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Site frequency spectrum of a rescued population under rare resistant mutations

Author

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  • Bonnet, Céline
  • Leman, Hélène

Abstract

The aim of this article is to study the impact of resistance acquisition on the distribution of neutral mutations in a cell population under therapeutic pressure. The cell population is modeled by a bi-type branching process. Initially, the cells all carry type 0, associated with a negative growth rate. Mutations towards type 1 are assumed to be rare and random, and lead to the survival of cells under treatment, i.e. type 1 is associated with a positive growth rate, and thus models the acquisition of a resistance. Cells also carry neutral mutations, acquired at birth and accumulated by inheritance, that do not affect their type. We describe the expectation of the ”Site Frequency Spectrum” (SFS), which is an index of neutral mutation distribution in a population, under the asymptotic of rare events of resistance acquisition and of large initial population. Precisely, we give asymptotically-equivalent expressions of the expected number of neutral mutations shared by both a small and a large number of cells. To identify the influence of relatives on the SFS, our work also lead us to study in detail subcritical binary Galton–Watson trees, where each leaf is marked with a small probability. As a by-product of this study, we thus provide the law of the generation of a randomly chosen leaf in such a Galton–Watson tree conditioned on the number of marks.

Suggested Citation

  • Bonnet, Céline & Leman, Hélène, 2024. "Site frequency spectrum of a rescued population under rare resistant mutations," Stochastic Processes and their Applications, Elsevier, vol. 176(C).
  • Handle: RePEc:eee:spapps:v:176:y:2024:i:c:s0304414924001273
    DOI: 10.1016/j.spa.2024.104421
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    References listed on IDEAS

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    1. Gunnarsson, Einar Bjarki & Leder, Kevin & Foo, Jasmine, 2021. "Exact site frequency spectra of neutrally evolving tumors: A transition between power laws reveals a signature of cell viability," Theoretical Population Biology, Elsevier, vol. 142(C), pages 67-90.
    2. Cheek, David & Antal, Tibor, 2020. "Genetic composition of an exponentially growing cell population," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6580-6624.
    3. Bertoin, Jean, 2010. "A limit theorem for trees of alleles in branching processes with rare neutral mutations," Stochastic Processes and their Applications, Elsevier, vol. 120(5), pages 678-697, May.
    4. Hwai-Ray Tung & Rick Durrett, 2021. "Signatures of neutral evolution in exponentially growing tumors: A theoretical perspective," PLOS Computational Biology, Public Library of Science, vol. 17(2), pages 1-12, February.
    5. Durrett, Richard & Moseley, Stephen, 2010. "Evolution of resistance and progression to disease during clonal expansion of cancer," Theoretical Population Biology, Elsevier, vol. 77(1), pages 42-48.
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