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The Limits of Natural Selection in a Nonequilibrium World
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Opinion
The Limits of Natural Selection in a Nonequilibrium World Yaniv Brandvain1 and Stephen I. Wright2,* Evolutionary theory predicts that factors such as a small population size or low recombination rate can limit the action of natural selection. The emerging field of comparative population genomics offers an opportunity to evaluate these hypotheses. However, classical theoretical predictions assume that populations are at demographic equilibrium. This assumption is likely to be violated in the very populations researchers use to evaluate selection's limits: populations that have experienced a recent shift in population size and/or effective recombination rates. Here we highlight theory and data analyses concerning limitations on the action of natural selection in nonequilibrial populations and argue that substantial care is needed to appropriately test whether species and populations show meaningful differences in selection efficacy. A move toward modelbased inferences that explicitly incorporate nonequilibrium dynamics provides a promising approach to more accurately contrast selection efficacy across populations and interpret its significance. Characterizing the Influence of Nonequilibrium Demographic History on the Efficacy of Natural Selection Despite the relentless action of natural selection, no organism is perfect. Understanding the factors that limit natural selection is a fundamental concern of population genetics [1]. These limits can inform the basis of human genetic diseases [2,3], the extinction of small [4,5], asexual [6], or selfing populations [7–10], the degradation of sex chromosomes [11], the evolution of gene [12] and genome structure [13–15], and the consequences of domestication [16–19]. For example, the history of population bottlenecks associated with range expansion might be responsible for the excess of potentially damaging and, in some cases, disease-causing [20,21] variants in historically bottlenecked human populations [21–26]. Similarly, an excess of putatively deleterious mutations in predominantly self-fertilizing plants suggests that purifying selection is limited in these taxa [27–30]. Because of its wide-ranging implications for micro- and macroevolution, conservation, plant and animal breeding, and human health, there has been much research on understanding the limits of selection. Classic theory predicts that smaller effective population sizes (see Glossary), higher ploidy levels, and lower effective recombination rates, among other factors, can limit the action of natural selection, driving populations toward lower mean fitness [1]. Population genomic datasets allow researchers to precisely identify and quantify putatively deleterious mutations, providing the opportunity for powerful tests of these hypotheses by investigating whether populations that differ in one or more of these features result in different patterns of divergence and variation for putatively deleterious mutations (many are reviewed in Table 1). However, there is growing recognition that inferring and interpreting differences in the efficacy of selection based on population genomic data can be more difficult than initially thought. Here we indicate the challenges in connecting differences in mutational patterns between taxa to differences in the action of natural selection (see Box 1 for a discussion of how researchers attempt to
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Trends Next-generation DNA and RNA sequencing datasets are enabling powerful genomic tests of the factors influencing the efficacy of natural selection against deleterious mutations. Theoretical advances have provided important insights into the extent to which demographic history influences selection strengths and genetic load. There is growing recognition that nonequilibrium demographic history can lead to spurious signals of increased genetic load. Model-based methods investigating the efficacy of selection, incorporating demographic history and uncertainty in the dominance of deleterious mutations, are being developed to provide further insights into the factors limiting selection in natural populations.
1 Department of Plant Biology, University of Minnesota, St[1_TD$IF] Paul, MN 55108, USA 2 Department of Ecology and Evolutionary Biology, University of Toronto, Toronto, ON M5S 3B2, Canada
*Correspondence: [email protected] (S.I. Wright).
http://dx.doi.org/10.1016/j.tig.2016.01.004 © 2016 Elsevier Ltd. All rights reserved.
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measure selection's limits). In particular, we highlight the complications that arise in attempts to infer limited efficacy of selection in nonequilibrial populations. There is growing recognition, particularly in the human population genomics literature, that nonequilibrium demography can complicate empirical tests for differences in the efficacy of selection from polymorphism data. This complication has led to considerable debate on the interpretation of genomic patterns [24,31–33]. For example, following a strong population bottleneck, sites under purifying selection are expected to recover equilibrium faster than neutral sites, which can lead to spurious signals of reduced efficacy of selection in bottlenecked populations [31,34,35]. Therefore, finding strong evidence for limited selection in such cases is difficult, particularly because theory predicts that population bottlenecks and expansions can have subtle and complex influences on selection. Although the confounding effects of nonequilibrium demography on our inference of relaxed selection is well appreciated in the human literature, we argue that such consideration must be extended to studies of other populations that have experienced a recent bottleneck, including domesticated species, those that have experienced a shift in mating system, and other candidates for relaxed selection. We argue that the field has yet to fully address these challenges, meaning that many examples purporting to provide evidence for selection limits remain ambiguous. Therefore, clarifying what is robust, genome-wide evidence for differences in selection, and improved understanding of between-species differences in fitness, will be a major task in the coming years. Below we outline both the promise and the challenges of using genomic data to test theory about the limits of natural selection and to investigate what forces are most important in imposing limits, especially as populations grow, shrink, and spread in our changing world.
Limits to Selection Theoretical Predictions of the Limits of Natural Selection The number and frequency of damaging mutations is determined by their introduction into a population by mutation, their stochastic change by drift, and their removal by selection. For strongly deleterious mutations in modestly sized populations, selection, mutation, and the mode of inheritance can describe the expected number and frequency of deleterious mutations, as well as the mutation load. For large-effect mutations, the predicted genetic load is simply a function of the mutation rate [36]; however, additional biological reality complicates this prediction [37]. For mutations with more subtle influences on fitness, stochasticity can overwhelm the action of selection as the number of independent chromosomes in a population decreases. Therefore, deleterious mutations are predicted to be more common in smaller populations (stronger effects of drift) and/or populations or genomic regions with lower recombination rates (less independence of selection on these chromosomes). Another constraint on selection's action is its ability to ‘see’ mutations. In diploids, deleterious variation can be hidden in the recessive state. In species or genomic regions with higher ploidy, a similar effect can occur and therefore selection may be unable to eliminate deleterious loss-of-function mutations that are hidden by functional gene copies. Together, population size, recombination rates, mutation rates, ploidy, and the mode of gene action interact to set the limits of selection, which we can hope to uncover from genomic data (Table 1). In this brief treatment, we neglect constraints in organismal design and the mutational landscape that can also impose limits on selection [1]. Uncovering these limits from genomic data presents an additional set of challenges orthogonal to the points below. Estimating Demographic History and Recombination Rates The basic predictors of the limits of natural selection – recombination rates, mutation rates, and historical population sizes – can, in principle, be precisely estimated from modern genomic data.
