Diffusion-mediated persistence in three-species competition models with heteroclinic cycles

Area of Science:

• Theoretical Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Ecological models often explore species competition and coexistence.
• Heteroclinic cycles represent complex, non-equilibrium dynamics in competitive systems.
• The role of spatial structure and refuges in maintaining biodiversity is crucial.

Purpose of the Study:

• To investigate the impact of a refuge patch on species persistence in a competitive system.
• To analyze the emergence of new heteroclinic cycles under diffusion.
• To determine conditions for global stability in a two-patch model with species diffusion.

Main Methods:

• Mathematical modeling of a two-patch system with three competing species.
• Analysis of heteroclinic cycles and their stability.
• Investigating the effects of diffusion rates between patches.

Main Results:

• A new heteroclinic cycle can emerge with diffusion, while the original cycle disappears.
• Persistence is possible under specific diffusion conditions, even if the competitive patch is unstable alone.
• Global stability is achieved for a specific model structure when the underlying cycle is a repeller.

Conclusions:

• Spatial structure, specifically a refuge, can rescue species persistence in competitive environments.
• Diffusion dynamics can fundamentally alter the stability and existence of ecological cycles.
• The model demonstrates the potential for complex population dynamics and stability through spatial coupling.