Methods to detect selection at the molecular level
Population size changes
Local adaptation, standing genetic variation, quantitative traits and multiple adaptive substitutions
Demographic context of selection and future directions
There has been an enormous increase in the amount of data on DNA sequence polymorphism available for many organisms in the last decade. New sequencing technologies provide great potential for investigating natural selection in plants using population genomic approaches. However, plant populations frequently show significant departures from the assumptions of standard models used to detect selection and many forms of directional selection do not fit with classical population genetics theory. Here, we explore the extent to which plant populations show departures from standard model assumptions, and the implications this has for detecting selection on molecular variation. A growing number of multilocus studies of nucleotide variation suggest that changes in population size, particularly bottlenecks, and strong subdivision may be common in plants. This demographic variation presents important challenges for models used to infer selection. In addition, selection from standing genetic variation and multiple independent adaptive substitutions can further complicate efforts to understand the nature of selection. We discuss emerging patterns from plant studies and propose that, rather than treating population history as a nuisance variable when testing for selection, the interaction between demography and selection is of fundamental importance for evolutionary studies of plant populations using molecular data.
Molecular population genetics is being invigorated by the ever-growing amount of nucleotide sequence data available. As a result, during the last two decades considerable efforts have been devoted to designing and applying analytical methods for detecting the footprint of natural selection at the molecular level. Finding genomic regions under selection is one of the first steps required to bridge the gap between the genotype and phenotype of adaptive traits, and is thus crucial for understanding the process of adaptation. Multilocus DNA sequence data also provide opportunities to gain detailed insight into population history and structure using explicit models that incorporate demographic features of populations. This presents an important challenge because both selection and population history have important influences on the amount and patterns of genetic variation. Studies of selection should ideally incorporate the confounding effects of demographic history, but studies of population history typically assume the absence of selection. Our review highlights this problem and discusses the progress and prospects for jointly inferring the role of population history and selection in plant populations.
Methods developed in the last 20 yr to test for selection on molecular variation mostly stem from the neutral theory of molecular evolution (Kimura, 1968, 1983). In a nutshell, the neutral theory posits that: the fate of segregating polymorphism is effectively determined by genetic drift, as most variation is neutral with regard to natural selection; fixed differences in alleles between species (divergence) are mostly neutral, with a negligible contribution from adaptive substitutions, and neutral loci are not affected by the effects of linked selection. Although this theory has stimulated much debate since its inception (Gillespie, 2000, 2001), it soon became widely used as a null hypothesis in molecular population genetics against which to test for selection. However, several crucial assumptions of the standard neutral model (hereafter SNM), namely no population structure, a constant population size and random mating make it a composite hypothesis (Nielsen, 2001; Garrigan et al., 2010). Thus, the mere rejection of neutrality does not point unambiguously to an effect of selection, but could also result from the violation of one (or several) of the aforementioned assumptions.
In parallel with attempts to test for the action of natural selection, considerable progress has been made in fitting explicit coalescent models to DNA sequence data for inferring demographic history (Hudson, 2002; Gutenkunst et al., 2009; Kuhner, 2009). These approaches allow for important inferences about the amount and timing of changes in population size, the extent of gene flow among populations and species (Hey & Nielsen, 2004; Kuhner, 2006; Hey, 2010), and the geographic structuring of populations (Charlesworth et al., 2003). These approaches have the potential to provide important quantitative insights into the process of speciation, the connectedness of populations, and the role of environmental factors, such as past climates, in influencing historical population dynamics.
Increasingly, methods to test for selection are being developed that explicitly take demography into account (Kim & Stephan, 2002; Jensen et al., 2005; Nielsen et al., 2005; De Mita et al., 2007; Eyre-Walker & Keightley, 2009). However, frequent and severe bottlenecks or extensive population subdivision are likely to strongly influence the power and ability to detect selection, and our understanding of these influences on testing for selection is still rather limited. For example, using simulations Städler et al. (2009) demonstrated how population subdivision can modify patterns of polymorphism and therefore affect the efficacy of tests of selection. Furthermore, departures from the classical model of directional selection also influence our ability to detect selection when it occurs. Here, we specifically explore the extent to which plant populations may be especially susceptible to violations of the assumptions of the SNM, and investigate the consequences that this may have for inferences of natural selection on molecular variation.
First, we outline the different methods that have been devised to detect the traces left by natural selection at the molecular level. We devote some effort to comparing these methods because our ability to detect selection at the molecular level depends critically on the types of data used and how robust the methods are to the underlying assumptions. We then explore violations of standard assumptions of the SNM and review recent evidence from multilocus data indicating that plant populations are indeed often susceptible to these violations. We also consider progress that has been made in developing methods to account for these violations. Finally, we conclude with a discussion of prospects and future directions in the field of plant population genomics, taking into account the increasing amount of data soon to be generated for a growing number of diverse species by next-generation sequencing techniques (Shendure & Ji, 2008; Wang et al., 2009).
II. Methods to detect selection at the molecular level
Natural selection has several types of effects on patterns of nucleotide variation, including on the level and structure of polymorphism, the amount of linkage disequilibrium (LD) around selected regions, the degree of population differentiation and the proportion and frequency of nonsynonymous substitutions (Table 1). The approaches used to examine DNA sequence variation can be distinguished by those that aim to detect the footprint of selection on linked neutral sites, and those that infer the action of selection directly on the sites themselves.
