\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$D^{*}_{uv}, D^{*}_{v}$\end{document}Duv∗,Dv∗, and D ∗ computed using empirical frequencies in a random sample of error-free gene trees converge in probability to an arbitrarily small radius of an additive matrix identical in topology to the true species tree; a consistent distance method with a safety radius [ 40 ] run on these matrices is a consistent estimator of the species tree topology.