Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$D^{*}_{uv}$\end{document}Duv∗ and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$D^{*}_{wz}$\end{document}Dwz∗ be two double anchored matrices produced using two disjoint pairs of anchors. If the two matrices are reduced to the n−4 leaves common between them (i.e., \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {L}^{\prime }=\mathcal {L}-\{u,v, w,z\}$\end{document}ℒ′=ℒ−{u,v,w,z}), we get two matrices that asymptotically converge to an additive matrix for the same tree topology (Corollary 1). The sum of two additive distance matrices that correspond to the same tree topology is also additive for the same topology. Thus, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$D^{*}_{uv}|\mathcal {L}^{\prime }+D^{*}_{wz}|\mathcal {L}^{\prime }$\end{document}Duv∗|ℒ′+Dwz∗|ℒ′ is asymptotically additive for the correct species tree. This provides a theoretical justification for our distance-sum approach. However, distances between four anchors and other leaves are missing in one of the matrices, and thus, their correct placement cannot be guaranteed.