Table 1. An incomplete list of approaches for detecting selection on DNA sequences (see the text for further discussion)
Level of diversity
Unusually low or high genetic diversity around the selected locus
High sensitivity to demographic assumptions
Site frequency spectrum (SFS) based-test
Modification in the relative proportions of low and high frequency mutations in the selected region
High sensitivity to demographic assumptions. High rate of false positives
Linkage disequilibrium (LD)
A rise in frequency of long haplotypes created by the increased LD around the selected region
Spurious signal of selection created by population structure. LD levels decrease rapidly after selective sweep is complete
Differences between the ratio of nonsynonymous to synonymous polymorphism and nonsynonymous to synonymous divergence
Cannot distinguish between past and current selection. Slightly deleterious mutations inflate polymorphism. Spurious signal of selection with population expansion and bottlenecks if there are slightly deleterious mutations
Increased or decreased population differentiation of a genomic region relative to the rest of the genome
Hierarchical genetic substructure creates false positives. Importance of the sampling scheme
1. Level and structure of polymorphism – effects of linked selection
Under classical models of positive directional selection, a new advantageous allele quickly spreads to fixation. As a result of hitchhiking effects, the variation at adjacent regions is reduced, as neutral alleles linked with the selected mutation become fixed (Maynard Smith & Haigh, 1974). Therefore, strong positive selection leaves a highly characteristic signature in the molecular data involving a reduction in diversity around the selected locus (see Wang et al., 1999 for a well-studied example in maize). By contrast, balancing selection caused by overdominance or negative frequency-dependent selection generates a peak of diversity near the site under selection, as has been shown for plant self-incompatibility loci (Ruggiero et al., 2008; Schierup & Vekemans, 2008) and disease resistance genes (Tian et al., 2002). The most prominent test using this information is the Hudson–Kreitman–Aguadé (HKA) test (Hudson et al., 1987). This test and its derivatives (Wright & Charlesworth, 2004; Innan, 2006) use polymorphism data from several loci and correct for differences in mutation rate by incorporating divergence information. Under neutrality, polymorphism and divergence are proportional because they both depend on the neutral mutation rate. Any excess or deficit in diversity could be indicative of the action of selection (balancing selection and positive selection, respectively) on at least one of the loci.
Several widely used neutrality tests rely on information given by the site frequency spectrum (SFS), which summarizes the allele frequencies of polymorphisms in the sample and whose shape is strongly affected by different forms of selection (Tajima, 1989; Fu & Li, 1993; Fay & Wu, 2000). For example, under a selective sweep there can be an excess of new low-frequency mutations following the fixation of an advantageous allele (Braverman et al., 1995). In addition, with recombination the SFS following a sweep exhibits an excess of high-frequency derived alleles compared with the neutral SFS (Fay & Wu, 2000), because neutral alleles become partially swept to fixation. By contrast, under balancing selection the SFS tends to be enriched in intermediate frequency alleles. Tests based on the SFS are among the most widely implemented, primarily because only polymorphism data is required, without the need for close outgroup sequences to control for mutation rates.
More advanced methods to detect selection have also been devised, such as the composite likelihood ratio test (CLRT) of Kim & Stephan (2002) or the goodness-of-fit (GOF) test of Jensen et al. (2005), which both use an explicit model of positive selection. It has been shown (Thornton & Jensen, 2007) that the application of these methods on a set of preselected loci showing extreme patterns of variation (as is often typical in population genetic studies) creates an ascertainment bias resulting in a high rate of false positives (i.e. loci inferred to be under selection when they are actually neutrally evolving). This ascertainment bias can be partly corrected (Thornton & Jensen, 2007). Nevertheless, a conceptual advantage of these approaches is that rather than simply rejecting the standard neutral model they allow for explicit comparisons of models of selection and neutrality.
In addition to detecting the fixation of advantageous mutations, researchers have also been interested in developing methods to detect the ongoing spread of an advantageous allele, known as a partial selective sweep. These methods also use LD information (Hudson et al., 1994; Sabeti et al., 2002; Voight et al., 2006) and are based on the principle that the sudden rise in frequency of a selected mutation leaves less time for recombination to break up the haplotype carrying the mutation than if the mutation was neutral. As a result, the observation of a high-frequency haplotype exhibiting an unusually long-ranging LD is a strong clue indicating the action of directional selection.
The final category of test is based on the concept of genetic hitchhiking applied to subdivided populations and traces back to Lewontin & Krakauer (1973). The idea is once again to detect outlier loci, but this time the quantity of interest is the level of differentiation exhibited between populations (FST). The rationale is that if selection favours different alleles in different populations, this should increase the allele frequency differences between populations (and therefore FST) compared with neutral loci (Charlesworth et al., 2003). On the other hand, if selection favours the same allele in different populations, a lower level of differentiation is expected than genetic drift acting alone. The main problem is therefore to determine the expected FST distribution under neutrality. Beaumont & Nichols (1996) and Vitalis et al. (2001) used coalescent simulations to determine the expected FST distribution. Recent Bayesian approaches involve more realistic scenarios in which the migration rate can differ between pairs of subpopulations (Beaumont & Balding, 2004; Foll & Gaggiotti, 2008).
2. Comparison of polymorphism and divergence for different classes of mutations
In addition to tests of the effect of linked selection on neutral diversity, comparisons of different classes of mutation allow for direct tests of selection at functional sites. The basic premise to this approach was first proposed by McDonald & Kreitman (1991, MK test) and is based on a comparison of two types of mutations both within (polymorphism) and between (divergence) species. Typically, synonymous and nonsynonymous mutations are compared, although in principle the test is applicable for any set of two categories for which one is neutral (Andolfatto, 2008). Under the neutral theory of molecular evolution, synonymous mutations are neutral whereas nonsynonymous mutations are either strongly deleterious or neutral. Under this model, deleterious nonsynonymous mutations contribute negligibly to polymorphism (they are readily eliminated by purifying selection) and the ratio of nonsynonymous (PA) to synonymous (PS) polymorphism () therefore reflects the proportion of new mutations that are neutral. Under complete neutrality, we expect the ratio of nonsynonymous (DA) to synonymous (DS) divergence () to be equal to f because the ratio for both polymorphism and divergence is a simple function of the fraction of neutral nonsynonymous mutations. However, if some of the nonsynonymous mutations are advantageous, there will be an excess of nonsynonymous divergence, and we can estimate the proportion of substitutions fixed by positive selection as (Charlesworth, 1994; Smith & Eyre-Walker, 2002). The MK test itself consists of applying a Fisher’s exact test to the contingency table with entries PA, PS, DA and DS; the idea being to determine whether the type of mutations (synonymous vs nonsynonymous) and their status (polymorphism vs divergence) are independent. If independence is rejected it indicates a departure from neutrality.
