The Annals of Applied Probability

Mutation frequencies in a birth–death branching process

David Cheek and Tibor Antal

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First, we revisit the stochastic Luria–Delbrück model: a classic two-type branching process which describes cell proliferation and mutation. We prove limit theorems and exact results for the mutation times, clone sizes and number of mutants. Second, we extend the framework to consider mutations at multiple sites along the genome. The number of mutants in the two-type model characterises the mean site frequency spectrum in the multiple-site model. Our predictions are consistent with previously published cancer genomic data.

Article information

Ann. Appl. Probab., Volume 28, Number 6 (2018), 3922-3947.

Received: November 2017
Revised: June 2018
First available in Project Euclid: 8 October 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J28: Applications of continuous-time Markov processes on discrete state spaces 92D10: Genetics {For genetic algebras, see 17D92} 92D20: Protein sequences, DNA sequences

Branching processes cancer population genetics


Cheek, David; Antal, Tibor. Mutation frequencies in a birth–death branching process. Ann. Appl. Probab. 28 (2018), no. 6, 3922--3947. doi:10.1214/18-AAP1413.

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