Bayesian phylogenetic inference via Markov chain Monte Carlo methods

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Bayesian phylogenetic inference via Markov chain Monte Carlo methods

Bob Mau,
Michael A. Newton ,
and Bret Larget

* Biometrics *, ** 5 **, 1-12, 1999.

Formerly Technical Report 961, Department of Statistics,
University of Wisconsin, Madison. First issued, June 1996.

### Abstract:

We consider standard stochastic models of evolution to describe
molecular data measured on a group of organisms.
Taking a Bayesian approach, we derive a Markov chain that can
sample from the posterior distribution of
the phylogenetic tree relating these organisms.
Transformation of the tree into a canonical
cophenetic matrix form suggests a simple Metropolis proposal distribution for selecting
candidate trees close to the current tree in the chain. We
illustrate the algorithm with restriction site data on nine plant species,
then extend to DNA sequences from thirty-two species of fish.
The algorithm appears to mix well in both examples,
generating reproducible estimates and credible sets
for the phylogeny.

*Key words:* Cophenetic matrix; Evolution; Kingman coalescent; Labeled
history; Metropolis-Hastings algorithm; Phylogeny reconstruction.