An important assumption underlying the MK test is that the fraction of nonsynonymous mutations that are nonneutral are strongly deleterious. However, in practice, a substantial fraction of nonsynonymous mutations might be slightly deleterious rather than strongly deleterious. The fate of nonsynonymous mutations is determined by both purifying selection and genetic drift. The result is that these mutations will be counted as polymorphism and sometimes reach fixation, although they will contribute more to polymorphism than to divergence, therefore biasing both estimates of f and α. The common method to reduce this bias has been to exclude rare polymorphisms from the analysis, because most weakly deleterious mutations will segregate at low frequency (Fay et al., 2001; Sella et al., 2009). Recently, several studies have developed likelihood methods to estimate the full distribution of fitness effects of deleterious amino acid changes using polymorphism and divergence data (Boyko et al., 2008; Eyre-Walker & Keightley, 2009). These methods allow for an estimate of α that fully accounts for the presence of slightly deleterious mutations.
Finally, the comparison of synonymous and nonsynonymous mutations can readily be extended to a phylogenetic context. The key quantity of interest here is where dN and dS are the nonsynonymous and synonymous substitution rates, respectively (for a review see Yang & Bielawski, 2000). The idea is quite simple, if there is no selection, synonymous and nonsynonymous substitutions should occur at the same rate and ω should equal 1. Under negative selection ω < 1 and under positive selection ω > 1. The likelihood framework allows estimation of ω and refinement of the model to various degrees. For example, ω can be allowed to vary among the branches of a phylogeny to assess if selection has been more important in one lineage than another, or among sites along the sequence, such that only some sites would be affected by positive selection.
III. Population size changes
One of the core assumptions of the SNM is constant population size, yet changes in population size are common in plant populations (Harper, 1977; Silvertown & Charlesworth, 2001). Population size changes can have a number of important effects on genetic variation that complicate inferences of selection (Tenaillon et al., 2004; Haddrill et al., 2005; Wright & Gaut, 2005; Teshima et al., 2006). First, changes in population size, particularly those resulting from population bottlenecks, increase the variance in levels of diversity among genes. This has the effect of increasing the number of false positive tests of genetic hitchhiking when the standard neutral model is assumed (Wright & Gaut, 2005; Andolfatto, 2008). Second, both bottlenecks and population expansion can skew the SFS in similar ways to natural selection, generating genome-wide departures from the SNM. Third, changes in population size will influence levels of LD (Wall et al., 2002). Therefore, molecular signatures characteristic of positive selection can also be generated by changes in population size.
How are different tests of selection likely to be affected by changes in population size? Overall MK-based tests are expected to be less sensitive to demographic assumptions than SFS or LD-based methods (McDonald & Kreitman, 1991). This follows from the fact that synonymous and nonsynonymous mutations are interspersed throughout the genome and should be affected in the same way by demographic events (Nielsen, 2005). However, an important assumption of the MK approach is that the fraction f of neutral mutations is constant over the timescale in which both polymorphism and divergence are being estimated. Indeed, it has been shown that artifactual evidence of adaptive evolution can be obtained with the MK test if some nonsynonymous mutations are slightly deleterious and there has been a population expansion or a bottleneck during divergence (Ohta, 1993; Eyre-Walker, 2002). Moreover, the removal of low-frequency polymorphisms aggravates this problem because it makes the MK test more sensitive to changes in effective population size (Eyre-Walker, 2002; Charlesworth & Eyre-Walker, 2008). Simulation studies also demonstrate that bottlenecks reduce the power to detect adaptive substitutions (Eyre-Walker & Keightley, 2009). Thus, the fraction of adaptive substitutions can be overestimated when significant population expansion occurs and underestimated if there is a recent population bottleneck.
Many plant species are self-compatible and/or capable of clonal reproduction, and this allows new populations to be founded by a very small number of individuals, sometimes only one, creating the potential for severe population bottlenecks during colonization events (Baker, 1955; Pannell & Barrett, 1998; Foxe et al., 2008). Similarly, founder events during speciation may also lead to strong population bottlenecks and, depending on the time since speciation, this could have important effects on patterns of neutral diversity (Gottlieb, 1973; Jakobsson et al., 2006). Although the general role of founder events in speciation has been questioned in recent years (Barton & Charlesworth, 1984; Coyne & Orr, 2004), two common modes of plant speciation, namely reproductive isolation resulting from the evolution of selfing and allopolyploid speciation, can involve origins from a small number of individuals (Jakobsson et al., 2006; Foxe et al., 2009). Given recent evidence that a significant percentage of plant speciation events involve polyploidy (Wood et al., 2009), there is thus the potential for many species to be recovering from severe speciation bottlenecks, although multiple origins of polyploids may not be uncommon (Soltis & Soltis, 1993). Finally, a major focus of studies of selection in plants has been on cultivated species, and for these lineages the domestication process is almost invariably accompanied by a loss of genetic variation through bottlenecks and strong artificial selection (Gaut & Clegg, 1993; Thuillet et al., 2005; Wright et al., 2005; Caicedo et al., 2007; Haudry et al., 2007).
A growing number of studies of nucleotide variation using coalescent models provide quantitative evidence for strong signatures of recent size changes in plant populations (Table 2). These studies take advantage of the development of coalescent methods to fit the data to demographic and speciation parameters. The basic approach involves varying the parameters associated with ancestral and present-day population sizes, and fitting the data to these parameters. Evidence for population bottlenecks associated with the evolution of selfing (Foxe et al., 2009; Ness et al., 2010) and allopolyploid speciation (Jakobsson et al., 2006) are consistent with the notion that founder events are likely to play an important role in many plant speciation events, especially in groups capable of long-distance dispersal.
