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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.

References

Durrett, R. (2004). Probability: Theory and Examples, 3rd edn. Duxbury press, Belmont, CA.Google Scholar
Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. 2, 2nd edn. John Wiley, New York.Google Scholar
Keilson, J. (1979). Markov Chain Models—Rarity and Exponentiality (Appl. Math. Sci. 28). Springer, New York.CrossRefGoogle Scholar
Koelle, K., Cobey, S., Grenfell, B. and Pascual, M. (2006). Epochal evolution shapes the phylodynamics of interpandemic influenza A (H3N2) in humans. Science 314, 1898–1903.CrossRefGoogle ScholarPubMed
Korber, B. et al. (2001). Evolutionary and immunological implications of contemporary HIV-1 variation. British Med. Bull. 58, 19–42.Google Scholar
Port, S. C. (1994). Theoretical Probability for Applications. John Wiley, New York.Google Scholar
Van Nimwegen, E. (2006). Influenza escapes immunity along neutral networks. Science 314, 1884–1886.Google Scholar