Is a nonlocal diffusion strategy convenient for biological populations in competition?

Annalisa Massaccesi, Enrico Valdinoci

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We study the viability 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 the introduction of a new nonlocal dispersal behavior is favored with respect to the local dispersal behavior of the resident population. 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 invade 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 distribution of the dispersal, thus suggesting that the shortage of resources and their unbalanced supply may be some of the basic environmental factors that favor nonlocal strategies.
Original languageEnglish
Pages (from-to)113-147
Number of pages35
JournalJournal of Mathematical Biology
Volume74
Issue number1-2
DOIs
Publication statusPublished - 2017
Externally publishedYes

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Nonlocal Diffusion
dispersal behavior
Biological systems
Linearization
Biological Models
Resources
Population
viability
environmental factors
Fractional Laplacian
Environmental Factors
Shortage
Reaction-diffusion System
Viability
Biological Systems
Linearly
Unstable
Strategy
Interaction

Cite this

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Is a nonlocal diffusion strategy convenient for biological populations in competition? / Massaccesi, Annalisa; Valdinoci, Enrico.

In: Journal of Mathematical Biology, Vol. 74, No. 1-2, 2017, p. 113-147.

Research output: Contribution to journalArticle

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