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- W4301675073 abstract "The Verhulst model is probably the best known macroscopic rate equation in population ecology. It depends on two parameters, the intrinsic growth rate and the carrying capacity. These parameters can be estimated for different populations and are related to the reproductive fitness and the competition for limited resources, respectively. We investigate analytically and numerically the simplest possible microscopic scenarios that give rise to the logistic equation in the deterministic mean-field limit. We provide a definition of the two parameters of the Verhulst equation in terms of microscopic parameters. In addition, we derive the conditions for extinction or persistence of the population by employing either the momentum-space spectral theory or the real-space Wentzel-Kramers-Brillouin (WKB) approximation to determine the probability distribution function and the mean time to extinction of the population. Our analytical results agree well with numerical simulations." @default.
- W4301675073 created "2022-10-05" @default.
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- W4301675073 date "2015-06-03" @default.
- W4301675073 modified "2023-09-30" @default.
- W4301675073 title "Stochastic dynamics and logistic population growth" @default.
- W4301675073 doi "https://doi.org/10.48550/arxiv.1506.01137" @default.
- W4301675073 hasPublicationYear "2015" @default.
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