A minimal compact description of the diversity index polytope

TL;DR

This paper characterizes the diversity index polytope for phylogenetic trees, providing a minimal description and exploring extensions for biodiversity measurement.

Contribution

It offers a combinatorial analysis of phylogenetic diversity indices to describe the diversity index polytope minimally and discusses its extensions.

Findings

Provided a minimal compact description of the diversity index polytope.

Analyzed the combinatorics of phylogenetic diversity indices.

Explored extensions of the polytope for broader biodiversity measurement.

Abstract

A phylogenetic tree is an edge-weighted binary tree, with leaves labelled by a collection of species, that represents the evolutionary relationships between those species. For such a tree, a phylogenetic diversity index is a function that apportions the biodiversity of the collection across its constituent species. The diversity index polytope is the convex hull of the images of phylogenetic diversity indices. We study the combinatorics of phylogenetic diversity indices to provide a minimal compact description of the diversity index polytope. Furthermore, we discuss extensions of the polytope to expand the study of biodiversity measurement.