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Effects of density-dependent migrations on stability of a two-patch predator-prey model
Abderrahim El Abdllaoui1, Pierre Auger, Bob W Kooi
1IRD, Institut de Recherche pour le Développement, U. R. GEODES, Centre de Recherche d'Ile de France, 32 Avenue Henri Varagnat, 93143 Bondy cedex, France. elabdll@bondy.ird.fr
Mathematical Biosciences
|July 3, 2007
Summary
This study simplifies predator-prey dynamics in two patches using aggregation methods. Density-dependent migration can lead to stable equilibria, limit cycles, or bistability between equilibrium and limit cycles.
Area of Science:
- Ecology
- Mathematical Biology
- Population Dynamics
Background:
- Predator-prey models are crucial for understanding ecological interactions.
- Migration patterns significantly influence population dynamics in spatially structured environments.
- Density-dependent migration introduces complex behaviors in ecological models.
Purpose of the Study:
- To develop and analyze a reduced predator-prey model in a two-patch environment with fast, density-dependent migration.
- To investigate the impact of different migration rates and density dependencies on population stability.
- To explore the emergence of complex dynamics such as limit cycles and bistability.
Main Methods:
- Utilized aggregation methods to simplify a two-patch predator-prey model with differing time scales for migration and local demography.
- Analyzed the stability of migration equilibria for various density-dependent migration rules.
- Performed numerical bifurcation analysis to compare the full and aggregated models and identify critical parameter values.
Main Results:
- Demonstrated the existence of a unique and stable migration equilibrium for a broad range of density-dependent migration rules.
- Confirmed the consistency between the full and aggregated models through bifurcation analysis.
- Observed that density-dependent migration can generate limit cycles and identified a Bautin bifurcation point leading to bistability.
Conclusions:
- The aggregation method effectively simplifies complex predator-prey dynamics in two-patch systems with fast migration.
- Density-dependent migration is a key factor driving complex population behaviors, including limit cycles and bistability.
- The findings provide insights into the ecological consequences of migration strategies in predator-prey interactions.
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