Extinction and quasi-stationarity in the Verhulst logistic model. |
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| Authors: | I N?sell |
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| Institution: | Department of Mathematics, The Royal Institute of Technology, Stockholm, S-100 44, Sweden. ingemar@math.kht.se |
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| 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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