Population stratification has long been recognized as a confounding factor in genetic association studies. Estimated ancestries, derived from multi-locus genotype data, can be used to perform a statistical correction for population stratification. One popular technique for estimation of ancestry is the model-based approach embodied by the widely applied program structure. Another approach, implemented in the program EIGENSTRAT, relies on Principal Component Analysis rather than model-based estimation and does not directly deliver admixture fractions. EIGENSTRAT has gained in popularity in part owing to its remarkable speed in comparison to structure. We present a new algorithm and a program, ADMIXTURE, for model-based estimation of ancestry in unrelated individuals. ADMIXTURE adopts the likelihood model embedded in structure. However, ADMIXTURE runs considerably faster, solving problems in minutes that take structure hours. In many of our experiments, we have found that ADMIXTURE is almost as fast as EIGENSTRAT. The runtime improvements of ADMIXTURE rely on a fast block relaxation scheme using sequential quadratic programming for block updates, coupled with a novel quasi-Newton acceleration of convergence. Our algorithm also runs faster and with greater accuracy than the implementation of an Expectation-Maximization (EM) algorithm incorporated in the program FRAPPE. Our simulations show that ADMIXTURE's maximum likelihood estimates of the underlying admixture coefficients and ancestral allele frequencies are as accurate as structure's Bayesian estimates. On real-world data sets, ADMIXTURE's estimates are directly comparable to those from structure and EIGENSTRAT. Taken together, our results show that ADMIXTURE's computational speed opens up the possibility of using a much larger set of markers in model-based ancestry estimation and that its estimates are suitable for use in correcting for population stratification in association studies.

/pdf/fast-model-based-estimation-of-ancestry-in-unrelated-1hvb7yh3n1.pdf

Fast model-based estimation of ancestry in unrelated individuals

Current methods for inferring population structure from genetic data do not provide formal significance tests for population differentiation. We discuss an approach to studying population structure (principal components analysis) that was first applied to genetic data by Cavalli-Sforza and colleagues. We place the method on a solid statistical footing, using results from modern statistics to develop formal significance tests. We also uncover a general “phase change” phenomenon about the ability to detect structure in genetic data, which emerges from the statistical theory we use, and has an important implication for the ability to discover structure in genetic data: for a fixed but large dataset size, divergence between two populations (as measured, for example, by a statistic like FST) below a threshold is essentially undetectable, but a little above threshold, detection will be easy. This means that we can predict the dataset size needed to detect structure.

/pdf/population-structure-and-eigenanalysis-46f957xkuu.pdf

Population structure and eigenanalysis

Genetic factors strongly affect susceptibility to common diseases and also influence disease-related quantitative traits. Identifying the relevant genes has been difficult, in part because each causal gene only makes a small contribution to overall heritability. Genetic association studies offer a potentially powerful approach for mapping causal genes with modest effects, but are limited because only a small number of genes can be studied at a time. Genome-wide association studies will soon become possible, and could open new frontiers in our understanding and treatment of disease. However, the execution and analysis of such studies will require great care.

Genome-wide association studies for common diseases and complex traits

Demographic models built from genetic data play important roles in illuminating prehistorical events and serving as null models in genome scans for selection. We introduce an inference method based on the joint frequency spectrum of genetic variants within and between populations. For candidate models we numerically compute the expected spectrum using a diffusion approximation to the one-locus, two-allele Wright-Fisher process, involving up to three simultaneous populations. Our approach is a composite likelihood scheme, since linkage between neutral loci alters the variance but not the expectation of the frequency spectrum. We thus use bootstraps incorporating linkage to estimate uncertainties for parameters and significance values for hypothesis tests. Our method can also incorporate selection on single sites, predicting the joint distribution of selected alleles among populations experiencing a bevy of evolutionary forces, including expansions, contractions, migrations, and admixture. We model human expansion out of Africa and the settlement of the New World, using 5 Mb of noncoding DNA resequenced in 68 individuals from 4 populations (YRI, CHB, CEU, and MXL) by the Environmental Genome Project. We infer divergence between West African and Eurasian populations 140 thousand years ago (95% confidence interval: 40–270 kya). This is earlier than other genetic studies, in part because we incorporate migration. We estimate the European (CEU) and East Asian (CHB) divergence time to be 23 kya (95% c.i.: 17–43 kya), long after archeological evidence places modern humans in Europe. Finally, we estimate divergence between East Asians (CHB) and Mexican-Americans (MXL) of 22 kya (95% c.i.: 16.3–26.9 kya), and our analysis yields no evidence for subsequent migration. Furthermore, combining our demographic model with a previously estimated distribution of selective effects among newly arising amino acid mutations accurately predicts the frequency spectrum of nonsynonymous variants across three continental populations (YRI, CHB, CEU).

/pdf/inferring-the-joint-demographic-history-of-multiple-34yl1aivyv.pdf

Inferring the joint demographic history of multiple populations from multidimensional SNP frequency data.

Individual differences in DNA sequence are the genetic basis of human variability. We have characterized whole-genome patterns of common human DNA variation by genotyping 1,586,383 single-nucleotide polymorphisms (SNPs) in 71 Americans of European, African, and Asian ancestry. Our results indicate that these SNPs capture most common genetic variation as a result of linkage disequilibrium, the correlation among common SNP alleles. We observe a strong correlation between extended regions of linkage disequilibrium and functional genomic elements. Our data provide a tool for exploring many questions that remain regarding the causal role of common human DNA variation in complex human traits and for investigating the nature of genetic variation within and between human populations.

https://science.sciencemag.org/content/sci/307/5712/1072.full.pdf

Whole-Genome Patterns of Common DNA Variation in Three Human Populations

Admixture mapping (also known as “mapping by admixture linkage disequilibrium,” or MALD) has been proposed as an efficient approach to localizing disease-causing variants that differ in frequency (because of either drift or selection) between two historically separated populations. Near a disease gene, patient populations descended from the recent mixing of two or more ethnic groups should have an increased probability of inheriting the alleles derived from the ethnic group that carries more disease-susceptibility alleles. The central attraction of admixture mapping is that, since gene flow has occurred recently in modern populations (e.g., in African and Hispanic Americans in the past 20 generations), it is expected that admixture-generated linkage disequilibrium should extend for many centimorgans. High-resolution marker sets are now becoming available to test this approach, but progress will require (a) computational methods to infer ancestral origin at each point in the genome and (b) empirical characterization of the general properties of linkage disequilibrium due to admixture. Here we describe statistical methods to estimate the ancestral origin of a locus on the basis of the composite genotypes of linked markers, and we show that this approach accurately estimates states of ancestral origin along the genome. We apply this approach to show that strong admixture linkage disequilibrium extends, on average, for 17 cM in African Americans. Finally, we present power calculations under varying models of disease risk, sample size, and proportions of ancestry. Studying ∼2,500 markers in ∼2,500 patients should provide power to detect many regions contributing to common disease. A particularly important result is that the power of an admixture mapping study to detect a locus will be nearly the same for a wide range of mixture scenarios: the mixture proportion should be 10%–90% from both ancestral populations.

https://www.cell.com/ajhg/pdf/S0002-9297(07)64363-8.pdf

Neil Hattangadi

Papers

Methods for high-density admixture mapping of disease genes.