  We propose a continuous model for evolutionary rate variation across sites
and over the tree and derive exact transition probabilities 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 taxa tree. Larger trees can be
evaluated using Monte-Carlo methods.
