Local enrichment and its nonlocal consequences for victim-exploiter metapopulations

Gur Yaari, Sorin Solomon, Marcelo Schiffer, Nadav M. Shnerb

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The stabilizing effects of local enrichment are revisited. Diffusively coupled host-parasitoid and predator-prey metapopulations are shown to admit a stable fixed point, limit cycle or stable torus with a rich bifurcation structure. A linear toy model that yields many of the basic qualitative features of this system is presented. The further nonlinear complications are analyzed in the framework of the marginally stable Lotka-Volterra model, and the continuous time analog of the unstable, host-parasitoid Nicholson-Bailey model. The dependence of the results on the migration rate and level of spatial variations is examined, and the possibility of "nonlocal" effect of enrichment, where local enrichment induces stable oscillations at a distance, is studied. A simple method for basic estimation of the relative importance of this effect in experimental systems is presented and exemplified.

Original languageEnglish
Pages (from-to)2553-2562
Number of pages10
JournalPhysica D: Nonlinear Phenomena
Issue number20
StatePublished - 15 Oct 2008

Bibliographical note

Funding Information:
We acknowledge helpful discussions with Marcel Holyoak. This work was supported by the EU 6th framework CO3 pathfinder and DAPHNet.


  • Bifurcation
  • Desynchronization
  • Enrichment
  • Host-parasite
  • Predator-prey dynamics
  • Spatial heterogeneity


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