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Tipping Cascades in a Multi-patch System with Noise and Spatial Coupling.

Abhishek Mallela1, Alan Hastings2,3

  • 1Department of Mathematics, University of California Davis, Davis, CA, 95616, USA. amallela@ucdavis.edu.

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Ecologists can forecast ecological tipping points using a spatial model. This study reveals that population coupling and spatial differences reduce early warning signals for population collapse.

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Environmental Science

Background:

  • Forecasting tipping points in spatially extended ecological systems is crucial.
  • Slowly declining populations are susceptible to cascading tipping points.
  • Understanding population dynamics under environmental change is vital.

Purpose of the Study:

  • To develop and analyze a spatial two-patch model for forecasting population collapse.
  • To investigate the impact of environmental stochasticity and spatial coupling on tipping point indicators.
  • To derive and evaluate candidate indicators for population extinction.

Main Methods:

  • Developed a spatial two-patch model with environmental stochasticity.
  • Employed geometric singular perturbation theory for a fast-slow version of the model.
  • Derived analytic expressions for indicators using spectral density analysis.
  • Evaluated indicator performance via simulation studies.

Main Results:

  • Coupling and spatial heterogeneity decrease the magnitude of early warning indicators.
  • The degree of population coupling influences summary statistics trends.
  • Analytic indicators show potential for forecasting population extinction.

Conclusions:

  • The developed spatial model and indicators offer insights into ecological tipping points.
  • Spatial structure significantly affects the detectability of impending population collapse.
  • The theoretical framework may be applicable to managing invasive species and other ecological challenges.