# Predicting the loss of phylogenetic diversity under non-stationary diversification 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).
Type de document :
Pré-publication, Document de travail
58 pages 3 figures. 2013
Domaine :

https://hal.archives-ouvertes.fr/hal-00833585
Contributeur : Amaury Lambert <>
Soumis le : jeudi 13 juin 2013 - 10:13:27
Dernière modification le : mercredi 21 mars 2018 - 18:56:48

### Identifiants

• HAL Id : hal-00833585, version 1
• ARXIV : 1306.2710

### Citation

Amaury Lambert, Mike Steel. Predicting the loss of phylogenetic diversity under non-stationary diversification models. 58 pages 3 figures. 2013. 〈hal-00833585〉

### Métriques

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