title: Tripartitions do not always discriminate phylogenetic networks.
abstract: Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of non-treelike evolutionary events, like recombination, hybridization, or lateral gene transfer. In a recent series of papers devoted to the study of reconstructibility of phylogenetic networks, Moret, Nakhleh, Warnow and collaborators introduced the so-called tripartition metric for phylogenetic networks. In this paper we show that, in fact, this tripartition metric does not satisfy the separation axiom of distances (zero distance means isomorphism, or, in a more relaxed version, zero distance means indistinguishability in some specific sense) in any of the subclasses of phylogenetic networks where it is claimed to do so. We also present a subclass of phylogenetic networks whose members can be singled out by means of their sets of tripartitions (or even clusters), and hence where the latter can be used to define a meaningful metric.
authors.affiliation: Department of Mathematics and Computer Science, University of the Balearic Islands, E-07122 Palma de Mallorca, Spain. gabriel.cardona@uib.es
authors.forename: Gabriel
authors.initials: G
authors.lastname: Cardona
authors.forename: Francesc
authors.initials: F
authors.lastname: Rosselló
authors.forename: Gabriel
authors.initials: G
authors.lastname: Valiente
mesh_terms: D019143:Evolution, Molecular; D008957:Models, Genetic; D010802:Phylogeny