Detecting signatures of positive selection in non-model species using genomic data

Detecting signatures of positive selection in non-model species using genomic data Abstract Understanding how natural selection shapes genetic variation in populations is of paramount importance in evolutionary biology. Affordable high-throughput sequencing now allows the generation of genome-wide data for non-model species, thereby stimulating research aimed at determining the genomic basis of adaptation to local environmental conditions. However, although these adaptive loci show characteristic signatures of positive selection, several other processes can lead to similar patterns, rendering the search for outlier loci a challenging task. Given that all these methods rely on different explicit (data requirements) or implicit (underlying population models) assumptions, they have limitations that often remain unknown to non-population geneticists. Simply applying different tests of selection to the generated data can yield unreliable results that include many false positives and negatives, therefore concealing the true evolutionary history. In this review, tailored for biologists with a standard background in mathematics entering the field of population genomics, we explain how signatures of positive selection emerge and describe the principles of state-of-the-art programs to detect these signatures. We highlight the promises and pitfalls of all approaches and provide practical recommendations based on simulation studies as well as various case studies from animals. Adaptation, population genetics, selection INTRODUCTION A central aim of evolutionary biology is to understand how different environmental conditions influence organismal diversity. Theoretical population genetics has generated a mathematical framework to predict patterns under neutral evolution for alleles and genotypes. Against this background, empirical and experimental data can be compared to estimate the relative importance of selection on the gene pool. However, for a long time, empirical and experimental molecular population genetics were comparatively data poor, being limited to a few populations/individuals and loci. The few studies based on genome-wide data on adaptation and divergence had typically focused on humans and on model species [e.g. Arabidopsis thaliana (L.) Heynh. and Drosophila melanogaster Meigen, 1830] or species of high economic value (e.g. cattle, dogs, wheat or corn; reviewed by Haasl & Payseur, 2016). Nowadays, genomic techniques such as restriction site-associated DNA sequencing (RADSeq; e.g. Wagner et al., 2013; Schweyen, Rozenberg & Leese, 2014), transcriptome sequencing (e.g. Cahais et al., 2012; Schunter et al., 2014) or selective enrichment using specific probes (Brandley et al., 2015) can be applied even if no prior genomic information exists. This ease in the gain of data has stimulated research into adaptation processes in non-model species ranging from microbes to vertebrates, and the resulting studies have greatly advanced our understanding of adaptation in experimental (e.g. Lenz et al., 2013) and natural populations (e.g. Colbourne et al., 2011; Read et al., 2013). To identify genomic regions involved in adaptation processes with confidence, it is important to distinguish signatures of positive selection from patterns shaped by neutral evolution and select appropriate statistical tests and software to screen for them. Aim of the Review There is an increasing number of different tests for the identification of positive selection at a micro-evolutionary scale, i.e. the detection of ongoing or recent selection within species. All the methods have different requirements, strengths and weaknesses, which are often difficult to evaluate for biologists coming more from ecological or applied disciplines with a standard mathematical background. Therefore, the aim of this review is to offer non-mathematicians an overview of the principles, requirements, dos and don’ts of different approaches. Only by understanding the underlying principles of the different test statistics is it possible to apply them in an adequate way; for example, choosing the right test for a certain question and by applying optimal settings for the tests. Using the wrong test for a given sampling set-up can lead, in the worst case, to a high rate of false positives, i.e. positive selection is detected although other factors have shaped the genetic diversity. This can result in avoidable high costs of follow-up studies analysing the biological meaning of a false positive sign of selection. Additionally, application of an unsuitable test can result in missed signals of selection (false negatives); for example, when the time since the onset of selection is too short or too long ago for the chosen test. GENOMIC SIGNATURES OF POSITIVE SELECTION Positive selection is defined as the process through which a new mutation or previously rare allele increases an individual’s fitness (reviewed by Nielsen et al., 2007; Vitti et al., 2013; López, Neira & Yáñez, 2015). One drastic form of positive selection is a hard selective sweep (Maynard Smith & Haigh, 1974; Fig. 1A). During a hard sweep, a new mutation with a strong selective advantage arises and is quickly driven to complete fixation in the population (Nielsen, 2005; Nielsen et al., 2007; Hohenlohe, Phillips & Cresko, 2010; Pritchard, Pickrell & Coop, 2010; Bank et al., 2014). Genetic polymorphisms adjacent to the site under selection ‘hitchhike’ together with the beneficial allele and thus co-increase in frequency. In the case of recombination, the new beneficial allele can become associated with neighbouring alleles that were previously linked to the alternative allele at the selected site, thereby introducing variability. As the process is very fast, recombination has only limited possibilities to break down physical linkage. In the final stage of a hard selective sweep, the entire population becomes fixed for the advantageous mutation. In the proximity of the site under selection, all other sites are also fixed if no recombination event occurs. Only those recombination events that connect the advantageous mutation to an alternative background are now visible, whereas those that involve the alternative allele at the selected site are lost. The probability of recombination events increases with the distance from the beneficial allele, leading to increased variability up- and downstream of the selected site. Figure 1. View largeDownload slide Changes in chromosomes during a selective sweep. A, hard selective sweep. B, soft selective sweep as a result of environmental changes, recurrent beneficial mutations or migration of individuals with beneficial alleles. Figure 1. View largeDownload slide Changes in chromosomes during a selective sweep. A, hard selective sweep. B, soft selective sweep as a result of environmental changes, recurrent beneficial mutations or migration of individuals with beneficial alleles. The genomic pattern of a hard sweep is characterized by low genetic diversity with an increase in low- and high-frequency variants, a long homozygous region and a high level of linkage disequilibrium (LD; Nielsen, 2005). However, LD is assumed to be high only if the analysed sites are compared within each region next to the favourable mutation, whereas a comparison between sites spanning the favourable mutation does not result in increased LD (Kim & Nielsen, 2004). The pattern originates from the different recombination events, which are assumed to be independent at both sites of favourable mutation. After fixation of the beneficial allele and linked variants, new mutations in the region together with recombination lead to a decay of the different characteristics of a selective sweep (Oleksyk et al., 2010). Although LD degrades very quickly, changes in the site frequency spectrum (SFS), meaning the increased proportion of low- and high-frequency-derived alleles, remain for a longer time (reviewed by Hohenlohe et al., 2010). Another, more common, form of positive selection is a soft selective sweep (Hermisson & Pennings, 2005; Pennings & Hermisson, 2006a; Fig. 1B). Here, the selected variants are not associated with a single genomic background but occur with several variants in close proximity. A soft sweep can be caused by three scenarios. First, selection can act on standing genetic variation when a change in the environmental conditions leads to a selective advantage of previously slightly deleterious or neutral genetic variants. Alternatively, different mutations in the same genomic region can have a similar selective advantage. The third possibility is that different individuals with the beneficial allele migrate into the population. All three scenarios lead to an increase in the frequency of different genomic backgrounds, which makes the genomic pattern in the region affected by a soft sweep less pronounced (i.e. more homogeneous) than for a hard sweep; hence, soft sweeps are more difficult to detect (Pennings & Hermisson, 2006b). CONFOUNDING FACTORS IN THE DETECTION OF POSITIVE SELECTION Purifying and Background Selection Besides positive selection, other types of selection influence the genomic pattern of variation. Purifying selection, also termed negative selection, is defined as the removal of deleterious alleles owing to their selective disadvantage (reviewed by Oleksyk et al., 2010; Vitti et al., 2013). If genetic variation at neighbouring sites is reduced owing to purifying selection on a deleterious allele, this selection mode is called background selection. The reduction in genetic variation can mimic some characteristics produced by a selective sweep, such as an increased proportion of low-frequency relative to intermediate-frequency alleles (Charlesworth et al., 1993). Hence, some methods cannot distinguish purifying or background selection from positive selection (Fu, 1997; Zeng et al., 2006). Balancing Selection Another form of selection is balancing selection, i.e. the maintenance of multiple alleles at the selected site (reviewed by Charlesworth, 2006; Fijarczyk & Babik, 2015). It can be caused by different mechanisms, such as heterozygote advantage (over-dominance), meaning an increased fitness of heterozygous individuals, or negative frequency-dependent selection, in which alleles mediate high fitness at a low frequency but where the fitness advantage is reduced with increased frequencies (Fijarczyk & Babik, 2015). Although the diversity pattern produced differs from selective sweeps, the early phase of balancing selection can be confused with some of the test statistics (Zeng et al., 2006). In this phase, the favoured alleles increase in frequency until they reach equilibrium, which can also lead to long homozygous regions similar to selective sweeps (Voight et al., 2006). A good review of methods to detect balancing selection is provided by Fijarczyk & Babik (2015). Demography Demographic changes in population size, such as bottlenecks or population expansions, also affect genetic variation and generate patterns that can resemble positive selection. For example, population growth leads to an excess of low-frequency alleles (Fu, 1997; Ramirez-Soriano et al., 2008), similar to a selective sweep. The pattern is generated by the larger effective population size that reduces the effects of genetic drift (i.e. the change in allele frequencies attributable to the random sampling of parents for the offspring of the following generation; see Hartl & Clark, 2007). Population bottlenecks are typically sharp reductions in population size, often followed by an expansion back to the original size. Depending on the strength of the bottleneck, different changes in the diversity patterns are expected (Ramirez-Soriano et al., 2008) owing to the varying influence of genetic drift and mutations. During a severe bottleneck, genetic variation decreases strongly as a result of the increased genetic drift in the contracted population, leading to a deficit in intermediate-frequency alleles. In the population growth phase, mutation generates new variation and the effects of genetic drift are reduced. The new variants are at a low frequency at first; therefore, many low-frequency variants are found compared with intermediate ones for several generations after a bottleneck. A weak bottleneck does not lead to a complete loss of the intermediate-frequency alleles (Depaulis et al., 2003). The subsequent population growth again increases low-frequency alleles. However, here, the proportion of intermediate-frequency alleles can exceed the low-frequency alleles. It was suggested that demographic processes could be distinguished from selective sweeps by quantifying the proportion of the genome showing a specific diversity pattern (reviewed by Nielsen, 2005; Hohenlohe et al., 2010). Demographic processes are assumed to affect the complete genome equally, whereas selective sweeps are assumed to affect only the selected site and the linked genomic region. However, some demographic scenarios can impact genomic regions unequally, resulting in an increased variance in neutral genetic variation, potentially mimicking characteristics of selective sweeps (Huber et al., 2016). One example is provided by bottlenecks of intermediate strength, after which most genomic regions will still contain several intermediate-frequency alleles (see above). However, by chance, some genomic regions may reveal a stronger reduction of intermediate-frequency alleles, which can be misinterpreted as a selective sweep. Migration Besides changes in population size, the strength and type of migration among adjacent populations can impact on genetic diversity (De Mita et al., 2013; Lotterhos & Whitlock, 2015; Vatsiou et al., 2016). The typical assumption is that in a scenario of positive selection with moderate migration, the beneficial allele becomes fixed in populations occurring in the selected environment, whereas populations in an alternative environment will have only low to intermediate frequencies of the beneficial allele or are fixed for the alternative allele. However, if migration between populations is high, the population in the neutral environment can be swamped by the beneficial allele, leading to a reduced population differentiation, similar to neutrality (Vatsiou et al., 2016). Alternatively, if only very few migrants are present, a strong population differentiation is found in the complete genome, leading to a similar differentiation pattern for selected and neutral genomic regions (Vatsiou et al., 2016). DATA REQUIREMENTS When designing a study to identify positive selection, it is important to consider directly the requirements of the desired test statistics, especially the number of sampled populations and individuals needed to obtain reliable results. Additionally, some test statistics require knowledge about ancestral and derived allele states; therefore, including an outgroup in the sample set has to be considered for such tests. Besides the sampling scheme, the chosen type of molecular markers, such as reduced representation approaches (e.g. RADseq), RNAseq or whole-genome resequencing, influences the quality of the results. Although genome resequencing is costly and bioinformatic analyses can be challenging and time consuming for large data sets, reduced representation approaches often have marker densities that are too low to detect the majority of selective sweeps (Tiffin & Ross-Ibarra, 2014; Lowry et al., 2017). RNAseq and exome capture methods rely on the sequencing of coding regions only and will therefore miss targets of positive selection involved in gene regulation unless they show strong LD (reviewed by Hoban et al., 2016). Additionally, some of the test statistics are based on information that is generally not available for species without genomic resources or non-model species, such as the known genomic position of the analysed loci, phased data sets or recombination maps. Methods to obtain these data are described in the following sections. Genomic Data Several methods to identify positive selection rely on known genomic positions of the analysed markers, either because the spatial pattern is relevant in the statistics (e.g. tests analysing changes in LD) or because the effect of selection cannot be identified at a single site, hence requiring several variants in the target region (e.g. tests based on changes in the SFS). This can be a central drawback for population geneticists working on non-model species because reference genomes needed for mapping approaches are often not available. To obtain information on genomic position of the loci, genome sequencing and assembly can be conducted, leading to long contigs (i.e. stretch of sequence from overlapping reads without gaps)/scaffolds (i.e. stretch of sequence build of several contigs including gaps). However, as very long scaffolds (ideally > 100 kb) are typically required for analyses integrating the genomic pattern of selection, a reasonable amount of sequencing effort is required (for a review on de novo genome sequencing see Ekblom & Wolf, 2014). We performed a survey of the most recent genome publications in the NCBI genome database to determine whether scaffolds would be sufficient for these types of analyses (Fig. 2). Only about half of the 100 most recently added genomes of non-model species had N50 values > 100 kb, meaning that half of the genome is represented by scaffolds with a size of at least 100 kb. Moreover, almost one-third of the genomes had N50 values < 10 kb, which makes them unsuitable for analyses of changes in the genomic diversity pattern. Figure 2. View largeDownload slide N50 values of recently generated genomes of non-model species. Data were retained from the NCBI genome database and filtered to include only data from animals with no other genome present at the same genus to excluded species with previous genomic resources. Additionally, mitochondrial genome sequencing projects were excluded. The 100 most recent data points are shown (published 25 November 2015–12 July 2017, access date 26 July 2017). If no scaffold data were available, the N50 value of the contigs was used. Figure 2. View largeDownload slide N50 values of recently generated genomes of non-model species. Data were retained from the NCBI genome database and filtered to include only data from animals with no other genome present at the same genus to excluded species with previous genomic resources. Additionally, mitochondrial genome sequencing projects were excluded. The 100 most recent data points are shown (published 25 November 2015–12 July 2017, access date 26 July 2017). If no scaffold data were available, the N50 value of the contigs was used. Haplotyping/Phasing A common requirement of methods based on LD is haplotypic information, i.e. phased data. These can be obtained using different approaches (for a review, see e.g. Browning & Browning, 2011). First, experimental phasing can be conducted by, amongst other methods, sequencing haploid cells (Fan et al., 2011), sequencing large-insert clones (Kitzman et al., 2011) or by high-throughput sequencing reads (e.g. Kuleshov et al., 2014; Madoui et al., 2015). However, these methods are often relatively cost and labour intensive (Browning & Browning, 2011). Second, related individuals can be genotyped and computationally phased (e.g. Stephens & Scheet, 2005; Brinza & Zelikovsky, 2008; Browning & Browning, 2009; Iliadis et al., 2010). The method works very accurately if trios composed of both parents and one offspring are used (Marchini et al., 2006). However, for many species and sampling designs, it is impossible to sample trios, e.g. if field samples are collected with unknown relationships. Furthermore, the costs of the study increase severalfold if only one individual of the related samples is needed to answer the question of the study, whereas the other individuals are sequenced only to obtain phased data (Browning & Browning, 2011). Third, algorithms can be applied to obtain phasing information using unrelated individuals (Scheet & Stephens, 2006; Brinza & Zelikovsky, 2008; Browning & Browning, 2009; Delaneau et al., 2013). These methods are the most affordable and feasible of the different methods described. They provide good phasing quality in small genomic regions for common single nucleotide polymorphisms (SNPs) if many specimens of a population are analysed (Browning & Browning, 2011). Recombination map Recombination maps are also required for some of the methods [e.g. integrated haplotype score (iHS), cross-population extended haplotype homozygosity (XP-EHH) and cross-population composite likelihood ratio test (XP-CLR)], because the recombination rate can vary strongly even at a small scale (McVean et al., 2004; Chan et al., 2012; Hellsten et al., 2013). Variation in the recombination rate can influence genetic diversity patterns, e.g. a reduced recombination rate increases LD locally (e.g. Voight et al., 2006). Additionally, genetic variation is reduced more rapidly by background selection or selective sweeps in regions with low recombination rates in comparison to regions with intermediate or high recombination rates (Hartl & Clark, 2007). If recombination rate variation is known, test statistics can be corrected, and an adequate estimation of positive selection is possible. Different methods exist to generate recombination maps (see, e.g. Baudat et al., 2013). Pedigree analyses can be conducted to estimate the recombination map by counting recombination events. They can be based on sampling and sequencing both parents as well as at least two offspring (e.g. Kong et al., 2002; Tsai et al., 2016). Alternatively, crossing of two individuals (P; later the grandparents), often originating from different subspecies or strains, can be performed (e.g. Tortereau et al., 2012; Reddy et al., 2014; Glazer et al., 2015). The offspring (F1) individuals are either interbred or, where possible, self-fertilized. Multiple offspring (F2) of one F1 cross are then sequenced in addition to the P individuals. The recombination rate can be estimated based on population data (reviewed by Stumpf & McVean, 2003). Given that samples are not directly related to each other, the number of recombination events cannot be counted as in pedigree analyses. Therefore, coalescent models have to be applied to infer the underlying genealogy of the different samples, incorporating recombination into the model. The model is, however, only able to estimate the population recombination rate, which includes the per generation recombination rate and the effective population size. To estimate the values of the per generation recombination rate [e.g. in centimorgan (cM)], the effective population size needs to be