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Splitting trees with neutral Poissonian mutations I: Small families

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  • Champagnat, Nicolas
  • Lambert, Amaury
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    Abstract

    We consider a neutral dynamical model of biological diversity, where individuals live and reproduce independently. They have i.i.d. lifetime durations (which are not necessarily exponentially distributed) and give birth (singly) at constant rate b. Such a genealogical tree is usually called a splitting tree [9], and the population counting process (Nt;t≥0) is a homogeneous, binary Crump–Mode–Jagers process.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304414911002778
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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 3 ()
    Pages: 1003-1033

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:3:p:1003-1033

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    Related research

    Keywords: Branching process; Coalescent point process; Splitting tree; Crump–Mode–Jagers process; Linear birth–death process; Allelic partition; Infinite alleles model; Poisson point process; Lévy process; Scale function; Regenerative set; Random characteristic;

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    1. 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.
    2. Geiger, Jochen, 1996. "Size-biased and conditioned random splitting trees," Stochastic Processes and their Applications, Elsevier, vol. 65(2), pages 187-207, December.
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    Cited by:
    1. 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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