A Metric for Phylogenetic Trees Based on Matching

Abstract

Comparing two or more phylogenetic trees is a fundamental task in computational biology. The simplest outcome of such a comparison is a pairwise measure of similarity, dissimilarity, or distance. A large number of such measures have been proposed, but so far all suffer from problems varying from computational cost to lack of robustness; many can be shown to behave unexpectedly under certain plausible inputs. For instance, similarity measures based on maximum agreement are too strict, while measures based on the elimination of rogue taxa work poorly when the proportion of rogue taxa is significant; distance measures based on edit distances under simple tree operations (such as nearest-neighbor interchange or subtree pruning and regrafting) are NP-hard; and the widely used Robinson-Foulds distance is poorly distributed and thus affords little discrimination, while also lacking robustness in the face of very small changes—reattaching a single leaf elsewhere in a tree of any size can instantly maximize the distance.

In this paper, we introduce an entirely new pairwise distance measure, based on matching, for phylogenetic trees. We prove that our measure induces a metric on the space of trees, show how to compute it in low polynomial time, verify through statistical testing that it is robust, and finally note that it does not exhibit unexpected behavior under the same inputs that cause problems with other measures. We also illustrate its usefulness in clustering trees, demonstrating significant improvements in the quality of hierarchical clustering as compared to the same collections of trees clustered using the Robinson-Foulds distance.