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December 2018 Mutation frequencies in a birth–death branching process
David Cheek, Tibor Antal
Ann. Appl. Probab. 28(6): 3922-3947 (December 2018). DOI: 10.1214/18-AAP1413

Abstract

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.

Citation

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David Cheek. Tibor Antal. "Mutation frequencies in a birth–death branching process." Ann. Appl. Probab. 28 (6) 3922 - 3947, December 2018. https://doi.org/10.1214/18-AAP1413

Information

Received: 1 November 2017; Revised: 1 June 2018; Published: December 2018
First available in Project Euclid: 8 October 2018

zbMATH: 06994410
MathSciNet: MR3861830
Digital Object Identifier: 10.1214/18-AAP1413

Subjects:
Primary: 60J80
Secondary: 60J28, 92D10, 92D20

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.28 • No. 6 • December 2018
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