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A multitype infinite-allele branching process with applications to cancer evolution

Part of: Markov processes

Published online by Cambridge University Press:  30 March 2016

Thomas O. McDonald  and
Marek Kimmel
Thomas O. McDonald*
Affiliation:
Rice University
Marek Kimmel*
Affiliation:
Rice University and Silesian University of Technology
*
∗ Postal address: Department of Statistics, Rice University, MS-138, P.O. Box 1892, Houston, TX 77251-1892, USA.
∗ Postal address: Department of Statistics, Rice University, MS-138, P.O. Box 1892, Houston, TX 77251-1892, USA.
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Abstract

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We extend the infinite-allele simple branching process of Griffiths and Pakes (1988) allowing the offspring to change types and labels. The model is developed and limit theorems are given for the growth of the number of labels of a specific type. We also discuss the asymptotics of the frequency spectrum. Finally, we present an application of the model's use in tumorigenesis.

Keywords

Infinite-allele branching processmultitype BGW processmodeling cancer evolutionpopulation geneticstumorigenesis

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J85: Applications of branching processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 52 , Issue 3 , September 2015 , pp. 864 - 876
Copyright
Copyright © 2015 by the Applied Probability Trust 

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