Testing for differences in polygenic scores in the presence of confounding.

Polygenic scores have become an important tool in human genetics, enabling the prediction of individuals' phenotypes from their genotypes. Understanding how the pattern of differences in polygenic score predictions across individuals intersects with variation in ancestry can provide insights into the evolutionary forces acting on the trait in question, and is important for understanding health disparities. However, because most polygenic scores are computed using effect estimates from population samples, they are susceptible to confounding by both genetic and environmental effects that are correlated with ancestry. The extent to which this confounding drives patterns in the distribution of polygenic scores depends on patterns of population structure in both the original estimation panel and in the prediction/test panel. Here, we use theory from population and statistical genetics, together with simulations, to study the procedure of testing for an association between polygenic scores and axes of ancestry variation in the presence of confounding. We use a general model of genetic relatedness to describe how confounding in the estimation panel biases the distribution of polygenic scores in a way that depends on the degree of overlap in population structure between panels. We then show how this confounding can bias tests for associations between polygenic scores and important axes of ancestry variation in the test panel. Finally, we use the understanding gained from this analysis to develop a method that uses patterns of genetic similarity between the two panels to guard against these biases, and show that this method can provide better protection against confounding than the standard PCA-based approach.

Polygenic score accuracy in ancient samples: Quantifying the effects of allelic turnover.

Polygenic scores link the genotypes of ancient individuals to their phenotypes, which are often unobservable, offering a tantalizing opportunity to reconstruct complex trait evolution. In practice, however, interpretation of ancient polygenic scores is subject to numerous assumptions. For one, the genome-wide association (GWA) studies from which polygenic scores are derived, can only estimate effect sizes for loci segregating in contemporary populations. Therefore, a GWA study may not correctly identify all loci relevant to trait variation in the ancient population. In addition, the frequencies of trait-associated loci may have changed in the intervening years. Here, we devise a theoretical framework to quantify the effect of this allelic turnover on the statistical properties of polygenic scores as functions of population genetic dynamics, trait architecture, power to detect significant loci, and the age of the ancient sample. We model the allele frequencies of loci underlying trait variation using the Wright-Fisher diffusion, and employ the spectral representation of its transition density to find analytical expressions for several error metrics, including the expected sample correlation between the polygenic scores of ancient individuals and their true phenotypes, referred to as polygenic score accuracy. Our theory also applies to a two-population scenario and demonstrates that allelic turnover alone may explain a substantial percentage of the reduced accuracy observed in cross-population predictions, akin to those performed in human genetics. Finally, we use simulations to explore the effects of recent directional selection, a bias-inducing process, on the statistics of interest. We find that even in the presence of bias, weak selection induces minimal deviations from our neutral expectations for the decay of polygenic score accuracy. By quantifying the limitations of polygenic scores in an explicit evolutionary context, our work lays the foundation for the development of more sophisticated statistical procedures to analyze both temporally and geographically resolved polygenic scores.

How well can we separate genetics from the environment?

A simulation study demonstrates a better method for separating genetic effects from environmental effects in genome-wide association studies, but there is still some way to go before this becomes a "solved" problem.

Measuring intolerance to mutation in human genetics.

In numerous applications, from working with animal models to mapping the genetic basis of human disease susceptibility, knowing whether a single disrupting mutation in a gene is likely to be deleterious is useful. With this goal in mind, a number of measures have been developed to identify genes in which protein-truncating variants (PTVs), or other types of mutations, are absent or kept at very low frequency in large population samples-genes that appear 'intolerant' to mutation. One measure in particular, the probability of being loss-of-function intolerant (pLI), has been widely adopted. This measure was designed to classify genes into three categories, null, recessive and haploinsufficient, on the basis of the contrast between observed and expected numbers of PTVs. Such population-genetic approaches can be useful in many applications. As we clarify, however, they reflect the strength of selection acting on heterozygotes and not dominance or haploinsufficiency.

Reduced signal for polygenic adaptation of height in UK Biobank.

Several recent papers have reported strong signals of selection on European polygenic height scores. These analyses used height effect estimates from the GIANT consortium and replication studies. Here, we describe a new analysis based on the the UK Biobank (UKB), a large, independent dataset. We find that the signals of selection using UKB effect estimates are strongly attenuated or absent. We also provide evidence that previous analyses were confounded by population stratification. Therefore, the conclusion of strong polygenic adaptation now lacks support. Moreover, these discrepancies highlight (1) that methods for correcting for population stratification in GWAS may not always be sufficient for polygenic trait analyses, and (2) that claims of differences in polygenic scores between populations should be treated with caution until these issues are better understood. Editorial note: This article has been through an editorial process in which the authors decide how to respond to the issues raised during peer review. The Reviewing Editor's assessment is that all the issues have been addressed (see decision letter).

Detecting Adaptive Differentiation in Structured Populations with Genomic Data and Common Gardens.

Adaptation in quantitative traits often occurs through subtle shifts in allele frequencies at many loci-a process called polygenic adaptation. While a number of methods have been developed to detect polygenic adaptation in human populations, we lack clear strategies for doing so in many other systems. In particular, there is an opportunity to develop new methods that leverage datasets with genomic data and common garden trait measurements to systematically detect the quantitative traits important for adaptation. Here, we develop methods that do just this, using principal components of the relatedness matrix to detect excess divergence consistent with polygenic adaptation, and using a conditional test to control for confounding effects due to population structure. We apply these methods to inbred maize lines from the United States Department of Agriculture germplasm pool and maize landraces from Europe. Ultimately, these methods can be applied to additional domesticated and wild species to give us a broader picture of the specific traits that contribute to adaptation and the overall importance of polygenic adaptation in shaping quantitative trait variation.