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Glossary p: the expected number of sequence differences between two chromosomes. pn: the expected number of sequence differences between two chromosomes at nonsynonymous sites within a species or population. ps: the expected number of sequence differences between two chromosomes at synonymous sites within a species or population. Distribution of fitness effects (DFE): the distribution of the proportion of new mutations in each class of selection coefficient. dN: the expected number of sequence differences between two chromosomes at nonsynonymous sites between species. dS: the expected number of sequence differences between two chromosomes at synonymous sites between species Effective population size (Ne): the effective number of breeding individuals. Gene surfing: the spread of new and standing mutations that are on the wave front of a range expansion; surfing by neutral or deleterious mutations mimics positive selection because they spread and fix over large areas. Genetic load: the difference between the average population fitness and the fitness of a mutationfree genotype.
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Table 1. Selected Examples of Genome-Wide Tests of Selection's Limits Factor
Theoretical Prediction
Comparison
Metric of Relaxed Selection
Refs
Significant Effect?
Effective population size
Small population sizes increase the effects of drift relative to selection [68]
Domesticated vs wild tomato
dN/dS
[69]
+
Domesticated vs wild sunflowers
pn/ps
[17]
+
Domesticated vs wild rice
[7_TD$IF]dN/[8_TD$IF]dS dN/[9_TD$IF]dS
[70] [16]
+ +
Domesticated vs wild horses
# Deleterious mutations/ind
[19]
+
Arabidopsis thaliana populations of different sizes
pn/ps
[71]
+
Yeast species of different sizes
Various
[72]
+
Human populations experiencing historical differences in population size
pn/ps (+ related summaries) pn/ps (+ related summaries) # Deleterious mutations/ind # Deleterious mutations/ind # Deleterious mutations/ind Predicted individual fitness
[25] [22] [31] [33] [52] [51,52]
+ + -
Low- vs highrecombination genomic regions
pn/ps, GERP scores dN/dS DFE pn/ps, dN/dS, DFE
[74] [75] [76] [77]
+
Selfing vs outcrossing species and populations
pn/ps, dN/dS, DFE # Stop codons, pn/ps dN/dS pn/ps dN/dS pn/ps DFE DFE
[78] [28] [10_TD$IF][28] [79] [79] [30] [27] [80]
+ +
dN/dS, pn/ps pn/ps
[29] [81]
+
Recombination rates
Reduced recombination will cause higher selective interference, weakening selection [73]
Asexual vs sexual populations
+ +
+ +
+ + + +
Tests of whether selection is weaker in populations with reduced effective population size or effective recombination rates. Response variables include the ratio of nonsynonymous to synonymous substitutions (dN/dS), the ratio of nonsynonymous to synonymous polymorphism pn/ps, and the inferred DFE.
For example, one diploid genome can provide a sketch of an entire population's history [38] and many sequences allow a fine-grained view of recent population sizes and migration rates [39–41]. Dense genotype data from many individuals provides precise characterization of the meiotic recombination landscape and whole-genome sequencing of parent–offspring trios can reveal the rate of spontaneous mutation [42,43], providing access to additional predictors of selection's limits. With such information, researchers can explore the relationship between the action of selection and population parameters of interest [31–33,44]. Quantifying the Limits to Selection A key measure of interest in evaluating the efficacy of selection is the genetic load – the difference between achieved fitness and maximum potential fitness. In theory one could test whether two populations differ in their load by comparing the fitness of individuals from these populations, and although the genetic load is not an exact measure of the historical action of selection, the efficacy of selection was likely to be more limited in the population with the larger load. In practice, however, comparing fitness of individuals adapted to different biotic and abiotic challenges is often
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Box 1. How Can We Quantify and Compare the Efficacy of Selection? Various metrics are applied to compare the efficacy of negative selection, but such comparisons have a number of challenges in their power and interpretation. The ratio of nonsynonymous to synonymous substitutions between species (dN/dS) is a common (and crude) measure of the strength of selection. Elevated dN/dS values are often interpreted as reflecting reduced efficacy of negative selection, but elevated dN/dS can also indicate elevated positive selection [48,82]. In addition, because new mutations accumulate slowly, we expect only modest differences in the number of deleterious mutations between recently diverged populations. Because most comparative population genomic studies focus on pairs of closely related populations (Table 1) between-species contrasts are often underpowered, limiting our ability to contrast contemporary differences in selection. Therefore, comparisons of intraspecific diversity at selected and neutral sites (e.g., pn/ps) fell into favor as a way to overcome this limitation. However, nonequilibrium demography can mislead this measure (Box 3). The use of evolutionary models to infer the DFE of deleterious mutations [62,63] is thus becoming increasingly widespread (Table 1). By combining information on the reduction in nonsynonymous diversity with the frequency distribution of nonsynonymous and synonymous mutations, these methods explicitly quantify the strength of selection against deleterious mutations rather than simply reporting a ratio of diversity levels at functional and neutral sites. However, cross-species comparisons of the DFE do not always generate straightforward interpretations of differences in the efficacy of selection. For example, one species can show increased proportions of both effectively neutral and strongly deleterious mutations compared with another [27]. Additionally, genomic data allow improved assessment of which mutations are likely to have deleterious effects [57]. Researchers can use algorithms (e.g., SIFT [59], MAPP [60]) that combine cross-species sequence conservation and functional predictions. Since tests of the limits of selection are focused on mutations with fitness effects, an improved search image for damaging mutations may increase the power of such tests. However, these methods inherently rely on sites subject to purifying selection over long macroevolutionary history and weakly selected sites that are more likely to be subject to shifts in the efficacy of selection could remain undetected, and beneficial changes in function can be confused for deleterious mutations.
unfeasible. As we describe below and in Box 1, annotated population genomic data may provide an alternative glimpse into the historical action of natural selection, and genome-informed inferences can, in principle, provide information about the genetic load in populations [37]. Such data allow precise estimation of the number and frequency of putatively deleterious mutations genome wide, potentially facilitating strong hypothesis testing regarding what factors influence the number and frequency of deleterious variants. The genome contains enough sites variable within or divergent among populations to investigate whether individuals from a given population carry more deleterious mutations than individuals in a different population. To test whether selection's limits differ between populations, species, or genomic regions, researchers often compare the number or frequency of putatively deleterious variants, perhaps weighted by their inferred effect on fitness, relative to putatively neutral ones and/or fit a model of demography and selection to such data (Box 1). The challenge, which we discuss in more detail below, is relating observed mutational patterns to the goal of quantifying and comparing historical selection. As we highlight in Box 1, this challenge is not trivial: there is currently no single agreed on measure of the efficacy of selection. Evidence of Selection's Limits Recent analyses of whole-genome data have attempted to test hypotheses of selection's limits (Table 1). Such tests take species, populations, or genomic regions that differ in some biological feature such as effective recombination rate, effective population size, and/or ploidy and ask whether there is a corresponding difference in the action of purifying selection as inferred from patterns of polymorphism and/or divergence. The results are somewhat mixed, with some studies purporting to find evidence for reduced efficacy of selection while others do not. In addition to variable results, the studies differ in how they test for relaxed selection. Moreover, tests of specific biological hypotheses can be quite different even when the explanatory variables are superficially similar. For example, both a severe
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recent bottleneck and a long-term small census size decrease the effective population size, but their predicted influence on selection is quite different (see below).
