Phylogenetic Network Dissimilarity Measures That Take Branch Lengths Into Account

Dissimilarity measures for phylogenetic trees have long been used for analyzing inferred trees and understanding the performance of phylogenetic methods. Given their importance, a wide array of such measures have been developed, some of which are based on the tree topologies alone, and others that also take branch lengths into account. Similarly, a number of dissimilarity measures of phylogenetic networks have been developed in the last two decades. However, to the best of our knowledge, all these measures are based solely on the topologies of phylogenetic networks and ignore branch lengths. In this paper, we propose two phylogenetic network dissimilarity measures that take both topology and branch lengths into account. We demonstrate the behavior of these two measures on pairs of related networks. Furthermore, we show how these measures can be used to cluster a set of phylogenetic networks obtained by an inference method, illustrating this application on the posterior sample of phylogenetic networks. Both measures are implemented in the publicly available software package PhyloNet.