estimated using a different approach. Furthermore, selection and demographic changes can affect the genealogy of samples and thus influence the estimation of the population recombination rate. Thus, their influence should be excluded using different estimates, such as the frequency of variants, i.e. the so-called ‘site frequency spectrum’ (SFS) or the level of diversity. An individual-based high-resolution genetic map can be produced by resequencing the whole genome of single sperm cells of an individual and thereby directly identifying meiotic crossing-overs (e.g. Lu et al., 2012; Wang et al., 2012). However, these tests identify the recombination rate only in males and are extremely cost intensive. DNA fragments associated with the enzymes involved in the recombination (a meiosis-specific recombinase and an enzyme involved in the formation of the double-strand break) can be separated from the rest of the genomic DNA and mapped to a reference genome, indicating genomic locations or recombination (e.g. Pan et al., 2011; Khil et al., 2012). In conclusion, different methods exist to obtain recombination maps or phased data required by several tests, which are typically unavailable for non-model species. However, all of these methods require investments in terms of time and budget. Furthermore, some cannot be conducted if laboratory breeding of the target species is impossible and relationships are unknown. Thus, the application of tests explicitly requiring a recombination map or phased data is somewhat limited, and their availability should be incorporated in the selection process for methods to detect positive selection. TEST STATISTICS TO DETECT POSITIVE SELECTION As mentioned in the section “Genomic signatures of positive selection”, selective sweeps influence different measures of genetic variation. On a micro-evolutionary scale, methods focusing on three measurements are commonly used: (1) linkage disequilibrium (LD); (2) site frequency spectrum (SFS); and (3) population differentiation-based tests. Most of the LD-based methods focus on long homozygous regions with high frequencies of certain haplotypes generated by hard sweeps (Sabeti et al., 2002; Garud et al., 2015). Variants of the tests incorporate different modifications, e.g. correcting for variation in the recombination rate (Sabeti et al., 2002), taking into account the derived and ancestral allele state (Voight et al., 2006), or using two populations instead of one (Sabeti et al., 2007). Other than long homozygous regions, selective sweeps also generate a specific spatial pattern of LD owing to the independent recombination events on both sides of the beneficial mutation, which is the target of the ω statistic (Kim & Nielsen, 2004). SFS-based methods rely on the assumption that selective sweeps affect the frequency of variants in a predictable manner, meaning an increased proportion of low- and high-frequency variants and a reduced proportion of intermediate-frequency variants. Many of the tests compare different estimates of the scaled population mutation rate (θ), which depend on different aspects of the SFS (e.g. Tajima, 1989; Fu & Li, 1993; Fay & Wu, 2000; Zeng et al., 2006). Although the estimates should result in similar values of θ under neutrality, selective sweeps affect the estimates unequally. Other tests compare the SFS of certain genomic regions with neutral assumptions on SFS based on the total data set (Nielsen et al., 2005; Boitard et al., 2013) or on data of a second population (Chen et al., 2010). Regions affected by a selective sweep are expected to deviate strongly from neutral assumptions. Population differentiation-based tests assume that populations occur in different environments and thus different selective regimes. Under positive selection mediated by these selective regimes, beneficial alleles and linked variants are expected to be present in high frequencies in the relevant populations, whereas they are present at intermediate to low frequencies in other populations. Thus, disproportionally high population differentiation for these loci is expected compared with neutral loci (Cavalli-Sforza, 1966; Lewontin & Krakauer, 1973). The test statistics differ mainly by the estimation of population differentiation, the underlying model of migration and the process to determine significance (Beaumont & Nichols, 1996; Foll & Gaggiotti, 2008; Excoffier et al., 2009; Bonhomme et al., 2010; Fariello et al., 2013). In addition to the three test categories described above that rely solely on genetic data, several other tests exist that analyse the correlation of population differentiation with environmental measurements. Such tests assume that an environmental gradient leading to positive selection is mirrored by the allele frequencies of the beneficial alleles, whereas neutral allele frequencies follow a different pattern. These tests are not considered in the present review but are dealt with elsewhere, e.g. by Manel et al. (2010), Schoville et al. (2012) and Rellstab et al. (2015). Choosing an Adequate Test Statistic The decision to apply a specific method and test category to identify positive selection in a data set depends on several criteria. First, data requirements of the tests have to be fulfilled (Table 1) as described above. Furthermore, the specific time at which a selective sweep occurred is important, because the different characteristics analysed in the tests show other detection rates for younger and older events of positive selection (reviewed by Biswas & Akey, 2006; Hohenlohe et al., 2010). The time since the onset of selection is commonly measured by the frequency of the beneficial allele (e.g. Zeng et al., 2006; Vatsiou et al., 2016). Linkage disequilibrium-based methods have optimal detection rates in a range from low beneficial allele frequency up to close to fixation, whereas the exact range depends on the method (Voight et al., 2006; Sabeti et al., 2007; Huff et al., 2010; Fariello et al., 2013; Ronen et al., 2013; Ma et al., 2015; Vatsiou et al., 2016). For example, population comparison methods have higher power close to fixation of the beneficial allele, whereas methods based on a single population have higher power at low beneficial allele frequencies (Sabeti et al., 2007; Tang et al., 2007; Fariello et al., 2013; Ronen et al., 2013; Fig. 3). Methods based on SFS comparing different estimates of θ show the highest statistical power when the frequency of the beneficial allele is approaching fixation in the analysed population (Simonsen et al., 1995; Fu, 1997; Zeng et al., 2006; Zeng et al., 2007b; Zhai et al., 2009; Ronen et al., 2013; Ferrer-Admetlla et al., 2014; Ma et al., 2015). However, methods that take into account the change in the spatial patterns of SFS attributable to selective sweeps have their maximal power at lower allele frequencies (Ronen et al., 2013; Ma et al., 2015; Vatsiou et al., 2016). For methods based on population differentiation, no results based on simulation studies were found. Nonetheless, they are assumed to perform best in a similar range to the SFS-based methods (Hohenlohe et al., 2010), because the difference in the allele frequency of the beneficial allele between populations in the selected and neutral environment is at its maximum in the time period shortly before and after fixation of the beneficial allele. Table 1. Overview of the requirements of the different methods commonly applied to detect micro-evolutionary patterns of positive selection Method Type of data Number of populations Genomic position Ancestral state/outgroup Recombination map Linkage disequilibrium-based methods  LRH Haplotypes One Yes No No  iHS Haplotypes One Yes Yes Yes  XP-EHH Haplotypes Two Yes No Yes  Rsb Genotypes or haplotypes Two Yes No No  H12 Genotypes One Yes No No  ω statistic Haplotypes One Yes No No  HapFLK Genotypes Multiple Yes No No Site frequency spectrum-based methods  Tajima’s D Genotypes or allele frequencies One Yes No No  Fu and Li’s tests Genotypes or allele frequencies One Yes Optional No  Fay and Wu’s H Genotypes or allele frequencies One Yes Yes No  CLR Allele frequencies One Yes Optional No  XP-CLR Allele frequencies Two Yes No Yes  Pool-HMM Pooled sequence data with quality score One Yes Optional No Population differentiation-based methods  FDist Allele frequencies Multiple No No No  BayeScan Allele frequencies Multiple No No No  FLK Allele frequencies Multiple No Optional No Method Type of data Number of populations Genomic position Ancestral state/outgroup Recombination map Linkage disequilibrium-based methods  LRH Haplotypes One Yes No No  iHS Haplotypes One Yes Yes Yes  XP-EHH Haplotypes Two Yes No Yes  Rsb Genotypes or haplotypes Two Yes No No  H12 Genotypes One Yes No No  ω statistic Haplotypes One Yes No No  HapFLK Genotypes Multiple Yes No No Site frequency spectrum-based methods  Tajima’s D Genotypes or allele frequencies One Yes No No  Fu and Li’s tests Genotypes or allele frequencies One Yes Optional No  Fay and Wu’s H Genotypes or allele frequencies One Yes Yes No  CLR Allele frequencies One Yes Optional No  XP-CLR Allele frequencies Two Yes No Yes  Pool-HMM Pooled sequence data with quality score One Yes Optional No Population differentiation-based methods  FDist Allele frequencies Multiple No No No  BayeScan Allele frequencies Multiple No No No  FLK Allele frequencies Multiple No Optional No CLR, composite likelihood ratio test; FLK, extended Lewontin and Krakauer test; iHS, integrated haplotype score; LRH, long-range haplotype test; XP-CLR, cross-population composite likelihood ratio test; XP-EHH, cross-population extended haplotype homozygosity. View Large Table 1. Overview of the requirements of the different methods commonly applied to detect micro-evolutionary patterns of positive selection Method Type of data Number of populations Genomic position Ancestral state/outgroup Recombination map Linkage disequilibrium-based methods  LRH Haplotypes One Yes No No  iHS Haplotypes One Yes Yes Yes  XP-EHH Haplotypes Two Yes No Yes  Rsb Genotypes or haplotypes Two Yes No No  H12 Genotypes One Yes No No  ω statistic Haplotypes One Yes No No  HapFLK Genotypes Multiple Yes No No Site frequency spectrum-based methods  Tajima’s D Genotypes or allele frequencies One Yes No No  Fu and Li’s tests Genotypes or allele frequencies One Yes Optional No  Fay and Wu’s H Genotypes or allele frequencies One Yes Yes No  CLR Allele frequencies One Yes Optional No  XP-CLR Allele frequencies Two Yes No Yes  Pool-HMM Pooled sequence data with quality score One Yes Optional No Population differentiation-based methods  FDist Allele frequencies Multiple No No No  BayeScan Allele frequencies Multiple No No No  FLK Allele frequencies Multiple No Optional No Method Type of data Number of populations Genomic position Ancestral state/outgroup Recombination map Linkage disequilibrium-based methods  LRH Haplotypes One Yes No No  iHS Haplotypes One Yes Yes Yes  XP-EHH Haplotypes Two Yes No Yes  Rsb Genotypes or haplotypes Two Yes No No  H12 Genotypes One Yes No No  ω statistic Haplotypes One Yes No No  HapFLK Genotypes Multiple Yes No No Site frequency spectrum-based methods  Tajima’s D Genotypes or allele frequencies One Yes No No  Fu and Li’s tests Genotypes or allele frequencies One Yes Optional No  Fay and Wu’s H Genotypes or allele frequencies One Yes Yes No  CLR Allele frequencies One Yes Optional No  XP-CLR Allele frequencies Two Yes No Yes  Pool-HMM Pooled sequence data with quality score One Yes Optional No Population differentiation-based methods  FDist Allele frequencies Multiple No No No  BayeScan Allele frequencies Multiple No No No  FLK Allele frequencies Multiple No Optional No CLR, composite likelihood ratio test; FLK, extended Lewontin and Krakauer test; iHS, integrated haplotype score; LRH, long-range haplotype test; XP-CLR, cross-population composite likelihood ratio test; XP-EHH, cross-population extended haplotype homozygosity. View Large Figure 3. View largeDownload slide Relevant time frames for analysing signatures of positive selection with the different methods. The time axis is scaled by the frequency of the beneficial allele. For the different methods, the exact range of beneficial allele frequencies with optimal performance depends on the simulation settings and thus the shown ranges are not exact thresholds, but only guidelines. CLR, composite likelihood ratio test; FLK, extended Lewontin and Krakauer test; iHS, integrated haplotype score; LD, linkage disequilibrium; LRH, long-range haplotype test; SFS, site frequency spectrum; XP-CLR, cross-population composite likelihood ratio test; XP-EHH, cross-population extended haplotype homozygosity. Figure 3. View largeDownload slide Relevant time frames for analysing signatures of positive selection with the different methods. The time axis is scaled by the frequency of the beneficial allele. For the different methods, the exact range of beneficial allele frequencies with optimal performance depends on the simulation settings and thus the shown ranges are not exact thresholds, but only guidelines. CLR, composite likelihood ratio test; FLK, extended Lewontin and Krakauer test; iHS, integrated haplotype score; LD, linkage disequilibrium; LRH, long-range haplotype test; SFS, site frequency spectrum; XP-CLR, cross-population composite likelihood ratio test; XP-EHH, cross-population extended haplotype homozygosity. Interpretation of Simulation Studies Multiple simulation studies were conducted to understand the behaviour of the different test statistics (e.g. Huff et al., 2010; De Mita et al., 2013; Ma et al., 2015; Vatsiou et al., 2016). To evaluate their results, three basic descriptors are important: true positive rate (TPR), false positive rate (FPR) and false discovery rate (FDR). The TPR or power of a test is calculated by identifying the loci found to be under selection, which were also simulated to be under selection (true positives). They are divided by the total number of loci simulated to be under selection. The FPR is defined as the proportion of false positives, meaning those loci found to be under selection but simulated neutrally, relative to the total number of neutral loci. The FDR describes the relationship of true positives to false positives by dividing the false positives by all loci that were found to be positive in the test. A small example to describe the difference between these three statistics is as follows. If a test on 900 neutral and 100 positive selected simulated loci results in 45 false positives, it equals an FPR of 0.05. In addition, if all 100 real positive selected loci (TPR of 1) are found to be positive, approximately two out of three of the loci found to be significant are true positives (FDR of 0.31). In contrast, if only 20 real positives are found (TPR of 0.2), this results in an FDR of 0.69, meaning that approximately two of the three loci found to be significant are false positives. Detailed Description of Test Statistics Choosing an adequate test statistic, conducting it correctly and interpreting its results reasonably depends on the general assumptions and requirements of the test. To this end, a basic understanding of the underlying calculation processes and the interpretation of results from simulation studies is inevitable. Therefore, in the next section, we describe several tests from each of the three categories using text and graphical summaries. In the descriptions, we focus on depicting data requirements and on the basic calculation processes. As many different tests exist, a subset was chosen to represent commonly used tests. For each of the main test categories, we provide information on the influence of different confounding factors on the individual test statistics based on simulation studies. The intention is to identify optimal conditions and the limitations of the single tests. Unfortunately, not all tests of a category were analysed for the same confounding factors and some of the simulation studies use different settings, sometimes leading to incomparable results. In a last section per test category, we give a short overview of recent applications of the tests to showcase research questions that can be asked with the methods and how the required data can be generated, focusing on animal species. Hence, the selected test cases can serve as starting points to facilitate researchers who are entering the field of adaptation research. Linkage Disequilibrium-Based Methods The extended haplotype homozygosity (EHH) concept (Sabeti et al., 2002; Fig. 4) Principle: Starting from a core region, the EHH assesses the homozygosity of the different extended haplotypes. The value is at its maximum for a low number of different haplotypes with unequal frequency distributions. Figure 4. View largeDownload slide Calculation process of the extended haplotype homozygosity (EHH) described by Sabeti et al. (2002). LD, linkage equilibrium. Figure 4. View largeDownload slide Calculation process of the extended haplotype homozygosity (EHH) described by Sabeti et al. (2002). LD, linkage equilibrium. A central concept for most methods that aim to identify loci under selection using LD patterns is the EHH concept (Sabeti et al., 2002). For the calculation, phase data are required, i.e. information that specifies which DNA bases are placed on the same of the two homologous chromosomes (in diploid organisms). The sequence of one of the two chromosomes is called a haplotype. The EHH calculation starts by defining a core region characterized by maximal LD, i.e. a region for which only one or a few core haplotypes exist and which does not show any sign of recombination (Sabeti et al., 2002). The core alleles can be either two variants of a single SNP (core SNP) or multiple variants of a region several base pairs long (core region), such as a gene. Next, the genomic region under investigation is extended to a certain SNP, X, and identical sequences from the core region until SNP X are clustered into identical extended haplotypes. Then, frequencies of the different extended haplotypes of a core allele are compared with each other. Thus, the EHH measures the probability that two randomly chosen haplotypes, with the same core allele, are homozygous (identical) over the complete range from the core allele to SNP X (Sabeti et al., 2002). Long-range haplotype (LRH) test (Sabeti et al., 2002; Fig. 5) Principle: Based on the EHH, the core allele frequencies are taken into account to identify regions that deviate from neutral expectations. Figure 5. View largeDownload slide Calculation process of the long-range haplotype (LRH) test described by Sabeti et al. (2002). EHH, extended haplotype homozygosity. Figure 5. View largeDownload slide Calculation process of the long-range haplotype (LRH) test described by Sabeti et al. (2002). EHH, extended haplotype homozygosity. Requirements: Haplotypes per individual of one population and multiple loci with genomic positions. To correct for variation in local recombination rates, the relative EHH (REHH) can be estimated, which incorporates the frequencies of the different core alleles per core region (Sabeti et al., 2002). The REHH is calculated by dividing the EHH of the tested core allele by the average EHH of all other core alleles, weighted by the core allele frequencies from a core region. The REHH was implemented in the LRH test (Sabeti et al., 2002), in which signatures of selective sweeps are identified through long genomic regions of high REHH values in combination with a high frequency of the core allele. For the test, the EHH is calculated first for the complete set of data starting at a core region, regardless of the core allele. When the EHH value falls within a certain range (usually 0.03–0.05), the SNP is used as SNP X. Now, the EHH values are calculated for all core alleles separately and REHH values are generated by incorporating the core allele frequencies. The process is repeated for different genomic regions. Two different approaches exist to identify core regions under selection, both taking into account REHH values and core allele frequencies. First, if the demographic population parameter estimates are known with some confidence, e.g. for typical model organisms, the neutral expectation of the REHH value can be generated using coalescence-based simulations (see, e.g. Sabeti et al., 2002). To identify genomic regions that are putatively under selection, the observed core haplotypes and the simulated data can be binned by their core allele frequencies. Next, within each bin, each observed REHH value is compared with all simulated values in the same bin to determine its rank. The rank is then translated into a P-value. Second, if the demographic history of the populations is less well known or genome-wide data are available, all tested genomic regions can be used to calculate the assumed neutral REHH value distribution (Sabeti et al., 2007; Piras et al., 2012; Meira et al., 2014). As for the first method, the REHH values can be divided into bins depending on their core allele frequency. The distribution of the REHH values within a bin can be standardised, i.e. have a mean of zero and a unit variance. Subsequently, the standard normal distribution can be used to assign P-values to the REHH values. Integrated haplotype score (iHS;Voight et al., 2006; Fig. 6) Principle: The EHH is integrated over the recombination distance independently for the ancestral and derived core alleles and then compared. Figure 6. View largeDownload slide Calculation process of the integrated haplotype score (iHS) described by Voight et al. (2006). EHH, extended haplotype homozygosity. Figure 6. View largeDownload slide Calculation process of the integrated haplotype score (iHS) described by Voight et al. (2006). EHH, extended haplotype homozygosity. Requirements: Haplotypes per individual of one population and multiple loci with genomic position, recombination map, and ancestral and derived allele status. The iHS is another method based on EHH values. It was developed by Voight et al. (2006) and incorporates the recombination distance (in centimorgan) into the statistics. Additionally, the alleles need to be classified according to their ancestral and derived status using an outgroup. In a first step, the test registers the point when the EHH values for the ancestral (A) and derived (D) core allele drop below a certain threshold (SNP XA and SNP XD, respectively). Next, the EHH values starting from the core allele to these SNPs are integrated over the recombination distance in centimorgan. Then, the log-ratio of the two areas is built by log10-transforming the division of the value for the ancestral allele by the value for the derived allele. Afterwards, the resulting value is standardised to have a mean of zero and a unit