The Dynamics of Two Diffusively Coupled Predator–Prey Populations

Abstract

I analyze the dynamics of predator and prey populations living in two patches. Within a patch the prey grow logistically and the predators have a Holling type II functional response. The two patches are coupled through predator migration. The system can be interpreted as a simple predator prey metapopulation or as a spatially explicit predator prey system. Asynchronous local dynamics are presumed by metapopulation theory. The main question I address is when synchronous and when asynchronous dynamics arise. Contrary to biological intuition, for very small migration rates the oscillations always synchronize. For intermediate migration rates the synchronous oscillations are unstable and I found periodic, quasi-periodic, and intermittently chaotic attractors with asynchronous dynamics. For large predator migration rates, attractors in the form of equilibria or limit cycles exist in which one of the patches contains no prey. The dynamical behavior of the system is described using bifurcation diagrams. The model shows that spatial predator prey populations can be regulated through the interplay of local dynamics and migration. ]

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

“…4B, and D). In this sense, our results can be added to those of Jansen (1995) (see also de Roos et al, 1991;Scheffer and de Boer, 1995;Nisbet et al, 1998;Jansen and de Roos, 2000;Jansen, 2001) who also proposed dispersal (without delay) as a potential resolution of the paradox of enrichment. The stabilizing effect of dispersal in these studies is weaker than it is in our model, however, as it only produces a decrease in the amplitude of the limit cycle, rather than stabilizing the equilibrium point.…”

Interacting populations : hosts and pathogens, prey and predators

“…6-4B, and D). In this sense, our results can be added to those of Jansen (1995) (see also de Roos et al, 1991;Scheffer & de Boer, 1995;Nisbet et al, 1998;Jansen, 2001) who also proposed dispersal (without delay) as a potential resolution of the paradox of enrichment. The stabilizing effect of dispersal in these studies is weaker than it is in our model, however, as it only produces a decrease in the amplitude of the limit cycle, rather than stabilizing the equilibrium point.…”

Invited Review - Fight on Plankton! or, Phytoplankton Shape and Size as Adaptive Tools to Get Ahead in the Struggle for Life

“…Future studies may attempt an integrated explanation of biomass responses and show the relative importance of different ecological factors like ontogenetic niche shifts (Mittelbach et al 1988), changes in community composition (Leibold 1996, Leibold et al 1997, Chase et al 2000, spatial refuge use (Jansen 2001), density dependence (Mittelbach et al 1988, Abrams 1993, adaptive foraging by herbivores (Abrams 1984(Abrams , 1991(Abrams , 1992(Abrams , 1993) and inducible defenses. More studies are needed that analyze the interactive effects of potentially important factors.…”