The phenotypes were simulated based on the additive model y = g + e in all scenarios using different values of MC and trait heritability (h2). In each simulation replicate, we simulated a trait with a heritability of 0.25 or 0.5 in all ancestries. Traits were simulated from MC (MC = 1000, 5000 and 10,000) causal variants sampled at random from the HapMap3 SNPs. We assumed the effect sizes of causal variants (β) were perfectly correlated across populations, i.e. ρb = 1. For each causal variant, β was sampled from a normal distribution with mean 0 and variance \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{h^2}}{{2p_{jl}(1 - p_{jl})M_{\mathrm{C}}}}$$\end{document}h22pjl(1−pjl)MC, where pjl is the MAF in jth causal variant in population l. For each individual, the genetic value g was defined such as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g = \mathop {\sum}\nolimits_{j = 1}^M {x_{jl}\beta _j}$$\end{document}g=∑j=1Mxjlβj, where xjl denotes the minor allele count (xjl equals to 0, 1 or 2) at the jth causal variant in population l. The environmental effect (e) was simulated using a
