Closed form modeling of evolutionary rates by exponential Brownian functionals

Nicolas Privault 1 Stéphane Guindon 2
2 MAB - Méthodes et Algorithmes pour la Bioinformatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : Accurate estimation of species divergence times from the analysis of genetic S equences relies on probabilistic models of evolution of the rate of molecular evolution. Importantly, while these models describe the sample paths of the substitution rates along a phylogenetic tree, only the (random) average rate can be estimated on each edge. For mathematical convenience, the stochastic nature of these averages is generally ignored. In this article we derive the probabilistic distribution of the average substitution rate assuming a geometric Brownian motion for the sample paths, and we investigate the corresponding error bounds via numerical simulations. In particular we confirm the validity of the gamma approximation proposed in Guindon (Syst Biol 62(1):22–34, 2013) for “small” values of the autocorrelation parameter.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-01233099
Contributor : Stephane Guindon <>
Submitted on : Tuesday, November 24, 2015 - 2:44:32 PM
Last modification on : Thursday, May 24, 2018 - 3:59:22 PM

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Nicolas Privault, Stéphane Guindon. Closed form modeling of evolutionary rates by exponential Brownian functionals. Journal of Mathematical Biology, Springer Verlag (Germany), 2015, 71 (6), pp.1387-1409. ⟨10.1007/s00285-015-0863-6⟩. ⟨lirmm-01233099⟩

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