Limits to Selection in Nonequilibrial Populations Theory in Nonequilibrial Populations Most results concerning the limits to selection assume demographic equilibrium. However, most populations are rarely at equilibrium. Many taxa that have been studied to test specific predictions of natural selection's limits have experienced a recent bottleneck (e.g., out-of-African human populations, domesticated plants and animals, plants that recently evolved a propensity to self-pollinate; Table 1). In these nonequilibrial populations, the effective population size estimated by sequence diversity (e.g., pairwise sequence diversity at synonymous sites) does not adequately summarize the complex predictions of population genetic theory. We summarize recent developments in population genetic theory addressing the limits of selection in nonequilibrium populations in Box 2. We also highlight the extension of these models to spatially expanding populations [26,45]. Overall, the theory summarized in Box 2 demonstrates that both a rapid decrease in population size followed by a fast recovery and a spatial population expansion will have subtle influences on the action of selection. If mutations have an additive effect on fitness, a recent bottleneck or population expansion will have a negligible effect on population fitness [31,33,46]. However, the case becomes more complex for recessive variants [24,45–47], where a short-term bottleneck can change a population's fitness. Thus, while longer-term reductions in effective population size are expected to have important effects on population mean fitness, the effects of shorter-term demographic bottlenecks followed by recovery depend in important ways on the dominance of deleterious mutations. Inferring Selection's Limits in Nonequilibrial Populations A reconsideration of what constitutes empirical evidence of reductions in the efficacy of selection has accompanied the development of theory described in Box 2. Importantly, one common measure of weakened selection – the relative ratio of putatively deleterious to putatively neutral variation within populations (e.g., pn/ps) can be particularly misled by recent bottlenecks. That is, because neutral variation approaches equilibrium more slowly than deleterious variation (Box 3), ratios of deleterious to neutral variation will be elevated in bottlenecked populations. Therefore, Box 2. Theory: Selection's Limits in Nonequilibrial Populations Most rare mutations are stochastically lost in the contraction phase of a bottleneck. Therefore, a recently bottlenecked population will retain few segregating deleterious mutations. However, those that survive the contraction are pushed to a higher frequency, and the average number of deleterious mutations per individual remains roughly constant after a population contraction [33,46,47]. Providing a bottlenecked population remains small, mildly deleterious mutations can accumulate; however, this effect is largely minor and transient, especially if the period of small population size is limited. The impact of a bottleneck on population fitness depends on the mode of gene action. Because the average number of deleterious mutations per individual is insensitive to recent bottlenecks, the genetic load induced by alleles with additive effects on fitness is also insensitive to brief bottlenecks [33,46]. By contrast, the higher frequency of alleles surviving a bottleneck means that the deleterious effects recessive mutations will be expressed, increasing the genetic load [46,47]. However, this burden is temporary: recessive variants return to equilibrium frequencies well before novel deleterious mutations drift to considerable frequencies [46]. Therefore, theory predicts a deficit in the per-individual number of deleterious recessive mutations in bottlenecked populations [47]. The impact of population expansions on the action of selection has also received much theoretical interest. Mutations arising on the geographical edge of an expanding population experience an evolutionary advantage with little regard to their fitness consequence, a phenomenon known as gene surfing [83–90]. The decline in fitness associated with deleterious mutations riding the wave front is called the expansion load [26,45]. Standing variants with additive effects on fitness do not contribute to the expansion load because drift does not influence expected allele frequencies [26,45]. However, new deleterious mutations with additive effects gradually accumulate at the wave front, generating an expansion load [26]. Additionally, standing recessive variants that ride the wave front increase the expansion load by exposing their fitness costs [45].
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Box 3. Population Contractions Generate a Relative Excess of Deleterious Variation, Regardless of the Efficacy of Selection Over time, mutation, drift, and selection generate an equilibrium distribution of allele frequencies across classes of functional elements in the genome. Major changes in population size shift genetic variation from this equilibrium by changing the number of chromosomes (in the population) that can be hit by mutation and in the face of population contractions, removing a large number of segregating mutations. The influence of demography on genome-wide patterns of variation is well known. However, the fact that this equilibrium is reached more quickly for deleterious mutations than neutral variants (Figure I) (see also [34,35,49]) has not been appreciated in our interpretation of the relative ratios of synonymous and nonsynonymous variation. In other words, segregating deleterious mutations are at a lower frequency at equilibrium than are weakly selected mutations and so deleterious mutations recover to their pre-bottleneck equilibrium levels faster than weakly selected mutations simply because their frequency was not high before the bottleneck.
Genec diversity X me, by strength of purifying selecon, starng with one chromsome Key: Neutral (s=0) s = 0.001 s = 0.01 s = 0.1
0.000
0.002
0.004
π%
0.006
0.008
0.010
The implications of this result for inferring reductions in the efficacy of selection are serious. We often evaluate evidence for differences in selection in recently bottlenecked populations using polymorphism patterns. The more rapid return of equilibrium variation at nonsynonymous than synonymous sites means that we could be misled to infer our hypothesized prediction; that is, we will infer that selection is relaxed following a bottleneck (elevated pn/ps) regardless of the actual process. Thus, a direct estimate of the number of putatively deleterious mutations can provide a stronger test of predictions of relaxed selection [31,33]. Alternatively, methods that estimate the distribution of fitness effects while explicitly controlling for nonequilibrium population history can be implemented [62,63,91–94].
