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Mutation frequencies in a birth–death branching process

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Original languageEnglish
Pages (from-to)3922–3947
Number of pages28
JournalAnnals of Applied Probability
Issue number6
Early online date8 Oct 2018
Publication statusPublished - Dec 2018


First, we revisit the stochastic Luria-Delbruck 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.

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