Abstract
Most of our understanding of the genetic basis of human adaptation is biased toward loci of large phenotypic effect. Genome wide association studies (GWAS) now enable the study of genetic adaptation in highly polygenic phenotypes. Here we test for polygenic adaptation among 187 worldwide human populations using polygenic scores constructed from GWAS of 34 complex traits. By comparing these polygenic scores to a null distribution under genetic drift, we identify strong signals of selection for a suite of anthropometric traits including height, infant head circumference (IHC), hip circumference (HIP) and waist-to-hip ratio (WHR), as well as type 2 diabetes (T2D). In addition to the known north-south gradient of polygenic height scores within Europe, we find that natural selection has contributed to a gradient of decreasing polygenic height scores from West to East across Eurasia, and that this gradient is consistent with selection on height in ancient populations who have contributed ancestry broadly across Eurasia. We find that the signal of selection on HIP can largely be explained as a correlated response to selection on height. However, our signals in IHC and WC/WHR cannot, suggesting a response to selection along multiple axes of body shape variation. Our observation that IHC, WC, and WHR polygenic scores follow a strong latitudinal cline in Western Eurasia support the role of natural selection in establishing Bergmann’s Rule in humans, and are consistent with thermoregulatory adaptation in response to latitudinal temperature variation.
One Sentence Summary Natural selection has lead to divergence in multiple quantitative traits in humans across Eurasian populations.
Main Text
Decades of research in anthropology have identified anthropometric traits that show potential evidence of biological adaptation to climatic conditions as humans spread around the world over the past hundred thousand years.1,2,3 However, it can be challenging to rule out environmental,4,5 as opposed to genetic variation, as the primary cause of these phenotypic differences.6 Even for pheno-types where there is some confidence that some of the phenotypic differences among populations are due in part to genetic differences, it is often hard to rule out genetic drift as an alterative explanation to selection.7,8,9 The development of population-genetic methods and genomic data resources during the last few decades has enabled the interrogation of adaptive hypotheses and has produced an expanding list of examples of plausible human adaptations.10,11 However, such approaches are often inherently limited to detecting adaptation in genetically simple traits via large allele frequency changes at a small number of loci, whereas many adaptations likely involve highly polygenic traits and so are undetectable by most approaches.12,13 Genome-wide association studies (GWAS) have now identified thousands of loci underlying the genetic basis of many complex traits.14,15,16 These studies offer an unprecedented opportunity to identify adaptation in recent human evolution by detecting subtle shifts in allele frequencies compounded over many GWAS loci.17,18,19,20,21,22,23
We conducted a broad screen for evidence of directional selection on variants that contribute to 34 polygenic traits by studying the distribution of their allele frequencies in dataset of 187 human populations (2158 individuals across 161 populations from the Human Origins Panel24 and 2504 individuals across 26 populations of the 1000 Genomes phase 3 panel25), making use of prior large-scale GWAS for these traits (see Table S1). We divided the genome into 1700 non-overlapping and approximately independent linkage blocks26 and choose the SNP with the highest posterior probability of association within the block.27,28 For each trait, we calculate a polygenic score for each population as a weighted sum of allele frequencies at each of these 1700 SNPs, with the GWAS effect sizes taken as the weights. Figure 1 shows the distribution of these scores for height across our population samples.