variance (iHS values). Strongly negative values suggest that the derived allele has swept through the population, whereas strongly positive values indicate the selection of the ancestral allele. Different approaches exist to identify genomic regions under selection. First, iHS values can be partitioned into bins depending on the number of SNPs per window, with the highest iHS values per bin being assumed to be significant (Pickrell et al., 2009; Eichstaedt et al., 2014). Second, iHS thresholds can be based on simulations (e.g. Voight et al., 2006; Colonna et al., 2014). For the test statistic, alleles have to be classified unambiguously into ancestral and derived state by comparison with the outgroup, i.e. the derived allele must be absent in the outgroup whereas the ancestral allele has to occur in the outgroup, and both alleles have to occur in the ingroup. Single nucleotide polymorphisms that cannot be assigned to ancestral or derived status are excluded from the analysis. The filtering step can substantially decrease the number of usable SNPs and thereby the total SNP density. Cross-population extended haplotype homozygosity (XP-EHH;Sabeti et al., 2007; Fig. 7) Principle: The EHH is calculated for two populations separately, integrated over recombination distance and compared in order to identify loci under selection in one of the two populations. Figure 7. View largeDownload slide Calculation process of the cross-population extended haplotype homozygosity (XP-EHH) described by Sabeti et al. (2007). EHH, extended haplotype homozygosity. Figure 7. View largeDownload slide Calculation process of the cross-population extended haplotype homozygosity (XP-EHH) described by Sabeti et al. (2007). EHH, extended haplotype homozygosity. Requirements: Haplotypes per individual of two populations and multiple loci with genomic position, and recombination map. Sabeti et al. (2007) suggested a population comparison approach to detect selection, the XP-EHH test. Genomic regions that underwent a selective sweep in one population but remained variable in the second population are targets of this method. First, a recombination distance cut-off (in centimorgan) for the EHH is calculated using all individuals of both populations. Similar to the iHS method, the EHH value is integrated over the recombination distance, separately for each of the two populations under study. Finally, a log-ratio of the integral for the first population relative to the integral of the second population is generated, which is standardised, similar to the iHS value. Extreme positive values indicate selection in the first population, whereas extreme negative values indicate selection in the second population. Selection is usually assumed to have affected the genomic regions with the proportion of the most extreme XP-EHH values (e.g. Ali et al., 2014; Zhao et al., 2016). Rsb test (Tang et al., 2007; Figs 8, 9) Principle: The Rsb test identifies loci under selection comparable to the XP-EHH test, but it can be applied with unphased data. Figure 8. View largeDownload slide Calculation process of the extended haplotype homozygosity of an individual single nucleotide polymorphism site (EHHS) described by Tang et al. (2007) using phased or unphased data. Figure 8. View largeDownload slide Calculation process of the extended haplotype homozygosity of an individual single nucleotide polymorphism site (EHHS) described by Tang et al. (2007) using phased or unphased data. Figure 9. View largeDownload slide Calculation process of the Rsb statistic described by Tang et al. (2007) based on the extended haplotype homozygosity of an individual single nucleotide polymorphism site (EHHS). Figure 9. View largeDownload slide Calculation process of the Rsb statistic described by Tang et al. (2007) based on the extended haplotype homozygosity of an individual single nucleotide polymorphism site (EHHS). Requirements: Genotypes or haplotypes per individual of two populations and multiple loci with genomic positions. Tang et al. (2007) developed another population comparison test to identify selective sweeps (Rsb). The test is based on the same idea as the XP-EHH test, assuming that a selective sweep occurred in only one of the two compared populations. In contrast to the other three tests, it does not require phasing information. In the first step, the EHH of an individual SNP site (EHHS) is calculated (Fig. 8). If phasing information is not available, the EHHS is based on the number of individuals that are homozygous, starting at the SNP site (core SNP) until a certain SNP, X, and weighted by the proportion of homozygous individuals at the SNP site. Otherwise, it is based on the count of the different haplotypes from the SNP site to SNP X and weighted by the similarity of the different allele counts at the SNP site. The following steps of the Rsb analysis are similar for both types of data using the corresponding EHHS values (Fig. 9). For each of the two compared populations, an SNP, X, is determined for which the EHHS value decreases below a certain limit (usually 0.1). Then, EHHS values are integrated over the physical distance (base pair distance) for each of the populations, and the log-ratio is built. These values are standardised to have a mean of zero and a unit variance [ln(Rsb) value]. Selection is commonly inferred using a standard normal distribution, which can be applied due to the normalisation of the ln(Rsb) values (e.g. Gautier & Naves, 2011; Flori et al., 2012; Roesti et al., 2015). To determine the desired threshold of ln(Rsb) values, the reciprocal of the P-value (1/P-value) is log10-transformed. For example, if a significance level of P < 0.0001 is chosen, all core SNPs with an ln(Rsb) ≥ 4 are assumed to be under positive selection in the first population. As selection can occur in both populations, the same threshold but negative (e.g. −4) indicates selection in the second population. H12 (Garud et al., 2015; Fig. 10) Principle: For a certain genomic region, the squared frequencies of the different haplotypes are summed, giving special weight to the two most common. Hard and soft sweeps can be distinguished by the impact of the most common haplotype on the summed frequencies. Figure 10. View largeDownload slide Calculation process of the H12 statistic described by Garud et al. (2015). Figure 10. View largeDownload slide Calculation process of the H12 statistic described by Garud et al. (2015). Requirements: Genotypes per individual of one population of multiple loci with genomic position. The test developed by Garud et al. (2015) is based, like the previous methods, on the expectation that selective sweeps will increase the haplotype homozygosity. However, the test does not focus on the number of different haplotypes and their lengths. It assumes that selective sweeps, especially soft sweeps, will not only increase the frequency of the most common, but also the second most common haplotype in a genomic region. The H12 statistic is calculated for a certain genomic window, meaning a specified number of SNPs. First, haplotypes and their frequencies are estimated from the genotype data. Hence, only homozygous SNPs are used, whereas heterozygous SNPs are set to ‘N’. Next, the frequency of the most common (p1) and the second most common (p2) haplotype are added. Finally, the squared frequencies of p1 and p2, i.e. (p1 + p2)2, are added to the squared frequencies of all other haplotypes, meaning p32 + p42…. This method of estimation gives special weight to the two most common haplotypes. Next, the window for the calculation is moved by a certain number of SNPs forward, and H12 is calculated for the next window. To determine the H12 level above which a selective sweep can be assumed, neutral data sets with the same characteristics as the analysed data set can be simulated and a threshold for a desired FPR estimated. When a pattern of selection is detected, a second statistic, H2/H1, can be used to determine whether it originated from a hard or soft sweep. Thus, for the calculation of H1, all haplotype frequencies are squared separately and added up (p12 + p22 + p32 + p42…). For H2, all haplotype frequencies are likewise squared separately and added up, starting from the second most common haplotype (p22 + p32 + p42…). Then, H2 is divided by H1. In a soft sweep, the influence of p1 should be less severe on the statistic, because more than one haplotype should be present at a high frequency. Hence, the value should be closer to one. In contrast, in a hard sweep, only one very common haplotype is mainly present; thus, H2 should be very small, resulting in a low value of H2/H1. As H2/H1 is, however, influenced by the absolute value of H12, it has to be normalised (Z′), so that its range is actually spanning from zero to one (Garud et al., 2015). Therefore, it is divided by its variance, which can be calculated based on the H12 value. ω statistic (Kim & Nielsen, 2004; Fig. 11) Principle: The LD within both flanking regions of the selected site is compared with the LD between flanking regions. Selective sweeps lead to high LD within but not between the flanking regions. Figure 11. View largeDownload slide Calculation process of the ω statistic described by Kim & Nielsen (2004). LD, linkage disequilibrium. Figure 11. View largeDownload slide Calculation process of the ω statistic described by Kim & Nielsen (2004). LD, linkage disequilibrium. Requirements: Haplotypes per individual of one population with genomic position. Selective sweeps generate a very specific LD pattern at sites neighbouring the beneficial allele, which can be captured by the ω statistic (Kim & Nielsen, 2004). Owing to the fast increase in frequency of the beneficial allele, genetic variation in the region under selection is only maintained by recombination during the selective sweep. When conceptually regarding a chromosome as two flanking regions adjacent to the selected site, a recombination event divides the chromosome into two parts: (1) the original genetic background of the selected site including one flanking region, the selected site and the second flanking region until the recombination breakpoint; and (2) the alternative genetic background, starting from the recombination breakpoint at the second flanking region. Hence, recombination will always affect only one side of the genomic region separated by the selected site per recombination event, leading to independent recombination patterns at both flanking sites. Therefore, LD should be high when comparing sites within one flanking region but low when comparing sites between the two flanking regions. The ω statistic is calculated by estimating the average LD (calculated as r2) of all possible comparisons of sites within both flanking regions divided by the average LD of all possible comparisons of sites between both flanking regions. If large genomic regions are analysed, the size of the flanking regions has to be specified. Furthermore, variations in the recombination rate and population mutation rate can affect the estimation for large genomic regions. Pavlidis et al., (2010) implemented a variable window size approach for the size of the analysed genomic region contributing to the ω statistic to account for these effects. Another implementation of the method was introduced by Alachiotis et al., (2012; OmegaPlus), allowing for the analysis of large whole-genome data sets. HapFLK (Fariello et al., 2013) Principle: The hapFLK method uses unphased data of multiple populations to determine cluster identities. These identities are than used to calculate a population differentiation statistic, which incorporates a kinship matrix representing the relationship between populations. Requirements: Genotypes per individual of multiple populations containing multiple loci with genomic position. For details, see hapFLK description in the ‘Population differentiation-based tests’ section. Simulation studies Simulations were applied to identify the optimal detection conditions for the different methods (e.g. Huff et al., 2010; Fariello et al., 2013; Vatsiou et al., 2016). A summary is given in Table 2. The simulation studies revealed that the methods can have very high FPR and FDR, if not conducted using their optimal parameter conditions (Huff et al., 2010; Pavlidis et al., 2010; Vatsiou et al., 2016). One important criterion for the different tests is the frequency of the beneficial allele, which represents the expected time since the onset of selection. For hard selective sweeps, all the above methods have different optimal frequencies of the beneficial allele at which the detection has the highest power. The LRH test performed best at low to intermediate allele frequencies, i.e. recent events (Huff et al., 2010; Fig. 3). The iHS performed best at intermediate allele frequencies (Voight et al., 2006; Ma et al., 2015; Vatsiou et al., 2016), whereas XP-EHH and the ω statistic performed best if the beneficial allele was close to or at fixation (Sabeti et al., 2007; Fariello et al., 2013; Ronen et al., 2013; Ma et al., 2015). HapFLK performed at high power in a wide range from intermediate to high beneficial allele frequencies, with a drop in statistical power close to fixation of the beneficial allele (Vatsiou et al., 2016). The connection of the performance of H12 and the beneficial allele frequency was not tested; however, a simulation study showed a loss in power with time after the cessation of selection (Garud et al., 2015). For Rsb, the optimal performance time was not analysed. Table 2. Summary of simulation study regarding linkage disequilibrium-based methods Parameter LRH iHS XP-EHH Rsb H12 ω hapFLK Best beneficial allele frequency Low to intermediate Intermediate Close to fixation Not tested Loss of power after cessation of selection Close to fixation Intermediate to high but not at fixation Bottleneck Not tested 0 Not tested Not tested Not tested − Not tested Expansion + 0 Not tested Not tested Not tested Not tested Not tested Migration rate Not tested − − − − Not tested Not tested − − Not tested Hierarchical structure of populations Not tested − − − − Not tested Not tested Not tested − − Detection of soft sweep Not tested − − − Not tested − Not tested − − Variation in local recombination rate 0 Incorporated Incorporated 0 Not tested Not tested Not tested Parameter LRH iHS XP-EHH Rsb H12 ω hapFLK Best beneficial allele frequency Low to intermediate Intermediate Close to fixation Not tested Loss of power after cessation of selection Close to fixation Intermediate to high but not at fixation Bottleneck Not tested 0 Not tested Not tested Not tested − Not tested Expansion + 0 Not tested Not tested Not tested Not tested Not tested Migration rate Not tested − − − − Not tested Not tested − − Not tested Hierarchical structure of populations Not tested − − − − Not tested Not tested Not tested − − Detection of soft sweep Not tested − − − Not tested − Not tested − − Variation in local recombination rate 0 Incorporated Incorporated 0 Not tested Not tested Not tested Impact on the methods is indicated (0, no impact; −, negative impact; +, positive impact). If a rating was possible among methods, a stronger negative impact is indicated by − − iHS, integrated haplotype score; LRH, long-range haplotype test, XP-EHH: cross-population extended haplotype homozygosity. View Large Table 2. Summary of simulation study regarding linkage disequilibrium-based methods Parameter LRH iHS XP-EHH Rsb H12 ω hapFLK Best beneficial allele frequency Low to intermediate Intermediate Close to fixation Not tested Loss of power after cessation of selection Close to fixation Intermediate to high but not at fixation Bottleneck Not tested 0 Not tested Not tested Not tested − Not tested Expansion + 0 Not tested Not tested Not tested Not tested Not tested Migration rate Not tested − − − − Not tested Not tested − − Not tested Hierarchical structure of populations Not tested − − − − Not tested Not tested Not tested − − Detection of soft sweep Not tested − − − Not tested − Not tested − − Variation in local recombination rate 0 Incorporated Incorporated 0 Not tested Not tested Not tested Parameter LRH iHS XP-EHH Rsb H12 ω hapFLK Best beneficial allele frequency Low to intermediate Intermediate Close to fixation Not tested Loss of power after cessation of selection Close to fixation Intermediate to high but not at fixation Bottleneck Not tested 0 Not tested Not tested Not tested − Not tested Expansion + 0 Not tested Not tested Not tested Not tested Not tested Migration rate Not tested − − − − Not tested Not tested − − Not tested Hierarchical structure of populations Not tested − − − − Not tested Not tested Not tested − − Detection of soft sweep Not tested − − − Not tested − Not tested − − Variation in local recombination rate 0 Incorporated Incorporated 0 Not tested Not tested Not tested Impact on the methods is indicated (0, no impact; −, negative impact; +, positive impact). If a rating was possible among methods, a stronger negative impact is indicated by − − iHS, integrated haplotype score; LRH, long-range haplotype test, XP-EHH: cross-population extended haplotype homozygosity. View Large The methods differ in their performance under different demographic scenarios. The LRH test was found to have a higher power for expansion than constant population size (Huff et al., 2010). However, the power was very low for all tested scenarios; hence, it has to be interpreted cautiously. For iHS, no impact of expansion was detected, whereas strong bottlenecks resulted in a decrease in power (Huff et al., 2010; Wang et al., 2014). The ω statistic was found to perform well for weak bottlenecks but is affected by strong ones (Alachiotis & Pavlidis, 2016). The division of a population into subpopulations is another factor that can potentially influence the performance of the different test statistics. For iHS and XP-EHH, high migration rates led to a poor performance (Vatsiou et al., 2016). In contrast, the FPR of the ω statistic decreased with increasing migration and thus decreasing differentiation between subpopulations, while the effect of migration on the power of the ω statistic was not tested (Jensen et al., 2007). If populations are structured hierarchically, the power of iHS, XP-EHH and hapFLK decreases. For the two-population method XP-EHH, the power was reduced more if the sampled populations originated from the same group than if they originated from different groups of hierarchically structured populations (Vatsiou et al., 2016). In addition to the performance of the test statistics to detect hard sweeps, they were also tested for their ability to detect soft sweeps in part. Here, a strong reduction in statistical power was found for iHS (Garud et al., 2015; Vatsiou et al., 2016) and likewise for the hapFLK (Fariello et al., 2013, 2017). In one study, XP-EHH was found to be almost unaffected, leading to a very good estimate in cases of high allele frequencies of the selected variant (Vatsiou et al., 2016). In contrast, Fariello et al. (2013) found a strong reduction in the power of XP-EHH. However, they averaged the power for all simulations with beneficial allele frequencies at the sampling time point > 0.6, which included samples with allele frequencies that were too low to be detected reliably by the XP-EHH test (Vatsiou et al., 2016). H12, which was designed to detect hard and soft sweeps, was able to detect soft sweeps in general (Garud et al., 2015). Nevertheless, very soft sweeps characterized by high initial allele frequency or a high number of selected variants in a genomic region could not be detected (Garud et al., 2015). Local variation in recombination rate, which impacts on LD, does not seem to influence the power of the LRH, iHS and Rsb methods (Tang et al., 2007; Huff et al., 2010). Furthermore, iHS and XP-EHH are corrected for such variation by integrating the statistic over the recombination distance in centimorgan (Voight et al., 2006; Sabeti et al., 2007). Examples Besides humans, LD-based tests were mainly applied to domesticated animal species and their relatives, such as cattle, sheep, pigs or honeybees (Haasl & Payseur, 2016). Commonly, several breeds were compared, and the underlying genetic basis of the different breed characteristics, such as productivity (e.g. Chen et al., 2016; Lim et al., 2016; Wragg et al., 2016) or morphology (Pfahler & Distl, 2015; Yuan et al., 2017), or adaptation to local conditions, such as climate (Yang et al., 2016) or parasites (Lee et al., 2016; Kim et al., 2017a), was the target of the studies. Owing to the high economic value of these species, genomic resources such as well-annotated reference genomes and recombination maps are available, simplifying the generation of large SNP data sets with high quality density. For most of the species, commercial SNP chips were present, which produced ~50000 (e.g. in cattle: Lim et al., 2016; Gurgul et al., 2016; or sheep: Zhao et al., 2016) to 600000 SNPs (e.g. in chickens: Liu et al., 2016; Fleming et al., 2017). Alternatively, genome resequencing approaches with an average coverage of 5–20x were applied, resulting in millions of suitable SNPs (Wang et al., 2016; Wragg et al., 2016; Yang et al., 2016). In addition to domesticated animals, LD-based methods were applied mainly on other species with high economic value, such as the tilapia fish (Xia et al., 2015), Atlantic salmon (Barson et al., 2015), salmon louse (Besnier et al., 2014) or tsetse fly (Gloria-Soria et al., 2016), and on typical model species, such as the house mouse (Didion et al., 2016), Drosophila melanogaster (Garud & Petrov, 2016; Merenciano et al., 2016) or the three-spine stickleback (Roesti et al., 2015; Marques et al., 2017). Two exceptions that do not fall in these two categories are studies on the Tasmanian devil (Epstein et al., 2016) and the crow species complex (Vijay et al., 2016). All but one species of the described examples possessed reference genomes prior to the study on selection, enabling genome resequencing (Xia et al., 2015; Vijay et al., 2016), commercial or customized SNP chips (Besnier et al., 2014; Barson et al., 2015; Didion et al., 2016) and RAD sequencing with high SNP densities (Epstein et al., 2016; Gloria-Soria et al., 2016). No reference genome was present for the salmon louse. Hence, lice from different locations were applied for genome sequencing for the generation of a new SNP array, which was subsequently used for genotyping. The underlying research questions of the studies were highly diverse, searching genomic patterns resulting from the adaptation to parasites (Gloria-Soria et al., 2016) and pesticides (Besnier et al., 2014), as well as selective sweeps originating from transmissible cancer (Epstein et al., 2016), genes under sexual conflict (Barson et al., 2015) and ‘selfish’ genes (Didion et al., 2016). Thus, although LD-based methods show promise for a high ability to detect relatively young selection events in particular and are applicable to a wide range of research questions, they were applied in only a very limited way to non-model species. This is most probably a result of the high data requirements, which currently cannot be fulfilled by any non-model species or species without high economic value. Commonly used programs with their requirements are shown in Table 3. Table 3. Programs commonly applied to calculate linkage disequilibrium-based statistics Program Methods Data requirements GUI Platform Link* hapbin EHH; iHS; XP-EHH Haplotype data; genomic position; recombination map; (one to two populations) No All (C++ compilation) 1 HapFLK HapFLK Allele frequency data; genomic position or recombination map; multiple populations; kinship matrix optional; outgroup optional No All (C++ compilation and Python) 2 iHS iHS Haplotype data; genomic position; recombination map; one population; ancestral allele state No All (C++ compilation) 3 rehh R-package EHH; iHS; XP-EHH; Rsb (phased data) Haplotype data; genomic position or recombination map; (one or multiple populations; ancestral allele state) No All (R) 4 SelectionHap Stats H12; H2/H1 Genotype data; genomic position No All (Python and R) 5 selscan EHH; iHS; XP-EHH Haplotype data; genomic position; recombination map; (one or multiple populations; ancestral allele state) No All 6 OmegaPlus ω statistic Haplotype data; genomic position; one population No Linux, Windows 7 XP-EHH XP-EHH Haplotype data; genomic position; recombination map; two populations No All (C++ compilation) 3 Program Methods Data requirements GUI Platform Link* hapbin EHH; iHS; XP-EHH Haplotype data; genomic position; recombination map; (one to two populations) No All (C++ compilation) 1 HapFLK HapFLK Allele frequency data; genomic position or recombination map; multiple populations; kinship matrix optional; outgroup optional No All (C++ compilation and Python) 2 iHS iHS Haplotype data; genomic position; recombination map; one population; ancestral allele state No All (C++ compilation) 3 rehh R-package EHH; iHS; XP-EHH; Rsb (phased data) Haplotype data; genomic position or recombination map; (one or multiple populations; ancestral allele state) No All (R) 4 SelectionHap Stats H12; H2/H1 Genotype data; genomic position No All (Python and R) 5 selscan EHH; iHS; XP-EHH Haplotype data; genomic position; recombination map; (one or multiple populations; ancestral allele state) No All 6 OmegaPlus ω statistic Haplotype data; genomic position; one population No Linux, Windows 7 XP-EHH XP-EHH Haplotype data; genomic position; recombination map; two populations No All (C++ compilation) 3 Data requirements only required for some methods of a program are placed in parenthesis. Data requirements of the program can differ from the requirements of the statistical test. EHH, extended haplotype homozygosity; iHS, integrated haplotype score; GUI, graphical user interfface; XP-EHH, cross-population extended haplotype homozygosity. *Links: (1) https://github.com/evotools/hapbin (2) https://forge-dga.jouy.inra.fr/projects/hapflk (3) http://hgdp.uchicago.edu/Software/ (4) https://cran.r-project.org/web/packages/rehh/index.html (5) https://github.com/ngarud/SelectionHapStats (6) https://github.com/szpiech/selscan (7) http://sco.h-its.org/exelixis/web/software/omegaplus/index.html. Last access to all links: 23.02.2018 View Large Table 3. Programs commonly applied to calculate linkage disequilibrium-based statistics Program Methods Data requirements GUI Platform Link* hapbin EHH; iHS; XP-EHH Haplotype data; genomic position; recombination map; (one to two populations) No All (C++ compilation) 1 HapFLK HapFLK Allele frequency data; genomic position or recombination map; multiple populations; kinship matrix optional; outgroup optional No All (C++ compilation and Python) 2 iHS iHS Haplotype data; genomic position; recombination map; one population; ancestral allele state No All (C++ compilation) 3 rehh R-package EHH; iHS; XP-EHH; Rsb (phased data) Haplotype data; genomic position or recombination map; (one or multiple populations; ancestral allele state) No All (R) 4 SelectionHap Stats H12; H2/H1 Genotype data; genomic position No All (Python and R) 5 selscan EHH; iHS; XP-EHH Haplotype data; genomic position; recombination map; (one or multiple populations; ancestral allele state) No All 6 OmegaPlus ω statistic Haplotype data; genomic position; one population No Linux, Windows 7 XP-EHH XP-EHH Haplotype data; genomic position; recombination map; two populations No All (C++ compilation) 3 Program Methods Data requirements GUI Platform Link* hapbin EHH; iHS; XP-EHH Haplotype data; genomic position; recombination map; (one to two populations) No All (C++ compilation) 1 HapFLK HapFLK Allele frequency data; genomic position or recombination map; multiple populations; kinship matrix optional; outgroup optional No All (C++ compilation and Python) 2 iHS iHS Haplotype data; genomic position; recombination map; one population; ancestral allele state No All (C++ compilation) 3 rehh R-package EHH; iHS; XP-EHH; Rsb (phased data) Haplotype data; genomic position or recombination map; (one or multiple populations; ancestral allele state) No All (R) 4 SelectionHap Stats H12; H2/H1 Genotype data; genomic position No All (Python and R) 5 selscan EHH; iHS; XP-EHH Haplotype data; genomic position; recombination map; (one or multiple populations; ancestral allele state) No All 6 OmegaPlus ω statistic Haplotype data; genomic position; one population No Linux, Windows 7 XP-EHH XP-EHH Haplotype data; genomic position; recombination map; two populations No All (C++ compilation) 3 Data requirements only required for some methods of a program are placed in parenthesis. Data requirements of the program can differ from the requirements of the statistical test. EHH, extended haplotype homozygosity; iHS, integrated haplotype score; GUI, graphical user interfface; XP-EHH, cross-population extended haplotype homozygosity. *Links: (1) https://github.com/evotools/hapbin (2) https://forge-dga.jouy.inra.fr/projects/hapflk (3) http://hgdp.uchicago.edu/Software/ (4) https://cran.r-project.org/web/packages/rehh/index.html (5) https://github.com/ngarud/SelectionHapStats (6) https://github.com/szpiech/selscan (7) http://sco.h-its.org/exelixis/web/software/omegaplus/index.html. Last access to all links: 23.02.2018 View Large Site Frequency Spectrum-Based Methods Tajima’s D (Tajima, 1989; Fig. 12) Principle: Two different estimates of the scaled population mutation rate are compared: the average nucleotide diversity and the number of segregating sites. Under neutrality, both estimates are expected to be similar, whereas positive selection leads to a higher proportion of segregating sites relative to the nucleotide diversity. Figure 12. View largeDownload slide Calculation process of Tajima’s D statistic described by Tajima (1989). θ, scaled population mutation rate. Figure 12. View largeDownload slide Calculation process of Tajima’s D statistic described by Tajima (1989). θ, scaled population mutation rate. Requirements: Genotypes per individual of one population containing one locus or multiple loci with genomic position. Tajima’s D test (Tajima, 1989) is based on the comparison of two different estimates for θ (scaled population mutation rate). If no selection acts on the tested DNA sequences and the population is in mutation–drift equilibrium (similar number of variants obtained through mutations and lost by drift), both estimates are expected to be similar. However, different changes in population size, e.g. expansion or bottlenecks, and different types of selection, e.g. positive selection, background selection or balancing selection, influence the two estimates of θ differently, leading to a test statistic that can be used to draw conclusions about population history. The first estimator is given by the average per nucleotide diversity of the DNA sequences (θπ). It can be estimated in two different ways: (1) the average number of pairwise nucleotide differences among all possible pairs of sequences is calculated; and (2) the sample frequency of the different allelic variants per site over all segregating sites corrected for sample size (unbiased estimation of heterozygosity) is applied. The second estimator for the scaled population mutation rate parameter is generated by counting all segregating sites in the DNA sequences (θS). Given that the number of segregating sites depends strongly on the number of sampled specimens, the value is corrected for sample size. For Tajima’s D statistic, the variable d is next calculated by subtracting the estimator based on the segregating site (θS) from the estimator based on the nucleotide differences (θπ). To generate the final test statistic (D), d is divided by its variance, which can be estimated based on the sample size and the number of segregating sites. Hence, the D-statistic is assumed to follow a standard normal distribution, with a mean of zero and a unit variance, which provides the basis to assign P-values to the test statistic. However, as D can take only limited values, the probability density function is better described by a beta distribution. The beta distribution is generated by using the maximum and minimum possible D-values based on the sample size. Resulting confidence limits for Tajima’s D based on the sample size (up to 140 sequences) can be found in table 2 in the original publication (Tajima, 1989). Alternatively, significance can be determined using coalescence simulations based on the sample size and either θπ or the number of segregating sites of the data set as input variables. Results are considered to be significant if an analysed locus falls within or below a certain percentage range of the lowest simulated values, or within or above the highest simulated values, respectively (e.g. using DnaSP; Rozas & Rozas, 1999). For window-based analyses of genome-wide data, a strong deviation of genomic regions from the average D-value can be used to define significance (e.g. Bellis et al., 2016). Significant negative D values indicate selective sweeps, among others. These values are caused by a low nucleotide diversity relative to the number of segregating sites, thus more low-frequency alleles than intermediate frequency alleles exist. Fu and Li’s D, D*, F and F* (Fu & Li, 1993; Fig. 13) Principle: Two different estimates of the scaled population mutation rate are compared, including estimates based on external and total branch length. Under neutrality, the two estimates are expected to be similar. In contrast, positive selection increases external branch length, whereas internal branch lengths are less affected. Figure 13. View largeDownload slide Calculation process of Fu and Li’s test statistics, namely D, D*, F and F*, described by Fu & Li (1993). θ, scaled population mutation rate. Figure 13. View largeDownload slide Calculation process of Fu and Li’s test statistics, namely D, D*, F and F*, described by Fu & Li (1993). θ, scaled population mutation rate. Requirements: Genotype data per individual of one population containing one locus or multiple loci with genomic position. Fu and Li’s D and F require an outgroup. All four statistics are based on the assumption that under neutrality, internal and external branch lengths of a population tree depend on θ (Fu & Li, 1993). In the case of a recent fixation of an advantageous allele owing to a selective sweep, younger branches, meaning mainly external branches, are expected to show an increased length because of a high amount of young mutations, whereas older branches, meaning mainly internal ones, are less affected by new mutations. The first statistic, Fu and Li’s D, thus compares the total branch length of the population tree, including internal and external branches, with the external branch length. As the dependency of the internal branch length from θ is also based on the number of sequences, a correction factor is included for the external branch length. For the test, the total branch length is estimated per site by the number of different nucleotides minus one, summed over all sites. If only biallelic SNPs are included, the total branch length is thus the number of segregating sites. The external branch length is estimated by the number of singleton mutations. These, however, can only be identified reliably using an outgroup. Otherwise, an ancestral allele occurring in only a single individual can be misinterpreted as a mutation in an external branch. As the test values depend on the sample size and the total branch length, it has to be divided by its variance to follow a normal distribution. The second test, Fu and Li’s D*, has the same underlying principle as Fu and Li’s D but does not require an outgroup. As it is not possible to determine whether singletons are ancestral, as described, a further correction term based on the same size is included. Similar to the D statistic, the test has to be normalised based on the sample size and the total branch length. The third test, Fu and Li’s F, assumes that the unbiased estimate of θ is the average number of pairwise nucleotide differences between all possible pairs of sequences (similar to θπ of Tajima’s D). Hence, the external branch lengths are subtracted from the estimate, requiring an outgroup. Similar to the previous tests, the value is normalised by dividing it by its variance, which is calculated based on the sample size and the total branch length. The last test, Fu and Li’s F*, has the same underlying principle as Fu and Li’s F but does not require an outgroup, as it uses singletons rather than the external branch length. Similar to D*, a correction for the number of samples is included in the test estimate. Again, the value is normalised by dividing it by its variance, which is calculated based on the sample size and the total branch length. The significance of all four tests can be estimated by the simulation of neutral data sets using either the segregating sites or the total branch length as an estimator of θ (e.g. using DnaSP; Rozas & Rozas, 1999). If a value falls below the 5% of the lowest simulated values, it is assumed to be significant. Significant values can indicate selective sweeps, but they can also indicate purifying selection or population expansion (Fu & Li, 1993). Fay and Wu’s H (Fay & Wu, 2000; Fig. 14) Principle: The scaled population mutation rate is estimated in two different ways, i.e. average homozygosity and average heterozygosity of the derived allele; the estimates are then compared. In the case of a selective sweep, an excess of high-frequency-derived alleles is expected, leading to a higher homozygosity estimate relative to the heterozygosity and thus to negative H values. Figure 14. View largeDownload slide Calculation process of Fay and Wu’s H statistic (Fay & Wu, 2000) and the standardised H (Zeng et al. 2006). θ, scaled population mutation rate. Figure 14. View largeDownload slide Calculation process of Fay and Wu’s H statistic (Fay & Wu, 2000) and the standardised H (Zeng et al. 2006). θ, scaled population mutation rate. Requirements: Genotypes per individual of one population containing one locus or multiple loci with genomic position. Ancestral and derived allele status. Similar to the two previously described tests, Fay and Wu’s H statistic (Fay & Wu, 2000) is based on the assumption that θ can be estimated with different parameters that all lead to similar results under neutrality but are differently influenced under demographic changes or selection. As before, θ is first estimated in Fay and Wu’s H statistic using the average per nucleotide diversity (θπ), calculated based on the average heterozygosity. Second, θ is estimated based on the average homozygosity of the derived alleles (θH). To assign alleles to either the ancestral or the derived state, an outgroup is explicitly needed for the test, which serves as a reference for the ancestral allele state. Both calculations of θ, θπ and θH, are based on counting the number of segregating sites with a certain derived allele: for θπ, the counted number of segregating sites with a certain derived allele count is multiplied by respective derived and ancestral allele counts. The division is repeated for all different derived allele counts and the results are summed. Finally, this sum is weighted by sample size. Owing to the incorporation of derived and ancestral allele count, segregating sites with intermediate allele frequencies contribute most to the θπ estimate. For θH, the number of segregating sites with a certain derived allele count is multiplied by the squared derived allele count. As for θπ, the results are summed for the different derived allele counts and weighted by sample size. Here, segregating sites with high derived allele frequencies contribute most to the θH estimate. Next, the H statistic is calculated by subtracting θH from θπ. Negative values indicate selective sweeps by an increased proportion of high-frequency alleles relative to intermediate-frequency alleles. The significance of the H statistic, i.e. significant deviation from the neutral assumption, is assessed by simulating neutral data sets using a coalescent approach. The simulation is conditioned on the number of segregating sites (as opposed to the nucleotide diversity). Values falling within or even below the lowest 5% of values from the empirical distribution are considered significant. Zeng et al. (2006) standardised the H statistic to have a mean of zero and a unit variance. For the standardisation, the estimation of the scaled population mutation rate by θH is slightly modified to θL. Instead of using the squared derived allele count for weighting the homozygosity-based estimator of θ, count data are used untransformed, i.e. unsquared. Furthermore, the correction by the sample size is slightly modified. Similar to the original H statistic, θL is subtracted from θπ. The value is divided by its variance, which can be estimated based on the sample size and the number of segregating sites. All subsequent steps of assessing significance of the H statistic remain identical. Composite likelihood ratio (CLR) test (Nielsen et al., 2005; Fig. 15) Principle: The method identifies selection by comparing a composite likelihood model with selection against a neutral model. Within the model of selection, the likelihood is maximized for different assumptions about the strength of selection, taking into account the spatial pattern of selective sweeps. Figure 15. View largeDownload slide Calculation process of the composite likelihood ratio (CLR) test described by Nielsen et al. (2005). SFS, site frequency spectrum. Figure 15. View largeDownload slide Calculation process of the composite likelihood ratio (CLR) test described by Nielsen et al. (2005). SFS, site frequency spectrum. Requirements Allele frequency data from one population and multiple loci with genomic position. A composite likelihood ratio test to detect selection using the SFS was developed by Nielsen et al. (2005; SweepFinder), comparing the likelihood of a model including selection with a neutral model for a certain genomic region. In order to do so, the analysed sequence is split into grids of a prespecified size and user-defined distances (in base pairs) in a first step. This requires knowledge of the physical position on the genome of markers such as individual SNPs rather than complete sequence information on large genomic regions. Within each of these grids, the likelihood of a model with selection (alternative model) is estimated per site (analysed site), assuming the selected site is at the centre of the grid. The marginal likelihood of the identified allele frequency at the analysed site is calculated as follows. It is assumed that the chromosome where the beneficial allele arose has the derived allele at the analysed site. As the selective sweep is assumed to have resulted in the fixation of the beneficial allele, all chromosomes with an ancestral allele at the analysed site must originate from lineages that have escaped the selective sweep by recombination with a chromosome carrying the beneficial allele at the selected site. Furthermore, some of the chromosomes having the derived allele at the analysed site may also originate from lineages that recombined with a lineage containing the beneficial allele at the selected site (although without a visible effect at the analysed site). Thus, for a certain size of recombinant fraction, the composition of lineages with ancestral and derived alleles at the analysed site can be inferred. For the calculation, all possible different sizes of these recombinant fractions are used, with the number of chromosomes having the ancestral allele at the analysed site as a minimum and the assumption that all alleles escaped the selective sweep by recombination at the analysed site as a maximum. For each possible size of recombinant fraction, the probability of having this size is estimated using assumptions about the position of the analysed site relative to the selected site, as well as α, a factor that includes the local recombination rate, the effective population size and the selection coefficient. Next, the probability of having the assumed derived allele frequency in the recombinant fraction (plus one lineage where the beneficial allele arose) is calculated. Hence, the SFS of the total data set is used as a probability distribution, because all lineages before the selective sweep are assumed to have had a similar probability to escape the sweep by recombination, and thus the allele frequencies in the recombinant fraction should represent the overall genomic distribution of allele frequencies. The results from steps 4 and 5 are multiplied by the probability that the beneficial allele arose on a chromosome carrying the derived allele, which is the proportion of derived alleles in the recombinant fraction. Steps 2–6 are repeated, assuming that the beneficial allele arose on a chromosome with an ancestral allele at the analysed site. Now the recombinant fraction consists of at least the number of chromosomes with the derived allele as the analysed site. In step 5, the probability of the assumed derived allele frequency in the recombinant fraction is still used, but it is multiplied in step 6 by the probability that the beneficial allele arose on a chromosome carrying the ancestral allele (hence, the proportion of ancestral alleles in the recombinant fraction). The resulting probabilities for the different sizes of recombinant fractions assuming that the beneficial allele arose on a chromosome with the ancestral