The theory of renewable resource management has traditionally focused on three basic questions: (1) "When should we harvest a renewable resource?" (2) "At what rate should we harvest?" and (3) "How can we achieve the desired rate in the face of economic, biological, and political constraints?" As a result of technological advances, however, a fourth question has recently been added to the list: (4) "Where should we harvest?" There is a rich quantitative theory to help guide managers as they attempt to answer the first three questions. The theory required for the fourth question, however, remains relatively undeveloped, particularly in the case where the resource is mobile (e.g. fish). The objective of this project is to build a useful mathematical theory that will provide rules of thumb for the spatial management of renewable resources. The principal investigators will develop mathematical models for the population dynamics of harvested, mobile resources. They will couple these to economically motivated optimization goals (e.g., rent maximization) and use methods for the optimal control of partial differential equations to analyze their models.
It is widely recognized that many renewable resources are being used at unsustainable rates. This is particularly true for marine fish. The research conducted under this project will help improve the management of these critical resources by contributing to a rigorous theoretical foundation for spatial management. Beyond its inherent societal relevance, this project will have broader impacts in the scientific community. This project will establish a new collaboration between the principal investigators. Their results will be widely distributed in the scientific literature.
