Long-range migrations and the resulting admixtures between populations have been important forces shaping human genetic diversity. Most existing methods for detecting and reconstructing historical admixture events are based on allele frequency divergences or patterns of ancestry segments in chromosomes of admixed individuals. An emerging new approach harnesses the exponential decay of admixture-induced linkage disequilibrium (LD) as a function of genetic distance. Here, we comprehensively develop LD-based inference into a versatile tool for investigating admixture. We present a new weighted LD statistic that can be used to infer mixture proportions as well as dates with fewer constraints on reference populations than previous methods. We define an LD-based three-population test for admixture and identify scenarios in which it can detect admixture events that previous formal tests cannot. We further show that we can uncover phylogenetic relationships among populations by comparing weighted LD curves obtained using a suite of references. Finally, we describe several improvements to the computation and fitting of weighted LD curves that greatly increase the robustness and speed of the calculations. We implement all of these advances in a software package, ALDER, which we validate in simulations and apply to test for admixture among all populations from the Human Genome Diversity Project (HGDP), highlighting insights into the admixture history of Central African Pygmies, Sardinians, and Japanese.

Interactions between genetic variants-epistasis-is pervasive in model systems and can profoundly impact evolutionary adaption, population disease dynamics, genetic mapping, and precision medicine efforts. In this work, we develop a model for structured polygenic epistasis, called coordinated epistasis (CE), and prove that several recent theories of genetic architecture fall under the formal umbrella of CE. Unlike standard epistasis models that assume epistasis and main effects are independent, CE captures systematic correlations between epistasis and main effects that result from pathway-level epistasis, on balance skewing the penetrance of genetic effects. To test for the existence of CE, we propose the even-odd (EO) test and prove it is calibrated in a range of realistic biological models. Applying the EO test in the UK Biobank, we find evidence of CE in 18 of 26 traits spanning disease, anthropometric, and blood categories. Finally, we extend the EO test to tissue-specific enrichment and identify several plausible tissue-trait pairs. Overall, CE is a dimension of genetic architecture that can capture structured, systemic forms of epistasis in complex human traits.

The human mutation rate is an essential parameter for studying the evolution of our species, interpreting present-day genetic variation, and understanding the incidence of genetic disease. Nevertheless, our current estimates of the rate are uncertain. Most notably, recent approaches based on counting de novo mutations in family pedigrees have yielded significantly smaller values than classical methods based on sequence divergence. Here, we propose a new method that uses the fine-scale human recombination map to calibrate the rate of accumulation of mutations. By comparing local heterozygosity levels in diploid genomes to the genetic distance scale over which these levels change, we are able to estimate a long-term mutation rate averaged over hundreds or thousands of generations. We infer a rate of 1.61 ± 0.13 × 10-8 mutations per base per generation, which falls in between phylogenetic and pedigree-based estimates, and we suggest possible mechanisms to reconcile our estimate with previous studies. Our results support intermediate-age divergences among human populations and between humans and other great apes.

Most Indian groups descend from a mixture of two genetically divergent populations: Ancestral North Indians (ANI) related to Central Asians, Middle Easterners, Caucasians, and Europeans; and Ancestral South Indians (ASI) not closely related to groups outside the subcontinent. The date of mixture is unknown but has implications for understanding Indian history. We report genome-wide data from 73 groups from the Indian subcontinent and analyze linkage disequilibrium to estimate ANI-ASI mixture dates ranging from about 1,900 to 4,200 years ago. In a subset of groups, 100% of the mixture is consistent with having occurred during this period. These results show that India experienced a demographic transformation several thousand years ago, from a region in which major population mixture was common to one in which mixture even between closely related groups became rare because of a shift to endogamy.

Austronesian languages are spread across half the globe, from Easter Island to Madagascar. Evidence from linguistics and archaeology indicates that the 'Austronesian expansion,' which began 4,000-5,000 years ago, likely had roots in Taiwan, but the ancestry of present-day Austronesian-speaking populations remains controversial. Here, we analyse genome-wide data from 56 populations using new methods for tracing ancestral gene flow, focusing primarily on Island Southeast Asia. We show that all sampled Austronesian groups harbour ancestry that is more closely related to aboriginal Taiwanese than to any present-day mainland population. Surprisingly, western Island Southeast Asian populations have also inherited ancestry from a source nested within the variation of present-day populations speaking Austro-Asiatic languages, which have historically been nearly exclusive to the mainland. Thus, either there was once a substantial Austro-Asiatic presence in Island Southeast Asia, or Austronesian speakers migrated to and through the mainland, admixing there before continuing to western Indonesia.