and with the derived allele are summed. In the next step, the marginal likelihoods of the different sites in the grid are multiplied, leading to the composite likelihood of the alternative model. As the values of the different components contributing to α, e.g. the strength of selection, are unknown, several values are tested, and the value for which the composite likelihood of the alternative model is at its maximum is chosen. The likelihood of the null model is estimated by calculating the SFS for all sites in the data set. The frequency distribution is set as the probability distribution of the site frequencies. Next, for each site in the grid, the respective probability of the identified allele frequency is determined, and the values are multiplied, leading to the composite likelihood of the null model. A composite likelihood ratio test is performed by dividing the logarithmic likelihood of the data under the alternative model by the logarithmic likelihood of the data under the null model (Pavlidis et al., 2008). To decide whether the difference between the alternative model and the null model is sufficient to indicate selection, simulations of the neutral expectations can be conducted. The respective parameters are estimated from the data, and the test statistics are calculated. The upper limit of the test statistics (e.g. 95%) generates the threshold for the neutral expectation. In 2013, the CLR algorithm was substantially extended by Pavlidis et al. (2013; SweeD). With this implementation, the neutral SFS can be calculated analytically following the theory of Živković & Stephan (2011), rather than being estimated empirically over the complete data set, if the demographic model is known with confidence. DeGiorgio et al. (2016) published another extension of the CLR algorithm (SweepFinder2). Amongst other modifications, invariable sites are included in the analysis, and variation in the recombination rate is taken into account by a recombination map. Furthermore, as variation in background selection has a strong impact on the SFS, it also enables the incorporation of a background selection map (B value map). Hence, for each site, the allele frequencies are rescaled with the B value. However, B value maps are currently available only for D. melanogaster (Comeron, 2014) and humans (McVicker et al., 2009). Cross-population composite likelihood ratio (XP-CLR) test (Chen et al., 2010; Fig. 16) Principle: In the XP-CLR test, a neutral reference population is used in a first step to predict allele frequency spectra for a target population under selection. Then, the observed data are compared against these predictions, and estimates are optimized using likelihood maximization. Figure 16. View largeDownload slide Calculation process of the cross-population composite likelihood ratio (XP-CLR) test described by Chen et al. (2010). SFS, site frequency spectrum; LD, linkage disequilibrium. Figure 16. View largeDownload slide Calculation process of the cross-population composite likelihood ratio (XP-CLR) test described by Chen et al. (2010). SFS, site frequency spectrum; LD, linkage disequilibrium. Requirements: Allele frequency data of two populations and multiple loci with genomic position. Only one of the two populations is assumed to be under positive selection. Recombination map. In the first step of the XP-CLR test developed by Chen et al. (2010), a grid size (in base pairs) is defined as a spacer between grid points, similar to the CLR method of Nielsen et al. (2005). In the calculation, these grid points are assumed potentially to be under selection. As the spatial pattern of changes in the SFS is considered in the test, windows of a user-defined size are analysed around the grid points to test for selection. The window size depends on the recombination distances (in centimorgan). Furthermore, to control for heterogeneity in the SNP density, a maximal number of SNPs per window can be defined. If the number of SNPs in the window exceeds the threshold, a random subset of SNPs is used. For each site in a window, a marginal likelihood is calculated based on modification of the Wiener process (Nicholson et al., 2002), which assumes that the allele frequency in the reference population together with information about the population history can be used to model SFS in the target population, as follows. Information about population history is approximated using the genome-wide data set (Racimo, 2016), and a neutral SFS is estimated. The neutral SFS is modified based on three parameters. First, a factor depending on the recombination fraction between the selected variant (grid point) and the analysed site is used, which is estimated based on the recombination distances provided. Second, the selection coefficient is incorporated. As it is unknown, different values are tested. Third, the initial frequency of the beneficial allele in the target population is considered using a very small, fixed value (1/20000). An increased proportion of high allele frequencies and of low allele frequencies characterizes the modified SFS. Alleles at linked sites occur at a high frequency when they are linked to the beneficial allele at the selected site at the beginning of the selective sweep, whereas alleles are expected at a low frequency when they are linked to the beneficial allele during the selective sweep by recombination. The modified SFS is used to calculate the likelihood that selection with the specified selection coefficient acted on the grid point, leading to the observed allele frequency at the analysed site. Therefore, the area under the SFS curve is integrated and, at the same time, weighted by the observed allele frequency. The marginal likelihood is down-weighted if adjacent SNPs are linked because of their close proximity, as they are not statistically independent. Hence, a correlation coefficient of each SNP is calculated based on the LD between the SNP and other SNPs in the window. The calculation is based on SNP data of the reference population only, because the correlation pattern is assumed to be unaffected by selection in that population. Chen et al. (2010) found that the down-weighting reduced the false positive rates. To estimate the composite likelihood of a specific window, the calculation described above is repeated for all SNPs in the window and the results are multiplied. As the selection coefficient is unknown, the composite likelihood is maximized for the analysed window by testing different values for the selection coefficient. The null model of the CLR is generated in a similar manner to the alternative model, but the selection coefficient is set to zero. Finally, the logarithmic composite likelihood of the alternative model is divided by the logarithmic composite likelihood of the null model. Windows with especially high XP-CLR scores are assumed to be under selection. Pool-HMM (Boitard et al., 2013; Fig. 17) Principle: A hidden Markov model (HMM) with three states, Neutral, Intermediate and Sweep, is applied, taking into account uncertainties in the allele counts attributable to sequencing errors. The model includes probabilities of changing between the different states (transition probability) and probabilities of finding certain allele frequencies given a certain state (emission probability). The most likely sequence of the states and the posterior probability of each site being associated with a selective sweep is estimated. Figure 17. View largeDownload slide Calculation process of the Pool-HMM statistic described by Boitard et al. (2013). θ, scaled population mutation rate; CLR, composite likelihood ratio test by Nielsen. Figure 17. View largeDownload slide Calculation process of the Pool-HMM statistic described by Boitard et al. (2013). θ, scaled population mutation rate; CLR, composite likelihood ratio test by Nielsen. Requirements: Sequence data with quality scores from a pool of individuals from one populations and multiple loci with genomic position. Similar to the CLR statistic of Nielsen et al. (2005), Pool-HMM assumes that the expected deviation from the SFS under a selective sweep can be estimated using the neutral SFS calculated from the complete data set (Boitard et al., 2013). In contrast to the method of Nielsen et al. (2005), however, an HMM is used to identify the spatial pattern of the selective sweep along the DNA fragment. An HMM is based on the assumption that a certain sequence of states underlies the data; in this case, Neutral, Intermediate and Sweep. The true sequence of the states is, however, unknown (hidden), but can be predicted by the observations of the allele frequencies at the different sites. A detailed explanation of HMM with an example can be found in the study by Eddy (2004). In general, the model is based on two components: the emission probabilities and the transition probabilities. The emission probabilities define the probability of finding a certain allele frequency for each of the three different states. The transition probabilities give the probability of staying in a certain state or changing to another state. The first step of the analysis is calculation of the neutral SFS, which is required for all three emission probability distributions. As Pool-HMM is based on pooled sequencing data of a known number of individuals, SNP calling of rare alleles is difficult, because they show similar frequencies to sequencing errors (Boitard et al., 2012). Hence, Pool-HMM incorporates uncertainties in the SFS, allowing the inclusion of low-frequency alleles. For the calculation, a certain fraction of all sites, comprising invariable as well as segregating sites, is selected (default: 10% of all sites). Per site, the probability of having a certain number of derived and ancestral alleles is calculated (or common and raw alleles, if no reference is given) by using the quality scores of the bases from the reads covering the site. These estimates are then used in an expectation maximization (EM) step to calculate the SFS, starting from a neutral expectation calculated based on a given value of θ. In the next step, the emission probabilities for Neutral, Intermediate and Sweep are calculated. For the Neutral emission probability, the neutral SFS is used. For the Intermediate and Sweep emission probabilities, the marginal likelihood calculation of the CLR (Nielsen et al., 2005) is applied for each possible number of derived alleles using two different values for α (Intermediate: α = 0.7; Sweep: α = 0.2) and the neutral SFS, leading to different predictions of the probability distribution. Subsequently, the transmission probabilities are estimated. For all states, the same probability to stay in the state (1 − k) is assumed. The probability to change from Neutral to Intermediate and from Sweep to Intermediate is also similar (k). The probability of changing from Intermediate to Neutral is similar to that from Intermediate to Sweep (k/2), whereas the probabilities of changing from Neutral to Sweep and vice versa are almost zero. The factor k (q in the study by Boitard et al., 2013) is defined by the user. However, a very small value (k < 0.1) is recommended in order to hinder a frequent change between states. Per segregating site, the probability of finding a certain state can be calculated. First, assuming a certain state at the previous site and a certain state at the present site, the according transition probability is used and scaled by the distance between sites. Next, similar to the neutral SFS calculation, not a certain derived allele count but rather a probability distribution for the different possible allele counts is estimated using read quality data. The allele count probability distribution is used to scale the emission probabilities of the assumed state at the present position. Both scaled transition probability and scaled emission probability are then multiplied by each other. The process can be repeated for all previous and present state combinations at a specific site. As the possible number of sequences of states is very high, and thus calculating the probability of all possible sequences is not feasible, especially for many segregating sites, a dynamic programming algorithm, the Viterbi algorithm (Rabiner, 1989), is used to estimate the most likely state sequence. A region is assumed to be affected by a selective sweep if the state Sweep is predicted at least once. Additionally, the posterior probability to find a selective sweep (state ‘Sweep’) at each site is estimated using the forward–backward algorithm. As the FDR of the analysis depends strongly on the value of k, and thus the change between the different states, it is recommended that neutral data sets should be simulated using the appropriate value of θ. Different values of k can then be tested and the FDR estimated, as no selective sweep should be observed. Simulation studies The performance of the different SFS-based methods was evaluated in several simulation-based studies (e.g. Zeng et al., 2006; Li, 2011; Ferrer-Admetlla et al., 2014; Wang et al., 2014; Ma et al., 2015). A summary can be found in Table 4. Pool-HMM was not studied in any simulation studies; however, a previous version was analysed (HMMB-SEG; by Boitard et al., 2009), which is assumed here to represent Pool-HMM. Additionally, as the underlying inference of the selected SFS is based on the algorithm of the CLR statistic, similar assumptions on sensitivity to bottlenecks or on the optimal allele frequency range can probably be made for Pool-HMM. From the four tests of Fu and Li, only one or two are often studied in a simulation study. As they are based on very similar assumptions and no major differences were detected in the simulation studies between the tests (Fu, 1997; Ma et al., 2015), we interpreted the results of the simulation studies for all four tests. For Tajima’s D and Fu and Li’s statistics, positive and negative values can indicate deviation from neutral assumptions. As negative values are indicative for selective sweeps, simulation studies testing the ability to detect signs of positive selection regard only significantly negative values rather than negative and positive values (e.g. Fu, 1997; Zeng et al., 2006; Wang et al., 2014). Table 4. Summary of simulation study results regarding site frequency spectrum-based methods Parameter Tajima’s D Fu and Li’s tests Fay and Wu’s H CLR by Nielsen XP-CLR Pool-HMM Best beneficial allele frequency Shortly before or at fixation Shortly before or at fixation At fixation or slightly later Shortly before fixation Wide range without very low and high frequencies Not tested Increased strength of selection + + + + + + Expansion − − − − − 0 Not tested Not tested Bottleneck − − − − − − − − Not tested Migration rate − − − − Not tested − Not tested Sampling scheme Not applicable Not applicable Not applicable Not applicable − Not applicable Background selection − Not tested − Not tested Not tested Not tested Balancing selection 0 Not tested − Not tested Not tested Not tested Recurrent selective sweeps − Not tested − − Not tested Not tested Soft sweep − − Not tested − − Not tested − Not tested Increased sample size + + + + (15 diploid individuals may be sufficient) Not tested Not tested Increased marker density + + Not tested + Not tested Not tested Distance to the selected site − Not tested − Not tested Not tested Not tested Errors attributable to recombination rate variation Not applicable Not applicable Not applicable − 0 Not applicable Errors in ancestral/derived allele status Not applicable Not tested − Not tested Not applicable Not tested Parameter Tajima’s D Fu and Li’s tests Fay and Wu’s H CLR by Nielsen XP-CLR Pool-HMM Best beneficial allele frequency Shortly before or at fixation Shortly before or at fixation At fixation or slightly later Shortly before fixation Wide range without very low and high frequencies Not tested Increased strength of selection + + + + + + Expansion − − − − − 0 Not tested Not tested Bottleneck − − − − − − − − Not tested Migration rate − − − − Not tested − Not tested Sampling scheme Not applicable Not applicable Not applicable Not applicable − Not applicable Background selection − Not tested − Not tested Not tested Not tested Balancing selection 0 Not tested − Not tested Not tested Not tested Recurrent selective sweeps − Not tested − − Not tested Not tested Soft sweep − − Not tested − − Not tested − Not tested Increased sample size + + + + (15 diploid individuals may be sufficient) Not tested Not tested Increased marker density + + Not tested + Not tested Not tested Distance to the selected site − Not tested − Not tested Not tested Not tested Errors attributable to recombination rate variation Not applicable Not applicable Not applicable − 0 Not applicable Errors in ancestral/derived allele status Not applicable Not tested − Not tested Not applicable Not tested Impact on the methods is indicated (0, no impact; −, negative impact; +, positive impact). If a rating was possible among methods, a stronger negative impact is indicated by − −. CLR, composite likelihood ratio test; XP-CLR, cross-population composite likelihood ratio test. View Large Table 4. Summary of simulation study results regarding site frequency spectrum-based methods Parameter Tajima’s D Fu and Li’s tests Fay and Wu’s H CLR by Nielsen XP-CLR Pool-HMM Best beneficial allele frequency Shortly before or at fixation Shortly before or at fixation At fixation or slightly later Shortly before fixation Wide range without very low and high frequencies Not tested Increased strength of selection + + + + + + Expansion − − − − − 0 Not tested Not tested Bottleneck − − − − − − − − Not tested Migration rate − − − − Not tested − Not tested Sampling scheme Not applicable Not applicable Not applicable Not applicable − Not applicable Background selection − Not tested − Not tested Not tested Not tested Balancing selection 0 Not tested − Not tested Not tested Not tested Recurrent selective sweeps − Not tested − − Not tested Not tested Soft sweep − − Not tested − − Not tested − Not tested Increased sample size + + + + (15 diploid individuals may be sufficient) Not tested Not tested Increased marker density + + Not tested + Not tested Not tested Distance to the selected site − Not tested − Not tested Not tested Not tested Errors attributable to recombination rate variation Not applicable Not applicable Not applicable − 0 Not applicable Errors in ancestral/derived allele status Not applicable Not tested − Not tested Not applicable Not tested Parameter Tajima’s D Fu and Li’s tests Fay and Wu’s H CLR by Nielsen XP-CLR Pool-HMM Best beneficial allele frequency Shortly before or at fixation Shortly before or at fixation At fixation or slightly later Shortly before fixation Wide range without very low and high frequencies Not tested Increased strength of selection + + + + + + Expansion − − − − − 0 Not tested Not tested Bottleneck − − − − − − − − Not tested Migration rate − − − − Not tested − Not tested Sampling scheme Not applicable Not applicable Not applicable Not applicable − Not applicable Background selection − Not tested − Not tested Not tested Not tested Balancing selection 0 Not tested − Not tested Not tested Not tested Recurrent selective sweeps − Not tested − − Not tested Not tested Soft sweep − − Not tested − − Not tested − Not tested Increased sample size + + + + (15 diploid individuals may be sufficient) Not tested Not tested Increased marker density + + Not tested + Not tested Not tested Distance to the selected site − Not tested − Not tested Not tested Not tested Errors attributable to recombination rate variation Not applicable Not applicable Not applicable − 0 Not applicable Errors in ancestral/derived allele status Not applicable Not tested − Not tested Not applicable Not tested Impact on the methods is indicated (0, no impact; −, negative impact; +, positive impact). If a rating was possible among methods, a stronger negative impact is indicated by − −. CLR, composite likelihood ratio test; XP-CLR, cross-population composite likelihood ratio test. View Large As the genetic diversity pattern generated by a single hard sweep changes over time, the detectability of a sweep by SFS-based methods depends on the time point of sampling. Hence, similar to LD-based methods, the time component in simulation studies is measured by the frequency of the beneficial allele (Fig. 3). For Tajima’s D and Fu and Li’s tests, a high power was found for high beneficial allele frequencies until some time after fixation, with the highest power shortly before or at fixation (Fu, 1997; Zeng et al., 2006; Zhai et al., 2009; Ronen et al., 2013). A similar time range was found for Fay and Wu’s H (Zeng et al., 2006), with some indications for a better detectability at later stages of the sweep, and the highest power after fixation of the beneficial allele (Ronen et al., 2013). In contrast, the power of the CLR statistic was highest shortly before but not ultimately at fixation, i.e. ideally, it can detect younger selective sweep events (Ronen et al., 2013; Ma et al., 2015). For the XP-CLR test, a high power has been reported for a large range of frequencies of the beneficial allele, besides very low and very high frequencies (Vatsiou et al., 2016). Thus, all tests show good results for the high beneficial allele frequencies, whereas patterns of positive selection in populations sampled very recently after the onset of selection, thus with a very low beneficial allele frequency, or some time after the end of the selective sweep, will not be identified correctly using this set of methods. Besides the time of sampling, the strength of selection is relevant for its detection. For all the methods described here, an increase in power with an increased strength of selection was described if a single hard selective sweep under an otherwise standard neutral model was analysed (Fu, 1997; Nielsen et al., 2005; Boitard et al., 2009; Chen et al., 2010; Pavlidis et al., 2010; Ferrer-Admetlla et al., 2014; Wang et al., 2014; Ma et al., 2015). Deviation in the demography of the sampled species from the standard neutral model can impact on the SFS in a similar manner to positive selection. Neutrality tests, such as Tajima’s D and Fu and Li’s tests, are used to detect not only signatures of selection but also demographic changes. In case of the application of neutrality tests for the detection of positive selection, the power to detect demographic changes is, however, undesired and thus scored as a false positive here. One demographic change that influences some part of the SFS in a similar way to a selective sweep is expansion. Both Tajima’s D and Fu and Li’s tests were found to detect expansions similar to selection (Fu, 1997; Zeng et al., 2006; Ferrer-Admetlla et al., 2014; Wang et al., 2014). The