Inferring phylogenetic networks to represent the tree of life expanded by hybridization edges is necessary because not all species follow the paradigm of vertical inheritance of their genetic material. Inference of phylogenetic trees is well established, but methods to infer explicit phylogenetic networks are still under development. Furthermore, testing whether gene tree discordance can be explained entirely by incomplete lineage sorting or we need to invoke reticulation events is still a difficult question.
We will address both problems with (i) a statistical method to infer phylogenetic networks from sequence data in a pseudolikelihood framework and (ii) a theoretical test to determine whether a species tree (or a species network) is a good fit for the gene tree discordance. The computation of the pseudolikelihood is based on quartets, with the following advantages: gene trees need not be rooted, and we avoid the burdensome calculation of the full likelihood, which is untractable on many species and many reticulations.