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Limit theorems for the site frequency spectrum of neutral mutations in an exponentially growing population

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  • Gunnarsson, Einar Bjarki
  • Leder, Kevin
  • Zhang, Xuanming

Abstract

The site frequency spectrum (SFS) is a widely used summary statistic of genomic data. Motivated by recent evidence for the role of neutral evolution in cancer, we investigate the SFS of neutral mutations in an exponentially growing population. Using branching process techniques, we establish (first-order) almost sure convergence results for the SFS of a Galton–Watson process, evaluated either at a fixed time or at the stochastic time at which the population first reaches a certain size. We finally use our results to construct consistent estimators for the extinction probability and the effective mutation rate of a birth–death process.

Suggested Citation

  • Gunnarsson, Einar Bjarki & Leder, Kevin & Zhang, Xuanming, 2025. "Limit theorems for the site frequency spectrum of neutral mutations in an exponentially growing population," Stochastic Processes and their Applications, Elsevier, vol. 182(C).
  • Handle: RePEc:eee:spapps:v:182:y:2025:i:c:s0304414925000043
    DOI: 10.1016/j.spa.2025.104565
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    References listed on IDEAS

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    1. Nicolas Champagnat & Amaury Lambert & Mathieu Richard, 2012. "Birth and Death Processes with Neutral Mutations," International Journal of Stochastic Analysis, Hindawi, vol. 2012, pages 1-20, December.
    2. 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).
    3. Foo, Jasmine & Leder, Kevin & Zhu, Junfeng, 2014. "Escape times for branching processes with random mutational fitness effects," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3661-3697.
    4. 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.
    5. 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.
    6. Xiaowei Wu & Marek Kimmel, 2013. "Modeling Neutral Evolution Using an Infinite-Allele Markov Branching Process," International Journal of Stochastic Analysis, Hindawi, vol. 2013, pages 1-10, March.
    7. Lambert, Amaury, 2018. "The coalescent of a sample from a binary branching process," Theoretical Population Biology, Elsevier, vol. 122(C), pages 30-35.
    8. 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.
    9. Ohtsuki, Hisashi & Innan, Hideki, 2017. "Forward and backward evolutionary processes and allele frequency spectrum in a cancer cell population," Theoretical Population Biology, Elsevier, vol. 117(C), pages 43-50.
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