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A stochastic model for phylogenetic trees. (English) Zbl 1180.60079
A stochastic model of the birth-death type is proposed for phylogenetic trees; the paper especially refers to influenza and HIV phylogenetic trees. Assumptions made in the paper are:
\(\bullet\) At each birth a fitness to new type from a fixed distribution is allowed,
\(\bullet\) At each death the type with smallest fitness is killed,
\(\bullet\) The process commence with a single type.
The paper does not develop distribution of tree which is a complex task. Instead the authors concentrate on developing theorems that are dependent on birth rate. They indicate that their results are consistent field observations.

60K35 Interacting random processes; statistical mechanics type models; percolation theory
92D30 Epidemiology
Full Text: DOI
[1] Durrett, R. (2004). Probability: Theory and Examples , 3rd edn. Duxbury press, Belmont, CA. · Zbl 0709.60002
[2] Feller, W. (1971). An Introduction to Probability Theory and Its Applications , Vol. 2, 2nd edn. John Wiley, New York. · Zbl 0219.60003
[3] Keilson, J. (1979). Markov Chain Models—Rarity and Exponentiality (Appl. Math. Sci. 28 ). Springer, New York. · Zbl 0411.60068
[4] 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.
[5] Korber, B. \et (2001). Evolutionary and immunological implications of contemporary HIV-1 variation. British Med. Bull. 58, 19–42.
[6] Port, S. C. (1994). Theoretical Probability for Applications . John Wiley, New York. · Zbl 0860.60001
[7] Van Nimwegen, E. (2006). Influenza escapes immunity along neutral networks. Science 314, 1884–1886.
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