Dispersal delays, predator–prey stability, and the paradox of enrichment
Dispersal delays, predator–prey stability, and the paradox of enrichment
Date
2007-03-26
Authors
Klepac, Petra
Neubert, Michael G.
van den Driessche, P.
Neubert, Michael G.
van den Driessche, P.
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Keywords
Delay-differential equations
Distributed delay
MacArthur-Rosenzweig model
Metapopulation dynamics
Paradox of enrichment
Stability
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.