Table 2. Studies of selection on multilocus sequence data that fit demographic models with population size changes
Approach for parameter inference
Patterns of genetic variation compared with Standard Neutral Model
Information regarding the level of population subdivision is indicated when available. ABC, Approximate Bayesian computation (see Fig. 1 and Marjoram & Tavare, 2006); IM, Isolation–Migration model (see Hey & Nielsen, 2004); MIMAR, MCMC estimation of the Isolation–Migration model Allowing for Recombination (see Becquet & Przeworski, 2007); LAMARC, Likelihood Analysis with Metropolis Algorithm using Random Coalescence (see Kuhner, 2006)
Glacial cycles can also cause colonization bottlenecks (Arabidopsis lyrata, see Ross-Ibarra et al., 2008) as well as rapid population expansion (Populus balsamifera, Keller et al., 2010). Detailed surveys involving very large samples have shown a strong signal of a recent founder event in North American populations of Arabidopsis thaliana, with stronger patterns of relatedness over extensive geographic regions compared with European populations (Platt et al., 2010). Studies of European A. thaliana are consistent with an advancing wave of colonization from east to west following glaciation (François et al., 2008). In domesticated species, there is strong evidence for population bottlenecks of varying severity from near-complete loss of variation in wheat (Thuillet et al., 2005; Haudry et al., 2007), to minimal signs of population bottlenecks in alfalfa (Muller et al., 2006). Although not exhaustive, Table 2 emphasizes how prevalent historical changes in population size are in many plant species, particularly those that are annual and self-compatible. Table 2 also shows evidence of bottlenecks for long-lived plant species such as trees, where even ancient bottlenecks can influence present-day patterns of polymorphism. With more comparative datasets of this kind, it will be interesting to quantitatively compare the extent of historical population size fluctuations and effective sizes among plant species that vary in life history and mating system.
As a result of growing recognition of the importance of population size changes, there is now increased effort to incorporate the basic ingredients of demography in building more realistic null models. The underlying idea is that whereas selection will only affect particular genes and the adjacent linked regions, demography affects the entire genome more or less evenly. Therefore, if one has a plausible demographic scenario for the populations of interest, it is – at least in principle – possible to simulate what the polymorphism pattern under this scenario is likely to be and look for outliers putatively under selection (see Box 1 for an explanation of this principle). This has been rendered possible by the increased availability of highly flexible simulation tools such as Hudson’s (2002) ms software. Most of these simulation tools use coalescent modelling of the genealogical history of the sample backward in time (Hudson, 1991), although a fast and efficient simulation program simulating entire populations forward in time has also been developed (Hernandez, 2008). More specifically, recent studies have aimed at detecting selection while explicitly modelling population size changes. As an example, Li & Stephan (2006) fitted a complex demographic model for Drosophila melanogaster populations, including a population expansion following the spread out of Africa and a bottleneck in Europe, using coalescent simulations conditioned on the observed joint SFS (see Section IV Population subdivision for more detail on the joint SFS) and proceeded to detect outliers.
Several attempts have been made to combine demographic fits of population size change with tests of selection in plant populations. For example, Wright et al. (2005) modelled the divergence of two populations (teosinte and maize) and estimated the bottleneck severity parameter (k) that best explained the maize data. Using a likelihood approach, they showed that a model allowing an additional class of genes under a more severe bottleneck was more likely than a model assuming a single bottleneck parameter for all genes, consistent with the idea that a subset of loci were under directional selection. Each locus was then given a posterior probability of being in the selected class, providing a ranked order list of candidate selected genes. Similarly, De Mita et al. (2007) calibrated a population expansion model in Medicago truncatula using a set of 24 reference loci through Approximate Bayesian Computation (ABC see Fig. 1). They then tested how a few candidate loci departed from the ‘neutral envelope’ simulated from the demographic model they identified.
It is important to appreciate that these approaches are only as good as the demographic model that is inferred. When outliers are identified they may be the result of a poor fit to the true demographic history rather than because of selection. An alternative and perhaps more powerful approach is to use many genes dispersed throughout the genome, and use a semi-nonparametric approach to identify regions with patterns of polymorphism that depart significantly from the rest of the genome (Nielsen et al., 2005). This method explicitly quantifies the departure of one genomic region from patterns of diversity (e.g. the SFS) across the genome, allowing for a more empirical measure of unusual patterns of local diversity within the genome. Although significance levels still require that a demographic model is specified, the method is quite robust to uncertainty in the underlying model, mitigating the dependence of results on exact inference of demographic history. However, as with any method for identifying unusual loci with an empirical distribution, this approach will tend to miss regions under selection if a substantial part of the genome is affected by recurrent selective sweeps (Sella et al., 2009). Although crucial, the assumption that selection must not be pervasive for this sort of test to have power is rarely mentioned explicitly. Nevertheless, this approach may provide one of the most robust means of identifying selected regions as genome-wide polymorphism datasets become increasingly available for plant populations.
IV. Population subdivision
Plants may be particularly susceptible to the effects of population structure because of their immobile habit, tendency to mate with near neighbours, and local dispersal of the majority of seeds in seed crops. Two major concerns arise when considering the effects of population structure on inferences of selection. First, as with population size changes discussed above, population subdivision creates departures from neutral expectations, and therefore increases the rate of false positives when scanning for selected regions. Second, restricted gene flow (Levin & Kerster, 1974) and/or contrasting selection pressures resulting in local adaptation (Linhart & Grant, 1996) across the species range may slow or prevent the global spread of advantageous alleles (Charlesworth et al., 2003). These effects can hinder the ability to detect selection, particularly in species-wide samples, where individuals are sampled extensively across the species distribution.
1. Models of population subdivision
In contrast to the efforts made to incorporate population size changes into studies of selection on nucleotide diversity, the fit of explicit models of population subdivision to data is still in its infancy. This problem is partly caused by the vast range of possible parameter space that needs to be considered in such models. Nevertheless, progress has been made in predicting the effects of population subdivision on neutral diversity under several limiting assumptions. One of the most common models of population subdivision is Wright’s island model, which assumes equal migration rates and population sizes across a constant number of subpopulations, or demes (Wright, 1931). The properties of the island model for a range of deme numbers from two to infinity have been considered in these models.
