dorsal/arxiv
View SchemaCoexistence versus extinction in the stochastic cyclic Lotka-Volterra model
| Authors | Tobias Reichenbach, Mauro Mobilia, Erwin Frey |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0605042 |
| URL | https://arxiv.org/abs/q-bio/0605042 |
| DOI | 10.1103/PhysRevE.74.051907 |
| Journal | Phys. Rev. E 74, 051907 (2006) |
Abstract
Cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity, see e.g. B. Kerr, M. A. Riley, M. W. Feldman and B. J. M. Bohannan [Nature {\bf 418}, 171 (2002)] and B. Kirkup and M. A. Riley [Nature {\bf 428}, 412 (2004)]. Through analytical methods supported by numerical simulations, we address this issue by studying the properties of a paradigmatic non-spatial three-species stochastic system, namely the `rock-paper-scissors' or cyclic Lotka-Volterra model. While the deterministic approach (rate equations) predicts the coexistence of the species resulting in regular (yet neutrally stable) oscillations of the population densities, we demonstrate that fluctuations arising in the system with a \emph{finite number of agents} drastically alter this picture and are responsible for extinction: After long enough time, two of the three species die out. As main findings we provide analytic estimates and numerical computation of the extinction probability at a given time. We also discuss the implications of our results for a broad class of competing population systems.
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"abstract": "Cyclic dominance of species has been identified as a potential mechanism to\nmaintain biodiversity, see e.g. B. Kerr, M. A. Riley, M. W. Feldman and B. J.\nM. Bohannan [Nature {\\bf 418}, 171 (2002)] and B. Kirkup and M. A. Riley\n[Nature {\\bf 428}, 412 (2004)]. Through analytical methods supported by\nnumerical simulations, we address this issue by studying the properties of a\nparadigmatic non-spatial three-species stochastic system, namely the\n`rock-paper-scissors\u0027 or cyclic Lotka-Volterra model. While the deterministic\napproach (rate equations) predicts the coexistence of the species resulting in\nregular (yet neutrally stable) oscillations of the population densities, we\ndemonstrate that fluctuations arising in the system with a \\emph{finite number\nof agents} drastically alter this picture and are responsible for extinction:\nAfter long enough time, two of the three species die out. As main findings we\nprovide analytic estimates and numerical computation of the extinction\nprobability at a given time. We also discuss the implications of our results\nfor a broad class of competing population systems.",
"arxiv_id": "q-bio/0605042",
"authors": [
"Tobias Reichenbach",
"Mauro Mobilia",
"Erwin Frey"
],
"categories": [
"q-bio.PE",
"cond-mat.stat-mech",
"physics.bio-ph"
],
"doi": "10.1103/PhysRevE.74.051907",
"journal_ref": "Phys. Rev. E 74, 051907 (2006)",
"title": "Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model",
"url": "https://arxiv.org/abs/q-bio/0605042"
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