Splitting trees with neutral Poissonian mutations II: Largest and oldest families

Nicolas Champagnat and Amaury Lambert

Stochastic Processes and their Applications, 2013, vol. 123, issue 4, 1368-1414

Abstract: We consider a supercritical branching population, where individuals have i.i.d. lifetime durations (which are not necessarily exponentially distributed) and give birth (singly) at constant rate. We assume that individuals independently experience neutral mutations, at constant rate θ during their lifetimes, under the infinite-alleles assumption: each mutation instantaneously confers a brand new type, called allele or haplotype, to its carrier. The type carried by a mother at the time when she gives birth is transmitted to the newborn.

Keywords: Branching process; Coalescent point process; Splitting tree; Crump–Mode–Jagers process; Linear birth–death process; Allelic partition; Infinite alleles model; Extreme values; Mixed Poisson point process; Cox process; Lévy process; Scale function (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2012.11.013

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