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  3. Research Domains
  5. Agricultural, Veterinary And Food Sciences
  7. Agriculture, Land And Farm Management
  9. Agricultural Production Systems Simulation
  11. The Power Of Allee Effects: Inducing Multistability And Oscillations In A Stoichiometric Producer-herbivore System

The power of Allee effects: inducing multistability and oscillations in a stoichiometric producer-herbivore system

Zhiwei Zhu1, Tao Feng2,3

  • 1School of Mathematical Science, Yangzhou University, Yangzhou, 225002, People's Republic of China.

Journal of Mathematical Biology
|February 27, 2025

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View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces a new producer-herbivore model, revealing how the Allee effect (a demographic challenge) creates complex ecosystem dynamics and can even cause population extinction. Managing this effect is key for biodiversity.

Area of Science:

  • Ecology
  • Mathematical Biology
  • Theoretical Ecology

Background:

  • Producer-herbivore interactions are crucial for ecosystem stability and biodiversity.
  • Positive density dependence, particularly the Allee effect, significantly impacts population dynamics.
  • Stoichiometric models offer a framework for understanding nutrient-driven ecological interactions.

Purpose of the Study:

  • To develop and analyze a novel stoichiometric producer-herbivore model incorporating the Allee effect.
  • To investigate the influence of key biological parameters on producer-herbivore dynamics.
  • To explore the conditions leading to multistability, oscillations, and population extinction.

Main Methods:

  • Rigorous mathematical analysis including well-posedness, nullcline analysis, and stability analysis.
Keywords:
Cooperative Allee effectMultistabilityOscillationProducer-herbivore system

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  • Numerical bifurcation analysis to examine parameter effects, especially light intensity.
  • Investigation of the Allee effect's severity and its impact on system dynamics.

    • Main Results:

    • The severity of the Allee effect drives complex dynamics, including multiple forms of bistability and tristability.
    • Severe Allee effects can lead to the extinction of both producer and herbivore populations.
    • Intermediate parameter levels (light intensity, growth rates, Allee saturation) can induce instability and oscillations, while low-severity Allee effects result in simpler dynamics.

    Conclusions:

    • Allee effect severity is a critical factor in determining producer-herbivore dynamics and ecosystem stability.
    • Effective management of the Allee effect is essential for conserving biodiversity and preventing undesirable ecological state transitions.
    • The model provides insights into how demographic factors can lead to complex population dynamics and potential extinctions.
    Stoichiometric