title: Predicting the loss of phylogenetic diversity under non-stationary diversification models.
abstract: For many species, 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 species, while the remaining N-K become extinct (N and K being random variables). 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→∞, both under the field of bullets model, and when K=kn is fixed and depends on n in such a way that kn/n converges to p. We also prove the convergence of this ratio as T→∞ in the supercritical, time-homogeneous case, where N simultaneously goes to ∞, thereby strengthening previous results of Mooers et al. (2012).
authors: Collège de France, Center for Interdisciplinary Research in Biology CNRS UMR 7241, Paris, France. Electronic address: amaury.lambert@upmc.fr.
authors: Amaury
authors: A
authors: Lambert
authors: Biomathematics Research Centre, University of Canterbury, Private Bag 4800, Christchurch, New Zealand. Electronic address: mike.steel@canterbury.ac.nz.
authors: Mike
authors: M
authors: Steel
mesh_terms: D044822:Biodiversity; D008954:Models, Biological; D010802:Phylogeny
keywords: Diversification process; Field of bullets model; Phylogenetic tree