0
1000
2000
3000
4000
5000
Gen
Figure I. pn Reaches Equilibrium Faster Than ps after a Population Bottleneck. Pairwise sequence diversity for a population of a constant size that begins with no variation (e.g., a population that has undergone[2_TD$IF] a contraction [3_TD$IF]that [4_TD$IF]wiped [5_TD$IF]out [6_TD$IF]all genetic diversity and then experiences an instantaneous expansion) with differing strengths of purifying selection. The blue or green lines are proxies for pn and the red and black lines are proxies for ps. At less than 2000 generations into the expansion, for example, pn/ps calculated using the green line (pn) to the red line (ps) must be interpreted with the caveat that the red line has not reached equilibrium. Our cartoon corresponds directly to the finding of Pennings et al. [35]: after a genome-wide sweep associated with drug resistance in HIV, the ratio of nonsynonymous to synonymous diversity (pn/ps) is high and decreases with time. This result reflects the more rapid approach to equilibrium under negative selection (pn) than with drift (ps) [34], presumably because deleterious mutations rise to a lower frequency.
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pn/ps measures in bottlenecked populations can generate statistical artifacts that mimic expectations of relaxed selection [31,33–35,48,49]. Simons et al. [33] and Do et al. [31] have therefore suggested that an increased number of deleterious mutations per individual, rather than the relative frequency of segregating variants, should be used to estimate selection's limits. However, while the number of putatively deleterious mutations is robust to artifacts induced by nonequilibrium demography, this measure neglects the frequency of mutations. Therefore, simply counting the number of deleterious mutations per individual does not reliably estimate the genetic load when deleterious mutations are partially recessive [24,33]. Because deleterious mutations are likely to be often recessive [50], and because theoretical results concerning selection in nonequilibrial populations depend on the mode of gene action, some authors have found the per-individual number of deleterious mutations measure to be an inadequate summary of the genetic load [24,45,51,52]. The challenges in estimating the genetic load has intensified debate on the extent to which selection has been limited in populations experiencing recent demographic shifts and particularly in out-of-African human populations [24,26,31–33,53]. Out-of-African human populations contain proportionately more putatively deleterious variation relative to neutral genetic diversity than African populations [25,26,54,55]. Counting the per-individual number of putatively deleterious derived mutations reveals subtle [52,56] or no [31,33] difference among populations. However, on average out-of-African populations are more homozygous for the derived, putatively deleterious mutations they do carry, and if these mutations are on average recessive, out-of-African populations may have an elevated mutation load [24,32,52]. More generally, most populations with recent dips in effective population size carry proportionally more putatively deleterious variation than closely related populations with large effective population sizes (Table 1). The observed increase in the proportion of putatively deleterious variation is consistent with expectations that selection is limited in populations with lower effective population sizes but can plausibly be induced by the artifacts discussed above. Accounting for nonequilibrium while considering the effects of dominance is therefore critical to our interpretation of the extent to which selection has been relaxed in bottlenecked populations. Promising Directions As a field, we have not yet identified how to best infer selection's limits. One creative approach weights genotypes by an estimate of their fitness costs under alternative dominance coefficients [52]. However, such attempts must admit the considerable uncertainty in estimates of both the mode of gene action and the fitness effect of mutations, which are usually inferred using crossspecies sequence conservation and/or functional predictions [57–60] and are not an actual fitness estimate. Similar challenges lie in the interpretation of other comparisons of selection efficacy in Table 1. Selfing populations, for example, rarely show evidence for higher rates of substitution at selected sites between species (using dN/dS), but more often show higher selected relative to neutral variation segregating within populations (see [61] and examples in Table 1). Domesticated organisms have similarly shown elevated proportions of selected variation compared with wild relatives. The extent to which these polymorphism patterns are a simple consequence of nonequilibrium demography without a corresponding increase in genetic load remains uncertain; however, recent studies in dogs [18] and horses [19] suggest that an increase in the genetic load has accompanied domestication. This supports the hypothesis that a higher genetic load is a ‘cost of domestication’ [16]. Model-based inference provides an alternative approach to comparing the efficacy of selection across populations and genomic regions. Of particular note is a popular set of models that
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estimate the distribution of fitness effects (DFE) of deleterious mutations while explicitly incorporating simple models of nonequilibrium demography [62,63]. The DFE approach has been recently harnessed to infer both an accumulation of modestly deleterious mutations and the purging of severely damaging mutations following the transition to self-fertilization [27]. However, DFE is improperly calibrated under complex demographic histories [62] and with recurrent selection [64]. Moreover, current DFE models assume an additive model of gene action and random mating, which can complicate interpretations of fitness differences across species in the presence of recessive mutations, especially across species that differ in ploidy and selfing rate [27,65].
Outstanding Questions
More explicit modeling of the joint effects of dominance, demography, and nonequilibrium transitions in population size and mating system will enable a more informed interpretation of selection from population genomic data. With realistic forward simulations incorporating nonequilibrium, mating system, and our uncertainty in selection and dominance parameters, we should be able to gain better insights into the scale and significance of selection differences. These comparisons in combination with model fitting may also in turn inform us about the distribution of dominance coefficients.
How rapidly can changes in population size and recombination drive major shifts in mean fitness and mutation load?
We caution, however, that the interpretation of results from model-based inference should be treated with care, as model misspecification can mislead inference. For example, some increase in the genetic load of out-of-African human populations is to likely reflect the introgression of deleterious alleles from archaic human populations [66,67] in which selection was likely to have been relaxed [31] and not accounting for this history of archaic introgression would seriously mislead models that aim to infer the extent to which population expansion has limited natural selection as some members of our species left Africa. Another possibility is that colonization bottlenecks and transitions in mating system are associated with reduced selection coefficients themselves, as shifts in environment and selective pressures free populations from historical selection pressures [30]. Distinguishing the role of effective population size change and differences in selection strengths adds a further challenge in interpretation.
Concluding Remarks As large-scale genomic datasets accumulate, there are exciting possibilities for investigating the extent to which populations and genomic regions differ in the strength of selection and how this affects the evolutionary process. Such analyses, however, highlight the difficulties in quantifying selection's limits, especially in nonequilibrial populations. In parallel with increasingly sophisticated model-based approaches to investigate population history using neutral diversity, it is becoming clear that simple comparisons of summaries of selected variation can give a limited or inaccurate picture of differences in selection. Future research addressing selection's limits will improve with explicit consideration of nonequilibrium conditions and mode of gene action; this will inform better understanding of the extent to which species differ in deleterious mutation accumulation (see Outstanding Questions). Meanwhile, we encourage researchers evaluating evidence for relaxed selection to present multiple analyses of their data and explicit modeling of demographic and mutational effects on fitness and to jointly consider the benefits and limitations of these approaches when interpreting their results. Acknowledgments The authors thank Suzanne McGaugh and Josh Schraiber for their comments and suggestions on the manuscript and Brian Charlesworth for helpful discussion.
