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Extinction and quasi-stationarity in the Verhulst logistic model.

Authors
  • Nåsell, I
Type
Published Article
Journal
Journal of theoretical biology
Publication Date
Jul 07, 2001
Volume
211
Issue
1
Pages
11–27
Identifiers
PMID: 11407888
Source
Medline
License
Unknown

Abstract

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.

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