Local enrichment and its nonlocal consequences for victim-exploiter metapopulations

TL;DR

This paper investigates how local enrichment in victim-exploiter metapopulations influences global stability, revealing complex bifurcation structures and nonlocal effects where local changes induce distant oscillations.

Contribution

It introduces a comprehensive analysis of local enrichment effects on metapopulation stability, including bifurcation analysis and the concept of nonlocal influence, supported by a simple estimation method.

Findings

Stable fixed points, limit cycles, and tori depend on migration rates.

Local enrichment can induce stable oscillations remotely.

A simple estimation method for nonlocal effects is proposed.

Abstract

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.