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## Bayesian inference on phylogeny and its impact on evolutionary biology. (2001)

Venue: | Science |

Citations: | 234 - 10 self |

### Citations

86 | London Ser. - Soc - 2009 |

46 |
Markov Chain Monte Carlo in Practice. Chapman and Hall: London,
- WR, Richardson, et al.
- 2006
(Show Context)
Citation Context ...l trees are considered a priori equally probable, and the likelihood is calculated under one of a number of standard Markov models of character evolution. The posterior probability, although easy to formulate, involves a summation over all trees and, for each tree, integration over all possible combinations of branch length and substitution model parameter values. It is all but impossible to do this analytically. Fortunately, a number of numerical methods are available that allow the posterior probability of a tree to be approximated, the most useful of which is Markov chain Monte Carlo [MCMC (4)]. MCMC has revolutionized Bayesian inference, with recent applications to Bayesian phylogenetic inference (1–3) as well as many other problems in evolutionary biology (5–7). The basic idea is to construct a Markov chain that has as its state space the parameters of the statistical model and a stationary distribution that is the posterior probability distribution of the parameters. For the phylogeny problem, the MCMC algorithm involves two steps: (i) A new tree is proposed by stochastically perturbing the current tree. (ii) This tree is then either accepted or rejected with a probability descr... |

43 |
Computing science and statistics,
- Geyer
- 1991
(Show Context)
Citation Context ...is, we wrote a computer program implementing the MCMC algorithm (8, 9). In particular, we implemented a variant of MCMC called Metropolis-coupled MCMC that is less prone to entrapment in local optima =-=(12)-=-. We applied the method to four large phylogenetic data sets that span the size range of many problems faced by systematists today (13–16). The smallest data set included 106 wingless sequences sample... |

32 |
Bayesian Data Analysis (Chapman &
- Gelman, Carlin, et al.
- 1995
(Show Context)
Citation Context ... can also be used to choose among evolutionary models. For example, Bayes factors— comparing the marginal likelihoods of two models— have proven to be useful in choosing among evolutionary models (24 ). One advantage of these methods is that the results are not conditional on an assumed topology being correct. The Markov chain simulation effectively treats the topology as a nuisance parameter by summing over trees. An exhaustive description of Bayesian methods of model choice is not feasible here, but we will illustrate one method that uses predictive densities–posterior predictive simulation (25). If an evolutionary model does a good job of explaining the observed DNA sequences, then data simulated under that model should be similar to the observations. Posterior predictive simulation tests the adequacy of a model by comparing a test statistic with the posterior predictive distribution of that statistic generated under the assumption that the model is correct. The test statistic should measure how well a model performs in predicting the observations. The posterior predictive distribution is approximated by simulating new observations by using parameter values sampled from the posterio... |

6 | Genetics 154, - Nielsen - 2000 |

5 | in Ecological Morphology: Integrative Organismal Biology, - Losos, Miles - 1994 |

4 |
Gilks et al., Eds., Markov Chain Monte Carlo
- R
- 1996
(Show Context)
Citation Context ...is analytically. Fortunately, a number of numerical methods are available that allow the posterior probability of a tree to be approximated, the most useful of which is Markov chain Monte Carlo [MCMC =-=(4)-=-]. MCMC has revolutionized Bayesian inference, with recent applications to Bayesian phylogenetic inference (1–3) as well as many other problems in evolutionary biology (5–7). The basic idea is to cons... |

4 |
et al., Genetics 155
- Yang
- 2000
(Show Context)
Citation Context ...st testing for the presence of positively selected sites with a likelihood ratio test, and then, if the test is significant, identifying positively selected sites by using an empirical Bayes approach =-=(31, 32)-=-. Empirical Bayes approaches differ from other Bayesian methods in that the prior distribution is determined, in part, by the data. The empirical Bayes approach has been useful in identifying positive... |

1 |
Interface Foundation,
- Geyer
- 1991
(Show Context)
Citation Context ...r posterior probabilities. Once such a sample is available, features that are common among the trees can be discerned. For example, the sample can be used to construct a consensus tree, with the posterior probability of the individual clades indicated on the tree. This is roughly equivalent to performing a maximum likelihood analysis with bootstrap resampling (3), but much faster. To illustrate this, we wrote a computer program implementing the MCMC algorithm (8, 9). In particular, we implemented a variant of MCMC called Metropolis-coupled MCMC that is less prone to entrapment in local optima (12). We applied the method to four large phylogenetic data sets that span the size range of many problems faced by systematists today (13–16). The smallest data set included 106 wingless sequences sampled from insects, whereas the largest included 357 atpB sequences sampled from plants. We assumed a general model of DNA substitution in the analyses (17, 18). This model allowed each nucleotide change to have its own rate and the nucleotide bases to have different frequencies. We allowed rates to vary across sites either by assuming that the rate at a site is a random variable drawn from a gamma di... |

1 | Zanotto et al., - M - 1996 |

1 |
thesis,
- Felsenstein
- 1968
(Show Context)
Citation Context ...nary Biology Centre, Uppsala University, Norbyv. 18D, SE-752 36 Uppsala, Sweden. 3Department of Biometrics, Cornell University, Ithaca, NY 14853–1643, USA. *To whom correspondence should be addressed. Email: johnh@brahms.biology.rochester.edu Table 1. The Bayesian approach to problems in phylogeny. Problem Bayesian approach Ref. Inferring phylogeny Find tree with maximum posterior probability; evaluate features in common among the sampled trees (1–3) Evaluating uncertainty in phylogenies Evaluate clade probabilities; form credible set containing trees whose cumulative probability sums to 0.95 (3, 40) Detecting selection Model substitution process on the codon and calculate probability of being in purifying or positively selected class; sample substitutions and count number of synonymous and nonsynonymous changes (29, 32) Comparative analyses Perform analysis on many trees, and weight results by the probability that each tree is correct (41–43) Divergence times Use fossils as a calibration. Infer divergence times by using a strict or relaxed molecular clock (44) Testing molecular clock Calculate Bayes factor for the clock versus no branch length restrictions (24) S C I E N C E ’ S C O M P ... |