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Spatial patterns of competing random walkers

AuthorsHernández-García, Emilio ; Heinsalu, Els ; López, Cristóbal
KeywordsNonlocal interactions
Pattern formation
Individual-based model
Niche space
Random walks
Lévy flights
Issue DateMar-2015
CitationEcological Complexity 21: 166-176 (2015)
Abstract© 2014 Elsevier B.V. We review recent results obtained from simple individual-based models of biological competition in which birth and death rates of an organism depend on the presence of other competing organisms close to it. In addition the individuals perform random walks of different types (Gaussian diffusion and Lévy flights). We focus on how competition and random motions affect each other, from which spatial instabilities and extinctions arise. Under suitable conditions, competitive interactions lead to clustering of individuals and periodic pattern formation. Random motion has a homogenizing effect and then delays this clustering instability. When individuals from species differing in their random walk characteristics are allowed to compete together, the ones with a tendency to form narrower clusters get a competitive advantage over the others. Mean-field deterministic equations are analyzed and compared with the outcome of the individual-based simulations.
Publisher version (URL)http://dx.doi.org/10.1016/j.ecocom.2014.06.005
Identifiersissn: 1476-945X
Appears in Collections:(IFISC) Artículos
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