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Opinion
The Limits of Natural Selection in a Nonequilibrium World Yaniv Brandvain1 and Stephen I. Wright2,* Evolutionary theory predicts that factors such as a small population size or low recombination rate can limit the action of natural selection. The emerging field of comparative population genomics offers an opportunity to evaluate these hypotheses. However, classical theoretical predictions assume that populations are at demographic equilibrium. This assumption is likely to be violated in the very populations researchers use to evaluate selection's limits: populations that have experienced a recent shift in population size and/or effective recombination rates. Here we highlight theory and data analyses concerning limitations on the action of natural selection in nonequilibrial populations and argue that substantial care is needed to appropriately test whether species and populations show meaningful differences in selection efficacy. A move toward modelbased inferences that explicitly incorporate nonequilibrium dynamics provides a promising approach to more accurately contrast selection efficacy across populations and interpret its significance. Characterizing the Influence of Nonequilibrium Demographic History on the Efficacy of Natural Selection Despite the relentless action of natural selection, no organism is perfect. Understanding the factors that limit natural selection is a fundamental concern of population genetics [1]. These limits can inform the basis of human genetic diseases [2,3], the extinction of small [4,5], asexual [6], or selfing populations [7–10], the degradation of sex chromosomes [11], the evolution of gene [12] and genome structure [13–15], and the consequences of domestication [16–19]. For example, the history of population bottlenecks associated with range expansion might be responsible for the excess of potentially damaging and, in some cases, disease-causing [20,21] variants in historically bottlenecked human populations [21–26]. Similarly, an excess of putatively deleterious mutations in predominantly self-fertilizing plants suggests that purifying selection is limited in these taxa [27–30]. Because of its wide-ranging implications for micro- and macroevolution, conservation, plant and animal breeding, and human health, there has been much research on understanding the limits of selection. Classic theory predicts that smaller effective population sizes (see Glossary), higher ploidy levels, and lower effective recombination rates, among other factors, can limit the action of natural selection, driving populations toward lower mean fitness [1]. Population genomic datasets allow researchers to precisely identify and quantify putatively deleterious mutations, providing the opportunity for powerful tests of these hypotheses by investigating whether populations that differ in one or more of these features result in different patterns of divergence and variation for putatively deleterious mutations (many are reviewed in Table 1). However, there is growing recognition that inferring and interpreting differences in the efficacy of selection based on population genomic data can be more difficult than initially thought. Here we indicate the challenges in connecting differences in mutational patterns between taxa to differences in the action of natural selection (see Box 1 for a discussion of how researchers attempt to
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Trends Next-generation DNA and RNA sequencing datasets are enabling powerful genomic tests of the factors influencing the efficacy of natural selection against deleterious mutations. Theoretical advances have provided important insights into the extent to which demographic history influences selection strengths and genetic load. There is growing recognition that nonequilibrium demographic history can lead to spurious signals of increased genetic load. Model-based methods investigating the efficacy of selection, incorporating demographic history and uncertainty in the dominance of deleterious mutations, are being developed to provide further insights into the factors limiting selection in natural populations.
1 Department of Plant Biology, University of Minnesota, St[1_TD$IF] Paul, MN 55108, USA 2 Department of Ecology and Evolutionary Biology, University of Toronto, Toronto, ON M5S 3B2, Canada
*Correspondence: [email protected] (S.I. Wright).
http://dx.doi.org/10.1016/j.tig.2016.01.004 © 2016 Elsevier Ltd. All rights reserved.
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measure selection's limits). In particular, we highlight the complications that arise in attempts to infer limited efficacy of selection in nonequilibrial populations. There is growing recognition, particularly in the human population genomics literature, that nonequilibrium demography can complicate empirical tests for differences in the efficacy of selection from polymorphism data. This complication has led to considerable debate on the interpretation of genomic patterns [24,31–33]. For example, following a strong population bottleneck, sites under purifying selection are expected to recover equilibrium faster than neutral sites, which can lead to spurious signals of reduced efficacy of selection in bottlenecked populations [31,34,35]. Therefore, finding strong evidence for limited selection in such cases is difficult, particularly because theory predicts that population bottlenecks and expansions can have subtle and complex influences on selection. Although the confounding effects of nonequilibrium demography on our inference of relaxed selection is well appreciated in the human literature, we argue that such consideration must be extended to studies of other populations that have experienced a recent bottleneck, including domesticated species, those that have experienced a shift in mating system, and other candidates for relaxed selection. We argue that the field has yet to fully address these challenges, meaning that many examples purporting to provide evidence for selection limits remain ambiguous. Therefore, clarifying what is robust, genome-wide evidence for differences in selection, and improved understanding of between-species differences in fitness, will be a major task in the coming years. Below we outline both the promise and the challenges of using genomic data to test theory about the limits of natural selection and to investigate what forces are most important in imposing limits, especially as populations grow, shrink, and spread in our changing world.
Limits to Selection Theoretical Predictions of the Limits of Natural Selection The number and frequency of damaging mutations is determined by their introduction into a population by mutation, their stochastic change by drift, and their removal by selection. For strongly deleterious mutations in modestly sized populations, selection, mutation, and the mode of inheritance can describe the expected number and frequency of deleterious mutations, as well as the mutation load. For large-effect mutations, the predicted genetic load is simply a function of the mutation rate [36]; however, additional biological reality complicates this prediction [37]. For mutations with more subtle influences on fitness, stochasticity can overwhelm the action of selection as the number of independent chromosomes in a population decreases. Therefore, deleterious mutations are predicted to be more common in smaller populations (stronger effects of drift) and/or populations or genomic regions with lower recombination rates (less independence of selection on these chromosomes). Another constraint on selection's action is its ability to ‘see’ mutations. In diploids, deleterious variation can be hidden in the recessive state. In species or genomic regions with higher ploidy, a similar effect can occur and therefore selection may be unable to eliminate deleterious loss-of-function mutations that are hidden by functional gene copies. Together, population size, recombination rates, mutation rates, ploidy, and the mode of gene action interact to set the limits of selection, which we can hope to uncover from genomic data (Table 1). In this brief treatment, we neglect constraints in organismal design and the mutational landscape that can also impose limits on selection [1]. Uncovering these limits from genomic data presents an additional set of challenges orthogonal to the points below. Estimating Demographic History and Recombination Rates The basic predictors of the limits of natural selection – recombination rates, mutation rates, and historical population sizes – can, in principle, be precisely estimated from modern genomic data.