Parallel altitudinal clines reveal trends in adaptive evolution of genome size in Zea mays.

While the vast majority of genome size variation in plants is due to differences in repetitive sequence, we know little about how selection acts on repeat content in natural populations. Here we investigate parallel changes in intraspecific genome size and repeat content of domesticated maize (Zea mays) landraces and their wild relative teosinte across altitudinal gradients in Mesoamerica and South America. We combine genotyping, low coverage whole-genome sequence data, and flow cytometry to test for evidence of selection on genome size and individual repeat abundance. We find that population structure alone cannot explain the observed variation, implying that clinal patterns of genome size are maintained by natural selection. Our modeling additionally provides evidence of selection on individual heterochromatic knob repeats, likely due to their large individual contribution to genome size. To better understand the phenotypes driving selection on genome size, we conducted a growth chamber experiment using a population of highland teosinte exhibiting extensive variation in genome size. We find weak support for a positive correlation between genome size and cell size, but stronger support for a negative correlation between genome size and the rate of cell production. Reanalyzing published data of cell counts in maize shoot apical meristems, we then identify a negative correlation between cell production rate and flowering time. Together, our data suggest a model in which variation in genome size is driven by natural selection on flowering time across altitudinal clines, connecting intraspecific variation in repetitive sequence to important differences in adaptive phenotypes.

Detecting Polygenic Adaptation in Admixture Graphs.

An open question in human evolution is the importance of polygenic adaptation: adaptive changes in the mean of a multifactorial trait due to shifts in allele frequencies across many loci. In recent years, several methods have been developed to detect polygenic adaptation using loci identified in genome-wide association studies (GWAS). Though powerful, these methods suffer from limited interpretability: they can detect which sets of populations have evidence for polygenic adaptation, but are unable to reveal where in the history of multiple populations these processes occurred. To address this, we created a method to detect polygenic adaptation in an admixture graph, which is a representation of the historical divergences and admixture events relating different populations through time. We developed a Markov chain Monte Carlo (MCMC) algorithm to infer branch-specific parameters reflecting the strength of selection in each branch of a graph. Additionally, we developed a set of summary statistics that are fast to compute and can indicate which branches are most likely to have experienced polygenic adaptation. We show via simulations that this method-which we call PolyGraph-has good power to detect polygenic adaptation, and applied it to human population genomic data from around the world. We also provide evidence that variants associated with several traits, including height, educational attainment, and self-reported unibrow, have been influenced by polygenic adaptation in different populations during human evolution.

A Coalescent Model for a Sweep of a Unique Standing Variant.

The use of genetic polymorphism data to understand the dynamics of adaptation and identify the loci that are involved has become a major pursuit of modern evolutionary genetics. In addition to the classical "hard sweep" hitchhiking model, recent research has drawn attention to the fact that the dynamics of adaptation can play out in a variety of different ways and that the specific signatures left behind in population genetic data may depend somewhat strongly on these dynamics. One particular model for which a large number of empirical examples are already known is that in which a single derived mutation arises and drifts to some low frequency before an environmental change causes the allele to become beneficial and sweeps to fixation. Here, we pursue an analytical investigation of this model, bolstered and extended via simulation study. We use coalescent theory to develop an analytical approximation for the effect of a sweep from standing variation on the genealogy at the locus of the selected allele and sites tightly linked to it. We show that the distribution of haplotypes that the selected allele is present on at the time of the environmental change can be approximated by considering recombinant haplotypes as alleles in the infinite-alleles model. We show that this approximation can be leveraged to make accurate predictions regarding patterns of genetic polymorphism following such a sweep. We then use simulations to highlight which sources of haplotypic information are likely to be most useful in distinguishing this model from neutrality, as well as from other sweep models, such as the classic hard sweep and multiple-mutation soft sweeps. We find that in general, adaptation from a unique standing variant will likely be difficult to detect on the basis of genetic polymorphism data from a single population time point alone, and when it can be detected, it will be difficult to distinguish from other varieties of selective sweeps. Samples from multiple populations and/or time points have the potential to ease this difficulty.

A population genetic signal of polygenic adaptation.

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.

Precise spatio-temporal regulation of the anthocyanin biosynthetic pathway leads to petal spot formation in Clarkia gracilis (Onagraceae).

Petal spots are widespread in angiosperms and are often implicated in pollinator attraction. Clarkia gracilis petals each have a single red-purple spot that contrasts against a pink background. The position and presence of spots in C. gracilis are determined by the epistatic interaction of alleles at two as yet unidentified loci. We used HPLC to identify the different pigments produced in the petals, and qualitative and quantitative RT-PCR to assay for spatio-temporal patterns of expression of different anthocyanin pathway genes. We found that spots contain different pigments from the remainder of the petal, being composed of cyanidin/peonidin-based, instead of malvidin-based anthocyanins. Expression assays of anthocyanin pathway genes showed that the dihydroflavonol-4-reductase 2 (Dfr2) gene has a spot-specific expression pattern and acts as a switch for spot production. Co-segregation analyses implicated the gene products of the P and I loci as trans-regulators of this switch. Spot pigments appear earlier in development as a result of early expression of Dfr2 and the flavonoid 3' hydroxylase 1 (F3'h1) gene. Pigments in the background appear later, as a result of later expression of Dfr1 and the flavonoid 3'-5' hydroxylase 1 (F3'5'h1) genes. The evolution of this spot production mechanism appears to have been facilitated by duplication of the Dfr gene and to have required substantial reworking of the anthocyanin pathway regulatory network.