a ∣ The variation in genome-wide ancestry in individuals from admixed populations is illustrated by using EIGENSOFT software to apply principal components analysis to admixed individuals. The samples were derived from HapMap 3 and the Human Genome Diversity Project (HGDP). The HapMap 3 samples included: West African (YRI, Yoruba in Ibadan, Nigeria), European (CEU, Utah residents with northern and western European ancestry from the CEPH collection), African American (ASW, African ancestry in Southwest USA) and Mexican American (MXL, Mexican ancestry in Los Angeles, California). For Native Americans, HGDP samples were used. Analyses were restricted to the intersection of HapMap 3 and HGDP marker sets. The results confirm that most African Americans lie on a cline of African and European ancestry with an average of 80% African and 20% European ancestry^1,2,29. The results also confirm that Mexican Americans lie on a cline of European and Native American ancestry with low levels of African ancestry: an average of 50% European, 45% Native American and 5% African ancestry^4,14,15. We caution that the positions of Native American individuals on this plot are complicated by recent European admixture (especially in Pima and Maya) and by population-specific drift (especially in Colombian, Karitiana and Surui populations). b ∣ Here, the variation in local ancestry in African Americans is illustrated by showing an individual (NA19919) from the ASW population as analysed by HAPMIX software²⁹ to estimate local ancestry on chromosome 1. The lengths of chromosomal segments of 0, 1 or 2 copies of European ancestry are consistent with previous estimates of an average of six generations since admixture in this population^1,2,29. We note that Latino populations have an average of 10–15 generations since admixture, leading to shorter chromosomal segments^4,14,15.

We computed the power of each method to attain genome-wide significance, which is defined based on a P value threshold of 5 × 10⁻⁸ for ATT, SUM and MIX and 1 × 10⁻⁵ for ADM (which has a decreased multiple hypothesis testing burden based on the lengths of chromosomal segments)^32,36 (see the figure). Our results are based on simulations of causal SNPs that are either randomly differentiated or highly differentiated (allele frequency difference >40% between Europeans and Africans). The simulations were performed starting with 100,000 random autosomal SNPs extracted from real genotypes in 6,209 African Americans³². Using a causal model with a genotypic odds ratio of 1.5, a total of 1,000 cases and 1,000 controls were simulated. As shown in the figure, MIX versus ATT produces a modest increase in power (41.3% versus 38%; 9% improvement) for randomly differentiated SNPs and a large increase in power (69.0% versus 55.3%; 25% improvement) for highly differentiated SNPs.