effect was strongest if a population differed significantly from its original size but had not yet reached mutation–drift equilibrium (Fu, 1997; Li, 2011). For Fay and Wu’s H statistic, only a small effect of expansion was detected (Zeng et al., 2006, 2007b; Li, 2011), which was strongest shortly after the expansion (Zeng et al., 2007b). The CLR statistic was found to be unaffected by expansions (Boitard et al., 2009). Another demographic change with a strong impact on the SFS are bottlenecks. For the evaluation of their effect, the strength, meaning the reduction in population size, duration and age of the bottleneck, meaning the time since the population size recovery, are important. Giving this complex interplay that, it is difficult to evaluate these from simulation studies. For Tajima’s D and Fu and Li’s tests, a higher impact of strong bottlenecks compared with weak ones was found (Wang et al., 2014; Alachiotis & Pavlidis, 2016), as well as a higher impact of old compared with young bottlenecks (Zeng et al., 2007a, b ; Li, 2011). For Fay and Wu’s H, a higher impact from younger compared with older bottlenecks was found by Zeng et al. (2007b) and Li (2011). In contrast, no effect on the power of the statistic for strong and weak bottlenecks was found by Wang et al. (2014), meaning that a time frame for the bottleneck was probably used, which did not impact on the statistic. The performance of the CLR statistic was only slightly affected by weak bottlenecks, but the influence increased with the strength of the bottleneck. Shallow and long bottlenecks decreased the power more than short but drastic ones (Pavlidis et al., 2010). Overall, recent bottlenecks with an intermediate strength had the highest influence on the CLR statistic (Boitard et al., 2009), because they cause large variation in the SFS, from which some can resemble selective sweeps (Jensen et al., 2005). The last tested method, XP-CLR, was also found to be slightly sensitive to bottlenecks (Ronen et al., 2013). When the time of the bottleneck relative to the onset of selection was analysed, all tested methods had the greatest power to detect selection if it occurred at the beginning of the bottleneck and not later (Ronen et al., 2013). The migration rate among subpopulations also impacts the test statistics. If only one subpopulation was sampled, Fay and Wu’s H was found to be the most sensitive, with the strongest effects at low migration rates, and thus high differentiation (Zeng et al., 2006, 2007b; Li, 2011). Although the general patterns were similar for Tajima’s D and Fu and Li’s tests, the proportion of false positives for selection was lower for these two methods (Zeng et al., 2006, 2007a, b; Li, 2011; Ferrer-Admetlla et al., 2014; Wang et al., 2014). The XP-CLR test is based on the comparison of two populations. If selection was strong and the migration rate very high, the power of the test decreased, as the beneficial allele swamped the reference population (Vatsiou et al., 2016). In contrast, a stronger differentiation and thus few migrants led to a decrease in power for cases where the selection was not very strong because of the increased genetic differentiation in the complete genome (Vatsiou et al., 2016). Here, the result also depended on the sampling scheme. First, if the target population was not under selection, but a nearby population was under selection, XP-CLR still detected selection if migration was sufficient between the two populations (Vatsiou et al., 2016). The more distant the target population compared with the population under selection, the lower was the detectability of the selective sweep. If populations were structured following a hierarchical island model, meaning that they were structured into groups, the power of the XP-CLR statistic also depended on the sample scheme. If the two populations were sampled from the same group, the power decreased for a beneficial allele at a low frequency, whereas the power remained almost unaffected for higher frequencies of the beneficial allele. If the samples originated from different groups, the pattern was similar, but the power was lower overall (Vatsiou et al., 2016). In another simulated scenario, the effect of sampling was tested for a stepping stones model with a heterogeneous environment (Vatsiou et al., 2016). This means that half of the simulated populations were under selection in a certain environment, whereas the other half occurred in a neutral environment. A high power for the XP-CLR test was found only if the reference population was in the neutral environment and the target population in the selected environment. Furthermore, a closer location of the reference population to the border of the selected environment increased the power. Otherwise, the neutral differentiation was very strong and affected the detection of selection (Vatsiou et al., 2016). Similar to certain demographic scenarios, other types of selection, such as purifying, background or balancing selection, have an impact on the SFS that is comparable to positive selection. Hence, Tajima’s D and Fu and Li’s neutrality tests were found to be sensitive against background selection, with increasing deleterious mutation rates leading to high impacts on the statistics (Fu, 1997; Zeng et al., 2006, 2007b). Fay and Wu’s H was found to be uninfluenced by background selection (Zeng et al., 2006, 2007b). In contrast, balancing selection showed a strong influence at the initial stage on Fay and Wu’s H, whereas Tajima’s D (negative values) was not as strongly influenced (Zeng et al., 2006). Besides a single hard sweep, different types of sweeps, such as recurrent hard sweeps or soft sweeps, can impact on a genomic region, resulting in more complex changes of the SFS. For recurrent hard sweeps, Tajima’s D and Fay and Wu’s H were able to identify positive selection only if the analysed region was not located between the selected sites of the two sweeps, but at the flanking regions (Chevin et al., 2008). The CLR statistic also had low power if several recurrent selective sweeps occurred in a population. The power increases with a decreasing strength of selection, as it will affect smaller parts of the genome and thus the neutral pattern can be estimated better (Pavlidis et al., 2010). For soft sweeps, Tajima’s D and Fay and Wu’s H were found generally to have low power, which decreased with an increased initial allele frequency of the beneficial allele (Ferrer-Admetlla et al., 2014; Wang et al., 2014). The power was best for the selection of intermediate strength (Ferrer-Admetlla et al., 2014). The XP-CLR test was found overall to have a high power to detect soft sweeps for a small range of intermediate frequencies of the beneficial variant at the sampling time point. As for Tajima’s D and Fay and Wu’s H, the power decreased as the initial allele frequency increased (Vatsiou et al., 2016). Although the factors described above depend on the population history and are often difficult to determine, other negative impacts on the test statistics based on the study design can be avoided. One factor is sample size. For Tajima’s D, Fu and Li’s tests and Fay and Wu’s H, an increase in power was shown with larger sample sizes (Simonsen et al., 1995; Li, 2011; Wang et al., 2014; Subramanian, 2016). Nevertheless, it is difficult to define a sufficient number of individuals. For example, Wang et al. (2014) found no increase in accuracy with > 30 diploid individuals for Tajima’s D and Fay and Wu’s H. In contrast, Li (2011) found an increase in the power of Tajima’s D, Fu and Li’s tests, and Fay and Wu’s H for up to 500 diploid individuals (upper test range); data from human exome capture indicated that the influence of sample size on the test statistic was not saturated for 500 exons (Subramanian, 2016). For CLR, no strong increase in power was detected for > 15 diploid individuals (Ma et al., 2015), whereas some increase in accuracy for determining the location of the selected site was visible in a range from 12 to 1000 haploid sequences. Similar to sample size, marker density can affect the accuracy of the tests. For Tajima’s D, Fu and Li’s tests and CLR, higher marker densities led to increased power (Ma et al., 2015). Another factor affecting the performance of the test statistics is the distance of the analysed region from the selected site, if the site is not included. For Tajima’s D and Fay and Wu’s H, it was shown that an increased distance leads to reduced power (Zeng et al., 2007a). Some of the methods need prior assumptions. For XP-CLR, a recombination map is required to incorporate changes in recombination rate along the chromosomes. However, it was shown to be relatively robust against incorrect estimates (Chen et al., 2010). For the CLR statistic, simulation of the neutral data set to determine significance requires knowledge of the recombination rate. Incorrect estimates led to the incorrect inference of the selection coefficient, whereas the null distribution of the test statistic itself was unaffected. Thus, regions showing particularly strong deviations from neutrality could still be identified (Nielsen et al., 2005). Fay and Wu’s H can be calculated only if ancestral/derived allele states are assigned using, for example, an outgroup, because the calculation is based on the homozygosity of the derived allele. This showed a strong increase in FPR with increasing misidentification (Zeng et al., 2007b). Examples Commonly, neutrality tests such as Tajima’s D or Fu and Li’s tests are applied to detect changes in population demography such as bottlenecks or expansions, rather than for the inference of selection, especially in studies using only one or a few genetic markers (e.g. Baldanzi et al., 2016; Rocha et al., 2016; Roy et al., 2016; Low et al., 2017). In addition, several studies applied neutrality tests to a single (Santolamazza et al., 2015; Bergamo et al., 2015; Chang et al., 2016) or a few candidate genes (Hemmer & Blumenstiel, 2016; Velenovsky et al., 2016; Almeida & DeSalle, 2017) to reveal patterns of positive selection. For instance, candidate genes assumed to be involved in speciation (Almeida & DeSalle, 2017) and insecticide resistance (Bergamo et al., 2015; Chang et al., 2016) or antifungal genes (Velenovsky et al., 2016) were studied using neutrality tests. Besides a few candidate genes that allow only the application of neutrality tests from the set of SFS-based statistics, a larger amount of data enables the application of the CLR-based tests and/or Pool-HMM. For example, one study analysed a large genomic region surrounding a candidate gene (> 50 kb) involved in the blanched coloration of white sand lizards, presumably as an adaptation to rapid environmental change, as well as hundreds of neutral loci, using a sequence capture approach (Laurent et al., 2016). Likewise, another study applied a sequence capture approach to re-examine > 1000 candidate genes presumably involved in ecotype formation in grey wolves, which were previously identified using a genome scan (Schweizer et al., 2016). Besides candidate gene sets, SFS-based methods have been applied to genome-wide data. In most cases, reference genomes were present, and data were generated by either pool- (Asgharian et al., 2015; Phillips et al., 2016; Dennenmoser et al., 2017) or individual-based (Martin et al., 2016; McGirr & Martin, 2017; Taye et al., 2017) genome resequencing. Alternatively, data were generated by RAD sequencing (Kamdem et al., 2017; Yang et al., 2017) or large SNP chips (Fu et al., 2016) or retrieved from previous studies (Freedman et al., 2016). In the case of the great tit, a de novo reference genome was generated and genome resequencing of several individuals was performed in a single study (Laine et al., 2016). Many of the studies were conducted on domesticated animals, inferring the genomic bases of artificial selection (e.g. dogs: Freedman et al., 2016; Yang et al., 2017; chickens: Wang et al., 2016; Fu et al., 2016; cattle: Kim et al., 2017a, b ; Taye et al., 2017). Additionally, several studies were conducted on Drosophila, for example studying selection in chemosensory gene families (Arguello et al., 2016) or the genetic basis of an extended lifespan (Michalak et al., 2017). Examples for targets of the studies in other species are genes involved in the adaptation to human-dominated environments in Anopheles gambiae (Kamdem et al., 2017), in adaptation to brackish water and freshwater habitats in prickly sculpin (Dennenmoser et al., 2017) or in the evolution of new feeding types in Caribbean pupfishes (McGirr & Martin, 2017). Moreover, many studies tried to identify genomic regions impacted by selection without an a priori assumption about the selective force (Culex pipiens: Asgharian et al., 2015; Heliconius melpomene: Martin et al., 2016; Asian house rat: Teng et al., 2016; African green monkey: Pfeifer, 2017). Typically used programs with their requirements are shown in Table 5. Table 5. Programs commonly applied to calculate site frequency spectrum-based statistics Program Methods Data requirements GUI Platform Link* Arlequin Tajima’s D Phased genotypic or haplotypic DNA sequences from one locus Yes in Windows All; project files with settings have to be generated using the GUI version for Windows 1 DnaSP Tajima’s D; Fu and Li’s tests; Fay and Wu’s H Genotypic (will be phased) or haplotypic DNA sequences from one locus; (outgroup) Yes Windows 2 Pool-HMM Pool-HMM Pooled NGS data from one population with quality scores; genomic position; ancestral allele state optional No All (Python) 3 PopGenome R package Tajima’s D; Fu and Li’s F*, D*; Fay and Wu’s H; CLR Haplotypic DNA sequences or phased or unphased SNP data with genomic position; one population No All (R) 4 PoPoolation Tajima’s D Pooled NGS data from one population with quality scores; genomic position No All (Perl) 5 SweeD CLR Allele frequency data; genomic position; one population; ancestral state optional No Linux 6 SweepFinder2 SweepFinder2 Allele frequency data; genomic position; one population; ancestral state optional; (recombination map; background selection map) No Linux 7 VCFtools Tajima’s D Genotype data; phased or unphased; genomic position; one population No Linux and Mac 8 XP-CLR XP-CLR Genotype data; phased or unphased; genomic position; two populations; recombination map No All (C++ compilation) 9 Program Methods Data requirements GUI Platform Link* Arlequin Tajima’s D Phased genotypic or haplotypic DNA sequences from one locus Yes in Windows All; project files with settings have to be generated using the GUI version for Windows 1 DnaSP Tajima’s D; Fu and Li’s tests; Fay and Wu’s H Genotypic (will be phased) or haplotypic DNA sequences from one locus; (outgroup) Yes Windows 2 Pool-HMM Pool-HMM Pooled NGS data from one population with quality scores; genomic position; ancestral allele state optional No All (Python) 3 PopGenome R package Tajima’s D; Fu and Li’s F*, D*; Fay and Wu’s H; CLR Haplotypic DNA sequences or phased or unphased SNP data with genomic position; one population No All (R) 4 PoPoolation Tajima’s D Pooled NGS data from one population with quality scores; genomic position No All (Perl) 5 SweeD CLR Allele frequency data; genomic position; one population; ancestral state optional No Linux 6 SweepFinder2 SweepFinder2 Allele frequency data; genomic position; one population; ancestral state optional; (recombination map; background selection map) No Linux 7 VCFtools Tajima’s D Genotype data; phased or unphased; genomic position; one population No Linux and Mac 8 XP-CLR XP-CLR Genotype data; phased or unphased; genomic position; two populations; recombination map No All (C++ compilation) 9 Data requirements only required for some methods of a program are placed in parenthesis. Data requirements of the program can differ from the requirements of the statistical test. CLR, composite likelihood ratio test; GUI, graphical user interface; XP-CLR, cross-population composite likelihood ratio test. *Links: (1) http://cmpg.unibe.ch/software/arlequin35/Arlequin35.html (2) http://www.ub.edu/dnasp (3) https://forge-dga.jouy.inra.fr/projects/pool-hmm (4) https://cran.r-project.org/web/packages/PopGenome/index.html (5) https://sourceforge.net/projects/popoolation (6) http://sco.h-its.org/exelixis/web/software/sweed (7) http://www.personal.psu.edu/mxd60/sf2.html (8) https://vcftools.github.io/man_latest.html (9) https://genetics.med.harvard.edu/reich/Reich_Lab/Software.html. Last access to all links: 23.02.2018. View Large Table 5. Programs commonly applied to calculate site frequency spectrum-based statistics Program Methods Data requirements GUI Platform Link* Arlequin Tajima’s D Phased genotypic or haplotypic DNA sequences from one locus Yes in Windows All; project files with settings have to be generated using the GUI version for Windows 1 DnaSP Tajima’s D; Fu and Li’s tests; Fay and Wu’s H Genotypic (will be phased) or haplotypic DNA sequences from one locus; (outgroup) Yes Windows 2 Pool-HMM Pool-HMM Pooled NGS data from one population with quality scores; genomic position; ancestral allele state optional No All (Python) 3 PopGenome R package Tajima’s D; Fu and Li’s F*, D*; Fay and Wu’s H; CLR Haplotypic DNA sequences or phased or unphased SNP data with genomic position; one population No All (R) 4 PoPoolation Tajima’s D Pooled NGS data from one population with quality scores; genomic position No All (Perl) 5 SweeD CLR Allele frequency data; genomic position; one population; ancestral state optional No Linux 6 SweepFinder2 SweepFinder2 Allele frequency data; genomic position; one population; ancestral state optional; (recombination map; background selection map) No Linux 7 VCFtools Tajima’s D Genotype data; phased or unphased; genomic position; one population No Linux and Mac 8 XP-CLR XP-CLR Genotype data; phased or unphased; genomic position; two populations; recombination map No All (C++ compilation) 9 Program Methods Data requirements GUI Platform Link* Arlequin Tajima’s D Phased genotypic or haplotypic DNA sequences from one locus Yes in Windows All; project files with settings have to be generated using the GUI version for Windows 1 DnaSP Tajima’s D; Fu and Li’s tests; Fay and Wu’s H Genotypic (will be phased) or haplotypic DNA sequences from one locus; (outgroup) Yes Windows 2 Pool-HMM Pool-HMM Pooled NGS data from one population with quality scores; genomic position; ancestral allele state optional No All (Python) 3 PopGenome R package Tajima’s D; Fu and Li’s F*, D*; Fay and Wu’s H; CLR Haplotypic DNA sequences or phased or unphased SNP data with genomic position; one population No All (R) 4 PoPoolation Tajima’s D Pooled NGS data from one population with quality scores; genomic position No All (Perl) 5 SweeD CLR Allele frequency data; genomic position; one population; ancestral state optional No Linux 6 SweepFinder2 SweepFinder2 Allele frequency data; genomic position; one population; ancestral state optional; (recombination map; background selection map) No Linux 7 VCFtools Tajima’s D Genotype data; phased or unphased; genomic position; one population No Linux and Mac 8 XP-CLR XP-CLR Genotype data; phased or unphased; genomic position; two populations; recombination map No All (C++ compilation) 9 Data requirements only required for some methods of a program are placed in parenthesis. Data requirements of the program can differ from the requirements of the statistical test. CLR, composite likelihood ratio test; GUI, graphical user interface; XP-CLR, cross-population composite likelihood ratio test. *Links: (1) http://cmpg.unibe.ch/software/arlequin35/Arlequin35.html (2) http://www.ub.edu/dnasp (3) https://forge-dga.jouy.inra.fr/projects/pool-hmm (4) https://cran.r-project.org/web/packages/PopGenome/index.html (5) https://sourceforge.net/projects/popoolation (6) http://sco.h-its.org/exelixis/web/software/sweed (7) http://www.personal.psu.edu/mxd60/sf2.html (8) https://vcftools.github.io/man_latest.html (9) https://genetics.med.harvard.edu/reich/Reich_Lab/Software.html. Last access to all links: 23.02.2018. View Large Population Differentiation-Based Methods FDist (Beaumont & Nichols, 1996; Fig. 18) Principle Neutral expectations of the population differentiation relative to heterozygosity are estimated from the data. The observed population differentiation per locus are compared against the neutral expectation, and loci that show a significant deviation from neutrality are assumed to be under selection. Figure 18. View largeDownload slide Calculation process of FDist described by Beaumont & Nichols (1996) and the modified versions implemented in LOSITAN (Antao et al., 2008) and in Arlequin (Excoffier et al., 2009; Excoffier & Lischer, 2010). FST, fixation index. Figure 18. View largeDownload slide Calculation process of FDist described by Beaumont & Nichols (1996) and the modified versions implemented in LOSITAN (Antao et al., 2008) and in Arlequin (Excoffier et al., 2009; Excoffier & Lischer, 2010). FST, fixation index. Requirements: Allele frequency data per population from multiple populations and multiple loci. The method FDist was developed by Beaumont & Nichols (1996). It is based on the idea that demographic processes influence differentiation between populations at all loci and alleles uniformly, whereas natural selection affects only specific loci and alleles in some populations (Cavalli-Sforza, 1966; Lewontin & Krakauer, 1973). First, the fixation index (FST value) is estimated, which is a measurement for the genetic differentiation of populations. In FDist, the calculation method described by Cockerham & Weir (1993) is applied, estimating average FST values over all populations for each locus. In short, the observed allele frequencies are used to calculate the average FST values. Thus, the average variance of allele frequencies between the populations is divided by the sum of the average variance within and between populations. Besides the allele frequencies, the number of sampled populations and the sample size are incorporated in the statistics. Positive selection is indicated by exceptionally high FST values relative to their heterozygosity. To test whether FST values are higher than expected, neutral data sets are generated, and the observed data are compared with these neutral exceptions. For this purpose, the average FST across all loci is estimated. To obtain an unbiased average, FST values are weighted by their heterozygosity, meaning the sum of the average variances of allele frequencies per locus within and between populations. Hence, each FST value is multiplied by its heterozygosity, and these products are summed. The total is divided by the sum of heterozygosity across all loci. Next, coalescent simulations under a simple island model as the underlying