Advances in Applied Probability

Conditional distributions and waiting times in multitype branching processes

H. K. Alexander

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In this paper we present novel results for discrete-time and Markovian continuous-time multitype branching processes. As a population develops, we are interested in the waiting time until a particular type of interest (such as an escape mutant) appears, and in how the distribution of individuals depends on whether this type has yet appeared. Specifically, both forward and backward equations for the distribution of type-specific population sizes over time, conditioned on the non\-appearance of one or more particular types, are derived. In tandem, equations for the probability that one or more particular types have not yet appeared are also derived. Brief examples illustrate numerical methods and potential applications of these results in evolutionary biology and epidemiology.

Article information

Adv. in Appl. Probab., Volume 45, Number 3 (2013), 692-718.

First available in Project Euclid: 30 August 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G99: None of the above, but in this section
Secondary: 92D15: Problems related to evolution 92D30: Epidemiology

Multitype branching process probability generating function waiting time escape mutant evolutionary biology epidemiology


Alexander, H. K. Conditional distributions and waiting times in multitype branching processes. Adv. in Appl. Probab. 45 (2013), no. 3, 692--718. doi:10.1239/aap/1377868535.

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