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Bistability in a tri-trophic food chain model: Basin stability perspective
Debarghya Pattanayak1, Arindam Mishra1, Syamal K Dana1
1Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India.
Chaos (Woodbury, N.Y.)
|August 3, 2021
Summary
Understanding food chain stability requires basin stability analysis, not just local or global methods. This study quantizes stability changes during transitions, revealing new control mechanisms in predator-prey dynamics.
Area of Science:
- Ecology
- Theoretical Ecology
- Mathematical Biology
Background:
- Food chain stability is crucial for ecosystem persistence against parameter changes.
- Local and conventional global stability analyses are insufficient for complex, multistable ecosystems.
- Transitions between stable states in food webs present significant analytical challenges.
Purpose of the Study:
- To provide precise insights into the dynamics of a tri-trophic food chain exhibiting bistability and transitions to monostability.
- To analyze system dynamics using basin stability to understand transitions leading to predator extinction.
- To quantitatively assess changes in basin stability and explore novel control mechanisms.
Main Methods:
- Revisiting a tri-trophic resource-consumer-predator food chain model.
- Employing basin stability analysis to investigate system dynamics.
- Generating bifurcation diagrams against key parameters with varied initial conditions.
Main Results:
- Identified parameter ranges for state persistence and complex dynamics.
- Quantified relative changes in basin areas during state transitions.
- Demonstrated a 'down-up' control phenomenon alongside 'bottom-up' and 'top-down' controls.
Conclusions:
- Basin stability analysis offers a more complete understanding of food chain dynamics, especially during state transitions.
- Quantitative basin stability estimates are vital for predicting ecosystem persistence.
- The identification of 'down-up' control expands the understanding of ecological regulation in food webs.
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