demographic process are conducted based on the estimated average FST value. Finally, the quantiles of the simulated data sets are calculated, and loci with FST values above the 0.975 quantile for their heterozygosity are expected to indicate positive selection (outlier), whereas loci with FST values below the 0.025 quantile are assumed to be under balancing selection. Using the software LOSITAN, Antao et al. (2008) introduced a graphical user interface (GUI) for the FDist approach. In addition, further modifications to obtain more precise neutral FST value estimates and a better fit of the neutral distribution to the average FST value were included (Antao et al., 2008). Excoffier et al. (2009) combined the FDist approach (Beaumont & Nichols, 1996) with a hierarchical island model, which resulted in improved outlier detection for hierarchically structured populations. The method was implemented in the software Arlequin (Excoffier & Lischer, 2010). BayeScan (Foll & Gaggiotti, 2008; Fig. 19) Principle: A Bayesian framework is applied to evaluate whether each locus is affected by selection. Using a reversible-jump Markov chain Monte Carlo (MCMC) approach, different model parameters are explored by jumping between a model including and excluding selection. The probability of the different models to explain the data is estimated. Figure 19. View largeDownload slide Calculation process of the software BayeScan by Foll & Gaggiotti (2008). Figure 19. View largeDownload slide Calculation process of the software BayeScan by Foll & Gaggiotti (2008). Requirements: Allele frequency data per population from multiple populations and multiple loci. The next test based on the population differentiation described here was developed by Foll & Gaggiotti (2008). For the remainder of this review, we only considered the described implementation for co-dominant markers because most modern population genetic or genomic studies are based on SNPs or longer DNA sequences. However, the method can also be used for dominant markers, such as amplified fragment length polymorphisms (AFLPs), but the conceptual framework is slightly different (Foll & Gaggiotti, 2008). In the Bayesian approach, called BayeScan, the model consists of three parts. First, the ancestral allele frequency (p) distribution is generated using an uninformative Dirichlet prior, which states that all ancestral allele frequencies are equally likely. It is based on the assumption that the current populations share a common historical migration pool from one ancestral population, which was not substructured. The assumption applies to a wide range of neutral demographic models (Beaumont, 2005). Second, to simulate demography, population-specific effects (β) are applied that influence the allele frequencies of all loci, leading to the overall population differentiation. Third, locus-specific effects (α) are included. They increase or decrease the genetic differentiation resulting from the population-specific effect at a specific locus. For neutral loci, the population-specific effects (β) are sufficient to explain their diversity patterns. For loci under selection, which are not only influenced by population-specific factors, such as changes in effective population size, additional locus-specific effects (α) are required as explanatory variables. Per generation of the MCMC process, the model of the previous generation is used to estimate new model parameters. The process is subdivided in parameter exchanges in the model and comparisons of likelihoods. Population-specific effect (β). The likelihood of the model including a different value for β relative to the model of the previous generation is calculated for the first population. To decide whether the new model with the changed parameter is accepted over the model from the previous generation, a random value from a uniform distribution (calibrated in the pilot runs) is taken, and the difference in the likelihood of the new model relative to the model of the previous generation has to be larger than the random value. If it holds true, the new value of β is accepted as part of the new model. Otherwise, the old value of the population-specific effect is used in the new model. Processes 1a and 1b are repeated for each population. The ancestral allele frequencies (pi) of each locus are updated in a similar way to the population-specific effects using the model resulting from process 1 as the old model. For the locus-specific effect (α), different approaches are used depending on whether a value is specified for a locus in the model of the previous generation (and thus of 2) or not. In both cases, the model including α (assuming selection) is tested against a model excluding α (neutral model). The continuous comparison of models with and without certain parameters in a Bayesian framework is called reversible-jump MCMC. If α is not part of the model from the previous generation for a locus, a new value is suggested and drawn from a Gaussian distribution. The likelihoods of the new (including α) and old model (without α) are compared. Here, the prior odds, which can be specified by the user, are included, stating that the model including α has to be at least the prior odds value times more likely than the model excluding α. If this is the case, α is included in the final model of the present generation; otherwise, it is excluded. If α is part of the model from the previous generation for a locus, an alternative value is suggested for α and, similar to processes 1 and 2, is tested against the old value of α. Next, the new model (regardless of whether the new α value was accepted or not) is compared with a model excluding α. Similar to 3a, depending on the differences of the likelihoods of the model including and excluding α and the defined prior odds, the locus-specific effect is part of the final model for a certain locus of the present generation. The defined burn-in and thinning interval specify the number of MCMC sampling generations. The statistics are calculated only from the set of models rather than from the models of all generations. Here, all generations of the burn-in are excluded from the sampling. Then, every xth generation (thinning) is sampled. The total number of generations is defined by the thinning interval multiplied by the defined sample number plus the burn-in. When the sampling process is finished, different statistics are calculated for each locus from the final subset of models. First, the posterior probability of a locus states how often the model including the locus-specific effect was accepted relative to all models in the final sampling set. Thus, a high posterior probability indicates a strong favour of the models including selection over the neutral models. Next, the q-value states below which FDR threshold the locus will be significantly identified as an outlier. Furthermore, the mean value of the locus-specific effects (α) is given for each locus. Additionally, using all α and β values, the average differentiation of each population to the ancestral population is calculated over all loci. Extended Lewontin and Krakauer test, FKL (Bonhomme et al., 2010; Fig. 20) Principle: The FLK method calculates a population differentiation statistic, which incorporates a kinship matrix representing the relationship between populations. Figure 20. View largeDownload slide Calculation process of the extended Lewontin and Krakauer (FLK) test described by Bonhomme et al. (2010). Figure 20. View largeDownload slide Calculation process of the extended Lewontin and Krakauer (FLK) test described by Bonhomme et al. (2010). Requirements: Allele frequency data per population from multiple populations and multiple loci. Outgroup data can be used. Data of known neutral loci can be used to generate neutral expectations. Bonhomme et al. (2010) developed the FLK test (extended Lewontin and Krakauer test). Its underlying neutral demographic model is based on the assumption that the splitting of a population generates two new populations. These two populations are expected each to have the same effective population size as the ancestral population (Xu, Atchley & Fitch, 1994). In the model, no migration is assumed between the two populations, and only genetic drift leads to changes in the allele frequencies; thus, the model can be represented by a population tree (Bonhomme et al., 2010). To compute the test statistics, the allele frequencies are used to calculate Reynolds’ genetic distance (Reynolds, Weir & Cockerham, 1983), which is then transferred into a population tree using the neighbour-joining algorithm (Saitou & Nei, 1987). The process can include an outgroup to root the tree, or midpoint rooting is performed if no outgroup is included in the data set. In the next step, the tree is used to generate a kinship matrix (F). Therefore, only that part of the tree with the populations of interest (excluding the outgroup, if part of the tree) is used. Per population, the F value (e.g. FPop1) is specified by adding together the length of all branches from the root of the reduced tree to the population. For population comparisons (e.g. fPop1,Pop2), the length of all branches that are shared between the two populations are summed up. Similar to the Lewontin–Krakauer test (Lewontin & Krakauer, 1973), the allele frequencies of the data set are now used to generate an FST-related statistic per locus, the FLK value. However, in the current test, the kinship matrix is included in the test statistic to correct for the assumed underlying demographic model. The resulting FLK values are assumed to be χ2 distributed, with the degrees of freedom defined by the number of populations used to build the kinship matrix minus one, or minus two if an outgroup is used. Using the χ2 distribution, a P-value can be assigned to each FLK value. If a large set of neutral loci is available, the FLK test allows an empirical FLK value distribution to be generated. Thus, the kinship matrix is estimated from the large data set, in a similar way as described above. Then, forward simulations are used to generate a large set of allele frequencies. Therefore, the effective population size and the split times of the simulation are chosen to result in allele frequencies that would generate the identified kinship matrix. Next, the simulated allele frequencies are used together with the kinship matrix to calculate the empirical FLK distribution with assigned confidence intervals. Here, the FLK values are analysed relative to the heterozygosity of the according simulated locus, comparable to the statistics based on Beaumont & Nichols (1996). Finally, the allele frequencies of a test data set, which includes loci potentially under selection, are used together with the kinship matrix to generate the observed FLK values. They are compared with the empirical FLK distribution, and loci outside the confidence interval are potentially under selection. HapFKL (Fariello et al., 2013; Fig. 21) Principle: The hapFLK method uses unphased data of multiple populations to determine cluster identities. These identities are then used to calculate a population differentiation statistic, which incorporates a kinship matrix representing the relationship between populations. Figure 21. View largeDownload slide Calculation process of the haplotype-based FLK test (hapFLK) described by Fariello et al. (2013) including the fastphase algorithm of Scheet & Stephens (2006). SNP, single nucleotid polymorphism. Figure 21. View largeDownload slide Calculation process of the haplotype-based FLK test (hapFLK) described by Fariello et al. (2013) including the fastphase algorithm of Scheet & Stephens (2006). SNP, single nucleotid polymorphism. Requirements: Genotypes per individual of multiple populations containing multiple loci with genomic positions. A modification of the FLK test was introduced by Fariello et al. (2013). The new test, called hapFLK, combines FST-outlier detection and haplotype-based selection inference. Therefore, genome-wide data are required, similar to other LD-based selection tests, as well as data from multiple populations. In the first step, the fastphase algorithm (Scheet & Stephens, 2006) is used. It estimates, for each individual at each locus, how likely it is to belong to a certain haplotype cluster given a certain total number of clusters. For the calculation, site- and population-specific model parameters (e.g. recombination rate and cluster frequency) and the cluster probability from the previous site are incorporated. Using an EM algorithm (Dempster et al., 1977), the models are optimized using several iteration steps. Finally, the cluster probabilities are averaged over all individuals of a population at a locus to generate the estimated average cluster frequencies per population. Given that EM algorithms can result in local likelihood maxima rather than in the global maximum (e.g. Wu, 1983), the complete procedure is repeated several times to obtain independent cluster frequency estimates. In the second step, the cluster frequencies resulting from the different fastphase algorithm runs are used independently to calculate the FLK statistics. In these analyses, the cluster frequencies represent the allele frequencies of multi-allele markers. The FLK (Bonhomme et al., 2010) algorithm is used as described above, with some small modifications. Next, the results based on the different independent FLK test calculations are averaged per locus to gain the hapFLK statistics. For the identification of outliers, the hapFLK values are standardised, and P-values as an indication for positive selection are assigned using standard normal distribution. As multiple populations are used in the calculation, it is of great interest to identify the population or populations that show signs of selection. Therefore, a population tree is calculated based on the cluster frequencies/SNP data at a significantly selected locus. The branch lengths of the trees are compared against the population tree calculated from all data using ordinary least squares. Populations experiencing selection are indicated by significantly different branch lengths of the locus tree relative to the whole data tree. Simulation studies Similar to the other two types of tests, population differentiation methods were subject to different simulation studies that aimed to evaluate the effect of, for example, the underlying demographic model or strength of selection on the performance of the methods. A summary can be found in Table 6. A key finding of these studies is that weak selection can hardly be detected by any of the methods (Narum & Hess, 2011; De Mita et al., 2013). However, hapFLK has not been included in such tests to date. Table 6. Summary of simulation study results regarding population differentiation-based methods Parameter FDist + LOSITAN Arlequin (hierarchical FDist) BayeScan FLK Weak selection − − − − Island model − Not tested − − Refugial populations − Not tested − − − Network model Not tested Not tested − Not tested Selfing − 0 − − Population differentiation pattern = selection pattern 0 0 0 Not tested Population differentiation pattern ≠ selection pattern 0 − 0 Not tested Neutral model parameterization − Not tested Not tested + Empirical P-value + Not tested + − Sample size ≥ 25 individuals from ≥ 10 populations Not tested ≥ 30 individuals from ≥ 6 populations Not tested Parameter FDist + LOSITAN Arlequin (hierarchical FDist) BayeScan FLK Weak selection − − − − Island model − Not tested − − Refugial populations − Not tested − − − Network model Not tested Not tested − Not tested Selfing − 0 − − Population differentiation pattern = selection pattern 0 0 0 Not tested Population differentiation pattern ≠ selection pattern 0 − 0 Not tested Neutral model parameterization − Not tested Not tested + Empirical P-value + Not tested + − Sample size ≥ 25 individuals from ≥ 10 populations Not tested ≥ 30 individuals from ≥ 6 populations Not tested Impact on the methods is indicated (0, no impact; −, negative impact; +, positive impact). If a rating was possible among methods, a stronger negative impact is indicated by − −. The results of hapFLK are shown in Table 2. FLK, extended Lewontin and Krakauer test View Large Table 6. Summary of simulation study results regarding population differentiation-based methods Parameter FDist + LOSITAN Arlequin (hierarchical FDist) BayeScan FLK Weak selection − − − − Island model − Not tested − − Refugial populations − Not tested − − − Network model Not tested Not tested − Not tested Selfing − 0 − − Population differentiation pattern = selection pattern 0 0 0 Not tested Population differentiation pattern ≠ selection pattern 0 − 0 Not tested Neutral model parameterization − Not tested Not tested + Empirical P-value + Not tested + − Sample size ≥ 25 individuals from ≥ 10 populations Not tested ≥ 30 individuals from ≥ 6 populations Not tested Parameter FDist + LOSITAN Arlequin (hierarchical FDist) BayeScan FLK Weak selection − − − − Island model − Not tested − − Refugial populations − Not tested − − − Network model Not tested Not tested − Not tested Selfing − 0 − − Population differentiation pattern = selection pattern 0 0 0 Not tested Population differentiation pattern ≠ selection pattern 0 − 0 Not tested Neutral model parameterization − Not tested Not tested + Empirical P-value + Not tested + − Sample size ≥ 25 individuals from ≥ 10 populations Not tested ≥ 30 individuals from ≥ 6 populations Not tested Impact on the methods is indicated (0, no impact; −, negative impact; +, positive impact). If a rating was possible among methods, a stronger negative impact is indicated by − −. The results of hapFLK are shown in Table 2. FLK, extended Lewontin and Krakauer test View Large A major difference in the various methods is the implicitly assumed underlying demographic model. However, it was found to have only a marginal influence on the performance of most methods, regardless of whether the simulated data mirrored the underlying demography of the method or not (Narum & Hess, 2011; De Mita et al., 2013; de Villemereuil et al., 2014; Vatsiou et al., 2016). At the same time, Lotterhos & Whitlock (2014) found that data generated under an island model, which is the underlying demographic model of FDist and part of the assumed model space in BayeScan, lead to only a low detection of true positives using FDist, FLK and BayeScan. On the contrary, De Mita et al. (2013) found detection rates for true positives of up to 100%. However, both studies used different parameters to generate the data. One of the major differences was the imposed selection pressure, which was unequal for the different loci in the study of Lotterhos & Whitlock (2014), in which only a few loci experienced strong selection. Thus, weak selection affecting the majority of the loci could have led to the overall low detection rate. Simulations including refuge populations led to high levels of false positives (> 15%) for BayeScan, whereas they had only minor effects on FDist and the FLK test (Lotterhos & Whitlock, 2014). The high amount of false positives was substantially reduced by increasing the prior odds of BayeScan from the default value of 10 to, for example, 10000 without reducing the number of true positives. As also found for other demographic scenarios, a general increase in the prior odds by some orders of magnitude could improve the reliability of the BayeScan results in studies trying to detect selection. For studies addressing selection on populations in riverine ecosystems, the study of Fourcade et al. (2013) is of high interest. The authors found that the proportion of detected outliers in river organisms is much higher compared with organisms living in other aquatic systems or terrestrial habitats. To validate the observation, they simulated different dispersal scenarios, including those that characterize river systems, by a demographic model with a network structure. The proportion of false positives found using BayeScan was up to 60% of the simulated neutral markers. Overall, a higher number of sampled demes resulted in an increase in the number of false positives. They concluded that the variance of the FST values is inflated by the river network structure relative to the neutral expectation, leading to these high false positive values. Another demographic factor that can potentially influence the detection of positive selection is selfing (De Mita et al., 2013). A negative impact on the detection of outliers was found for all of the tested methods, with the exception of the method of Excoffier et al. (2009). The strength of the influence depended on the underlying demographic model, with a major impact if the data were generated under the island model. The pattern of the environmental gradient forcing positive selection relative to the pattern of neutral differentiation was also tested for its effects on outlier detection (Narum & Hess, 2011; de Villemereuil et al., 2014). If the underlying simulated environmental gradient follows the same pattern as neutral differentiation, stronger differentiation with a similar pattern is assumed at selected loci relative to neutral ones, whereas different patterns between both types of loci are expected otherwise. For the method of Excoffier et al. (2009), only loci under selection showing the same pattern of differentiation as the neutral loci were detected as outliers (Narum & Hess, 2011), whereas BayeScan and FDist were also able to detect selection in cases were both patterns differed (Narum & Hess, 2011; de Villemereuil et al., 2014). To improve population differentiation-based tests, Lotterhos & Whitlock (2014) compared two different methods. First, a set of putatively neutral loci, e.g. loci within non-coding regions, were used to parameterize the neutral null model (neutral parameterization). One example is the calculation of the mean FST value required in FDist by using only neutral loci. However, a reduction in the accuracy occurred if the data did not match the neutral expectations of the island model. The same was found for the optimized mean FST estimation, which is optional in LOSITAN. For the FLK test, neutral parameterization is achieved by using the neutral data set to calculate the kinship matrix. This resulted in a better outlier detection, especially if many selected loci were part of the data set. Second, an empirical P-value can be estimated if a very large set of putatively neutral loci is available. This enables the calculation of test statistics using neutral loci to generate neutral expectations. Then, the putatively selected loci are compared with the null distribution. The approach led to a strong decrease of false positive rates for FDist, BayeScan and FLK, but the number of true positives was also