A phase transition for a random cluster model on phylogenetic trees.

Elchanan Mossel; Mike Steel

doi:10.1016/j.mbs.2003.10.004

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A phase transition for a random cluster model on phylogenetic trees.

Elchanan Mossel·Mike Steel

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Abstract

We investigate a simple model that generates random partitions of the leaf set of a tree. Of particular interest is the reconstruction question: what number k of independent samples (partitions) are required to correctly reconstruct the underlying tree (with high probability)? We demonstrate a phase transition for k as a function of the mutation rate, from logarithmic to polynomial dependence on the size of the tree. We also describe a simple polynomial-time tree reconstruction algorithm that applies in the logarithmic region. This model and the associated reconstruction questions are motivated by a Markov model for genomic evolution in molecular biology.

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Cluster Analysis Evolution, Molecular Markov Chains Models, Genetic Phylogeny Journal Article Research Support, Non-U.S. Gov't

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Elchanan Mossel, Mike Steel. 2004. A phase transition for a random cluster model on phylogenetic trees.. https://doi.org/10.1016/j.mbs.2003.10.004

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