A cubic-time algorithm for computing the trinet distance between level-1 networks

In evolutionary biology, phylogenetic networks are constructed to represent the evolution of species in which reticulate events are thought to have occurred, such as recombination and hybridization. It is therefore useful to have efficiently computable metrics with which to systematically compare such networks. Through developing an optimal algorithm to enumerate all trinets displayed by a level-1 network (a type of network that is slightly more general than an evolutionary tree), here we propose a cubic-time algorithm to compute the trinet distance between two level-1 networks. Employing simulations, we also present a comparison between the trinet metric and the so-called Robinson-Foulds phylogenetic network metric restricted to level-1 networks. The algorithms described in this paper have been implemented in JAVA and are freely available at https://www.uea.ac.uk/computing/TriLoNet.