Splitting trees with neutral Poissonian mutations I: Small families

Nicolas Champagnat and Amaury Lambert

Stochastic Processes and their Applications, 2012, vol. 122, issue 3, 1003-1033

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.

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 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2011.11.002

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