The Sackin Index of Simplex Networks

Abstract

A phylogenetic network is a simplex network if the child of every reticulation node is a network leaf and each tree node has at most one reticulation node as its child. 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 Θ(n7 / 4) in the uniform model.