Optimal harvesting under stochastic fluctuations and critical depensation

Area of Science:

• Ecology
• Population Dynamics
• Mathematical Biology

Background:

• Stochastic population models are crucial for understanding ecological dynamics.
• The Allee effect, a phenomenon where population growth rate decreases at low densities, significantly impacts population viability.
• Optimal harvesting strategies aim to maximize yield while ensuring long-term sustainability.

Purpose of the Study:

• To derive the optimal harvesting strategy for a stochastically fluctuating population exhibiting an Allee effect.
• To determine the harvesting thresholds and strategy value that maximize expected cumulative yield until extinction.
• To analyze the influence of the Allee effect and discounting on harvesting policies and extinction probability.

Main Methods:

• Utilized stochastic calculus to model population fluctuations.
• Applied the theory of linear diffusions to derive optimal control strategies.
• Analyzed the impact of an Allee effect on harvesting thresholds and strategy value.

Main Results:

• Identified two optimal harvesting thresholds: one for initiating harvesting and a lower one for immediate population depletion due to the Allee effect.
• Demonstrated that discounting increases harvesting incentives, leading to a higher probability of rapid population extinction.
• The derived optimal strategy value quantifies the maximum expected cumulative yield under the specified conditions.

Conclusions:

• The presence of an Allee effect fundamentally alters optimal harvesting strategies by introducing a critical lower threshold for population depletion.
• Discounting economic factors significantly influences harvesting decisions, potentially accelerating population extinction.
• These findings are vital for developing effective and sustainable resource management policies in ecologically sensitive populations.