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Pattern Formation in Mesic Savannas.

Denis Patterson1,2,3, Simon Levin4,5, Ann Carla Staver6,7

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|November 27, 2023
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Summary
This summary is machine-generated.

Spatial resource limitation in forest-savanna models can lead to pattern formation. This study reveals subcritical bifurcations and multistability, challenging homogeneous dynamics and informing savanna ecosystem modeling.

Keywords:
Integro-differential equationsPattern formationSavannaSpatial modelingVegetation dynamics

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Area of Science:

  • Ecological modeling
  • Mathematical biology
  • Spatial dynamics

Background:

  • The standard forest-savanna model typically exhibits homogeneous solutions.
  • Spatial processes are crucial for understanding ecosystem dynamics.
  • Resource limitation is a key factor in ecosystem stability.

Purpose of the Study:

  • To investigate pattern-forming bifurcations in a spatially extended forest-savanna model.
  • To analyze the impact of spatial resource limitation on ecosystem dynamics.
  • To explore conditions leading to multistability in savanna ecosystems.

Main Methods:

  • Analysis of a nonlinear partial integro-differential equation system.
  • Numerical simulations to explore pattern formation.
  • Continuation methods to study bifurcations and parameter dependencies.

Main Results:

  • Spatial resource limitation (e.g., water, nutrients, herbivory) can induce pattern formation.
  • Subcritical pattern-forming bifurcations were identified.
  • Significant regions of multistability were observed under realistic parameter regimes.

Conclusions:

  • Spatially extended models with resource limitation offer richer dynamics than homogeneous models.
  • Understanding pattern formation and multistability is vital for savanna ecosystem management.
  • Developing unifying mathematical models for savannas across rainfall gradients remains a challenge.