Asymptotic genealogy of a critical branching process

Details Asymptotic genealogy of a critical branching process Asymptotic genealogy of a critical branching process

2005-03-25

arxiv.org/abs/math/0503577v1

Annals of Applied Probability 2004, Vol. 14, No. 4, 2120-2148

Mathematics

Probability

30 pages

Scientific paper

10.1214/105051604000000486

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.

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