A parsimony-based metric for phylogenetic trees

In evolutionary biology various metrics have been defined and studied for comparing phylogenetic trees. Such metrics are used, for example, to compare competing evolutionary hypotheses or to help organize algorithms that search for optimal trees. Here we introduce a new metric dpdp on the collection of binary phylogenetic trees each labeled by the same set of species. The metric is based on the so-called parsimony score, an important concept in phylogenetics that is commonly used to construct phylogenetic trees. Our main results include a characterization of the unit neighborhood of a tree in the dpdp metric, and an explicit formula for its diameter, that is, a formula for the maximum possible value of dpdp over all possible pairs of trees labeled by the same set of species. We also show that dpdp is closely related to the well-known tree bisection and reconnection (tbr) and subtree prune and regraft (spr) distances, a connection which will hopefully provide a useful new approach to understanding properties of these and related metrics.