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Title: Is a nonlocal diffusion strategy convenient for biological populations in competition?
Authors: Massaccesi, AnnalisaValdinoci, Enrico
Issue Date: 2015
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik, Volume 2092, ISSN 2198-5855
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: We study the convenience of a nonlocal dispersal strategy in a reaction-diffusion system with a fractional Laplacian operator. We show that there are circumstances - namely, a precise condition on the distribution of the resource - under which a nonlocal dispersal behavior is favored. In particular, we consider the linearization of a biological system that models the interaction of two biological species, one with local and one with nonlocal dispersal, that are competing for the same resource. We give a simple, concrete example of resources for which the equilibrium with only the local population becomes linearly unstable. In a sense, this example shows that nonlocal strategies can become successful even in an environment in which purely local strategies are dominant at the beginning, provided that the resource is sufficiently sparse. Indeed, the example considered presents a high variance of the distribu- tion of the dispersal, thus suggesting that the shortage of resources and their unbalanced supply may be some of the basic ingredients that favor nonlocal strategies.
Keywords: Fractional equations; population dynamics
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik

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