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The colors indicate the marginal posterior mean estimate of the selection parameter for variants associated with the corresponding trait with red indicating an increase in trait-increasing variant frequency, and blue indicating a decrease in trait-increasing variant frequency. PolyGraph then consistently converged on the appropriate joint distribution of selection parameters.
When the branches were simulated to be longer 0.
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We also observe that using a nonsparse prior i. We were concerned about false positive estimates of selection when the graph is misspecified. To assess this, we simulated a graph like the one shown in Figure 3C but with no selection. We first run PolyGraph while correctly specifying the topology and the branch lengths of length equal to 0. Then, we simulated a graph with the same topology but with each branch having length equal to 0. Finally, we simulated the same graph but with each branch having length equal to 0.
With increasingly stronger misspecification of the branch lengths, we observe that the behavior of some of the posterior estimates becomes more erratic. We also simulated a neutral graph as in Figure 3C but pretended that population A had not been sampled, and that the graph was incorrectly estimated to be a three-population tree like the one in Figure 3A. This topological misspecification slightly affected the inference of neutrality in one of the five simulations Figure S32 in File S1 , and we do not discard the possibility of other incorrect types of topologies that could also generate wrong inferences.
We therefore stress that the admixture graph—especially the branch lengths—relating the populations under study should be correctly estimated before running PolyGraph. We also advise to run the MCMC only when there is significant evidence for selection based on the statistic Berg and Coop , which does not need an admixture graph as input, as it uses the full genome-wide covariance matrix to model the expected amount of drift separating each of the populations.
We tested our method on sets of associated variants from 43 GWAS on 42 different traits Table S1 in File S1 ; two of the GWAS are for age at menarche that were previously assembled as part of a meta-analysis studying the genetic correlations between such traits Pickrell et al. The meta-analysis split the genome into approximately independent linkage disequilibrium blocks Berisa and Pickrell For each block with a posterior probability of containing an association [obtained from fgwas Pickrell ], the SNP with the maximum posterior probability of being the causative variant was extracted.
For our first analysis, we did not attempt to model any admixture events. We took trait-associated variants to be under polygenic adaptation if the P -value for the corresponding Berg and Coop statistic testing for overall selection among the populations was where n is the number of assessed GWASs. Traits with associated variants that passed this criterion are shown in Table 1. These were: height Wood et al. To account for possible artifacts arising from the ascertainment scheme for each GWAS, we also generated samples in which we randomly switched the sign of the estimated effect size for all trait-associated SNPs.
This serves to preserve the genetic architecture of each trait, while removing the effect of selection. We computed a second P -value of the observed by comparing it to these samples Table 1. The P -values of the statistic obtained from a distribution for each branch are shown in Table S2 in File S1.
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However, this is only a consequence of the MCMC showing alternate strong support for selection in either one or the other branch at different points in the run, but only weak support for selection in both branches simultaneously Figure S35 in File S1 , suggesting we are unable to discern which among these is the correct configuration. We plotted poly-graphs for all traits that passed the significance criterion in the seven-leaf tree Figure 4. Poly-graphs for trait-associated variants that show significant evidence for polygenic adaptation in the seven-leaf tree built using Genomes allele frequency data.
The results from both alternative sets of panels are very similar to our original tree.
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The best-fitting combination was a mixture of the terminal branch leading to CEU and the terminal branch leading to PEL , the latter of which is the panel with the highest amount of Native American ancestry in the Genomes Project Auton et al. Here, we recapitulated many of our previous findings from the seven-leaf tree Figure S39 in File S1 and Table 1 , like selection on variants associated with height and educational attainment.
Poly-graphs of the five-leaf admixture graph are shown in Figure 5. Poly-graphs for trait-associated variants that show significant evidence for polygenic adaptation in the five-leaf admixture graph built using Genomes allele frequency data. To make sure there were no artifacts due to GWAS ascertainment Berg and Coop , we also generated an empirical null distribution produced using samples, each containing SNPs that were frequency-matched to the trait-associated SNPs, using their allele frequency in CEU.
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We computed the statistic for each of these samples, to obtain an empirical P -value in Table 1. We do not observe a value of as high as the one observed in the real data, for either height, educational attainment, or self-reported unibrow Figure 6. We generated an empirical null distribution by sampling SNPs from the genome that matched the CEU allele frequency of the SNPs associated with educational attainment, self-reported unibrow, and height.
We generated samples this way, and computed the statistic for each sample, using the population panels from Figure 4. The value observed in the real data are depicted with a red line. We also plot the density of the corresponding distribution blue line for comparison. To test how robust our results were to our modeling assumptions, we also performed a simpler two-tailed binomial sign test between every pair of Genomes panels.
The assumption here is that—for every panel X and Y—we should observe roughly equal number of trait-increasing alleles at higher frequency in X than in Y as trait-decreasing alleles at higher frequency in X than in Y, under a model of neutrality with respect to the effect size sign Orr This test only uses information about the sign of the effect estimates of each SNP, not their magnitudes, and does not use information about genome-wide drift parameters between each population.
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Thus, it is bound to have less power than the or MCMC tests. The P -values for these pairwise binomial tests are shown in Tables S4—S8 in File S2 for all traits that were found to have significant evidence of selection using the statistic. For ease of visualization, we also plotted, for each panel, the number of pairwise tests involving that panel that resulted in a P -value Figures S40—S44 in File S1. We were interested in verifying how sensitive different proportions of missing data i.
First, we simulated different proportions of missing trait-associated SNPs, ranging from to with step sizes of For each of 10, simulations under each missing data scenario, we assessed how often the polygenic score for unibrow and educational attainment in CHB was higher than the polygenic score for CEU, like we observe in the Genomes data.
Height follows the opposite pattern with CEU having a higher polygenic score than CHB , so in that case we assessed how often its polygenic score in CEU was higher than in CHB, across the 10, simulations for each scenario.
Note that we built these scores using only the SNPs used in our selection tests. The results are in Figure S45 in File S1. For example, we see that—even with missing data—the polygenic scores for either of the three traits preserve the observed relationship of inequality between CEU and CHB almost of the time. Finally, we simulated a situation in which some proportion of the signs of the effect size estimates were misassigned.
To understand how the signal of selection was distributed among our SNPs, we plotted the absolute value of the effect sizes of trait-associated SNPs for height, educational attainment, and self-reported unibrow, as a function of the difference in frequency observed between CHB and CEU, polarized with respect to the trait-increasing allele in each SNP Figure 7. We find that, in the case of self-reported unibrow, there are three variants of large effect with large frequency differences contributing to a higher polygenic score in CHB: rs, rs, and rs These are genes involved in pigmentation and skin development, and all three have documented signatures of selective sweeps causing strong allele frequency differences between Europeans and East Asians Bersaglieri et al.
After removing SNPs with large absolute effect size values , the P -value of the statistic for these variants remains significant. When looking at the other two sets variants associated with height and educational attainment , the signal of selection is more uniformly distributed among the SNPs, with no strong outliers of large effect with large frequency differences Figure 7.
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