Local enrichment and its nonlocal consequences for victim-exploiter metapopulations

Details Local enrichment and its nonlocal consequences for victim-exploiter metapopulations Local enrichment and its nonlocal consequences for victim-exploiter metapopulations

2008-03-14

arxiv.org/abs/0803.2210v2

Biology

Quantitative Biology

Populations and Evolution

25 pages, 13 figures, to appear physica D 2008

Scientific paper

10.1016/j.physd.2008.04.004

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.

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