Affiliations: Department of Mathematics and Computer Science, University of the Balearic Islands, E-07122 Palma de Mallorca, Spain. {adria.alcala,merce.llabres,cesc.rossello}@uib.es, pau@rullan.cat
Note: [] Address for correspondence: Department of Mathematics and Computer Science, University of the Balearic Islands, E-07122 Palma de Mallorca, Spain
Abstract: In general, a phylogenetic network is a graphical representation of an evolutionary history that involves reticulate events like recombinations, hybridizations, or lateral gene transfers. Tree-child reticulate networks (TC networks) are a special class of phylogenetic networks that allow to represent evolutionary histories where, despite the existence of such reticulate events, every ancestral species has some descendant through mutations. In this paper we establish two equivalent characterizations of the families of clusters of TC networks. These characterizations yield a simple, polynomial-time algorithm that decides whether a given family of clusters on a set of taxa is the family of clusters of some TC network or not, and, when the answer is positive, outputs a TC network that is a minimal reticulate network representing this family of clusters. This algorithm is based on the notion of cluster network introduced by Huson and Rupp, and it has been implemented in a Python package and a companion web tool, which are freely available on the web.
