Exact Enumeration of Phylogenetic Networks: The Tree-Child, Reticulation-Visible and Orchard Hierarchy
This research develops a unified framework to exactly count three types of phylogenetic networks: Tree-Child (TC), Reticulation-Visible (RV), and Orchard networks. It establishes a hierarchy between them, provides explicit counting formulas for differences between RV and TC networks, and proves asymptotic scaling laws for their growth as the number of leaves increases.