Phylogenetic degrees for Jukes-Cantor model

TL;DR

This paper investigates the algebraic degrees of phylogenetic varieties under the Jukes-Cantor model, providing combinatorial methods to compute the volumes of associated polytopes, which reveal the model's geometric properties.

Contribution

It introduces two combinatorial approaches to compute the volumes of polytopes related to the Jukes-Cantor model's phylogenetic varieties, advancing understanding of their algebraic degrees.

Findings

Derived formulas for phylogenetic degrees of the Jukes-Cantor model.

Provided combinatorial algorithms for polytope volume computation.

Enhanced geometric understanding of phylogenetic models.

Abstract

Jukes-Cantor model is one of the most meaningful statistical models from a biological perspective. We are interested in computing the algebraic degrees for phylogenetic varieties, which we call phylogenetic degrees, associated to the Jukes-Cantor model and any tree. As these varieties are toric, their geometry is hidden in the associated polytopes. For this reason, we provide two different combinatorial approaches to compute the volume for these polytopes.