The Sackin Index of Simplex Networks

A phylogenetic network is a simplex (or 1-component tree-child) network if the child of every reticulation node is a network leaf. Simplex networks are a superclass of phylogenetic trees and a subclass of tree-child networks. Generalizing the Sackin index to phylogenetic networks, we prove that the expected Sackin index of a random simplex network is asymptotically $\Omega(n^{7/4})$ in the uniform model.