Theoretical basis of admixture GWAS study designs. (a) Populations 1 and 2 are two parental populations in which there has been no gene flow historically. When these populations interbreed the subsequent F1 population includes heterozygotes. Over the course of 5 or 10 generations the chromosome of any given Fn population offspring will include a combination of parental chromosomal `bands'. Some loci are associated with a disease (such as B) and others are not (such as A). (b, c) In a typical GWAS, association testing identifies whether a given allele (such as T at SNP2) is associated with increased risk for having a disease; this is shown as allele frequencies in the table. (c) If the ancestral frequency of T at SNP2 is different in two parental populations (1 and 2) and if it is associated with disease, then the population with higher frequencies of this allele will also have higher risk for disease. One can thus expect to observe higher incidences of disease in individuals carrying the T allele and also higher incidence of disease in individuals from population 1, in which the T allele is more frequent. This is the premise of admixture association studies. By ascertaining local ancestry one can determine if an allele that is much more common in one population may be associated with disease risk. In (b), in a locus with no evidence of association with disease, admixture analysis would find that the minor allele frequencies (and percentages of individuals of either ancestral populations) do not differ between cases and controls. (d) Graph of the allele frequencies along the genome. The relative frequency of the allele from population 1 differs between the cases and the controls only at the locus associated with the disease/phenotype. Thus, in admixed populations, by determining the local ancestry in the cases versus controls, one can determine if there is an association between an allele associated with ancestry and disease liability.