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Glossary p: the expected number of sequence differences between two chromosomes. pn: the expected number of sequence differences between two chromosomes at nonsynonymous sites within a species or population. ps: the expected number of sequence differences between two chromosomes at synonymous sites within a species or population. Distribution of fitness effects (DFE): the distribution of the proportion of new mutations in each class of selection coefficient. dN: the expected number of sequence differences between two chromosomes at nonsynonymous sites between species. dS: the expected number of sequence differences between two chromosomes at synonymous sites between species Effective population size (Ne): the effective number of breeding individuals. Gene surfing: the spread of new and standing mutations that are on the wave front of a range expansion; surfing by neutral or deleterious mutations mimics positive selection because they spread and fix over large areas. Genetic load: the difference between the average population fitness and the fitness of a mutationfree genotype.
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Table 1. Selected Examples of Genome-Wide Tests of Selection's Limits Factor
Theoretical Prediction
Comparison
Metric of Relaxed Selection
Refs
Significant Effect?
Effective population size
Small population sizes increase the effects of drift relative to selection [68]
Domesticated vs wild tomato
dN/dS
[69]
+
Domesticated vs wild sunflowers
pn/ps
[17]
+
Domesticated vs wild rice
[7_TD$IF]dN/[8_TD$IF]dS dN/[9_TD$IF]dS
[70] [16]
+ +
Domesticated vs wild horses
# Deleterious mutations/ind
[19]
+
Arabidopsis thaliana populations of different sizes
pn/ps
[71]
+
Yeast species of different sizes
Various
[72]
+
Human populations experiencing historical differences in population size
pn/ps (+ related summaries) pn/ps (+ related summaries) # Deleterious mutations/ind # Deleterious mutations/ind # Deleterious mutations/ind Predicted individual fitness
[25] [22] [31] [33] [52] [51,52]
+ + -
Low- vs highrecombination genomic regions
pn/ps, GERP scores dN/dS DFE pn/ps, dN/dS, DFE
[74] [75] [76] [77]
+
Selfing vs outcrossing species and populations
pn/ps, dN/dS, DFE # Stop codons, pn/ps dN/dS pn/ps dN/dS pn/ps DFE DFE
[78] [28] [10_TD$IF][28] [79] [79] [30] [27] [80]
+ +
dN/dS, pn/ps pn/ps
[29] [81]
+
Recombination rates
Reduced recombination will cause higher selective interference, weakening selection [73]
Asexual vs sexual populations
+ +
+ +
+ + + +
Tests of whether selection is weaker in populations with reduced effective population size or effective recombination rates. Response variables include the ratio of nonsynonymous to synonymous substitutions (dN/dS), the ratio of nonsynonymous to synonymous polymorphism pn/ps, and the inferred DFE.
For example, one diploid genome can provide a sketch of an entire population's history [38] and many sequences allow a fine-grained view of recent population sizes and migration rates [39–41]. Dense genotype data from many individuals provides precise characterization of the meiotic recombination landscape and whole-genome sequencing of parent–offspring trios can reveal the rate of spontaneous mutation [42,43], providing access to additional predictors of selection's limits. With such information, researchers can explore the relationship between the action of selection and population parameters of interest [31–33,44]. Quantifying the Limits to Selection A key measure of interest in evaluating the efficacy of selection is the genetic load – the difference between achieved fitness and maximum potential fitness. In theory one could test whether two populations differ in their load by comparing the fitness of individuals from these populations, and although the genetic load is not an exact measure of the historical action of selection, the efficacy of selection was likely to be more limited in the population with the larger load. In practice, however, comparing fitness of individuals adapted to different biotic and abiotic challenges is often
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Box 1. How Can We Quantify and Compare the Efficacy of Selection? Various metrics are applied to compare the efficacy of negative selection, but such comparisons have a number of challenges in their power and interpretation. The ratio of nonsynonymous to synonymous substitutions between species (dN/dS) is a common (and crude) measure of the strength of selection. Elevated dN/dS values are often interpreted as reflecting reduced efficacy of negative selection, but elevated dN/dS can also indicate elevated positive selection [48,82]. In addition, because new mutations accumulate slowly, we expect only modest differences in the number of deleterious mutations between recently diverged populations. Because most comparative population genomic studies focus on pairs of closely related populations (Table 1) between-species contrasts are often underpowered, limiting our ability to contrast contemporary differences in selection. Therefore, comparisons of intraspecific diversity at selected and neutral sites (e.g., pn/ps) fell into favor as a way to overcome this limitation. However, nonequilibrium demography can mislead this measure (Box 3). The use of evolutionary models to infer the DFE of deleterious mutations [62,63] is thus becoming increasingly widespread (Table 1). By combining information on the reduction in nonsynonymous diversity with the frequency distribution of nonsynonymous and synonymous mutations, these methods explicitly quantify the strength of selection against deleterious mutations rather than simply reporting a ratio of diversity levels at functional and neutral sites. However, cross-species comparisons of the DFE do not always generate straightforward interpretations of differences in the efficacy of selection. For example, one species can show increased proportions of both effectively neutral and strongly deleterious mutations compared with another [27]. Additionally, genomic data allow improved assessment of which mutations are likely to have deleterious effects [57]. Researchers can use algorithms (e.g., SIFT [59], MAPP [60]) that combine cross-species sequence conservation and functional predictions. Since tests of the limits of selection are focused on mutations with fitness effects, an improved search image for damaging mutations may increase the power of such tests. However, these methods inherently rely on sites subject to purifying selection over long macroevolutionary history and weakly selected sites that are more likely to be subject to shifts in the efficacy of selection could remain undetected, and beneficial changes in function can be confused for deleterious mutations.
unfeasible. As we describe below and in Box 1, annotated population genomic data may provide an alternative glimpse into the historical action of natural selection, and genome-informed inferences can, in principle, provide information about the genetic load in populations [37]. Such data allow precise estimation of the number and frequency of putatively deleterious mutations genome wide, potentially facilitating strong hypothesis testing regarding what factors influence the number and frequency of deleterious variants. The genome contains enough sites variable within or divergent among populations to investigate whether individuals from a given population carry more deleterious mutations than individuals in a different population. To test whether selection's limits differ between populations, species, or genomic regions, researchers often compare the number or frequency of putatively deleterious variants, perhaps weighted by their inferred effect on fitness, relative to putatively neutral ones and/or fit a model of demography and selection to such data (Box 1). The challenge, which we discuss in more detail below, is relating observed mutational patterns to the goal of quantifying and comparing historical selection. As we highlight in Box 1, this challenge is not trivial: there is currently no single agreed on measure of the efficacy of selection. Evidence of Selection's Limits Recent analyses of whole-genome data have attempted to test hypotheses of selection's limits (Table 1). Such tests take species, populations, or genomic regions that differ in some biological feature such as effective recombination rate, effective population size, and/or ploidy and ask whether there is a corresponding difference in the action of purifying selection as inferred from patterns of polymorphism and/or divergence. The results are somewhat mixed, with some studies purporting to find evidence for reduced efficacy of selection while others do not. In addition to variable results, the studies differ in how they test for relaxed selection. Moreover, tests of specific biological hypotheses can be quite different even when the explanatory variables are superficially similar. For example, both a severe
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recent bottleneck and a long-term small census size decrease the effective population size, but their predicted influence on selection is quite different (see below).