slightly decreased for the FLK test. With real data, however, an accurate estimation of empirical P-values is complicated, because prior knowledge of neutrality is required. Another factor influencing the test accuracy is sample size. Commonly, population differentiation methods are applied to pairs of populations (e.g. Bongaerts et al., 2017; Dennenmoser et al., 2017; Pujolar et al., 2017; Tigano et al., 2017). For BayeScan, sample sizes of 30 individuals from six or more populations each were recommended (Foll & Gaggiotti, 2008). Furthermore, the program was found to have a low power to detect selection if only two populations with high population differentiation were sampled (Foll & Gaggiotti, 2008). Likewise, for FDist, the use of 25 diploid individuals from at least ten subpopulations each was recommended, and the subpopulations should not be adjacent and samples should not be taken repeatedly from populations with correlated alleles (Beaumont & Nichols, 1996). Furthermore, it was shown that application of the FDist algorithm in LOSITAN resulted in high false positive rates if only a few populations and biallelic SNPs were used, particularly at low migration rates (Flanagan & Jones, 2017). In contrast to all other population differentiation-based methods, for hapFLK the genomic position needs to be known, similar to the linkage-based selection test. Therefore, some of its strength and limitations to detect selection are described in the respective section. In short, hapFLK performs well in detecting hard selective sweeps, whereas its power decreases with an increased initial allele frequency at soft sweeps (Fariello et al., 2013; Vatsiou et al., 2016). Complex demographic scenarios did not have a strong influence. Compared with FLK, which does not require information on genomic position, hapFLK was superior if the site under selection was not directly included in the data set. This is commonly the case, e.g. if SNP chips are used or the SNP data sets are generated via reduced representation genomic libraries, such as RADSeq or genotype-by-sequencing (Fariello et al., 2013). If the selected site was included, the FLK test performed better than hapFLK. However, too high marker densities result in a correlation among data, e.g. at very high SNP densities, decreased the power of FLK but did not affect hapFLK as strongly (Fariello et al., 2017). Examples Population differentiation tests do not require information on the genomic position of the analysed markers, besides hapFLK. Thus, the methods were commonly applied to AFLP and microsatellite data, as well as to SNP data sets. As the number of case studies is very high, we focus on studies using SNP data, generated using various methods. Frequently, reduced representation methods, such as RAD (e.g. Cammen et al., 2015; Guo, Li & Merilä, 2016; Bernardi et al., 2016) and its spin-offs such as ddRAD (e.g. Lavretsky et al., 2015; Portnoy et al., 2015; Lal et al., 2016), 2b-RAD (e.g. Galaska et al., 2017; Paterno et al., 2017) or NextRAD (e.g. Bray & Bocak, 2016; Bongaerts et al., 2017), were applied to generate data sets with hundreds to thousands of SNPs. Moreover, RNA sequencing was conducted to generate expression data but also to call SNPs, which were subsequently subjected to population differentiation tests (e.g. Berdan et al., 2015; Eierman & Hare, 2016). If SNPs were already known, as for domesticated animals, or identified by previous candidate gene studies, SNP arrays were applied, ranging from small sets of 96 (e.g. Bekkevold et al., 2016; Pedersen et al., 2017) to tens of thousands of SNPs (Stronen et al., 2015; Berg et al., 2016; Brito et al., 2017). Of course, the necessary data can also be produced by genome resequencing (Wragg et al., 2016; Pinharanda et al., 2017). As no previous genomic knowledge is required for some of the methods used for SNP generation, population differentiation-based methods have been applied to a diverse set of taxa, including corals (e.g. Bongaerts et al., 2017; Thomas et al., 2017), molluscs (e.g. Lal et al., 2016; Van Wyngaarden et al., 2017), crustaceans (e.g. Benestan et al., 2016; Laurent et al., 2016), insects (e.g. Berdan et al., 2015; Onyango et al., 2016), fish (e.g. Gaither et al., 2015; Portnoy et al., 2015), birds (e.g. Shultz et al., 2016; Pan et al., 2017) and mammals (e.g. Cammen et al., 2015; Stronen et al., 2015). As diverse as the set of taxa are the underlying research questions. Common targets of genome scans are genes involved in adaptation to local environments (Portnoy et al., 2015; Stronen et al., 2015; Guo et al., 2016), the formation of ecotypes (Berg et al., 2016; Bernatchez et al., 2016; Ravinet et al., 2016) or speciation (Berdan et al., 2015; Gaither et al., 2015; Bernatchez et al., 2016). Additionally, a wide range of more frequently applied studies used population differentiation-based tests to identity the genetic basis of artificial selection (e.g. Wragg et al., 2016; Purfield et al., 2017), assess the pattern of genetic diversity for conservation management (Carreras et al., 2017; Van Wyngaarden et al., 2017) or identify the origin of captured individuals (e.g. Gilbey et al., 2016; Montes et al., 2017). Typically used programs with their requirements are shown in Table 7. Table 7. Programs commonly applied to calculate population differentiation-based statistics Program Methods Data requirements GUI Platform Link* Arlequin FDist; Excoffier et al. (2009) Genotype data or allele frequency data; multiple populations Yes in Windows Windows, Mac, Linux; project file with settings has to be generated using the GUI version for Windows 1 BayeScan v2.1 BayeScan Allele frequency data; multiple populations No All 2 HapFLK HapFLK; FLK Genotype data; multiple populations; kinship matrix optional; outgroup optional; (genomic position or recombination map; pseudo-positions can be used for FLK) No All (C++ compilation and Python) 3 LOSITAN FDist with modifications (LOSITAN) Genotype data; multiple populations Yes All platforms (Java Web Start application needs Internet connection) can be compiled 4 PopGenome R package BayeScan Phased or unphased genotype data; multiple population; genomic pseudo-positions can be used No All (R) 5 Program Methods Data requirements GUI Platform Link* Arlequin FDist; Excoffier et al. (2009) Genotype data or allele frequency data; multiple populations Yes in Windows Windows, Mac, Linux; project file with settings has to be generated using the GUI version for Windows 1 BayeScan v2.1 BayeScan Allele frequency data; multiple populations No All 2 HapFLK HapFLK; FLK Genotype data; multiple populations; kinship matrix optional; outgroup optional; (genomic position or recombination map; pseudo-positions can be used for FLK) No All (C++ compilation and Python) 3 LOSITAN FDist with modifications (LOSITAN) Genotype data; multiple populations Yes All platforms (Java Web Start application needs Internet connection) can be compiled 4 PopGenome R package BayeScan Phased or unphased genotype data; multiple population; genomic pseudo-positions can be used No All (R) 5 Data requirements only required for some methods of a program are placed in parenthesis. Data requirements of the program can differ from the requirements of the statistical test. FLK, extended Lewontin and Krakauer test; GUI, graphical user interface. *Links: (1) http://cmpg.unibe.ch/software/arlequin35/Arlequin35.html; (2) http://cmpg.unibe.ch/software/BayeScan; (3) https://forge-dga.jouy.inra.fr/projects/hapflk; (4) http://popgen.net/soft/lositan; (5) https://cran.r-project.org/web/packages/PopGenome/index.html. Last access to all links: 23.02.2018. View Large Table 7. Programs commonly applied to calculate population differentiation-based statistics Program Methods Data requirements GUI Platform Link* Arlequin FDist; Excoffier et al. (2009) Genotype data or allele frequency data; multiple populations Yes in Windows Windows, Mac, Linux; project file with settings has to be generated using the GUI version for Windows 1 BayeScan v2.1 BayeScan Allele frequency data; multiple populations No All 2 HapFLK HapFLK; FLK Genotype data; multiple populations; kinship matrix optional; outgroup optional; (genomic position or recombination map; pseudo-positions can be used for FLK) No All (C++ compilation and Python) 3 LOSITAN FDist with modifications (LOSITAN) Genotype data; multiple populations Yes All platforms (Java Web Start application needs Internet connection) can be compiled 4 PopGenome R package BayeScan Phased or unphased genotype data; multiple population; genomic pseudo-positions can be used No All (R) 5 Program Methods Data requirements GUI Platform Link* Arlequin FDist; Excoffier et al. (2009) Genotype data or allele frequency data; multiple populations Yes in Windows Windows, Mac, Linux; project file with settings has to be generated using the GUI version for Windows 1 BayeScan v2.1 BayeScan Allele frequency data; multiple populations No All 2 HapFLK HapFLK; FLK Genotype data; multiple populations; kinship matrix optional; outgroup optional; (genomic position or recombination map; pseudo-positions can be used for FLK) No All (C++ compilation and Python) 3 LOSITAN FDist with modifications (LOSITAN) Genotype data; multiple populations Yes All platforms (Java Web Start application needs Internet connection) can be compiled 4 PopGenome R package BayeScan Phased or unphased genotype data; multiple population; genomic pseudo-positions can be used No All (R) 5 Data requirements only required for some methods of a program are placed in parenthesis. Data requirements of the program can differ from the requirements of the statistical test. FLK, extended Lewontin and Krakauer test; GUI, graphical user interface. *Links: (1) http://cmpg.unibe.ch/software/arlequin35/Arlequin35.html; (2) http://cmpg.unibe.ch/software/BayeScan; (3) https://forge-dga.jouy.inra.fr/projects/hapflk; (4) http://popgen.net/soft/lositan; (5) https://cran.r-project.org/web/packages/PopGenome/index.html. Last access to all links: 23.02.2018. View Large DISCUSSION Tests for positive selection can deliver no, few or hundreds of candidate markers. The question is, how reliable are these results? Does the failure to identify candidate loci reveal the absence of local adaptation, and do high numbers of candidate loci indicate strong positive selection? To address these questions, it is of crucial importance to understand the reliability of the different test statistics. This will be discussed in the first section of the Discussion. In the second section, we outline strategies for subsequent candidate marker validation. Finally, we end with a short conclusion and outlook summarising the key points identified in this review. Reliability of the Results from Tests for Positive Selection The reliability of screens for signatures of positive selection not only depends on the requirements described above but is also influenced by the underlying assumptions of the different statistical tests. Applying tests in conditions that explicitly violate the underlying assumptions can make the tests useless. For example, if the time since the onset of selection, and thus the beneficial allele frequency, is in the wrong range for the test, selection cannot be identified (Fig. 3). Violating the underlying demographic assumptions or an inadequate sampling scheme can also result in many false positives. The consequences of these biases affect both the conceptual and the practical level. Failing to identify loci under selection can lead to the misinterpretation of population history and incorrect results. Besides incorrect scientific inferences, incorrectly identified loci under selection (false positives) can produce high follow-up costs if candidate loci are subsequently studied experimentally. It is important to consider the scale, even for a moderate FPR of 5%. As genome-wide inferences are typically made with high-throughput data, meaning that thousands of loci are analysed, an FPR of 5% can result in up to several hundred incorrectly identified loci. A possible solution to circumvent misidentification is the combination of several test statistics with different characteristics. One example is the DH test (Zeng et al., 2006), which combines two tests from the SFS category. It integrates the comparison of low- to intermediate-frequency alleles based on Tajima’s D (Tajima, 1989) with the high- to intermediate-frequency comparison based on Fay & Wu’s H (Fay & Wu, 2000). Both high- and low-frequency alleles are assumed to be sensitive to alternative confounding factors, and the combination was shown to be less sensitive then the individual tests (Zeng et al., 2006, 2007a). Alternatively, tests from different categories can be combined as suggested by Grossman et al. (2010). Their approach joins the LD-based tests iHS (Voight et al., 2006) and XP-EHH (Sabeti et al., 2007) with an estimation of the FST value and two additional tests. The different statistics were found to be almost uncorrelated in neutral genomic regions and weakly correlated at neutral loci within selected regions. At the selected site and at tightly linked neutral loci, all tests indicated selection for the settings used. Thus, Grossman et al. (2010) implemented all five tests in a composite likelihood statistic. However, the test requires the simulation of data under neutral assumptions to compute likelihood tables (Utsunomiya et al., 2013). Additional knowledge about the population history is needed to generate a calibrated demographic model, which is probably unavailable for most species. Therefore, an alternative approach was described by Utsunomiya et al. (2013) using iHS (Voight et al., 2006), Rsb (Tang et al., 2007) and two other tests. Rather than building a composite likelihood ratio, the P-values of the individual tests were combined in a meta-analysis. Ma et al. (2015) developed another modification of the idea by Grossman et al. (2010). Rather than computing likelihood tables, the test accounts for the correlation of the different statistics by a correlation factor using neutral simulations. All three methods assume that the combined tests indicate selection for the same loci. In contrast, the method of González-Rodríguez et al. (2016) explicitly assumes that different tests detect different patterns of selection and thus other loci. They combined the results of 11 test statistics in a factorial analysis, and loci with exceptionally high values in one of the resulting three canonical axes were assumed to be under selection. Nonetheless, how different confounding factors influence the summary statistics remains to be tested for all four tests. Besides the overall reliability of the results, another insecurity in the outcome of tests for positive selection is the exact location of the selected site. As alleles at neutral sites are subject to genetic hitchhiking along with the beneficial allele, variability patterns similar to the selected site can arise in its proximity. The accuracy of the exact location of the selected site differs for the individual tests (Grossman et al., 2010). An important point to consider when it comes to assigning function to the identified loci potentially under selection, e.g. via ontology searches, is that the selected site may not necessarily be part of the analysed sites. Sequencing only a subset of variants, e.g. by using SNP chips or by reducing the genomic complexity with methods such as RADSeq, may have led to the inclusion of only neighbouring sites rather than the selected site itself. Additionally, if the time of sampling is after the fixation of the beneficial allele, it cannot be detected as a variable in single population studies. Validation of Positive Selection Owing to the uncertainties discussed above, the identified sites under positive selection cannot be taken for granted, but further validation is required. A first step could be the critical re-evaluation of data quality, because poor-quality reads can mimic patterns of positive selection (e.g. Taberletet al., 1999; Mallick et al., 2009). Likewise, an ascertainment bias can result in modified diversity patterns and high FPR (Nielsen et al., 2005; Kelley, 2006; Thornton & Jensen, 2007). An ascertainment bias occurs when the set of SNPs for the analyses is selected based on a small data set, for example not including all populations, which is then used to genotype larger data sets, e.g. by using chip-based SNP inference (Clark et al., 2005). If the ascertainment process is known, the data can be at least partly corrected against biases (e.g. Nielsen, 2004; Clark et al., 2005). After a thorough check of the data quality (e.g. Phred quality score, minimal locus coverage per individual, minor allele frequency per locus or minimal number of individuals sequenced for a locus) and the exclusion of disturbing factors, such as ascertainment biases, potential functions of the loci under selection can be characterized. Therefore, not only the locus itself but also the genomic regions surrounding the candidate loci should be taken into account. If a reference genome is available, the loci can be mapped against a functionally annotated genome (e.g. Besnier et al., 2014; Gutierrez et al., 2016; Laporte et al., 2016; Ravinet et al., 2016). Alternatively, if no reference genome is available and only short DNA fragments for a fraction of the genome were sequenced, as in the RADSeq approaches, a homology search can be conducted with Blast (Altschul et al., 1990), as performed by Bourret et al. (2013). Identified genes present in the candidate regions can be compared against databases that hold information about gene functionality, such as Gene Ontology (GO; Ashburner et al., 2000), Swiss-Prot (The UniProt Consortium, 2015) or InterPro (Mitchell et al., 2015). The resulting hits can be inspected descriptively for any enrichment. However, the enrichment could be biased by the complete data set rather than the candidate regions. Therefore, either a random subset (Ravinet et al., 2016) or the complete data set (Bourret et al., 2013; Pujolar et al., 2015; Laporte et al., 2016) should be processed in the same way as the candidate loci. The list of candidate regions can be compared against the resulting lists from the neutral loci and tested for significant enrichment of certain pathways in the candidate regions. Although the indication of selection acting on several genes with the same functionality is a strong hint, negative results do not necessarily indicate false positive candidate loci. First, a mutation in a single locus could lead to a selective advantage rather than multi-gene selection. Alternatively, mutations in non-protein-coding regions, which are involved in the regulation of gene expression, for example, can also lead to selective advantages (Andolfatto, 2005). In general, tests for functional enrichment have to be used with caution, because false positives indicating an enrichment can still be interpreted to make biological sense (Pavlidis et al., 2012). Besides further testing of the candidate loci using bioinformatic tools, resequencing of promising candidate loci can yield insights into their quality (e.g. Schweizer et al., 2016); however, this means additional time and cost efforts. First, intrinsic problems of the genotype methods, such as allele dropout attributable to mutations in the restriction site for RADSeq methods, can lead to incorrect estimations of genetic diversity (Gautier et al., 2013; Schweyen et al., 2014). Resequencing of candidate regions using alternative approaches could be used to rule out these effects. Additionally, fine mapping of genomic regions can help to identify the causative mutation. This was done, for example, in the study by Chan et al. (2010), revealing an enhancer rather than the assumed candidate gene itself to be under selection. Additionally, further sampling efforts of more populations can be used to eliminate false positives if the pattern of evolution is replicated among the populations owing to the same selective force (Hohenlohe et al., 2010). Furthermore, sampling multiple time points can be especially valuable to obtain insight into changes owing to selective sweeps (Bank et al., 2014). The final validation of the effect of candidate loci can be achieved by experimentally proving their influence on fitness (see review by Vitti et al., 2013). This can be done by creating transgenic organisms, for example (e.g. Chan et al., 2010). Although these tools were mainly applicable to model species, new progress in the field of gene editing, such as the CRISPR-Cas9 system, will probably open up the applications to non-model species (Huang et al., 2016). Conclusions Test statistics from three different categories were introduced, explained and critically discussed in this review: LD-based tests, SFS-based tests and population differentiation-based tests. All tests of one category analyse a similar characteristic change in genetic diversity caused by positive selection. However, the tests differ in their underlying assumptions and thus in their data requirements and results. Some of the tests require additional data, such as recombination maps, which can hardly be provided for many non-model organisms. To generate these data, it is an advantage if the analysed organisms can either be bred in the laboratory or if the exact relationships between the different individuals can be examined easily. Incorrect settings and assumptions can lead to high FPR and low power for all tests. Hence, we argued that a basic understanding of the different test statistics is of pivotal importance to design molecular evolutionary and ecological studies. Owing to the potentially high error rates, the recovered candidate loci should be subjected to additional analyses before accepting them to be under positive selection. Some small steps leading to greater confidence, such as improving the statistical design needed for certain tests or a posteriori double-checking of sequencing quality, can be conducted easily. Other steps, such as experimental validation, are time, labour and money intensive. They will probably be performed in follow-up studies only if a well-validated candidate locus is of high interest. ACKNOWLEDGEMENTS We thank two anonymous referees for their helpful comments on this review paper. H.W. and F.L. are supported by a grant from the Kurt Eberhard Bode Foundation (GeneStream). REFERENCES Alachiotis N , Pavlidis P . 2016 . Scalable linkage-disequilibrium-based selective sweep detection: a performance guide . GigaScience 5 : 7 . Google Scholar CrossRef Search ADS Alachiotis N , Stamatakis A , Pavlidis P . 2012 . 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Detecting signatures of positive selection in non-model species using genomic data