These polygenic scores should not be viewed as phenotypic predictions across populations. For example, the Maasai and Biaka pygmy populations have similar polygenic scores despite having dramatic differences in height.29 Discrepancies between polygenic scores and actual phenotypes may be expected to occur either because of purely environmental influences on phenotype, as well as gene-by-gene and gene-by-environment interactions. We also expect that the accuracy of these scores when viewed as predictions should decay with genetic distance from Europe (where the GWAS were carried out), due to changes in the structure of linkage disequilibrium (LD) between causal variants and tag SNPs picked up in GWAS, and because GWAS are biased toward discovering intermediate frequency variants, which will explain more variance in the region they are mapped in than outside of it. These caveats notwithstanding, the distribution of polygenic scores across populations can still be informative about the history of natural selection on a given phenotype,18 and a number of striking patterns are visible in their distribution. For example, there is a strong gradient in polygenic height scores running from east to west across Eurasia (Figure 1)
To explore whether patterns observed in the polygenic scores were caused by natural selection, we tested whether the observed distribution of polygenic scores across populations could plausibly have been generated under a neutral model of genetic drift. To understand this null model, consider that a neutrally evolving allele is expected to be at the same frequency in a set of independently evolving sub-populations. However, due to genetic drift, sub-populations will deviate from this frequency, with the variance of the sub-population frequencies given by FSTp (1 – p) where p is the ancestral allele frequency, and FST is Wright’s “fixation index,”30 which can be measured from genome-wide data.17,31 Our polygenic scores sum the additive contributions of a large number of unlinked loci, which under our null model will experience genetic drift independently. Therefore, under a model of genetic drift, the polygenic score of each of a set of independent sub-populations will be normally distributed, with variance of VAFST (here, VA is the additive genetic variance of polygenic scores the ancestral population). Our test is based on a generalization of this simple relation in which we account for both variance and covariance among multiple populations that exhibit non-independence due to common descent, migration, and admixture over the history of human evolution. Specifically, we model the joint distribution of polygenic scores as multivariate normal and use a generalized variance statistic (QX) to measure the over-dispersion of polygenic scores relative to the neutral prediction, which is taken as evidence in favor of natural selection driving difference among populations in polygenic scores (see Methods and our previous study18 for details). Our approach is similar to classic tests of adaptation on phenotypes measured in common gardens, which rely on comparisons of the within and among-population additive genetic variance for phenotypes and neutral markers, i.e. QST/FST comparisons.32,33,34 Importantly, the neutral distribution we derive holds independent of whether the loci truly influence the trait in an additive manner (with respect to each other or the environment), and whether the GWAS loci are truly causal or merely imperfect tags. However, population structure in the original GWAS panels can confound signals of polygenic adaptation.18,20 Modern methods are generally considered to be effective at controlling for the effects of population structure,35 and we proceed assuming that it has been adequately accounted for in the original GWAS panels.
We applied our test to each of the 34 traits across all populations, as well as within nine restricted regional groupings (Figure 2 and Table S3). Using our test across all populations as a general test for the impact of selection anywhere in the dataset, we find 5 signals of selection after controlling for multiple testing (p < 0.05/34). The traits involved include height, infant head circumference (IHC), hip circumference (HIP), waist-hip ratio (WHR), and type 2 diabetes (T2D). Although the sixth-strongest signal, waist circumference (WC), failed to meet the multiple-testing correction, we include it in subsequent analyses due to its obvious connection to WHR. We also found signals of selection on polygenic scores constructed for waist and hip circumference and waist-hip ratio when adjusted for BMI (Table S3), but we focus on the unadjusted versions for ease of interpretation. We do not replicate a previously reported signal of selection on BMI within Europe, but also note that the previous study used many more SNPs than we have in constructing polygenic scores, which likely explains the difference.20 In each case of significant over-dispersion, the signal represents a small but systematic shift in allele frequency of a few percent across many loci, which would be undetectable by standard population-genetic tests for selection (see Table S6), such that the majority of the variance in polygenic scores is within populations as opposed to among populations (see Table S4).
The predominantly European ascertainment of GWAS loci can lead to apparent deviations from neutrality. Therefore all p values in Figure 2 and throughout the paper are derived from comparing test statistics against frequency-matched empirical controls, unless otherwise stated (see Text S1.3). This empirical matching is an important control. For example, the distribution of polygenic scores for Schizophrenia show a signal of over-dispersion under the naive null hypothesis, but not after controlling for the effects of ascertainment. More generally, the ascertainment and selection against disease phenotypes pose difficulties for the interpretation of tests of differentiation. Thus, although we see a signal of selection for decreased T2D polygenic scores in Europe, the interpretation of this signal likely requires the development of more explicit models of selection on disease traits (section S1.4).
The Geography of Selection on Height
In addition to the known signal of a gradient of increased polygenic height score in northern Europeans relative to southern Europeans (latitude correlation within Europe p = 6.3 × 10−6, see S2 and Methods for statistical details),17,18,19,20,36 we also find evidence that that natural selection has impacted polygenic height scores well outside of modern Europe. Polygenic height scores decline sharply from west to east across Eurasia in a way that cannot be predicted by a neutral model (longitude correlation across Eurasia, p = 4.46 × 10−15; Figure 1), and they are overdispersed within each of our four population clusters (north, south/central, east, and west) across Asia, as well among Native Americans (Figure 2). A natural question is whether this broadly Eurasian signal represents multiple independent episodes of selection on the genetic basis of height, or ancient selection on one or just a few populations, with modern signals across Eurasia reflecting variation in the extent to which modern populations derive ancestry from these ancient populations. For example, the signal of selection on height in East Asia is driven entirely by the Tu population sample (p = 0.4329 after they are removed), who have the highest polygenic height score among East Asian samples. Does this unusually high polygenic score reflect recent selection, or the fact that the Tu derive a proportion of their ancestry from an ~800-year-old admixture event involving a population resembling modern Europeans37?
