SMILE

Stochastic Models for the Inference of Life Evolution

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

Lambert, A., Steel, M.

Journal of Theoretical Biology

2013

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).

Bibtex

@article{lambert_predicting_2013,
Author = {Lambert, Amaury and Steel, Mike},
Title = {Predicting the loss of phylogenetic diversity under
non-stationary diversification models},
Journal = {Journal of Theoretical Biology},
Volume = {337},
Pages = {111--124},
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).},
doi = {10.1016/j.jtbi.2013.08.009},
issn = {1095-8541},
language = {eng},
month = nov,
pmid = {23973477},
year = 2013
}

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