Theory and simulation studies using the island model emphasize the importance of sampling schemes when considering the effect of subdivision on patterns of genetic variation. Perhaps counter-intuitively, samples taken from a single subpopulation under this model often exhibit a high variance in the amount of diversity, increased LD and highly skewed allele frequencies because of the immigration of unusual alleles (Städler et al., 2008). This situation is accentuated as the rate of migration decreases, as migration events generate distinct haplotypes. By contrast, ‘scattered’ samples consisting of a single sample per deme for many demes are more likely to approximate neutral coalescent processes, particularly with a large number of demes (Wakeley, 2003). ‘Pooled’ samples, consisting of more than one sample per population for multiple populations, create patterns that are intermediate between the two. Careful consideration is required in plant species with broad geographical ranges as to the most suitable sampling scheme for molecular studies.
The results obtained for the island model of migration are not restricted to this form of population subdivision. De & Durrett (2007) modelled a stepping-stone model of population structure, where migration is more likely to occur between local populations. They found that local population samples created strongly skewed SFS and a strong excess of LD, potentially generating spurious signatures of selection. Recent theoretical work suggests that models with a large numbers of demes and those with more biologically realistic forms of population structure may converge with results from the island model (Matsen & Wakeley, 2006). However, when population size changes and/or extinction and recolonization processes (metapopulation dynamics) are added to these models, skewed allele frequencies also become a feature of scattered samples (Pannell, 2003; Städler et al., 2009).
Biologically realistic models of population structure are not only problematic for standard tests of hitchhiking at neutral sites, but they can also influence tests that have been traditionally thought to be more robust to demographic assumptions. For example, metapopulation processes have been shown to increase the variation across loci in levels of differentiation, which could lead to an excess of false positives when using population structure statistics to test for local adaptation (Pannell, 2003). Moreover, in situations where population structure is hierarchical, for example, where samples are obtained from several populations within each of several broad geographic regions, a naive use of FST-based tests of local adaptation results in a large proportion of false positives (Excoffier et al., 2009). Finally, using MK approaches Gossmann et al. (2010) found that under a two-deme island model a pooled sample of alleles from both populations generated a spurious signature of positive selection, whereas a single-deme sample under this model did not. However, where a large number of demes are sampled (many-demes limit) MK-based inferences on the strength of selection are robust to subdivision, either with scattered or within-population samples (Wakeley, 2003). In general, models suggest that sampling broadly from many demes will provide the best approach for inferring historical patterns of selection across the genome.
2. The extent of subdivision in plant populations
Concerns about the effect of subdivision on inferences of selection present a number of pressing questions to workers interested in the population genomics of plant adaptation. To what extent is subdivision strong enough in plant populations to create problems for inferring selection at the molecular level? Do most species conform to the ‘many-deme’ or ‘few-deme’ models of population structure? How extensive is gene flow in plant populations? Despite extensive work on measuring population differentiation in plants both at the ‘ecotype’ level through common garden and transplant studies (Langlet, 1971; Linhart & Grant, 1996) and at marker loci (Hamrick & Godt, 1996), we are still some way from being able to answer these questions with confidence.
Levels of population differentiation are typically quantified using a variant of Wright’s FST parameter, which measures the proportion of variation in a sample that is distributed among populations. However, it is important to realize that estimates of FST (and its relatives such as GST and others) applied to genetic variation data are not strictly measures of differentiation (Charlesworth, 1998; Jost, 2008, 2009). This is because these measures are highly influenced by the amount of within-population diversity of the markers that are used. Putting aside these mathematical misconceptions, a number of additional caveats should be borne in mind. Under an idealized island model, FST is a simple function of effective population size and the migration rate. As a result, it has been commonly used to estimate rates of gene flow among populations. However, departures from the island model assumptions are likely to be common in plants, making quantitative inferences of gene flow difficult (Whitlock & McCauley, 1999). In the extreme case, recently diverged populations with no gene flow will have low values of FST, causing an erroneous inference of high migration rates. For example, Ross-Ibarra et al. (2008) used a coalescent model of divergence with no gene flow to pairs of A. lyrata populations from North America and Europe. This provided a good fit to simulations of the observed data, even among population pairs with low FST values. Thus, in this case a fit to the island model implies a rate of gene flow greater than one migrant per generation, whereas the data are more consistent with a model of no gene flow since divergence c. 6000 yr ago. Given the common occurrence of range expansion and contraction following glaciation, recent divergence with low levels of gene flow would appear to be a reasonable alternative hypothesis to explain their data.
Despite these caveats, interspecific comparisons of levels of molecular differentiation from various types of markers are consistent with expectations based on mating systems and predicted differences in gene flow. Outcrossing populations typically exhibit lower levels of differentiation than selfing populations, and local samples show less differentiation than those sampled over a broader geographical area (Morjan & Rieseberg, 2004). Multilocus estimates of population differentiation in plants using single nucleotide polymorphisms (SNPs) generally display comparable levels of differentiation to previous studies of FST using other markers (average FST = 0.32, Morjan & Rieseberg, 2004). In addition to quantifying differentiation by FST using populations as units, new cluster-based approaches that assign individuals to populations by minimizing levels of LD have been widely implemented (Pritchard et al., 2000; Gao et al., 2007; Huelsenbeck & Andolfatto, 2007). The general picture to emerge from these studies suggests that plant populations typically cluster into broader regional groupings, and it is not uncommon to find a multilevel hierarchy of geographic structuring revealed by varying the number of clusters and/or treating regional populations separately (Nordborg et al., 2005; Ross-Ibarra et al., 2008; Ness et al., 2010).
3. Accounting for subdivision in tests of selection
When testing for selection, several conflicting sampling solutions have been proposed to account for population structure. On one hand, scattered population samples from many populations, ignoring within-population diversity, may best approximate a neutral coalescent process under a broad range of models (Wakeley, 2003; Städler et al., 2008). However, scattered samples do not allow for the investigation of local adaptation and for this goal within-population samples are required (Siol et al., 2008; Bomblies et al., 2010; Turner et al., 2010). This stems from the fact that local adaptation results in levels of differentiation around genes under selection that is greater than expected for neutrally evolving regions. Furthermore, taking samples from multiple populations does not rule out hierarchical population structure; in an extreme example where the species is split into two geographic clusters it could reflect sampling from two demes, leading to genome-wide departures from neutrality (Excoffier et al., 2009). Similarly, if a species is structured as an ancestral, refugial or source population and an advancing wave of colonizing populations (François et al., 2008), it is not clear that a scattered sample will best reflect the history of selection. Combining both within and between population samples should allow for in-depth characterization of population history. Furthermore, integrating data from multiple within-population samples affords the most powerful approach for modelling both population history and selection. Of course, this requires considerable sequencing effort and cost.
