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Model Averaging and Bayes Factor Calculation of Relaxed Molecular Clocks in Bayesian Phylogenetics

By Wai Lok Sibon Li and Alexei J. Drummond


We describe a procedure for model averaging of relaxed molecular clock models in Bayesian phylogenetics. Our approach allows us to model the distribution of rates of substitution across branches, averaged over a set of models, rather than conditioned on a single model. We implement this procedure and test it on simulated data to show that our method can accurately recover the true underlying distribution of rates. We applied the method to a set of alignments taken from a data set of 12 mammalian species and uncovered evidence that lognormally distributed rates better describe this data set than do exponentially distributed rates. Additionally, our implementation of model averaging permits accurate calculation of the Bayes factor(s) between two or more relaxed molecular clock models. Finally, we introduce a new computational approach for sampling rates of substitution across branches that improves the convergence of our Markov chain Monte Carlo algorithms in this context. Our methods are implemented under the BEAST 1.6 software package, available at

Topics: Research Articles
Publisher: Oxford University Press
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Provided by: PubMed Central

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  1. (2009). (11 co-authors).
  2. (2007). A general comparison of relaxed molecular clock models. Mol Biol Evol.
  3. (1924). A mathematical theory of evolution, based on the conclusions of Dr.
  4. (1997). A nonparametric approach to estimating divergence times in the absence of rate constancy.
  5. (2007). A reversible jump method for Bayesian phylogenetic inference with a nonhomogeneous substitution model. Mol Biol Evol.
  6. (2009). An examination of phylogenetic models of substitution rate variation among lineages.
  7. (1997). Application of inverse Gaussian distribution to occupational exposure data. Ann Occup Hyg.
  8. (1994). Approximate Bayesian inference with the weighted likelihood bootstrap.
  9. (1997). Back to the future: a synthesis of strepsirrhine systematics. Evol Anthropol.
  10. (1995). Bayes factors.
  11. (1999). Bayesian model averaging and model search strategies.
  12. (1999). Bayesian model averaging: a tutorial. Stat Sci.
  13. (2004). Bayesian phylogenetic model selection using reversible jump Markov chain Monte Carlo. Mol Biol Evol.
  14. (2009). Bayesian phylogeography finds its roots. PLoS Comput Biol.
  15. (2010). Bayesian random local clocks, or one rate to rule them all.
  16. (2001). Bayesian selection of continuous-time Markov chain evolutionary models. Mol Biol Evol.
  17. (2007). BEAST: Bayesian evolutionary analysis by sampling trees.
  18. (1995). Biometry: the principles and practice of statistics in biological research.
  19. (1993). Body size, metabolic rate, generation time, and the molecular clock.
  20. (2008). Confirming the phylogeny of mammals by use of large comparative sequence data sets. Mol Biol Evol.
  21. (2004). Congruent mammalian trees from mitochondrial and nuclear genes using Bayesian methods. Mol Biol Evol.
  22. (2002). Convergence assessment for reversible jump MCMC samplers.
  23. (1999). Convergence assessment for reversible jump MCMC simulations.
  24. (1985). Dating of the human-ape splitting by a molecular clock of mitochondrial DNA.
  25. (1998). Early metazoan divergence was about 830 million years ago.
  26. (2002). Effects of models of rate evolution on estimation of divergence dates with special reference to the metazoan 18S ribosomal RNA phylogeny. Syst Biol.
  27. (1998). Estimating divergence dates from molecular sequences. Mol Biol Evol.
  28. (1998). Estimating the rate of evolution of the rate of molecular evolution.
  29. (2003). Estimation of divergence times for major lineages of primate species.
  30. (1985). Evidence for higher rates of nucleotide substitution in rodents than in man.
  31. (1965). Evolutionary divergence and convergence in proteins.
  32. (1995). Historical development of the Newton-Raphson method.
  33. (1995). Improved dating of the human/ chimpanzee separation in the mitochondrial DNA tree: heterogeneity among amino acid sites.
  34. (2007). Inferring speciation times under an episodic molecular clock. Syst Biol.
  35. (2011). Joint inference of microsatellite mutation models, population history and genealogies using transdimensional Markov Chain Monte Carlo.
  36. (2009). Language phylogenies reveal expansion pulses and pauses in Pacific settlement.
  37. (2001). Mammalian phylogeny: genes and supertrees. Curr Biol.
  38. (1994). Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: approximate methods.
  39. Model Averaging for Phylogenetic Relaxed Molecular Clocks ·
  40. (2008). Modelling heterotachy in phylogenetic inference by reversible-jump Markov chain Monte Carlo.
  41. (2001). On the relationship between Markov chain Monte Carlo methods for model uncertainty.
  42. (2005). Orthologous repeats and mammalian phylogenetic inference. Genome Res.
  43. (2007). OrthoMaM: a database of orthologous genomic markers for placental mammal phylogenetics.
  44. (2006). Primate molecular divergence dates. Mol Phylogenet Evol.
  45. (1986). Rates of DNA sequence evolution differ between taxonomic groups.
  46. (1996). Rates of nucleotide substitution in primates and rodents and the generation-time effect hypothesis. Mol Phylogenet Evol.
  47. (1992). Relative rates of nucleotide substitution at the rbcl locus of monocotyledonous plants.
  48. (2006). Relaxed phylogenetics and dating with confidence.
  49. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination.
  50. (2007). Robust time estimation reconciles views of the antiquity of placental mammals. PLoS One.
  51. (2007). Seq-Gen: an application for the Monte Carlo simulation of DNA sequence evolution along phylogenetic trees.
  52. (1986). Some probabilistic and statistical problems in the analysis of DNA sequences.
  53. (1978). The hat matrix in regression and ANOVA. Am Stat.
  54. (2010). Unified framework to evaluate panmixia and migration direction among multiple sampling locations.

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