Generalization of Phylogenetic Matching Metrics with Experimental Tests of Practical Advantages

The ability to quantify a dissimilarity of different phylogenetic trees is required in various types of phylogenetic studies, for example, such metrics are used to assess the quality of phylogeny construction methods and to define optimization criteria in supertree building algorithms. In this article, starting from the already described concept of matching metrics, we define three new metrics for rooted phylogenetic trees. One of them, Matching Pair Jaccard (MPJ) distance, is still purely topological, but we now utilize the Jaccard index set dissimilarity measure in its construction. This modification substantially changes the structural features of the metric space. In particular, we investigate the properties of the previously known Matching Cluster Jaccard (MCJ) and the new MPJ metrics, such as the asymptotic behavior of their expected distance between two random trees, the space diameter, and the change of a distance after a single leaf relocation. The other two metrics, Matching Cluster Weight-aware (MCW) and Matching Cluster Jaccard Weight-aware (MCJW) distances, are the first propositions of generalization of matching metrics designed for rooted phylogenies with branch lengths. The experimental tests of the practical utility of the phylogenetic metrics show the superiority of MCJ, MPJ over the previous best tree comparison method. To define the MCW and MCJW metrics, we introduce a general method for constructing matching metrics for weighted rooted phylogenetic trees.