Per study ancestry variation, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_{{lk}}$$\end{document}Clk is calculated using MDS on the basis of allele frequency. We defined the genetic distance between two studies, that is, study k and k′, with J variants, as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${d}_{k{k}^{{\prime} }}=\sqrt{{\sum }_{j}{\left({f}_{{jk}}-{f}_{j{k}^{{\prime} }}\right)}^{2}},$$\end{document}dkk′=∑jfjk−fjk′2, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f}_{{jk}}$$\end{document}fjk and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f}_{j{k}^{{\prime} }}$$\end{document}fjk′ are the allele frequency for the jth variant for study k and k′, respectively. We fit models with 0, 1, 2, 3 and 4 MDS components and combined the results using a minimal P value approach (see Extended Data Fig. 1a for a visual representation of the first four MDS components).
