The Annals of Applied Probability

Asymptotic genealogy of a critical branching process

Lea Popovic

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Abstract

Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the smallest subtree containing the genealogy of the extant individuals together with the genealogy of the recorded extinct individuals. We introduce a novel representation of such subtrees in terms of a point-process, and provide asymptotic results on the distribution of this point-process as the number of extant individuals increases. We motivate the study within the scope of a coherent analysis for an a priori model for macroevolution.

Article information

Source
Ann. Appl. Probab., Volume 14, Number 4 (2004), 2120-2148.

Dates
First available in Project Euclid: 5 November 2004

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1099674091

Digital Object Identifier
doi:10.1214/105051604000000486

Mathematical Reviews number (MathSciNet)
MR2100386

Zentralblatt MATH identifier
1062.92048

Subjects
Primary: 60J85: Applications of branching processes [See also 92Dxx]
Secondary: 60J65: Brownian motion [See also 58J65] 92D15: Problems related to evolution

Keywords
Critical branching process Galton–Watson process random tree point process Brownian excursion genealogy

Citation

Popovic, Lea. Asymptotic genealogy of a critical branching process. Ann. Appl. Probab. 14 (2004), no. 4, 2120--2148. doi:10.1214/105051604000000486. https://projecteuclid.org/euclid.aoap/1099674091


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