Marina Garrote López: Identifiability of Level-1 Species Networks from Gene Tree Quartets

Abstract: Phylogenetic networks offer a more realistic representation of evolutionary relationships, than phylogenetic trees, when events such as hybridization and horizontal gene transfer are involved. Methods employing quartet concordance factors, the probabilities of four-taxon gene tree topologies, have emerged as powerful tools for inferring these complex networks. While earlier studies have provided initial insights into the identifiability of certain network aspects, a complete picture of what can and cannot be uniquely determined in level-1 phylogenetic networks under the network multispecies coalescent model has remained incomplete. In this talk, we address this gap by presenting a comprehensive analysis of the identifiability of level-1 networks. By investigating the algebraic varieties defined by quartet concordance factors, we achieve a complete understanding of which topological structures and numerical parameters of level-1 networks are identifiable and, crucially, which are not. In particular, we will provide answers to several open questions concerning 3-cycles. This definitive characterization of identifiability is fundamentally important for developing and applying rigorous inference methods.