dorsal/arxiv
View SchemaFluctuations and Correlations in Lattice Models for Predator-Prey Interaction
| Authors | Mauro Mobilia, Ivan T. Georgiev, Uwe C. Tauber |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0508043 |
| URL | https://arxiv.org/abs/q-bio/0508043 |
| DOI | 10.1103/PhysRevE.73.040903 |
| Journal | Phys. Rev. E 73, 040903(R) (2006) |
Abstract
Including spatial structure and stochastic noise invalidates the classical Lotka-Volterra picture of stable regular population cycles emerging in models for predator-prey interactions. Growth-limiting terms for the prey induce a continuous extinction threshold for the predator population whose critical properties are in the directed percolation universality class. Here, we discuss the robustness of this scenario by considering an ecologically inspired stochastic lattice predator-prey model variant where the predation process includes next-nearest-neighbor interactions. We find that the corresponding stochastic model reproduces the above scenario in dimensions 1< d \leq 4, in contrast with mean-field theory which predicts a first-order phase transition. However, the mean-field features are recovered upon allowing for nearest-neighbor particle exchange processes, provided these are sufficiently fast.
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"abstract": "Including spatial structure and stochastic noise invalidates the classical\nLotka-Volterra picture of stable regular population cycles emerging in models\nfor predator-prey interactions. Growth-limiting terms for the prey induce a\ncontinuous extinction threshold for the predator population whose critical\nproperties are in the directed percolation universality class. Here, we discuss\nthe robustness of this scenario by considering an ecologically inspired\nstochastic lattice predator-prey model variant where the predation process\nincludes next-nearest-neighbor interactions. We find that the corresponding\nstochastic model reproduces the above scenario in dimensions 1\u003c d \\leq 4, in\ncontrast with mean-field theory which predicts a first-order phase transition.\nHowever, the mean-field features are recovered upon allowing for\nnearest-neighbor particle exchange processes, provided these are sufficiently\nfast.",
"arxiv_id": "q-bio/0508043",
"authors": [
"Mauro Mobilia",
"Ivan T. Georgiev",
"Uwe C. Tauber"
],
"categories": [
"q-bio.PE",
"cond-mat.stat-mech",
"physics.soc-ph",
"q-bio.QM"
],
"doi": "10.1103/PhysRevE.73.040903",
"journal_ref": "Phys. Rev. E 73, 040903(R) (2006)",
"title": "Fluctuations and Correlations in Lattice Models for Predator-Prey Interaction",
"url": "https://arxiv.org/abs/q-bio/0508043"
},
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