Dynamics of a consumer-resource reaction-diffusion model : Homogeneous versus heterogeneous environments

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Consumer-resource models are crucial for understanding population dynamics.
• Previous research by Zhang et al. (2017) highlighted differences in resource distribution effects.
• Contrasting predictions exist for resource distribution impacts on population abundance (Lou, 2006 vs. Zhang et al., 2017).

Purpose of the Study:

• To analyze the dynamics of a consumer-resource reaction-diffusion model in homogeneous and heterogeneous environments.
• To establish global stability of steady states in homogeneous settings.
• To investigate the existence, stability, and persistence of solutions in heterogeneous environments.

Main Methods:

• Analysis of reaction-diffusion equations.
• Global stability analysis for constant steady states.
• Investigation of positive steady states and time-dependent solutions for heterogeneous environments.

Main Results:

• Global stability of constant steady states confirmed for homogeneous environments.
• Unique spatial resource limitation identified in heterogeneous environments.
• Consumer diffusion can increase population abundance in heterogeneous environments for small/high yield rates, but not intermediate ones.

Conclusions:

• Environmental heterogeneity significantly alters consumer-resource dynamics compared to homogeneous settings.
• Spatial resource distribution and consumer diffusion play critical roles in determining population abundance.
• Model predictions offer new insights into ecological interactions and resource management.