dorsal/arxiv
View SchemaStochastic models in population biology and their deterministic analogs
| Authors | A. J. McKane, T. J. Newman |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0501022 |
| URL | https://arxiv.org/abs/q-bio/0501022 |
| DOI | 10.1103/PhysRevE.70.041902 |
| Journal | Phys. Rev. E 70, 041902 (2004) |
Abstract
In this paper we introduce a class of stochastic population models based on "patch dynamics". The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean field theories, which are generally valid as the patch size becomes very large. These models may be used to formulate a broad range of biological processes in both spatial and non-spatial contexts. Here, we concentrate on two-species competition. We present both a mathematical analysis of the patch model, in which we derive the precise form of the competition mean field equations (and their first order corrections in the non-spatial case), and simulation results. These mean field equations differ, in some important ways, from those which are normally written down on phenomenological grounds. Our general conclusion is that mean field theory is more robust for spatial models than for a single isolated patch. This is due to the dilution of stochastic effects in a spatial setting resulting from repeated rescue events mediated by inter-patch diffusion. However, discrete effects due to modest patch sizes lead to striking deviations from mean field theory even in a spatial setting.
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"abstract": "In this paper we introduce a class of stochastic population models based on\n\"patch dynamics\". The size of the patch may be varied, and this allows one to\nquantify the departures of these stochastic models from various mean field\ntheories, which are generally valid as the patch size becomes very large. These\nmodels may be used to formulate a broad range of biological processes in both\nspatial and non-spatial contexts. Here, we concentrate on two-species\ncompetition. We present both a mathematical analysis of the patch model, in\nwhich we derive the precise form of the competition mean field equations (and\ntheir first order corrections in the non-spatial case), and simulation results.\nThese mean field equations differ, in some important ways, from those which are\nnormally written down on phenomenological grounds. Our general conclusion is\nthat mean field theory is more robust for spatial models than for a single\nisolated patch. This is due to the dilution of stochastic effects in a spatial\nsetting resulting from repeated rescue events mediated by inter-patch\ndiffusion. However, discrete effects due to modest patch sizes lead to striking\ndeviations from mean field theory even in a spatial setting.",
"arxiv_id": "q-bio/0501022",
"authors": [
"A. J. McKane",
"T. J. Newman"
],
"categories": [
"q-bio.PE"
],
"doi": "10.1103/PhysRevE.70.041902",
"journal_ref": "Phys. Rev. E 70, 041902 (2004)",
"title": "Stochastic models in population biology and their deterministic analogs",
"url": "https://arxiv.org/abs/q-bio/0501022"
},
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