Mutation frequencies in a birth-death branching process
نویسندگان
چکیده
First, we revisit a classic two-type branching process which describes cell proliferation and mutation; widespread application has been seen in cancer and microbial modelling. As the mutation rate tends to zero and the population size to infinity, the mutation times converge to a Poisson process. This yields the number of mutants and clone sizes. Other limits and exact results are also explored. Second, we extend the model to consider mutations at multiple sites on 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 genomic data from tumours.
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