Predicting the loss of phylogenetic diversity under non-stationary diversification models

TL;DR

This paper develops explicit formulas to predict the loss of phylogenetic diversity under non-stationary models of diversification, accounting for time-dependent speciation and extinction rates, and different species sampling scenarios.

Contribution

It introduces new mathematical formulas for expected phylogenetic diversity loss under complex, non-stationary diversification models with random extinction scenarios.

Findings

Explicit formulas for expected remaining PD under various models.

Convergence results for the ratio of remaining to initial PD as the number of species grows.

Strengthening previous results on PD loss in supercritical, time-homogeneous models.

Abstract

For many taxa, the current high rates of extinction are likely to result in a significant loss of biodiversity. The evolutionary heritage of biodiversity is frequently quantified by a measure called phylogenetic diversity (PD). We predict the loss of PD under a wide class of phylogenetic tree models, where speciation rates and extinction rates may be time-dependent, and assuming independent random species extinctions at the present. We study the loss of PD when $K$ contemporary species are selected uniformly at random from the $N$ extant species as the surviving taxa, while the remaining $N-K$ become extinct. We consider two models of species sampling, the so-called field of bullets model, where each species independently survives the extinction event at the present with probability $p$, and a model for which the number of surviving species is fixed. We provide explicit formulae for the expected remaining PD in both models, conditional on $N=n$, conditional on $K=k$, or conditional on both events. When $N=n$ is fixed, we show the convergence to an explicit deterministic limit of the ratio of new to initial PD, as $n\to\infty$, both under the field of bullets model, and when $K=k_n$ is fixed and depends on $n$ in such a way that $k_n/n$ converges to $p$. We also prove the convergence of this ratio as $T\to\infty$ in the supercritical, time-homogeneous case, where $N$ simultaneously goes to $\infty$, thereby strengthening previous results of Mooers et al. (2012).