True quartet probabilities are not known. Instead, we empirically use \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\overline {p}(ab.uv)=\frac {1}{k}|\{t:\mathcal {G}|ab.uv\in \mathcal {Q}^{t}\}|$\end{document}p¯(ab.uv)=1k|{t:G|ab.uv∈Qt}|. Empirical frequencies inferred from gene trees converge in probability to true values as the number of genes increases; thus, it is easy to show (proof omitted):