The stage-structured predator-prey model and optimal harvesting policy

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Predator-prey interactions are fundamental to ecosystem stability.
• Stage structure (e.g., juvenile and adult) significantly influences population dynamics.
• Understanding species interactions is crucial for conservation and resource management.

Purpose of the Study:

• To develop a mathematical model for a two-species predator-prey system with distinct life stages.
• To establish criteria for the permanence and extinction of both predator and prey populations.
• To determine optimal harvesting policies for sustainable coexistence.

Main Methods:

• Formulation of a mathematical model incorporating stage structure and predator-prey relationships.
• Analysis of model dynamics to derive conditions for population permanence and extinction.
• Application of optimal control theory to find sustainable harvesting strategies.

Main Results:

• The study provides necessary and sufficient conditions for the coexistence and extinction of the two species.
• An optimal harvesting policy is derived, balancing population levels and resource utilization.
• A critical harvesting threshold is identified for ensuring long-term sustainable development.

Conclusions:

• The mathematical model effectively captures the complex dynamics of stage-structured predator-prey systems.
• The findings offer valuable insights for managing harvested populations and maintaining ecosystem balance.
• The identified harvesting strategies promote ecological sustainability and resource viability.