Optimal control of species augmentation in a competition model

Area of Science:

• Mathematical Ecology
• Conservation Biology
• Optimal Control Theory

Background:

• Endangered species face extinction risks from competitive interactions and the Allee effect, exacerbated by climate change.
• Existing mathematical models inadequately address augmentation strategies for species survival in competitive environments.
• There is a critical need for effective strategies to safeguard vulnerable populations against environmental pressures.

Purpose of the Study:

• To develop and analyze an optimal control strategy for a continuous-time competition model featuring strong Allee effects.
• To maximize the target species population at the final time while considering the costs associated with control measures.
• To investigate cost-effective augmentation strategies for endangered species conservation.

Main Methods:

• Formulation of a continuous-time competition model incorporating the Allee effect.
• Application of Pontryagin's Maximum Principle to derive optimal control characterizations.
• Numerical simulations using the forward-backward sweep method for approximate solutions.

Main Results:

• Optimal control strategies were derived to maximize target species populations.
• The study identified cost-minimization approaches for species translocation and augmentation.
• Numerical simulations provided insights into the dynamics of the model and the effectiveness of the proposed strategies.

Conclusions:

• The developed optimal control framework offers a viable approach for managing endangered species in competitive environments with Allee effects.
• Integrating cost-benefit analyses into conservation strategies is essential for practical implementation.
• This research highlights the importance of mathematical modeling in addressing conservation challenges posed by climate change and interspecific competition.