To test whether the height signal within Asia is due to a selective event shared with Europeans, we predicted the polygenic height scores across Asia given the deviation of European populations from the Asian mean, and each of the Asian sample’s genome-wide relationship to the European samples (see Figure 3, and Methods for details). We find that this prediction conditioned on Europeans are sufficient to explain most the divergence between the Tu and the other East Asian populations in our dataset (see sky blue dots in Figure 3), and eliminate the signal of selection among East Asian populations (p = 0.099 after conditioning). In fact, all signals of differential selection on height across Asia can be eliminated using these conditional predictions (p = 0.2019 after conditioning). This suggests that most of the selected divergence in our polygenic height scores across Eurasia can be attributed either to events which are predominantly ancestral to modern Europeans (but which have impacted other regions via admixture), or which lie along an early lineage which has contributed ancestry broadly across Eurasia.
To further investigate the history of selection on height, we examined polygenic height scores in a set of ancient DNA samples from Western Eurasia19,38,39 (for more detail see Text S1.5, Figure S9, and Figure S10). We find that the Eurasian selective gradient in genetic height scores was long established, with many ancient Western Eurasian population samples (particularly those with significant hunter-gatherer or Yamnaya steppe ancestry) having significantly greater polygenic height scores than modern East Asian populations in our dataset (e.g. Yamnaya-Samara vs Han Chinese pairwise p = 0.011). In fact, European hunter-gatherer samples appear to have significantly higher polygenic height scores than any modern European population (e.g. CEU vs Caucasus hunter-gatherers pairwise p = 0.017 and CEU vs Western European hunter-gatherers pairwise p = 0.007, see Text S1.5). Our results do not support Mathieson and colleagues’19 suggestion of selection for reduced height in Iberian Neolithic samples relative to Anatolian Neolithic (p = 0.90, with the Iberians actually having a higher score than the Anatolians, see also40). Our results seem most consistent with the idea there was selection for increased height in the history of the yamnaya and hunter-gatherer populations, and that modern signals of divergence result from variation in the proportion of this ancestry that has been inherited across the continent.
Selection on Body Shape Polygenic Scores
As four out of the next five strongest signals beyond height also represent anthropometric traits, we focus the remainder of our efforts on these phenotypes. Due to genetic correlations between traits, it is possible that signals of selection on two (or more) distinct phenotypes actually represent only a single episode of selection, where one trait responds indirectly to selection on the correlated trait. Because the genetic correlation with height varies among these phenotypes (HIP: r = 0.39, IHC: r= 0.268, WC: r = 0.22, and WHR: r = –0.08),41,42 we expect a priori that signals for more tightly correlated phenotypes are more likely due to a correlated response to selection on height, whereas for example the WHR signal is more likely to be independent.
To test whether the new signals we observe represent selective events distinguishable from the height signal, we developed a multi-trait extension to our null model based on the quantitative-genetic multivariate-selection model of Lande and Arnold43 (see Methods and Supplementary Text Section S1.6). We condition on the observed polygenic height scores, and test whether the signal of selection on a second trait is still significant after accounting for a genetic correlation with height (a non-significant p-value is consistent with a correlated response to selection on height). Applying this test to our entire panel of populations, we find that conditioning on height ablates much of the signal for HIP (p = 0.0186) and WC (p = 0.0059), whereas signals in IHC (p = 1.11 × 10−5) and WHR (p = 3.57 × 10−8) are less affected. Restricting to European populations only, height is better able to explain HIP (p = 0.1152), WC (p = 0.0104), and IHC (0.0051) signals, while the signal of selection on WHR remains strong even after conditioning on height (p = 1.92 × 10−8). WHR is genetically correlated with HIP (r = 0.316) and WC (r = 0.729), but not with IHC (r = 0.01).41,42 Conditioning on WHR is sufficient to explain WC (global p = 0.1523, Europe p = 0.5178), but signals in HIP, IHC, and height are all independent of WHR (Table S4). Together, these results suggest that we can distinguish the action of natural selection along a minimum of two phenotypic dimensions (i.e. height and WHR, or unmeasured phenotypes closely correlated to them). The signal of selection observed for HIP is likely due to selection on height, and the WC signal is probably due to selection on a combination of height and WHR (or closely correlated phenotypes; we provide additional evidence for this claim in supplement section S1.6.2). Whereas IHC shows some evidence of being influenced by selection on height, a correlated response to height seems not to fully explain this signal.
