This study sought to address whether natural selection has differentiated allele frequencies and LD scores of complex traits associated SNPs among worldwide populations more than expected under drift. To this end, we established a strategy to test whether the among-population variation in allele frequency or LD score at the trait-associated SNPs is significantly higher than that at MAF-matched and LD-matched control SNPs. We detected significant signals in allele frequencies in the GERA populations for height (\(P = 2.46 \times 10^{ - 5}\)), WHRadjBMI (\(P = 2.77 \times 10^{ - 4}\)), and SCZ (\(P = 3.96 \times 10^{ - 5}\)) (Table 1) and significant signals in LD for height (\(P = 2.01 \times 10^{ - 6}\)) and SCZ (\(P = 5.16 \times 10^{ - 18}\)) (Table 2). There are two plausible models that are compatible with the observed results: 1) the trait itself has undergone natural selection; 2) variants affecting the trait have been under selection because of their pleiotropic effects on fitness, and variants with larger effects on the trait tend to be more differentiated via such pleiotropic effects41.

Height is a classic complex trait. Previous studies have shown that height-associated SNPs have been under natural selection and that this might contribute to the mean height differences among EUR populations4,16,19,20,21. Our results suggest that the phenotypic differences in height among AFR, EAS, and EUR populations are also partially due to natural selection on height-associated SNPs (Fig. 2 and Supplementary Fig. 2). The mean PRS of AFR was higher than that of EAS but lower than that of EUR, consistent with the observed phenotypic differences in mean height1. Waist-to-hip ratio is an anthropometric index of abdominal obesity. Previous studies have shown that after adjusting for BMI, European Americans tend to have a larger amount of visceral fat on average than African Americans35,36 but a lower amount than those of Asian descent6,34. This finding could be explained by the enrichment of the WHRadjBMI-increasing alleles in EAS as shown in our results; we did not have enough power to detect difference between EUR and AFR (Fig. 2 and Supplementary Fig. 2). It is worth noting that, compared with height, direct measurements of WHRadjBMI are not widely available for worldwide populations and are less consistent across studies, which may be related to insufficient sample sizes42,43 or the influence of environmental factors44. For SCZ, the enrichment of risk alleles in AFR (Fig. 2 and Supplementary Fig. 2) identified by our analyses appears to support the reported discrepancy in the prevalence of SCZ between African Americans and European Americans31,32. Moreover, Fearon et al.33 found that, among the ethnic minority groups in the UK, the incidence rate ratios (IRRs) for SCZ (adjusted by age and sex) in individuals of Chinese descent (IRR = 3.5) is higher than non-British Whites (IRR=2.5) and lower than individuals of African descent (IRR = 9.1 for African-Caribbean and 5.8 for Black African), consistent with our findings. However, the diagnosis of SCZ can be potentially biased by non-genetic factors, such as socioeconomic status and access to hospitalization31.

The trait-associated SNPs used to detect signatures of natural selection were ascertained from EUR-based meta-analyses of GWAS. Such ascertainment might be biased because F ST is a function of MAF and the MAF or LD properties of the trait-associated SNPs could be different from that of the non-associated SNPs26,45. For example, SNPs with higher MAF in EUR tend to have higher power to be detected at a certain significance level, resulting in a difference in mean F ST even in the absence of natural selection. This potential bias can be mitigated by matching the control SNPs with the associated SNPs by MAF and LD score. Via simulations, we confirmed that inflation did not occur in the test statistics under the null model (Supplementary Fig. 1a). Our F ST enrichment results are unlikely to be driven by the EUR bias because among the traits that showed significant signal in the F ST enrichment test (Table 1) only height showed higher mean fTIA in EUR than non-EUR (mean fTIA was higher in EAS for WHRadjBMI and higher in AFR for SCZ compared to EUR) (Fig. 3). Moreover, we did not observe a correlation between the worldwide F ST (using the AFR, EAS and EUR samples in 1000G) and EUR F ST (using the CEPH, Finnish, British, Spanish, and Tuscan samples in 1000G-EUR) for the trait-associated SNPs that show evidence of selection (Supplementary Fig. 6). This result suggests that the differentiation of PRS in global populations is unlikely to be confounded by the biases in the estimated SNP effects due to population stratification in EUR. In addition, genetic drift that takes place during particular demographic events (e.g., population bottleneck or expansion in Europeans) would result in a difference in the frequency spectrum between the causal variants and neutral variants46. The difference, however, was very unlikely lead to a bias in our results because there was no difference in MAF between the trait-associated SNPs and the matched control SNPs. It is confirmed by simulation that there was no inflation in the F ST enrichment test-statistics when the causal variants were simulated to have lower MAF than null SNPs in the absence of selection (A and B in Supplementary Table 4 and Supplementary Fig. 7a). We further demonstrated by simulation that the F ST enrichment analysis method was robust to different levels of heritability (C and D in Supplementary Table 4 and Supplementary Fig. 7b), different degrees of LD between causal variants (Supplementary Figs. 8 and 9), different strategies of sampling control SNPs (matching the control SNPs with the trait-associated SNPs by only MAF computed from EUR or by both MAF and LD scores computed from AFR; Supplementary Fig. 10), or whether the causal variants were included in the analysis (Supplementary Fig. 11). We also applied different strategies of matching control SNPs to the analyses of real data and observed little differences in results (Supplementary Table 5). In addition, we compared the variance of F ST values of a set of associated SNPs with a random set of control SNPs (with MAF and LD matched) across 100 independently simulated traits and did not observe a significant difference in variance of F ST values between the trait-associated SNPs and control SNPs, regardless of whether the traits were simulated based on a single variant or multiple variants at each of the 1,000 causal loci (Supplementary Fig. 12).

