  The Tree of Life is the graphical structure that represents the evolutionary
process from single-cell organisms at the origin of life to the vast
biodiversity we see today. Reconstructing this tree from genomic sequences is
challenging due to the variety of biological forces that shape the signal in
the data, and many of those processes like incomplete lineage sorting and
hybridization can produce confounding information. Here, we present the
mathematical version of the identifiability proofs of phylogenetic networks
under the pseudolikelihood model in SNaQ. We establish that the ability to
detect different hybridization events depends on the number of nodes on the
hybridization blob, with small blobs (corresponding to closely related species)
being the hardest to be detected. Our work focuses on level-1 networks, but
raises attention to the importance of identifiability studies on phylogenetic
inference methods for broader classes of networks.
