Two results on expected values of imbalance indices of phylogenetic trees

TL;DR

This paper derives explicit formulas for the expected values of two imbalance indices, Colless and Sackin, in phylogenetic trees generated under the Yule and uniform models, respectively.

Contribution

It provides the first explicit formulas for the expected Colless and Sackin indices under these common models of phylogenetic tree generation.

Findings

Explicit formula for the expected Colless index under the Yule model.

Explicit formula for the expected Sackin index under the uniform model.

Enhances understanding of tree imbalance measures in phylogenetics.

Abstract

We compute an explicit formula for the expected value of the Colless index of a phylogenetic tree generated under the Yule model, and an explicit formula for the expected value of the Sackin index of a phylogenetic tree generated under the uniform model.