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Invasive behaviour under competition via a free boundary model: a numerical approach
Kamruzzaman Khan1,2, Shuang Liu3, Timothy M Schaerf1
1School of Science and Technology, University of New England, Armidale, NSW, 2351, Australia.
Journal of Mathematical Biology
|August 5, 2021
Summary
When two invasive species invade simultaneously, numerical simulations reveal four possible outcomes. Successful invasion by both species leads to a "chase-and-run coexistence" dynamic, with invaders forming circular patterns in 2D.
Area of Science:
- Mathematical Biology
- Ecology
- Computational Science
Background:
- Investigates the complex dynamics of simultaneous biological invasions.
- Extends theoretical research on the diffusive Lotka-Volterra competition system with free boundaries.
- Builds upon prior work on weak-strong competition and 'chase-and-run coexistence'.
Purpose of the Study:
- To numerically explore all possible scenarios of two competing invasive species.
- To analyze the influence of initial conditions on invasion dynamics.
- To examine model behavior under environmental perturbations and in different spatial dimensions.
Main Methods:
- Employs numerical simulations based on the diffusive Lotka-Volterra competition system.
- Utilizes the level set method for 2D cases without radial symmetry.
- Applies the front tracking method for other spatial dimensions and symmetries.
Main Results:
- Identified four potential long-term dynamics for competing invasive species.
- Confirmed 'chase-and-run coexistence' as the sole outcome when both species successfully invade.
- Demonstrated model robustness to periodic environmental variations and observed circular population spread in 2D.
Conclusions:
- Numerical simulations provide crucial insights into biological invasion phenomena.
- Findings offer a foundation for future theoretical investigations and model refinement.
- Highlights the potential for applying these models to real-world biological invasion problems.
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