A consumer-resource competition model with a state-dependent delay and stage-structured consumer species

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Consumer-resource interactions are fundamental in ecological systems.
• Maturity delays can significantly impact population dynamics.
• Stage-structured models are crucial for understanding species with distinct life stages.

Purpose of the Study:

• To develop a novel consumer-resource competition model incorporating a state-dependent maturity delay.
• To analyze the mathematical properties of the model, including well-posedness and equilibria.
• To investigate the stability and global attractivity of the coexistence equilibrium.

Main Methods:

• Development of a mathematical model with one resource and two stage-structured consumer species.
• Analysis of the model's well-posedness and existence/uniqueness of equilibria.
• Linearized stability analysis of equilibria and derivation of conditions for global attractivity.

Main Results:

• The model directly links resource levels to consumer maturity time via a correction term.
• Existence and uniqueness of all equilibria were established.
• Sufficient conditions for the global attractivity of the coexistence equilibrium were determined.

Conclusions:

• The developed model provides a new framework for studying consumer-resource dynamics with state-dependent maturity.
• The analysis offers insights into the stability and persistence of competing consumer species.
• Findings contribute to a deeper understanding of ecological competition under complex life-history traits.