Notes on the birth-death prior with fossil calibrations for Bayesian estimation of species divergence times.
Constructing a multi-dimensional prior on the times of divergence (the node ages) of species in a phylogeny is not a trivial task, in particular, if the prior density is the result of combining different sources of information such as a speciation process with fossil calibration densities. Yang & Rannala (2006 Mol. Biol. Evol 23, 212-226. (doi:10.1093/molbev/msj024)) laid out the general approach to combine the birth-death process with arbitrary fossil-based densities to construct a prior on divergence times. They achieved this by calculating the density of node ages without calibrations conditioned on the ages of the calibrated nodes. Here, I show that the conditional density obtained by Yang & Rannala is misspecified. The misspecified density can sometimes be quite strange-looking and can lead to unintentionally informative priors on node ages without fossil calibrations. I derive the correct density and provide a few illustrative examples. Calculation of the density involves a sum over a large set of labelled histories, and so obtaining the density in a computer program seems hard at the moment. A general algorithm that may provide a way forward is given.This article is part of the themed issue 'Dating species divergences using rocks and clocks'.
School of Biological and Chemical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK Department of Genetics, Evolution and Environment, University College London, Gower Street, London W1C 6BT, UK m.dosreisbarros@qmul.ac.uk.
Mario
0000-0001-9514-3976
M
Dos Reis
D000818:Animals; D001499:Bayes Theorem; D005075:Biological Evolution; D002138:Calibration; D019143:Evolution, Molecular; D005580:Fossils / Q000033:anatomy & histology*; D010802:Phylogeny; D013997:Time Factors
Bayesian method; birth–death process; divergence time; molecular clock; phylogeny; time prior