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

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Date
2007-03-26
Author
Klepac, Petra 
Neubert, Michael G. 
van den Driessche, P. 
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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.
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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