Maximum sustainable yield of a nonlinear population model with continuous age structure

Area of Science:

• Population Dynamics
• Mathematical Biology
• Ecology

Background:

• Maximum sustainable yield (MSY) is crucial for fisheries and wildlife management.
• Age-structured population models are essential for accurate biological assessments.
• Density dependence significantly impacts population dynamics and resource management.

Purpose of the Study:

• To investigate the maximum sustainable yield problem for density-dependent, age-structured populations.
• To analyze population dynamics using the nonlinear McKendrick model.
• To determine optimal harvesting strategies without magnitude constraints.

Main Methods:

• Utilized the nonlinear McKendrick model of population dynamics, as introduced by Gurtin and MacCamy.
• Investigated density-dependent population dynamics.
• Analyzed the unconstrained harvesting term within the population model.

Main Results:

• Demonstrated that the maximum sustainable yield problem for this model possesses an optimal solution.
• Identified that the optimal solution is achievable through a bimodal harvesting policy.
• Confirmed consistency with previous findings for the nonlinear Leslie model.

Conclusions:

• An optimal harvesting strategy exists for density-dependent, age-structured populations modeled by the nonlinear McKendrick equation.
• Bimodal harvesting policies represent an effective approach to achieving maximum sustainable yield.
• The findings align with established ecological modeling principles, reinforcing the nonlinear Leslie model results.