The Annals of Probability

Subtree prune and regraft: A reversible real tree-valued Markov process

Steven N. Evans and Anita Winter

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We use Dirichlet form methods to construct and analyze a reversible Markov process, the stationary distribution of which is the Brownian continuum random tree. This process is inspired by the subtree prune and regraft (SPR) Markov chains that appear in phylogenetic analysis.

A key technical ingredient in this work is the use of a novel Gromov–Hausdorff type distance to metrize the space whose elements are compact real trees equipped with a probability measure. Also, the investigation of the Dirichlet form hinges on a new path decomposition of the Brownian excursion.

Article information

Ann. Probab., Volume 34, Number 3 (2006), 918-961.

First available in Project Euclid: 27 June 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J25: Continuous-time Markov processes on general state spaces 60J75: Jump processes
Secondary: 92B10: Taxonomy, cladistics, statistics

Dirichlet form continuum random tree Brownian excursion phylogenetic tree Markov chain Monte Carlo simulated annealing path decomposition excursion theory Gromov–Hausdorff metric Prohorov metric


Evans, Steven N.; Winter, Anita. Subtree prune and regraft: A reversible real tree-valued Markov process. Ann. Probab. 34 (2006), no. 3, 918--961. doi:10.1214/009117906000000034.

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