  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.
