A population genetic signal of polygenic adaptation

Abstract

Adaptation in response to selection on polygenic phenotypes may occur via subtle allele frequencies shifts at many loci. Current population genomic techniques are not well posed to identify such signals. In the past decade, detailed knowledge about the specific loci underlying polygenic traits has begun to emerge from genome-wide association studies (GWAS). Here we combine this knowledge from GWAS with robust population genetic modeling to identify traits that may have been influenced by local adaptation. We exploit the fact that GWAS provide an estimate of the additive effect size of many loci to estimate the mean additive genetic value for a given phenotype across many populations as simple weighted sums of allele frequencies. We use a general model of neutral genetic value drift for an arbitrary number of populations with an arbitrary relatedness structure. Based on this model, we develop methods for detecting unusually strong correlations between genetic values and specific environmental variables, as well as a generalization of [Q(ST)/F(ST)] comparisons to test for over-dispersion of genetic values among populations. Finally we lay out a framework to identify the individual populations or groups of populations that contribute to the signal of overdispersion. These tests have considerably greater power than their single locus equivalents due to the fact that they look for positive covariance between like effect alleles, and also significantly outperform methods that do not account for population structure. We apply our tests to the Human Genome Diversity Panel (HGDP) dataset using GWAS data for height, skin pigmentation, type 2 diabetes, body mass index, and two inflammatory bowel disease datasets. This analysis uncovers a number of putative signals of local adaptation, and we discuss the biological interpretation and caveats of these results.

Figure 1. A schematic representation of the flow of our method.

The boxes colored blue are items provided by the investigator (GWAS SNP effect sizes, the frequency of the GWAS SNPs across populations, and a environmental variable). The boxes colored red make use of random SNPs sampled to match the GWAS set as described in “Choosing null SNPs” in the methods section. For each box featuring a calculated quantity a set of equation numbers are provided for the relevant calculation. The Z score uses the untransformed genetic values, rather than the transformed genetic values, but this relationship is not depicted in the figure for the sake of readability.

Figure 2. Power of our statistics as compared to alternative approaches.

(A) across a range of selection gradients () of latitude, and when we hold constant at 0.14 and (B) decrease , the genetic correlation between the trait of interest and the selected trait, (C) vary the number of loci, and (D) vary the number of loci while holding the fraction of variance explained constant. Bottom panels show power of the Z-test and approaches to detect selection affecting (E) a single population, and (F) multiple populations in a given region. See main text for simulation details.

Figure 3. Histogram of the empirical null distribution of for each trait, obtained from genome-wide resampling of well matched SNPs.

The mean of each distribution is marked with a vertical black bar and the observed value is marked by a red arrow. The expected density is shown as a black curve.

Figure 4. The two components of for the height dataset, as described by the left and right terms in (14).

The null distribution of each statistic is shown as a histogram. The mean value is shown as a black bar, and the observed value as a red arrow.

Figure 5. Visual representation of outlier analysis at the regional and individual population level for (A) height, (B) skin pigmentation, (C) body mass index, (D) type 2 diabetes, (E) Crohn's disease and (F) ulcerative colitis.

For each geographic region we plot the expectation of the regional average, given the observed values in the rest of the dataset as a grey dashed line. The true regional average is plotted as a solid bar, with darkness and thickness proportional to the regional Z score. For each population we plot the observed value as a colored circle, with circle size proportional to the population specific Z score. For example, in (A), one can see that estimated genetic height is systematically lower than expected across Africa. Similarly, estimated genetic height is significantly higher (lower) in the French (Sardinian) population than expected, given the values observed for all other populations in the dataset.

Figure 6. Estimated genetic height (A) and skin pigmentation score (B) plotted against winter PC2 and absolute latitude respectively.

Both correlations are significant against the genome wide background after controlling for population structure (Table 2).

Figure 7. Estimated genetic risk score for Crohn's disease (A) and ulcerative colitis (B) risk plotted against summer PC2.

Both correlations are significant against the genome wide background after controlling for population structure (Table 2). Since a large proportion of SNPs underlying these traits are shared, we note that these results are not independent.