Additional file 1: Algorithm S4 shows DISTIQUE’s targeted sampling strategy for choosing a subset of all possible anchor pairs. Let d 1…d r denote the degree of polytomies in the consensus tree, indexed arbitrarily. For each polytomy i, we randomly partition its d i clusters into sets of size two; if d i is odd, we randomly choose a cluster and pair it with the remaining cluster. Then, we randomly choose one species from each cluster. This produces \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lceil \frac {d_{i}}{2}\rceil $\end{document}⌈di2⌉ pairs of anchors for each polytomy i. The total number of anchors is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$m={\sum _{1}^{r}} \lceil \frac {d_{i}}{2}\rceil =O(n)$\end{document}m=∑1r⌈di2⌉=O(n) (Additional file 1: Lemma S2). Each anchor pair is used to resolve all polytomies on the path between them in the consensus tree. This processes may be repeated several rounds (a user-specified input parameter).