Extinction times for a birth-death process with weak competition
Journal article, 2013

We consider a birth-death process with birth rates i lambda and death rates i mu+i(i-1)theta, where i is the current state of the process. A positive competition rate theta is assumed to be small. In the supercritical case where lambda > mu, this process can be viewed as a demographic model for a population with high carrying capacity around (lambda-mu)/theta. The article reports in a self-contained manner on the asymptotic properties of the time to extinction for this logistic branching process as theta -> 0. All three reproduction regimes lambda > mu, lambda < mu, and lambda = mu are studied.

carrying capacity

logistic branching process

coupling method

time to extinction

birth-death process


Serik Sagitov

Chalmers, Mathematical Sciences, Mathematical Statistics

University of Gothenburg

A. Shaimerdenova

Al Farabi Kazakh National University

Lithuanian Mathematical Journal

0363-1672 (ISSN) 1573-8825 (eISSN)

Vol. 53 2 220-234

Stochastic models of gene and species trees

Swedish Research Council (VR) (2010-5623), 2011-01-01 -- 2013-12-31.

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