Let i denote (diploid) individuals and s index SNPs. Individual i is assigned global ancestry proportion θi from some distribution F(.) with mean E[θi] = θ and variance σ2θ. Given θi, an individual is assigned maternal and paternal local ancestries γi,s,M and γi,s,P at each SNP (0 or 1 copies of European ancestry), from Bernoulli distribution Ber(θi). Given local ancestries γi,s,M, γi,s,P and allele frequencies ps,o, ps,1 at SNP s in populations 0 and 1, individuals are assigned maternal genotypes gi,s,M =γi,s,M Zi,s,1 + (1-γi,s,M) Zi,s,0 where Zi,s,0∼Ber(ps,0) and Zi,s,1∼Ber(ps,1), and similarly for paternal genotypes. The diploid genotype gi,s= gi,s,P+ gi,s,M (0, 1 or 2), and the diploid local ancestry γi,s = γi,s,P+γi,s,M (0, 1 or 2).