A significant advance for selection models with structured populations is the use of the multidimensional allele frequency spectrum (or joint frequency spectrum, Li & Stephan, 2006). This is a natural extension of the SFS discussed in the first section, and describes the joint distribution of polymorphisms across populations. Fig. 2 shows the joint frequency spectrum for two populations having diverged from a common ancestral population. However, the principle can be extended to any number of populations by using a P-dimensional matrix. The advantage of the multidimensional SFS is that it provides a more complete summary of the data than traditional SFS summary statistics or FST, which can all be calculated from the multidimensional SFS.
The use of the multidimensional SFS was first introduced by Li & Stephan (2006) in the context of demographic model fitting in a two-population scenario involving Drosophila (and see Hernandez et al., 2007; Gutenkunst et al., 2009; Nielsen et al., 2009). Gutenkunst et al. (2009) used a diffusion approximation to fit demographic parameters to the multipopulation SFS. Even though the diffusion framework is in theory applicable to any number of populations, in practice computational issues associated with solving the multidimensional diffusion equation limit its implementation to three. However, simulation approaches could be used to extend to any number of populations, and the use of the multidimensional SFS represents an improvement in our ability to fit realistic demographic scenarios, and use information present in the data more efficiently to test for selection in a demographic context.
Nielsen et al. (2009) used information encapsulated in the two-dimensional SFS to propose a new test of neutrality (which they termed the G2D test) that they applied to human genetic data to identify loci subject to local adaptation. A feature of this test is that the null hypothesis is directly derived from the background pattern of variation in the data, similar to the authors’ previous work on single populations (Nielsen et al., 2005). This approach avoids relying on a potentially mis-specified population genetic model. More specifically, the test quantifies the fit of the multi-dimensional SFS for a particular genomic region with the global multidimensional SFS observed throughout the genome through the calculation of a (composite) likelihood ratio test. The critical values of the test statistic are determined using coalescent simulations under the demographic model identified from the genome-wide data. It should be noted that although the authors use the composite likelihood ratio test in the case of a two-dimensional frequency spectrum, their approach is readily applicable to higher-dimensional problems, the limiting factor being once again computational feasibility.
The potential to detect the footprint of selection using the G2D test remains to be investigated for a range of demographic scenarios. However, as noted by Nielsen et al. (2009), the test should be sensitive to any deviations from neutrality, therefore it should be able to detect various modifications of the multidimensional SFS shape according to the form of natural selection, including purifying selection and local positive selection. It would be interesting to know under what circumstances there is enough power to detect different forms of selection. As an example, Fig. 3 shows the effect of a selective sweep in a derived bottlenecked population. The scenario is similar to the one considered in Thornton & Jensen (2007) and Innan & Kim (2008). Thornton & Jensen (2007) considered a number of summary statistics and concluded that under this type of scenario FST was the most powerful statistic for identifying outlier loci compared with statistics based on the frequency spectrum. However, they did not consider using the full joint-frequency spectrum of the two populations. Fig. 3 suggests that the net effect of the selective sweep is to decrease the proportion of shared polymorphisms and to increase the proportion of fixed differences between populations. Whether the signal is strong enough to be detected as statistically significant depends on parameters such as divergence time, migration rate between the populations and the intensity and duration of the bottleneck.
Some progress towards identifying genes under positive selection using structured populations has been achieved using large-scale plant population genomics data. For example, Toomajian et al. (2006) used a nonparametric approach to show high haplotype sharing at two independently derived loss-of function alleles at the flowering time gene FRI in European populations of A. thaliana. Similarly, Turner et al. (2010) used two pairs of local populations of A. lyrata to screen for candidate loci thought to be involved with local adaptation to serpentine soils. Although these kinds of approaches lack explicit demographic models and are thus nonparametric, the outlier loci that are identified should be enriched for the targets of selection. Integrating the results from such approaches with functional data (e.g. quantitative trait loci (QTL) mapping, association mapping, gene annotation) will provide a powerful approach for the identification of targets of positive selection in plant genomes.
V. Local adaptation, standing genetic variation, quantitative traits and multiple adaptive substitutions
A substantial amount of adaptation in plant populations may arise from variation that departs from the idealized model of positive selection. Under the standard model of a selective sweep, a new beneficial mutation arises in a population as a single copy and increases in frequency owing to natural selection of constant strength and direction (Maynard Smith & Haigh, 1974). The extent to which this is typical of most adaptive events remains to be determined, but it is likely that a significant fraction of adaptive evolution does not proceed in this way. First, many adaptations may originate from standing genetic variation that has been present in a population for some time before the new selective episode that assembles the adaptation being considered (this is referred to as a soft selective sweep; Orr & Betancourt, 2001; Hermisson & Pennings, 2005; Pritchard et al., 2010). Second, well-developed population subdivision can slow the spread of an advantageous mutation, making it more likely that an alternative adaptive mutation will occur in a distinct local population before spread of the first advantageous allele through gene flow. Third, fluctuation in the strength and mode of selection across space (diversifying selection resulting in local adaptation) and time violates a simple model of constant selection resulting in the rapid spread of a new beneficial mutation across the species (Harder & Johnson, 2009). Finally, even though there is a growing literature identifying mutations of major effect on phenotype, many adaptive traits are likely to be polygenic, especially those associated with life history.
