A balance index for phylogenetic trees based on quartets

Abstract

We define a new balance index for phylogenetic trees based on the symmetry of the evolutive history of every quartet of leaves. This index makes sense for polytomic trees and it can be computed in time linear in the number of leaves. We compute its maximum and minimum values for arbitrary and bifurcating trees, and we provide exact formulas for its expected value and variance for bifurcating trees under Fords -model and Aldous {beta}-model and for arbitrary trees under the -{gamma}-model.