Dispersal delays, predator–prey stability, and the paradox of enrichment
Date
2007-03-26Metadata
Show full item recordCitable URI
https://hdl.handle.net/1912/1580As published
https://doi.org/10.1016/j.tpb.2007.02.002Keyword
Delay-differential equations; Distributed delay; MacArthur-Rosenzweig model; Metapopulation dynamics; Paradox of enrichment; StabilityAbstract
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/1912/1580Related items
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