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Stability switching and hydra effect in a predator-prey metapopulation model.

Nicolas Bajeux1, Bapan Ghosh2

  • 1Université Côte d'Azur, Inria, INRAE, CNRS, Sorbonne Université, Biocore team, Sophia Antipolis, France; Department of Mathematics, University of Manitoba, Winnipeg, Canada.

Bio Systems
|September 20, 2020
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Summary

Spatial heterogeneity in predator-prey models can induce stability switching and the hydra effect. These phenomena, not seen in non-spatial models, emerge from unbalanced dispersal rates between patches.

Keywords:
Dissimilar dispersalHarvestingPatchy modelSpatial heterogeneityStability

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Predator-prey interactions are fundamental to ecosystem stability.
  • Spatial heterogeneity can significantly influence population dynamics.
  • The Rosenzweig-MacArthur (RM) model is a cornerstone for studying predator-prey systems.

Purpose of the Study:

  • To investigate the impact of spatial heterogeneity on predator-prey dynamics using a metapopulation model.
  • To explore how unbalanced dispersal rates between patches affect ecological stability.
  • To identify novel phenomena arising from spatial structure in harvesting strategies.

Main Methods:

  • Formulation of a Rosenzweig-MacArthur (RM) predator-prey model incorporating dispersal for both prey and predator.
  • Definition and analysis of partially mixed spatial models with asymmetric dispersal rates.
  • Examination of independent harvesting strategies applied to heterogeneous environments.

Main Results:

  • Spatial heterogeneity, induced by dissimilar dispersal rates, can stabilize unstable equilibria.
  • The study identified two phenomena absent in non-spatial models: stability switching and the hydra effect.
  • Stability switching occurs when harvesting effort causes a stable state to become unstable and then re-stabilize.
  • The hydra effect was observed, where harvesting a predator-rich patch increased overall predator biomass.

Conclusions:

  • Spatial heterogeneity is a critical factor that can fundamentally alter predator-prey dynamics.
  • The metapopulation model demonstrates that unbalanced dispersal can lead to emergent phenomena like stability switching and the hydra effect.
  • These findings highlight the importance of considering spatial structure in ecological management and conservation strategies.