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Approximation of the allelic frequency spectrum in general supercritical branching populations

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  • Henry, Benoit

Abstract

We consider a branching population with arbitrary lifetime distribution and Poissonian births. Moreover, individuals experience mutations at Poissonian rate. This mechanism leads to a partition of the population by type: the allelic partition. We focus on the frequency spectrum A(k,t) which counts the number of families of size k at time t. Our main goal is to study the asymptotic error made in some approximations of the frequency spectrum.

Suggested Citation

  • Henry, Benoit, 2021. "Approximation of the allelic frequency spectrum in general supercritical branching populations," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 192-225.
    • Handle: RePEc:eee:spapps:v:132:y:2021:i:c:p:192-225
    DOI: 10.1016/j.spa.2020.10.008
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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. Champagnat, Nicolas & Lambert, Amaury, 2012. "Splitting trees with neutral Poissonian mutations I: Small families," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 1003-1033.
    3. Champagnat, Nicolas & Lambert, Amaury, 2013. "Splitting trees with neutral Poissonian mutations II: Largest and oldest families," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1368-1414.
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