Journal
JOURNAL OF THEORETICAL BIOLOGY
Volume 211, Issue 1, Pages 11-27Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1006/jtbi.2001.2328
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We formulate and analyse a stochastic version of the Verhulst deterministic model for density-dependent growth of a single population Three parameter regions with qualitatively different behaviours are identified. Explicit approximations of the quasi-stationary distribution and of the expected time to extinction are presented in each of these regions. The quasi-stationary distribution is approximately normal, and the time to extinction is long, in one of these regions. Another region has a short time to extinction and a quasi-stationary distribution that is approximately truncated geometric. A third region is a transition region between these two. Here the time to extinction is moderately long and the quasi-stationary distribution has a more complicated behaviour. Numerical illustrations are given. (C) 2001 Academic Press.
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