dorsal/arxiv
View SchemaExtinction Rates for Fluctuation-Induced Metastabilities : A Real-Space WKB Approach
| Authors | David A. Kessler, Nadav M. Shnerb |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0611049 |
| URL | https://arxiv.org/abs/q-bio/0611049 |
| DOI | 10.1007/s10955-007-9312-2 |
Abstract
The extinction of a single species due to demographic stochasticity is analyzed. The discrete nature of the individual agents and the Poissonian noise related to the birth-death processes result in local extinction of a metastable population, as the system hits the absorbing state. The Fokker-Planck formulation of that problem fails to capture the statistics of large deviations from the metastable state, while approximations appropriate close to the absorbing state become, in general, invalid as the population becomes large. To connect these two regimes, a master equation based on a real space WKB method is presented, and is shown to yield an excellent approximation for the decay rate and the extreme events statistics all the way down to the absorbing state. The details of the underlying microscopic process, smeared out in a mean field treatment, are shown to be crucial for an exact determination of the extinction exponent. This general scheme is shown to reproduce the known results in the field, to yield new corollaries and to fit quite precisely the numerical solutions. Moreover it allows for systematic improvement via a series expansion where the small parameter is the inverse of the number of individuals in the metastable state.
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"abstract": "The extinction of a single species due to demographic stochasticity is\nanalyzed. The discrete nature of the individual agents and the Poissonian noise\nrelated to the birth-death processes result in local extinction of a metastable\npopulation, as the system hits the absorbing state. The Fokker-Planck\nformulation of that problem fails to capture the statistics of large deviations\nfrom the metastable state, while approximations appropriate close to the\nabsorbing state become, in general, invalid as the population becomes large. To\nconnect these two regimes, a master equation based on a real space WKB method\nis presented, and is shown to yield an excellent approximation for the decay\nrate and the extreme events statistics all the way down to the absorbing state.\nThe details of the underlying microscopic process, smeared out in a mean field\ntreatment, are shown to be crucial for an exact determination of the extinction\nexponent. This general scheme is shown to reproduce the known results in the\nfield, to yield new corollaries and to fit quite precisely the numerical\nsolutions. Moreover it allows for systematic improvement via a series expansion\nwhere the small parameter is the inverse of the number of individuals in the\nmetastable state.",
"arxiv_id": "q-bio/0611049",
"authors": [
"David A. Kessler",
"Nadav M. Shnerb"
],
"categories": [
"q-bio.PE"
],
"doi": "10.1007/s10955-007-9312-2",
"title": "Extinction Rates for Fluctuation-Induced Metastabilities : A Real-Space WKB Approach",
"url": "https://arxiv.org/abs/q-bio/0611049"
},
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