2013/06/12 by Amaury Lambert, Lambert, Amaury, Mike Steel +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Earth and Planetary Sciences · #Evolution and Genetic Dynamics #Evolution and Paleontology Studies #FOS: Biological sciences #Populations and Evolution (q-bio.PE) #q-bio.PE
paper · pdf · doi:10.48550/arxiv.1306.2710
58 pages 3 figures
arxiv created 2013/06/12 · openalex publication_date 2013/06/12 · arxiv updated 2013/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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→∞, 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).