  Phylogenetic networks are necessary to represent the tree of life expanded by
edges to represent events such as horizontal gene transfers, hybridizations or
gene flow. Not all species follow the paradigm of vertical inheritance of their
genetic material. While a great deal of research has flourished into the
inference of phylogenetic trees, statistical methods to infer phylogenetic
networks are still limited and under development. The main disadvantage of
existing methods is a lack of scalability. Here, we present a statistical
method to infer phylogenetic networks from multi-locus genetic data in a
pseudolikelihood framework. Our model accounts for incomplete lineage sorting
through the coalescent model, and for horizontal inheritance of genes through
reticulation nodes in the network. Computation of the pseudolikelihood is fast
and simple, and it avoids the burdensome calculation of the full likelihood
which can be intractable with many species. Moreover, estimation at the
quartet-level has the added computational benefit that it is easily
parallelizable. Simulation studies comparing our method to a full likelihood
approach show that our pseudolikelihood approach is much faster without
compromising accuracy. We applied our method to reconstruct the evolutionary
relationships among swordtails and platyfishes ($Xiphophorus$: Poeciliidae),
which is characterized by widespread hybridizations.
