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    Dispersal delays, predator–prey stability, and the paradox of enrichment

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    stabilizing_dispersal_delays_TPB_2006_revision.pdf (5.263Mb)
    Date
    2007-03-26
    Author
    Klepac, Petra  Concept link
    Neubert, Michael G.  Concept link
    van den Driessche, P.  Concept link
    Metadata
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    Citable URI
    https://hdl.handle.net/1912/1580
    As published
    https://doi.org/10.1016/j.tpb.2007.02.002
    Keyword
     Delay-differential equations; Distributed delay; MacArthur-Rosenzweig model; Metapopulation dynamics; Paradox of enrichment; Stability 
    Abstract
    It takes time for individuals to move from place to place. This travel time can be incorporated into metapopulation models via a delay in the interpatch migration term. Such a term has been shown to stabilize the positive equilibrium of the classical Lotka-Volterra predator{prey system with one species (either the predator or the prey) dispersing. We study a more realistic, Rosenzweig-MacArthur, model that includes a carrying capacity for the prey, and saturating functional response for the predator. We show that dispersal delays can stabilize the predator{prey equilibrium point despite the presence of a Type II functional response that is known to be destabilizing. We also show that dispersal delays reduce the amplitude of oscillations when the equilibrium is unstable, and therefore may help resolve the paradox of enrichment.
    Description
    Author Posting. © Elsevier B.V., 2007. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Theoretical Population Biology 71 (2007): 436-444, doi:10.1016/j.tpb.2007.02.002.
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    Suggested Citation
    Preprint: Klepac, Petra, Neubert, Michael G., van den Driessche, P., "Dispersal delays, predator–prey stability, and the paradox of enrichment", 2007-03-26, https://doi.org/10.1016/j.tpb.2007.02.002, https://hdl.handle.net/1912/1580
     

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