The Sackin Index of Simplex Networks

TL;DR

This paper extends the Sackin index to simplex networks, a class of phylogenetic networks, and proves that the expected index grows asymptotically as Omega(n^{7/4}) in the uniform model.

Contribution

It introduces a generalization of the Sackin index to simplex networks and establishes its asymptotic behavior in the uniform model.

Findings

Expected Sackin index grows as Omega(n^{7/4})

Simplex networks are a superclass of phylogenetic trees

Asymptotic analysis of index in network models

Abstract

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.