Dynamics of consumer-resource reaction-diffusion models: single and multiple consumer species

Area of Science:

• Ecology
• Mathematical Biology
• Theoretical Ecology

Background:

• A single-species consumer-resource reaction-diffusion model was previously studied.
• An analytical study on its dynamics proposed a conjecture regarding global dynamics for small yield rates.

Purpose of the Study:

• To resolve the conjecture on the global dynamics of the consumer-resource model for small yield rates.
• To investigate the dynamics of a multi-species consumer-resource model with indirect competition.
• To determine if competitive exclusion occurs in such multi-species systems.

Main Methods:

• Analytical investigation of reaction-diffusion models.
• Mathematical analysis of dynamical systems.
• Exploration of ecological models in homogeneous and heterogeneous environments.

Main Results:

• The conjecture on the global dynamics for small yield rates is completely settled.
• In the multi-species model, all consumer species are shown to persist uniformly.
• The phenomenon of competitive exclusion is demonstrated to not occur in this model.

Conclusions:

• The global dynamics of the single-species model are fully understood.
• The multi-species model demonstrates stable coexistence, challenging traditional competition exclusion principles.
• The model's behavior is characterized across different environmental conditions.