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Feasibility and stability in large Lotka Volterra systems with interaction structure
Xiaoyuan Liu1, George W A Constable1, Jonathan W Pitchford1
1Department of Mathematics, University of York, York, YO10 5DD, United Kingdom.
Physical Review. E
|June 17, 2023
Summary
Complex system stability is better understood by combining random matrix theory (RMT) and feasibility approaches. Increasing predator-prey interactions enhances stability in generalized Lotka-Volterra models.
Area of Science:
- Ecology
- Theoretical Ecology
- Mathematical Biology
Background:
- Complex system stability is crucial for ecological dynamics.
- Linear stability analysis and feasibility are two key approaches to study system stability.
- Both methods emphasize the role of interaction structure.
Purpose of the Study:
- To demonstrate the complementary nature of random matrix theory (RMT) and feasibility approaches.
- To analyze how interaction structures influence stability in generalized Lotka-Volterra (GLV) models.
Main Methods:
- Analytical derivations.
- Numerical simulations.
- Application of random matrix theory (RMT).
- Feasibility analysis in generalized Lotka-Volterra (GLV) models.
Main Results:
- Feasibility in GLV models increases with more predator-prey interactions.
- Increased competition or mutualism negatively impacts feasibility.
- These structural changes significantly affect the stability of the GLV model.
Conclusions:
- RMT and feasibility analyses offer complementary insights into complex system stability.
- Interaction structure, particularly predator-prey dynamics, is a critical determinant of ecological stability.
- Findings provide a more comprehensive understanding of ecological model stability.
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