Functional genomics data has the potential to increase GWAS power by identifying SNPs that have a higher prior probability of association. Here, we introduce a method that leverages polygenic functional enrichment to incorporate coding, conserved, regulatory, and LD-related genomic annotations into association analyses. We show via simulations with real genotypes that the method, functionally informed novel discovery of risk loci (FINDOR), correctly controls the false-positive rate at null loci and attains a 9%-38% increase in the number of independent associations detected at causal loci, depending on trait polygenicity and sample size. We applied FINDOR to 27 independent complex traits and diseases from the interim UK Biobank release (average N = 130K). Averaged across traits, we attained a 13% increase in genome-wide significant loci detected (including a 20% increase for disease traits) compared to unweighted raw p values that do not use functional data. We replicated the additional loci in independent UK Biobank and non-UK Biobank data, yielding a highly statistically significant replication slope (0.66-0.69) in each case. Finally, we applied FINDOR to the full UK Biobank release (average N = 416K), attaining smaller relative improvements (consistent with simulations) but larger absolute improvements, detecting an additional 583 GWAS loci. In conclusion, leveraging functional enrichment using our method robustly increases GWAS power.

Both polygenicity (many small genetic effects) and confounding biases, such as cryptic relatedness and population stratification, can yield an inflated distribution of test statistics in genome-wide association studies (GWAS). However, current methods cannot distinguish between inflation from a true polygenic signal and bias. We have developed an approach, LD Score regression, that quantifies the contribution of each by examining the relationship between test statistics and linkage disequilibrium (LD). The LD Score regression intercept can be used to estimate a more powerful and accurate correction factor than genomic control. We find strong evidence that polygenicity accounts for the majority of the inflation in test statistics in many GWAS of large sample size.

Linear mixed models are a powerful statistical tool for identifying genetic associations and avoiding confounding. However, existing methods are computationally intractable in large cohorts and may not optimize power. All existing methods require time cost O(MN(2)) (where N is the number of samples and M is the number of SNPs) and implicitly assume an infinitesimal genetic architecture in which effect sizes are normally distributed, which can limit power. Here we present a far more efficient mixed-model association method, BOLT-LMM, which requires only a small number of O(MN) time iterations and increases power by modeling more realistic, non-infinitesimal genetic architectures via a Bayesian mixture prior on marker effect sizes. We applied BOLT-LMM to 9 quantitative traits in 23,294 samples from the Women's Genome Health Study (WGHS) and observed significant increases in power, consistent with simulations. Theory and simulations show that the boost in power increases with cohort size, making BOLT-LMM appealing for genome-wide association studies in large cohorts.

The Roma people, living throughout Europe and West Asia, are a diverse population linked by the Romani language and culture. Previous linguistic and genetic studies have suggested that the Roma migrated into Europe from South Asia about 1,000-1,500 years ago. Genetic inferences about Roma history have mostly focused on the Y chromosome and mitochondrial DNA. To explore what additional information can be learned from genome-wide data, we analyzed data from six Roma groups that we genotyped at hundreds of thousands of single nucleotide polymorphisms (SNPs). We estimate that the Roma harbor about 80% West Eurasian ancestry-derived from a combination of European and South Asian sources-and that the date of admixture of South Asian and European ancestry was about 850 years before present. We provide evidence for Eastern Europe being a major source of European ancestry, and North-west India being a major source of the South Asian ancestry in the Roma. By computing allele sharing as a measure of linkage disequilibrium, we estimate that the migration of Roma out of the Indian subcontinent was accompanied by a severe founder event, which appears to have been followed by a major demographic expansion after the arrival in Europe.

Southern and eastern African populations that speak non-Bantu languages with click consonants are known to harbour some of the most ancient genetic lineages in humans, but their relationships are poorly understood. Here, we report data from 23 populations analysed at over half a million single-nucleotide polymorphisms, using a genome-wide array designed for studying human history. The southern African Khoisan fall into two genetic groups, loosely corresponding to the northwestern and southeastern Kalahari, which we show separated within the last 30,000 years. We find that all individuals derive at least a few percent of their genomes from admixture with non-Khoisan populations that began ∼1,200 years ago. In addition, the East African Hadza and Sandawe derive a fraction of their ancestry from admixture with a population related to the Khoisan, supporting the hypothesis of an ancient link between southern and eastern Africa.