title: Continuous and tractable models for the variation of evolutionary rates.
abstract: We propose a continuous model for variation in the evolutionary rate across sites and over the phylogenetic tree. We derive exact transition probabilities of substitutions under this model. Changes in rate are modelled using the CIR process, a diffusion widely used in financial applications. The model directly extends the standard gamma distributed rates across site model, with one additional parameter governing changes in rate down the tree. The parameters of the model can be estimated directly from two well-known statistics: the index of dispersion and the gamma shape parameter of the rates across sites model. The CIR model can be readily incorporated into probabilistic models for sequence evolution. We provide here an exact formula for the likelihood of a three-taxon tree. The likelihoods of larger trees can be evaluated using Monte-Carlo methods.
authors.affiliation: Department of Mathematics and Statistics, McGill University, Montréal, Canada.
authors.forename: Thomas
authors.initials: T
authors.lastname: Lepage
authors.forename: Stephan
authors.initials: S
authors.lastname: Lawi
authors.forename: Paul
authors.initials: P
authors.lastname: Tupper
authors.forename: David
authors.initials: D
authors.lastname: Bryant
mesh_terms: D001483:Base Sequence; D019143:Evolution, Molecular; D008390:Markov Chains; D008957:Models, Genetic; D009010:Monte Carlo Method; D010802:Phylogeny