The quantitative genetics perspective on adaptation is quite different from what has been described so far in our review. Indeed, adaptation is most commonly viewed as the outcome of selection operating at many loci for a given trait (Fisher, 1930; Lynch & Walsh, 1998). The consequences of quantitative inheritance on the traces left by positive selection at the sequence level have been surprisingly under-investigated. A few studies (Latta, 1998; Le Corre & Kremer, 2003; Chevin & Hospital, 2008) have started to fill the gap by demonstrating that the dynamics of a beneficial mutation affecting a quantitative trait depends not only on its own selection coefficient (the parameter encapsulating the beneficial or deleterious effect of a particular mutation), but also on the genetic variation for this trait at other loci. These studies highlight the fact that strong selection on a quantitative phenotype may not necessarily translate to strong selection on a single locus influencing the trait.
Selection from standing genetic variation may be particularly likely under conditions of rapid environmental change or in the colonization of new environments, such as when invasive species are introduced to new regions (Barrett et al., 2008). Under these circumstances the timescale involved may limit the introduction of new beneficial mutations. Innan & Kim (2004) studied the case of a domestication event, where a previously neutral or slightly deleterious trait in the wild progenitor is strongly favoured by artificial selection (e.g. selection for nonshattering habit in domesticated cereals; Glémin & Bataillon, 2009). Another instance investigated by the same authors (Innan & Kim, 2008) is the local colonization of a novel environment from an ancestral population following a bottleneck (the scenario is depicted in Fig. 2 where the parental population is in the environment of origin and the derived population experiences different selective pressures). The take-home message from these analyses and others (Hermisson & Pennings, 2005; Przeworski et al., 2005; Pennings & Hermisson, 2006) is that the ‘typical’ signatures of positive selection (reduced levels of polymorphisms in linked regions, increased LD and skewed SFS) exhibit more variance and that many loci under selection are likely to go undetected, depending on the selection coefficient and the initial frequency of the mutation when selection commenced.
Although there are still relatively few examples of adaptive mutations that have been cloned and characterized in plants, a number of those that have been identified suggest that more complex models of adaptation may be the norm. For example, a recent study of trichome evolution in A. lyrata demonstrated parallel loss of trichomes in Swedish and Russian populations, through independent loss-of-function mutations in the glb1 gene (Kivimaki et al., 2007). Similarly, variation in flowering time in A. thaliana is mediated, in part, by numerous independent loss-of-function alleles with different geographic distributions and constitutes one of the most well-studied examples of loss-of-function mutations with large phenotypic effects (Alonso-Blanco et al., 2005). Large numbers of independent loss-of-function mutations have similarly been identified in studies of candidate plant disease-resistance genes (Gos & Wright, 2008). Finally, in Petunia loss-of-function alleles involved in flower colour have arisen several times independently and have mediated a shift in the types of pollinators attracted to populations (Hoballah et al., 2007). These results suggest that the rate of adaptive mutation may exceed the rate of migration, particularly for loss-of-function changes.
Finally, given the common occurrence of hybridization in plants, gene introgression is likely to be another important source of adaptive genetic variation. Although this possibility was noted early on by Stebbins (1971) and introgression has been well-documented in plants (Baack & Rieseberg, 2007), it has proven more difficult to establish introgression for adaptive alleles. A convincing example concerns regulatory genes controlling the shape of florets that have been introgressed from Senecio squalidus to Senecio vulgaris and which enhance pollinator attraction (Kim et al., 2008; Chapman & Abbott, 2010). Also, in sunflowers herbivore resistance has been transferred from Helianthus debilis to Helianthus annuus (Whitney et al., 2006). It is probable that the relative paucity of well-studied examples of adaptive introgression does not accurately reflect the true frequency of such events in plant adaptation.
All of these findings highlight the fact that the signature of positive selection may often be more local and complex than is generally assumed in standard population genetic models. However, some recent progress has been made in developing methods to better detect selection from standing genetic variation. Innan & Kim (2008) demonstrated that pairwise comparisons of ancestral and derived populations greatly increase the power to detect selection on standing variation. Thus, methods using the joint SFS of ancestral and derived populations (Fig. 2) will likely provide increased power to detect selection following an environmental change or after a colonization event. This also emphasizes the importance of targeted, local population samples in conjunction with further development of methods such as those using LD to identify the targets of recent positive selection (Pennings & Hermisson, 2006; Toomajian et al., 2006) and those based on between-population differentiation (Thornton & Jensen, 2007; Ross-Ibarra et al., 2008; Chen et al., 2010). Thus, while scattered samples from many populations may provide the closest match to standard neutral expectations, local sampling combined with explicit demographic models will also be crucial for the realistic understanding of selection dynamics in structured populations.
VI. Demographic context of selection and future directions
During the first phase of plant molecular population genetics involving one or a small number of genes, rejection of the standard neutral model (SNM) was most often interpreted as resulting from selection rather than because of departures from demographic assumptions (Wright & Gaut, 2005). Since then important progress has been made in developing methods to fit demographic models to population genomic data, and in attempts to ‘control for demography’ in searching for the footprint of selection at the molecular level. In comparison with other groups of organisms, multilocus population genetic studies of plants, while still sparse, have provided surprisingly little definitive evidence for positive selection at the genome level. In particular, few studies have identified genes putatively under selection using patterns of neutral variation. The failure to detect genes under selection may be in part result from inherent features of many plants (e.g. immobility, hermaphroditism, clonal propagation) that make them especially vulnerable to demographic violations of the SNM assumptions and to departures from standard models of selective sweeps.
Given the evidence for the prevalence of population structure and the dynamic nature of population size in many plant species, it is likely that population history itself plays an important role in the nature, direction and efficacy of natural selection. Low levels of gene flow enhance the potential for local adaptation (Ronce & Kirkpatrick, 2001), while severe population bottlenecks and small effective population size (Ne, Charlesworth, 2009) are expected to reduce the efficacy of positive and negative selection. Recently expanding populations may be subject to high rates of adaptive evolution owing to range expansion (Karasov et al., 2010), but may also be susceptible to bottleneck effects in the newly colonized area that could limit adaptive potential. Thus, understanding demographic history provides more than simply a way to generate the appropriate null model in testing for selection, but is also essential for formulating appropriate hypotheses and models for the detailed action of natural selection.