We observed from the LD score calculation in GERA that there were three regions (on chromosomes 6, 11 and 17) presenting extremely large LD scores (Supplementary Fig. 13). The chr6 region (Supplementary Fig. 14a) harbors genes that encode the major histocompatibility complex (MHC; hg19 chr6:28,477,797-33,448,354), a well-known protein complex that is essential for the immune response. It is not surprising that the MHC locus has been under selection47. The chr17 region (Supplementary Fig. 14b) harbors an inversion (hg16 chr17:44.1-45.0 Mb) that almost exclusively occurs in EUR and has been shown to be under positive selection in Icelandic females48. The chr11 region (Supplementary Fig. 14c) stretches over the centromere with a length >10 Mb, and it contains multiple polymorphic inversions49. More than half of the genes contained in this region (48–60 Mb; Supplementary Fig. 14d) are olfactory receptor genes (ORs) (186 ORs/308 genes)50. This gene family has been found to show the greater evolutionary acceleration between humans and chimpanzees than other functional gene classes, such as nuclear transport and reproduction51. Moreover, this region included a large number of nearly independent SNPs that show pleiotropic effects on HDL cholesterol and height (Supplementary Fig. 14d).

Nevertheless, several limitations were associated with this study. First, the F ST enrichment test is underpowered for highly polygenic traits because some of the control SNPs might be in LD with the causal variants by chance under a polygenic model (as demonstrated by the deviation of fTIA differences in the control SNPs from the expected values for height and SCZ; Fig. 3). Fortunately, the loss of power was remedied by the use of data from studies with very large sample sizes (Supplementary Table 1). Second, the GWAS summary statistics used in this study were generated from EUR samples (see the discussion of EUR bias above). This is because non-EUR GWAS of large sample size (on a similar scale as the sample sizes of the EUR GWAS used in this study) are not available for most complex traits. If there is genetic heterogeneity between EUR and non-EUR populations, the PRS computed in AFR and EAS based on SNP effects estimated from EUR studies will be biased37,38. We showed that this potential bias could be mitigated by the fTIA analysis, which ignores the magnitude of estimated SNP effects (Fig. 3 and Supplementary Fig. 3). In fact, the results from the fTIA analysis (Fig. 3 and Supplementary Fig. 3) were largely consistent with those from the PRS analysis (Fig. 2 and Supplementary Fig. 2), suggesting that the direction of genetic differentiation as indicated by the PRS for height, WHRadjBMI, or SCZ is unlikely to be substantially biased by the between-population differences in SNP effects52. In addition, our result that the EUR F ST was almost independent of the global F ST (Supplementary Fig. 6) implies that the mean values of PRS in non-EUR samples were not biased by possible confounding in the estimated SNP effects owing to population stratification in EUR. Third, because we tested the mean F ST (or LDCV) across all the associated loci against that of the control SNPs, we could not distinguish whether the population differentiation of mean F ST (or LDCV) at the trait-associated variants (more than expected by drift) is due to natural selection on different loci, the same loci but different alleles, or the same alleles but different levels of selection pressure in different populations. Fourth, regarding to the type of selection on the trait-associated variants, our results seem to indicate that the excess of genetic differentiation at the trait-associated SNPs is a consequence of local selection (different alleles are favored in different populations). However, we cannot rule out the possibility that the increase in F ST (or LDCV) at the trait-associated SNPs is due to background selection53 (i.e., those SNPs are in LD with causal variants under negative selection). This is confirmed by forward simulation using SLiM54 (Methods). The simulation result shows that background selection reduces genetic diversity and increases between-population differentiation at genetic variants in LD with the variants under negative selection (Supplementary Fig. 15). Last, we used the F ST and LDCV enrichment analyses to assess the excess of population genetic differentiation at the trait-associated loci as a means to detect signature of natural selection. These analyses, however, cannot determine when the selection occurred in the history of human evolution and whether there are other types of natural selection within a population. Studies in progress have developed methods to model polygenic selection in an admixture graph (representing of the historical divergences and admixture events in the human populations through time) to infer which branches are most likely to have experienced polygenic selection55, and to model the relationship between variance in SNP effect and MAF to detect signatures of negative selection on variants associated with complex traits56,57.

In summary, we proposed a robust statistical approach to test whether SNPs associated with a complex trait of interest are more differentiated across worldwide populations than MAF-matched and LD-matched control SNPs, and used the results to infer whether the trait-associated genetic variants have undergone natural selection. Our simulations indicated that the test statistics of the proposed approach were not inflated under the null model of random drift. Using this approach, we identified that for height, WHRadjBMI, and SCZ, the trait-associated alleles were differentiated significantly more than the matched control, in directions consistent with those of phenotypic differentiation. We showed that the results were robust to the potential biases in ascertaining the trait-associated SNPs (e.g., population stratification in EUR). These results support our hypothesis that the observed phenotypic differentiation among worldwide populations is (at least partly) genetic and a consequence of natural selection on the trait-associated variants because of selection on the trait or through their pleiotropic effects on fitness since the divergence of these populations16. Our findings further suggest that natural selection has also driven differentiation in LD among populations at genomic loci associated with height and SCZ. These findings expand our understanding of the role of natural selection in shaping the genetic architecture of complex traits in human populations. The methods developed in this study are general and applicable to other complex traits, including endophenotypes, such as gene expression and DNA methylation.