Signals of divergence for both IHC and WHR polygenic scores are confined mostly to Europe and West Asia. For both traits the null model gives a significantly improved fit to the data when conditioned on Europe to explain West Asia and similar when conditioning on West Asia to explain Europe (Table S5). This suggests that, as is the case for Eurasian height scores, a substantial fraction of the divergence in IHC and WHR polygenic scores among modern populations across western Eurasia reflects divergence among ancient populations and subsequent mixture rather than recent selection.
Bergmann’s Rule and Thermoregulatory Adaptation
For both IHC and WHR, the selective signal in Western Eurasia can be captured in large part by strong, positive latitudinal clines (p = 3.16 × 10−15 for IHC and p = 3.16 × 10−7 for WHR; Figure 5). These clines in polygenic scores support independent phenotypic evidence for larger and wider bodies and rounder skulls at high latitudes,44,1,45,2,46,47,3 consistent with Bergmann’s Rule,48,49 and add genetic support for a thermoregulatory hypothesis for morphological adaptation, whereby individuals in colder environments are thought to have adapted to improve heat conservation by decreasing their surface area to volume ratio.
A broad range of selective mechanisms have been proposed to act on height variation.50 Because we do not detect any signal of selection on age at menarche, we think it unlikely that the height signal represents a correlated response due to life-history mediated selection on age at reproductive maturity.51 It has also been suggested that selection on height may be explained as a thermoregulatory adaptation.50 However, because the surface area to volume ratio is approximately independent of height,52,2 the effect of height SNPs on this ratio is mediated almost entirely through their effect on circumference (hip and/or waist; see section S1.8). Because the signal of selection on height cannot be explained by conditioning on hip and waist circumference, it seems that the thermoregulation hypothesis cannot fully explain the signal of selection on height.
A second eco-geographic rule relevant to height is Allen’s rule,53 which predicts relatively shorter limbs in colder environments, again consistent with adaptation on the basis of thermoregulation. In support of this, human populations in colder environments are observed to have proportionally shorter legs, compared to those in warmer environments.45,54 However, we detect no signal of selection on polygenic scores for the ratio of sitting to standing height (SHR); a measure of leg length relative to total body height.55 Indeed, by combining our height SNPs with their effect on SHR, we find a strong signal that both increases in leg length and torso length underlie the selective signal on height from North to South within Europe, and from East to West across Eurasia (see S1.9). This again suggests that thermoregulatory concerns are unlikely to fully explain signals of selection for height.
Discussion
The study of polygenic adaptation provides new avenues for the study of human evolution, and promises a synthesis of physical anthropology and human genetics. Here, we provide the first population genetic evidence for selected divergence in height polygenic scores among Asian populations. We also provide evidence of selected divergence in IHC and WHR polygenic scores within Europe and to a lesser extent Asia, and show that both hip and waist circumference have likely been influenced by correlated selection on height and waist-hip ratio. Finally, signals of divergence among Asian populations can be explained in terms of differential relatedness to Europeans, which suggests that much of the divergence we detect predates the major demographic events in the history of modern Eurasian populations, and represents differential inheritance from ancient populations which had already diverged at the time of admixture. Note that because modern non-admixed east Asian populations only show significant evidence of divergence in pairwise comparisons to western populations (ancient or modern) that have been selected up in height (Figure S10), our results do not support a hypothesis of selection for decreased height in east Asia.
However, the fact that we cannot detect departures from neutrality outside of those associated with broad scale variation in European ancestry across Asia should not be taken as evidence that such events have not occurred, merely that if they exist, we cannot currently detect them using GWAS variants mapped in Europe. We should expect to be better-powered to detect selective events in populations more closely related to Europeans for two reasons. First, changes in the structure of linkage disequilibrium (LD) across populations should lead GWAS variants to tag causal variation best in populations genetically close to the European-ancestry GWAS panels.56 Second, gene-by-environment and gene-by-gene interactions can lead to changes in the additive effects of individual loci among populations,57 and therefore in the way that they respond to selection on the phenotype. We expect that these difficulties can be overcome or mitigated in the future through a combination of well-powered GWAS in multiple populations of non-European ancestry, access to a wider array of ancient DNA samples, and improved frameworks for the interpretation of signals of polygenic adaptation.23
The existence of latitudinal trends in the polygenic scores for WHR and IHC support the notion that some of the clinal phenotypic variation in body shape typically thought to represent thermoreg-ulatory adaptation can be attributed to genetic variation driven by selection, while the ability of simple models to unify signals across broad geographic regions again suggests that these patterns could have been generated by a limited number of selective events. Evidence for adaptation on the basis of specific environmental pressures is most convincing when multiple populations independently converge on the same phenotype in the face of the same environmental pressure, a pattern for which we currently lack evidence. Therefore, while our evidence is consistent with adaptation to temperature environments, alternative explanations (e.g. adaptation to diet) are plausible.
