecular scale , it is understood that adaptation should induce more genetic changes at amino acid altering sites in the genome , compared to amino acid–preserving sites . The ratio of substitution rates at such sites , denoted dN/dS , is therefore commonly used to detect proteins undergoing adaptation . This test was originally developed for application to distantly diverged genetic sequences , the differences among which represent substitutions along independent evolutionary lineages . Nonetheless , the dN/dS statistics are also frequently applied to genetic sequences sampled from a single population , the differences among which represent transient polymorphisms , not substitutions . Here , we show that the behavior of the dN/dS statistic is very different in these two cases . In particular , when applied to sequences from a single population , the dN/dS ratio is relatively insensitive to the strength of natural selection , and the anticipated signature of adaptive evolution , dN/dS>1 , is violated . These results have implications for the interpretation of genetic variation sampled from a population . In particular , these results suggest that microbes may experience substantially stronger selective forces than previously thought .