Computing phylogenetic trees using topologically related minimum spanning trees

Choi et al. [2] introduced a minimum spanning tree (MST)-based method called CLGrouping, for constructing tree-structured probabilistic graphical models, a statistical framework that is commonly used for inferring phylogenetic trees. While CLGrouping works correctly if there is a unique MST, we observe an indeterminacy in the method in the case that there are multiple MSTs. We demonstrate the indeterminacy of CLGrouping using a synthetic quartet tree and a tree over primate genera. The indeterminacy of CLGrouping can be removed if the input MST shares a topological relationship with the corresponding phylogenetic tree. We introduce so-called vertex order based MSTs (VMSTs) that are guaranteed to have the desired topological relationship. We relate the number of leaves in the VMST to the degree of parallelism that is offered by CLGrouping. We provide polynomial-time algorithms for constructing VMSTs and for selecting a VMST with the optimal number of leaves. Submitted: November 2016 Reviewed: April 2017 Revised: May 2017 Accepted: August 2017 Final: September 2017 Published: October 2017 Article type: Regular paper Communicated by: F. Vandin PK’s work has been funded in part by the German Center for Infection Research (DZIF, German Ministry of Education and Research Grants No. TTU 05.805, TTU 05.809) E-mail addresses: [email protected] (Prabhav Kalaghatgi) [email protected] (Thomas Lengauer) 1004 Kalaghatgi & Lengauer Computing phylogenetic trees . . .