Phylogenetic networks are a generalization of evolutionary trees that can be used to represent reticulate processes such as hybridization and recombination. Here, we introduce a new approach called TriLoNet (Trinet Level- one Network algorithm) to construct such networks directly from sequence alignments which works by piecing together smaller phylogenetic networks. More specifically, using a bottom up approach similar to Neighbor-Joining, TriLoNet constructs level-1 networks (networks that are somewhat more general than trees) from smaller level-1 networks on three taxa. In simulations, we show that TriLoNet compares well with Lev1athan, a method for reconstructing level-1 networks from three-leaved trees. In particular, in simulations we find that Lev1athan tends to generate networks that overestimate the number of reticulate events as compared with those generated by TriLoNet. We also illustrate TriLoNet's applicability using simulated and real sequence data involving recombination, demonstrating that it has the potential to reconstruct informative reticulate evolutionary histories. TriLoNet has been implemented in JAVA and is freely available at https://www.uea.ac.uk/computing/TriLoNet.

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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

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