Limits to Selection in Nonequilibrial Populations Theory in Nonequilibrial Populations Most results concerning the limits to selection assume demographic equilibrium. However, most populations are rarely at equilibrium. Many taxa that have been studied to test specific predictions of natural selection's limits have experienced a recent bottleneck (e.g., out-of-African human populations, domesticated plants and animals, plants that recently evolved a propensity to self-pollinate; Table 1). In these nonequilibrial populations, the effective population size estimated by sequence diversity (e.g., pairwise sequence diversity at synonymous sites) does not adequately summarize the complex predictions of population genetic theory. We summarize recent developments in population genetic theory addressing the limits of selection in nonequilibrium populations in Box 2. We also highlight the extension of these models to spatially expanding populations [26,45]. Overall, the theory summarized in Box 2 demonstrates that both a rapid decrease in population size followed by a fast recovery and a spatial population expansion will have subtle influences on the action of selection. If mutations have an additive effect on fitness, a recent bottleneck or population expansion will have a negligible effect on population fitness [31,33,46]. However, the case becomes more complex for recessive variants [24,45–47], where a short-term bottleneck can change a population's fitness. Thus, while longer-term reductions in effective population size are expected to have important effects on population mean fitness, the effects of shorter-term demographic bottlenecks followed by recovery depend in important ways on the dominance of deleterious mutations. Inferring Selection's Limits in Nonequilibrial Populations A reconsideration of what constitutes empirical evidence of reductions in the efficacy of selection has accompanied the development of theory described in Box 2. Importantly, one common measure of weakened selection – the relative ratio of putatively deleterious to putatively neutral variation within populations (e.g., pn/ps) can be particularly misled by recent bottlenecks. That is, because neutral variation approaches equilibrium more slowly than deleterious variation (Box 3), ratios of deleterious to neutral variation will be elevated in bottlenecked populations. Therefore, Box 2. Theory: Selection's Limits in Nonequilibrial Populations Most rare mutations are stochastically lost in the contraction phase of a bottleneck. Therefore, a recently bottlenecked population will retain few segregating deleterious mutations. However, those that survive the contraction are pushed to a higher frequency, and the average number of deleterious mutations per individual remains roughly constant after a population contraction [33,46,47]. Providing a bottlenecked population remains small, mildly deleterious mutations can accumulate; however, this effect is largely minor and transient, especially if the period of small population size is limited. The impact of a bottleneck on population fitness depends on the mode of gene action. Because the average number of deleterious mutations per individual is insensitive to recent bottlenecks, the genetic load induced by alleles with additive effects on fitness is also insensitive to brief bottlenecks [33,46]. By contrast, the higher frequency of alleles surviving a bottleneck means that the deleterious effects recessive mutations will be expressed, increasing the genetic load [46,47]. However, this burden is temporary: recessive variants return to equilibrium frequencies well before novel deleterious mutations drift to considerable frequencies [46]. Therefore, theory predicts a deficit in the per-individual number of deleterious recessive mutations in bottlenecked populations [47]. The impact of population expansions on the action of selection has also received much theoretical interest. Mutations arising on the geographical edge of an expanding population experience an evolutionary advantage with little regard to their fitness consequence, a phenomenon known as gene surfing [83–90]. The decline in fitness associated with deleterious mutations riding the wave front is called the expansion load [26,45]. Standing variants with additive effects on fitness do not contribute to the expansion load because drift does not influence expected allele frequencies [26,45]. However, new deleterious mutations with additive effects gradually accumulate at the wave front, generating an expansion load [26]. Additionally, standing recessive variants that ride the wave front increase the expansion load by exposing their fitness costs [45].
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Box 3. Population Contractions Generate a Relative Excess of Deleterious Variation, Regardless of the Efficacy of Selection Over time, mutation, drift, and selection generate an equilibrium distribution of allele frequencies across classes of functional elements in the genome. Major changes in population size shift genetic variation from this equilibrium by changing the number of chromosomes (in the population) that can be hit by mutation and in the face of population contractions, removing a large number of segregating mutations. The influence of demography on genome-wide patterns of variation is well known. However, the fact that this equilibrium is reached more quickly for deleterious mutations than neutral variants (Figure I) (see also [34,35,49]) has not been appreciated in our interpretation of the relative ratios of synonymous and nonsynonymous variation. In other words, segregating deleterious mutations are at a lower frequency at equilibrium than are weakly selected mutations and so deleterious mutations recover to their pre-bottleneck equilibrium levels faster than weakly selected mutations simply because their frequency was not high before the bottleneck.
Genec diversity X me, by strength of purifying selecon, starng with one chromsome Key: Neutral (s=0) s = 0.001 s = 0.01 s = 0.1
0.000
0.002
0.004
π%
0.006
0.008
0.010
The implications of this result for inferring reductions in the efficacy of selection are serious. We often evaluate evidence for differences in selection in recently bottlenecked populations using polymorphism patterns. The more rapid return of equilibrium variation at nonsynonymous than synonymous sites means that we could be misled to infer our hypothesized prediction; that is, we will infer that selection is relaxed following a bottleneck (elevated pn/ps) regardless of the actual process. Thus, a direct estimate of the number of putatively deleterious mutations can provide a stronger test of predictions of relaxed selection [31,33]. Alternatively, methods that estimate the distribution of fitness effects while explicitly controlling for nonequilibrium population history can be implemented [62,63,91–94].