1 Methods
1.1 Population Genetics Datasets
We downloaded the 1000 genomes phase 3 release data from the 1000 genomes ftp portal.25 We also used data from the Human Origins fully public panel24 which was imputed from the 1000 Genomes phase 3 as reference, using the Michigan imputation server,58 and restricting to SNPs with an imputation quality score (in terms of predicted r2) of 0.8 or greater (pers. comm. Joe Pickrell). The original genotype data can be downloaded from the Reich lab website. This combined dataset represent samples from 2504 people from 26 populations in the 1000 Genomes dataset and 2158 people across 161 populations from the Human Origins dataset, for a total of 4662 samples from 187 populations (S2). For global analyses we include all 187 populations. In regional analyses we exclude populations with a significant recent (i.e. < 500 years) African/non-African admixture to avoid confounding admixture with signals of recent selection within regions (see S2 and S1 for the regions).
1.2 Selection of GWAS SNPs
We took public GWAS results for a set of traits28 and combined them with additional anthropometric traits from the GIANT consortium and a subset of Early Growth phenotypes contributed by EGG Consortium. Table S1 gives a full list of the traits included in this study and the relevant references. For each trait we selected a set of SNPs with which to construct our polygenic scores as follows. For each SNP, we calculated an approximate Bayes factor summarizing the evidence for association at that SNP via the method of Wakefield,59 following Pickrell et al.28 (see their supplementary note section 1.2.1). We then used a published set of 1700 non-overlapping linkage disequilibrium blocks26 to divide the genome, after which we selected the single SNP with the strongest approximate Bayes factor in favor of association within each block to carry forward for analyses.
1.3 Polygenic Scores and Null Model
Given a set of L SNPs associated with a trait (L ≈ 1700), we construct the vector of polygenic scores across all M = 187 populations by taking the sum of allele frequencies across the L sites (the vector at site ℓ), weighting each allele’s frequency by its effect on the trait (αℓ) to give For each trait, we construct a null model for the joint distribution of polygenic scores across populations, assuming where . Here p̅ℓ is the mean allele frequency across all population samples (weighting all population samples equally), and F is the M × M population-level genetic covariance matrix.18 All polygenic scores are plotted in centered standardized form .
We use the Mahalanobis distance of from its distribution under the null as a natural test statistic to assess the ability of the null model to explain the data (see Berg and Coop (2014)18 for an extended discussion). This test statistic should be X2 with M – 1 degrees of freedom under neutrality. However, in practice we are concerned that the ascertainment of GWAS loci may invalidate our null model, so we compare the test statistic to an empirical null (see Section S1.3)
1.4 Latitudinal and Longitudinal Correlations
We also test for selection-driven correlations between geographic variables (e.g. latitude) and a subset of our polygenic scores (see Berg and Coop (2014)18 and Section S1.1 for more details of the test). We take the standardized geographic variable and polygenic scores, and then rotate these vectors by the inverse Cholesky decomposition of the relatedness matrix F. These rotated vectors are in a reference frame where the populations represent independent contrasts under the neutral model. We take as our test statistic the covariance of these rotated vectors. We calculate the significance of the statistic by comparing to a null distribution generated by calculating null sets of polygenic scores assembled from resampled SNPs with derived frequency matched to the CEU population sample so as to mimic the effects of the GWAS ascertainment.
