The Annals of Applied Probability

Asymptotic genealogy of a critical branching process

Lea Popovic

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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

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

First available in Project Euclid: 5 November 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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

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