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Route to chaos in multi-species ecosystems.

Robin Delabays1, Philippe Jacquod1,2,3

  • 1School of Engineering, University of Applied Sciences of Western Switzerland HES-SO, CH-1950 Sion, Switzerland.

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Summary

Mathematical ecosystem models show that increasing interaction variability can lead to complex dynamics like chaos, preserving biodiversity. This route to chaos is common in species-rich systems with dominant predator-prey interactions.

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Dynamical Systems Theory

Background:

  • Ecosystem models often focus on equilibrium states.
  • Persistent dynamics, including limit cycles and chaos, are observed in real and modeled ecosystems.
  • Understanding the drivers of complex ecosystem dynamics is crucial.

Purpose of the Study:

  • To investigate species-rich mathematical models of ecosystems.
  • To explore the emergence of limit cycles and chaotic dynamics from interspecies interaction variability.
  • To unify diverse population dynamics within a single model framework.

Main Methods:

  • Analysis of species-rich mathematical ecosystem models.
  • Investigation of Hopf bifurcations and parameter tuning.
  • Application of random matrix theory arguments.
  • Numerical simulations to observe population dynamics.

Main Results:

  • Increasing interaction variability drives limit cycles and strange attractors.
  • Chaotic dynamics (positive Lyapunov exponent) emerge with increased variability.
  • Limit cycles and strange attractors can maintain biodiversity by preventing species extinction.
  • This route to chaos is prevalent in predator-prey dominated systems.

Conclusions:

  • A unifying model framework explains diverse population dynamics.
  • Interspecies interaction variability is a key driver of complex ecosystem dynamics.
  • The findings suggest a generic scenario for chaos in large, species-rich ecosystems.