A key framework for understanding the influence of population history and subdivision on selection is through consideration of the many factors influencing effective population size, a crucial parameter in population genetics theory determining the intensity of genetic drift (Wakeley, 2008). Population genetic theory predicts that in species characterized by low Ne, a larger proportion of slightly deleterious and slightly advantageous mutations will be effectively neutral. This stems from the fact that the fate of a selected mutation is determined by two parameters, Ne, which determines the intensity of genetic drift, and s, the coefficient of selection. More precisely, mutations for which the product Nes is approximately equal to 1 behave as if they are neutral. As a result, in low-Ne species the efficacy of selection is reduced and the fate of weakly selected mutations is determined more by genetic drift (Ellegren, 2009). Furthermore, in such species the input of mutations will also be lower and beneficial mutations therefore arise less frequently. Depending on the shape of the distribution of fitness effects for deleterious and beneficial mutations, a moderate difference in effective population size could potentially lead to a substantial change in the number of effectively neutral mutations and thus affect the efficacy of natural selection (Kassen & Bataillon, 2006; Bachtrog, 2008; Woolfit, 2009). Thus, low effective populations sizes could influence the intensity of selection on molecular variation.
In general agreement with these basic predictions, it appears that organisms exhibiting higher rates of adaptive evolution and purifying selection may generally be those for which Ne tends to be large (Ellegren, 2009). Fig. 4 illustrates the estimated level of adaptive substitutions for diverse species, using MK-based approaches (Boyko et al., 2008; Eyre-Walker & Keightley, 2009), against the logarithm of their effective population sizes, estimated using neutral polymorphism. At the broadest taxonomic scale there seems to be a correlation between Ne and α, similar to the relation that has been found between Ne and the level of purifying selection (see Fig. 1 in Wright & Andolfatto, 2008). However, this figure highlights that many plant species show evidence for relatively low effective population sizes compared with other model systems and relatively few provide evidence for significant adaptive evolution (Bustamante et al., 2002; Nordborg et al., 2005; Schmid et al., 2005; Kim et al., 2007; Foxe et al., 2008; Gossmann et al., 2010 although see Strasburg et al., 2009; Ingvarsson, 2010; Slotte et al., 2010). It should be noted that these estimates of Ne assume the standard equilibrium neutral model, and thus do not fully account for recent demographic history or population subdivision. In this context is notable that there is little evidence for significant population structure or bottlenecks in the three plant species (Capsella grandiflora, Populus tremula, Helianthus annuus see Table 2) in which there is evidence for high rates of adaptive protein evolution. However, more data points from species with varying demographic histories are clearly needed to better resolve the interaction between demography and adaptive protein evolution in plants.
Disentangling the relative influence of population size, demographic changes and population structure will be difficult because many species with small population sizes also exhibit strong population differentiation and size fluctuations (Nordborg et al., 2005; Muller et al., 2008; Ross-Ibarra et al., 2008; Liti et al., 2009). Furthermore, low rates of species-wide adaptive substitution do not necessarily imply low rates of adaptive evolution. Widespread local adaptation can only be inferred using targeted population samples and currently MK tests do not have a clear analogue at the within-population level, although recent studies that have compared levels of population differentiation at coding vs noncoding regions appear promising (Coop et al., 2009). Finally, as noted by Karasov et al. (2010), Ne estimates from neutral polymorphisms represent the harmonic average over a very long period of time and are thus sensitive to periods of low population size. This can lead to very different estimates of effective population size using levels of neutral variability compared with demographic approaches, which may more accurately reflect current effective population size (see Charlesworth, 2009). Thus, while the patterns shown in Fig. 4 highlight the possible importance of effective population size on rates of adaptive evolution, changes in population size and population subdivision likely have a confounding influence.
Exciting as the past decade has been in giving us new insights into the genomic structure of plant populations, the advent of so-called ‘next-generation’ sequencing holds even more promise. These new techniques generate quantities of data that are orders of magnitude greater than classic sequencing methods and they are now being increasingly applied in the field of population genomics (Simmons et al., 2008; Keightley et al., 2009; Hohenlohe et al., 2010). The continuous decline in sequencing costs, increase in coverage and length of reads, along with the development of powerful de novo assembly algorithms for species without a reference genome should allow a broader diversity of plants to be investigated in the near future, including studies of nonmodel species. In particular, it will soon be possible to assay species with diverse life-history traits spanning a much larger range of Ne values, population histories and patterns of subdivision.
Evolutionary analysis of genomic data is still in its infancy and many formidable challenges face the field of evolutionary bioinformatics (for a thorough review, see Pool et al., 2010). The first involves the sheer number of sequences that must be dealt with, which imposes a strong constraint on bioinformatic automation and computational demand. The comparison of observed patterns of variation at thousands of loci makes it all the more difficult to avoid false positives, and inclusion of sequencing errors (appearing as rare SNPs) can skew diversity estimates and the SFS, perhaps leading to spurious inferences. One possible solution is removing rare variants (Turner et al., 2010), but for many analyses low frequency SNPs are of direct interest when testing for the action of selection.
It thus appears that for the first time in population genetics history, the limiting factor is the availability of methods and models and not the data on which to address evolutionary questions. However, such methods are beginning to appear (Jiang et al., 2009; Haubold et al., 2010) and more will surely follow. Even if the challenges are daunting, there are grounds for optimism. The parallel improvement of next-generation sequencing techniques and computational and analytical tools should allow large-scale interspecific comparisons of the historical and contemporary context in which selection operates at the molecular level. These approaches will yield important insights into the interactions between demography and adaptive evolution in plant populations.
We thank our colleagues Aneil Agrawal, Asher Cutter, Rob Ness and John Stinchcombe for valuable discussions on population genomics and for help with references. Thanks also to Stéphane De Mita and Tanja Slotte who provided advice on an earlier version of this manuscript. MS was supported by a post-doctoral fellowship from the Canada Research Chair’s program to SCHB; SIW and SCHB acknowledge support from NSERC Discovery Grants.