Collaborative Research: Spatial Theory for Renewable Resource Economics

可再生资源管理的理论传统上集中在三个基本问题上：（1）“我们应该什么时候收获可再生资源？“（2）“我们应该以什么样的速度收获？如何在经济、生物和政治约束下达到预期的速率？然而，由于技术的进步，最近又增加了第四个问题：（4）“我们应该在哪里收获？“有丰富的定量理论可以帮助指导管理者试图回答前三个问题。 然而，第四个问题所需的理论仍然相对不成熟，特别是在资源是移动的的情况下（例如鱼）。 该项目的目标是建立一个有用的数学理论，将提供经验法则的空间管理可再生资源。 主要调查人员将为收获的移动的资源的种群动态建立数学模型。 他们将把这些与经济动机的优化目标（例如，租金最大化），并使用偏微分方程的最优控制方法来分析其模型。人们普遍认为，许多可再生资源正在以不可持续的速度使用。对于海洋鱼类来说尤其如此。 在该项目下进行的研究将有助于通过为空间管理奠定严格的理论基础来改善这些关键资源的管理。 除了其固有的社会相关性，该项目将在科学界产生更广泛的影响。该项目将在主要研究者之间建立新的合作关系。 他们的研究结果将在科学文献中广泛传播。

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.