Properties of biodiversity indices that model future extinction risk

TL;DR

This paper generalizes biodiversity indices used to predict future extinction risks, expanding their applicability to various biodiversity measures and providing explicit statistical descriptions, with an application to crocodilian phylogeny.

Contribution

It introduces a generalized framework for biodiversity indices like HED and HEDGE, applicable to phylogenetic networks and feature diversity, with explicit mean and variance calculations.

Findings

Generalized HED(GE) indices for broader biodiversity measures.

Explicit formulas for mean and variance of biodiversity measures.

Application to crocodilian phylogeny demonstrating practical use.

Abstract

The loss of biodiversity due to the likely widespread extinction of species in the near future is a focus of current concern in conservation biology. One approach to measure the impact of this extinction is based on the predicted loss of phylogenetic diversity. These predictions have become a focus of the Zoological Society of London's 'EDGE2' program for quantifying biodiversity loss and involves considering the HED (heightened evolutionary distinctiveness) and HEDGE (heightened evolutionary distinctiveness and globally endangered) indices. Here, we show how to generalise the HED(GE) indices by expanding their application to more general settings (to phylogenetic networks, to feature diversity on discrete traits, and to arbitrary biodiversity measures). We provide a simple and explicit description of the mean and variance of such measures, and illustrate our results by an application to the phylogeny of all 27 extant Crocodilians. We also derive various equalities for feature diversity, and an inequality if species extinction rates are correlated with feature types.