1.5 Two-Trait Conditional Tests
Because some of the traits we examine are genetically correlated with one another, we were concerned that signals of selection observed for one trait might reflect a response to selection on another correlated trait. To determine whether genetic correlations might be responsible for some of our signals, we developed a multitrait extension to our neutral model that accounts for genetic covariance among traits. The extension is on the framework of Lande and Arnold.43
If and are vectors of polygenic scores for two different traits constructed according to equation (1), and the matrix contains these vectors as columns, then under neutrality the distribution of Z is approximately matrix normal where the matrix μ contains the trait-specific means, F gives the population covariance structure among rows as in the single trait model, and G is the among trait additive genetic covariance matrix, the “G matrix” of multivariate quantitative genetics,43 estimated for a population ancestral to all populations in the sample. The diagonal elements of the 2 × 2 G matrix are given by the VA parameters from above in the single trait model and the off-diagonal element (CA,12) corresponds to the additive genetic covariance between the two traits. Given this null model for the joint distribution of the two traits, we can construct a conditional model for the distribution of polygenic scores for trait 1, given the polygenic score observed for trait 2, as Given a value of CA,12 we can then use these conditional means and variances in equation (3) to form a conditional QX statistic and compare it to its null distribution. We take the failure to reject neutrality on the basis of the conditional QX statistic as consistent with the hypothesis that any response to selection observed for trait 1 is a result of selection on trait 2. Some of the traits we study have non-linear allometric relationships with each other, but because our polygenic scores are linear by construction our tests are robust to this non-linearity (see S1.7).
We experimented with estimating CA,12 on the basis of SNPs that overlap between the two traits in each genomic block. However, we were concerned about this approach to estimating genetic correlations not being a sufficient joint model for cases in which different SNPs within a block affected the two traits but were in linkage disequilibrium with one another, and therefore do not drift independently. To deal with this issue, we represent the genetic covariance among populations as where ρ represents the genetic correlation between the two sets of polygenic scores. We pursued a conservative strategy, testing a range of values for ρ along a dense grid from -1 to 1 to ask whether any assumed genetic correlation between polygenic scores could plausibly allow one trait to be explained as a correlated response to another. As a further conservative measure, we allowed the genetic correlation used to calculate the conditional variance (Eq (7)) to be equal to zero, while allowing the p used to compute the conditional mean (Eq (6)) was not. This is a conservative approach, as it fits our conditional prediction to the mean, but allows the variance of the null model to remain as large as the unconditional model. The conditional two-trait p-values we present in the text, and the CI shown in two-trait Figure 4 and in the supplement, use this conservative approach. In practice our values of ρ are consistent with estimates of genetic correlations obtained from the LDscore approach,41,42 given that our polygenic scores capture only a fraction of the total genetic variance for each trait.
1.6 Single Trait Conditional Null Model
We also developed an extension of the null model for a single trait to test whether two (or more) signals of selection detected in different geographic regions might reflect a single ancestral event that occurred in an ancient population that has contributed ancestry broadly to modern populations.
Assume for example that we have detected a signal of selection among the population samples from region A (e.g. Europe) and among the population samples from (e.g. Asia), and we would like to test whether the signal detected in region B is due to a selective event that is also responsible for generating a signal of selection in region A. We first reorganize our samples into two blocks for the two regions Where μB is the mean polygenic score in the set of populations being tested, the F•,•s refer to the sub-matrices of the relatedness matrix F, and F itself has been recentered at the mean of the test set (i.e. region B). Then the conditional distribution of polygenic scores in region B given the polygenic scores observed in region A is The conditional mean, reflects the best predictions of population means in region B given the values observed in region A, whereas the conditional covariance matrix FB|A reflects the scale and form of the variance around this expectation that arises from drift that is independent of drift in the ancestry of populations in region A.
We can then test for over-dispersion of polygenic score in region given the observed polygenic scores in region A by using and FB|A in (3) to construct a conditional QX score. We judge the statistical significance of this conditional QX score by comparing it to a frequency matched dataset, as with the standard test. We interpret a non-significant conditional QX score for region B as evidence that any selective signal of overdispersion in B is well explained by genome-wide allele-sharing with A. We view this as evidence that the selection signal in B overlaps that in A, due to selection in shared ancestral populations and admixture.
In Figure 3 we plot the observed polygenic scores for Asia against the predicted polygenic scores for Asia (B), conditional on the Europe population sample polygenic scores (A). The error bars are 95% CIs for each population sample, obtained from the variances on the diagonal of VAFB|A.
Acknowledgements
We thank the Coop Lab and Doc Edge, Iain Mathieson, Emily Josephs, Joe Pickrell, Molly Prze-worski, Jeff Ross-Ibarra, Guy Sella, and Tim Weaver for helpful discussions and feedback on earlier drafts. The work was supported in part by an NSF GRFP (to JJB), the UC Davis Anthropology department (XZ), and National Institute of General Medical Sciences of the National Institutes of Health under award numbers R01 GM108779 and R01 grant GM115889.