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A Stochastic Model for Phylogenetic Trees

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Thomas M. Liggett  and
Rinaldo B. Schinazi
Thomas M. Liggett*
Affiliation:
University of California, Los Angeles
Rinaldo B. Schinazi*
Affiliation:
University of Colorado
*
∗Postal address: Department of Mathematics, University of California, Los Angeles, CA 90095-1555, USA.
∗∗Postal address: Department of Mathematics, University of Colorado, Colorado Springs, CO 80933-7150, USA. Email address: schinazi@math.uccs.edu
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Abstract

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We propose the following simple stochastic model for phylogenetic trees. New types are born and die according to a birth and death chain. At each birth we associate a fitness to the new type sampled from a fixed distribution. At each death the type with the smallest fitness is killed. We show that if the birth (i.e. mutation) rate is subcritical, we obtain a phylogenetic tree consistent with an influenza tree (few types at any given time and one dominating type lasting a long time). When the birth rate is supercritical, we obtain a phylogenetic tree consistent with an HIV tree (many types at any given time, none lasting very long).

Keywords

Phylogenetic treeinfluenzaHIVstochastic model

MSC classification

Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 2 , June 2009 , pp. 601 - 607
Copyright
Copyright © Applied Probability Trust 2009 

Footnotes

Partially supported by NSF grant DMS-0701396.

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