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Extinction and Quasi-stationarity in the Verhulst Logistic Model

✍ Scribed by INGEMAR NÅSELL

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
310 KB
Volume
211
Category
Article
ISSN
0022-5193

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✦ Synopsis

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 di!erent behaviours are identi"ed. 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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