Article

Continuous and tractable models of the variation of evolutionary rates. Math Biosci

Department of Mathematics and Statistics, McGill University, Montréal, Canada.
Mathematical Biosciences (Impact Factor: 1.49). 03/2006; 199(2):216-33. DOI: 10.1016/j.mbs.2005.11.002
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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.

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Available from: Stephan Lawi, Aug 30, 2015
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    • "Under a 'relaxed-clock' model, substitution rates change over the tree in a constrained manner, thus separating the rate and time parameters associated with each branch and allowing inference of lineage divergence times. A considerable amount of effort has been directed at modeling lineage-specific substitution rate variation, with many different relaxed-clock models described in the literature [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]. When such models are coupled with a model on the distribution of speciation events over time (e.g., the Yule model [20] or birth-death process [21]), molecularsequence data can then inform the relative rates and node ages in a phylogenetic analysis. "
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    • "Others assume that branch-specific rates are drawn from a single underlying distribution, such as a lognormal, gamma, or exponential distribution, the parameters of which are estimated from the data (Drummond et al. 2006; Lepage et al. 2007; Rannala and Yang 2007). The available relaxed-clock methods have been compared in several reviews (Magalí on 2004; Welch and Bromham 2005; Lepage et al. 2006; Rutschmann 2006), and their performance has been assessed in a number of studies (e.g., Ho et al. 2005; Drummond et al. 2006; Lepage et al. 2007). The new relaxed-clock methods have also introduced more flexible techniques for incorporating calibrations, leading to a lively discussion about approaches to calibrating estimates of divergence times (Graur and Martin 2004; Hedges and Kumar 2004; Donoghue and Benton 2007; Ho 2007). "
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