0
1000
2000
3000
4000
5000
Gen
Figure I. pn Reaches Equilibrium Faster Than ps after a Population Bottleneck. Pairwise sequence diversity for a population of a constant size that begins with no variation (e.g., a population that has undergone[2_TD$IF] a contraction [3_TD$IF]that [4_TD$IF]wiped [5_TD$IF]out [6_TD$IF]all genetic diversity and then experiences an instantaneous expansion) with differing strengths of purifying selection. The blue or green lines are proxies for pn and the red and black lines are proxies for ps. At less than 2000 generations into the expansion, for example, pn/ps calculated using the green line (pn) to the red line (ps) must be interpreted with the caveat that the red line has not reached equilibrium. Our cartoon corresponds directly to the finding of Pennings et al. [35]: after a genome-wide sweep associated with drug resistance in HIV, the ratio of nonsynonymous to synonymous diversity (pn/ps) is high and decreases with time. This result reflects the more rapid approach to equilibrium under negative selection (pn) than with drift (ps) [34], presumably because deleterious mutations rise to a lower frequency.
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pn/ps measures in bottlenecked populations can generate statistical artifacts that mimic expectations of relaxed selection [31,33–35,48,49]. Simons et al. [33] and Do et al. [31] have therefore suggested that an increased number of deleterious mutations per individual, rather than the relative frequency of segregating variants, should be used to estimate selection's limits. However, while the number of putatively deleterious mutations is robust to artifacts induced by nonequilibrium demography, this measure neglects the frequency of mutations. Therefore, simply counting the number of deleterious mutations per individual does not reliably estimate the genetic load when deleterious mutations are partially recessive [24,33]. Because deleterious mutations are likely to be often recessive [50], and because theoretical results concerning selection in nonequilibrial populations depend on the mode of gene action, some authors have found the per-individual number of deleterious mutations measure to be an inadequate summary of the genetic load [24,45,51,52]. The challenges in estimating the genetic load has intensified debate on the extent to which selection has been limited in populations experiencing recent demographic shifts and particularly in out-of-African human populations [24,26,31–33,53]. Out-of-African human populations contain proportionately more putatively deleterious variation relative to neutral genetic diversity than African populations [25,26,54,55]. Counting the per-individual number of putatively deleterious derived mutations reveals subtle [52,56] or no [31,33] difference among populations. However, on average out-of-African populations are more homozygous for the derived, putatively deleterious mutations they do carry, and if these mutations are on average recessive, out-of-African populations may have an elevated mutation load [24,32,52]. More generally, most populations with recent dips in effective population size carry proportionally more putatively deleterious variation than closely related populations with large effective population sizes (Table 1). The observed increase in the proportion of putatively deleterious variation is consistent with expectations that selection is limited in populations with lower effective population sizes but can plausibly be induced by the artifacts discussed above. Accounting for nonequilibrium while considering the effects of dominance is therefore critical to our interpretation of the extent to which selection has been relaxed in bottlenecked populations. Promising Directions As a field, we have not yet identified how to best infer selection's limits. One creative approach weights genotypes by an estimate of their fitness costs under alternative dominance coefficients [52]. However, such attempts must admit the considerable uncertainty in estimates of both the mode of gene action and the fitness effect of mutations, which are usually inferred using crossspecies sequence conservation and/or functional predictions [57–60] and are not an actual fitness estimate. Similar challenges lie in the interpretation of other comparisons of selection efficacy in Table 1. Selfing populations, for example, rarely show evidence for higher rates of substitution at selected sites between species (using dN/dS), but more often show higher selected relative to neutral variation segregating within populations (see [61] and examples in Table 1). Domesticated organisms have similarly shown elevated proportions of selected variation compared with wild relatives. The extent to which these polymorphism patterns are a simple consequence of nonequilibrium demography without a corresponding increase in genetic load remains uncertain; however, recent studies in dogs [18] and horses [19] suggest that an increase in the genetic load has accompanied domestication. This supports the hypothesis that a higher genetic load is a ‘cost of domestication’ [16]. Model-based inference provides an alternative approach to comparing the efficacy of selection across populations and genomic regions. Of particular note is a popular set of models that
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estimate the distribution of fitness effects (DFE) of deleterious mutations while explicitly incorporating simple models of nonequilibrium demography [62,63]. The DFE approach has been recently harnessed to infer both an accumulation of modestly deleterious mutations and the purging of severely damaging mutations following the transition to self-fertilization [27]. However, DFE is improperly calibrated under complex demographic histories [62] and with recurrent selection [64]. Moreover, current DFE models assume an additive model of gene action and random mating, which can complicate interpretations of fitness differences across species in the presence of recessive mutations, especially across species that differ in ploidy and selfing rate [27,65].
Outstanding Questions
More explicit modeling of the joint effects of dominance, demography, and nonequilibrium transitions in population size and mating system will enable a more informed interpretation of selection from population genomic data. With realistic forward simulations incorporating nonequilibrium, mating system, and our uncertainty in selection and dominance parameters, we should be able to gain better insights into the scale and significance of selection differences. These comparisons in combination with model fitting may also in turn inform us about the distribution of dominance coefficients.
How rapidly can changes in population size and recombination drive major shifts in mean fitness and mutation load?
We caution, however, that the interpretation of results from model-based inference should be treated with care, as model misspecification can mislead inference. For example, some increase in the genetic load of out-of-African human populations is to likely reflect the introgression of deleterious alleles from archaic human populations [66,67] in which selection was likely to have been relaxed [31] and not accounting for this history of archaic introgression would seriously mislead models that aim to infer the extent to which population expansion has limited natural selection as some members of our species left Africa. Another possibility is that colonization bottlenecks and transitions in mating system are associated with reduced selection coefficients themselves, as shifts in environment and selective pressures free populations from historical selection pressures [30]. Distinguishing the role of effective population size change and differences in selection strengths adds a further challenge in interpretation.
Concluding Remarks As large-scale genomic datasets accumulate, there are exciting possibilities for investigating the extent to which populations and genomic regions differ in the strength of selection and how this affects the evolutionary process. Such analyses, however, highlight the difficulties in quantifying selection's limits, especially in nonequilibrial populations. In parallel with increasingly sophisticated model-based approaches to investigate population history using neutral diversity, it is becoming clear that simple comparisons of summaries of selected variation can give a limited or inaccurate picture of differences in selection. Future research addressing selection's limits will improve with explicit consideration of nonequilibrium conditions and mode of gene action; this will inform better understanding of the extent to which species differ in deleterious mutation accumulation (see Outstanding Questions). Meanwhile, we encourage researchers evaluating evidence for relaxed selection to present multiple analyses of their data and explicit modeling of demographic and mutational effects on fitness and to jointly consider the benefits and limitations of these approaches when interpreting their results. Acknowledgments The authors thank Suzanne McGaugh and Josh Schraiber for their comments and suggestions on the manuscript and Brian Charlesworth for helpful discussion.
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