  Species networks generalize the notion of species trees to allow for
hybridization or other lateral gene transfer. Under the Network Multispecies
Coalescent Model, individual gene trees arising from a network can have any
topology, but arise with frequencies dependent on the network structure and
numerical parameters. We propose a new algorithm for statistical inference of a
level-1 species network under this model, from data consisting of gene tree
topologies, and provide the theoretical justification for it. The algorithm is
based in an analysis of quartets displayed on gene trees, combining several
statistical hypothesis tests with combinatorial ideas such as a quartet-based
intertaxon distance appropriate to networks, the NeighborNet algorithm for
circular split systems, and the Circular Network algorithm for constructing a
splits graph.
