%0 Journal Article
%A dos Reis, Mario
%T Notes on the birth–death prior with fossil calibrations for Bayesian estimation of species divergence times
%D 2016
%R 10.1098/rstb.2015.0128
%J Philosophical Transactions of the Royal Society B: Biological Sciences
%V 371
%N 1699
%X 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’.
%U http://rstb.royalsocietypublishing.org/content/royptb/371/1699/20150128.full.pdf