Natural resources, such as forests, fish, land, and biodiversity, while renewable, are being pushed to the brink and beyond by sectorial mismanagement and the resulting cumulative impacts on the macroscopic environmental and ecosystem conditions. For many, the solution is to take a more holistic or ecosystem-based approach to management (EBM).
While this approach seems intuitive, there are many unanswered questions as to the information and modeling requirements for implementing EBM and the potential impacts both at a micro and macroscopic level that it would have on the sustainability of natural resources and the communities that rely on them. It is clear that EBM requires a synthesis of our understanding of ecology and economics, which are both complex systems in their own right. Each has its own highly developed mathematical models and modeling approaches.
Methods from optimal control have been applied in the context of fisheries and forestry, as exemplified by the classic text by Colin Clark, Mathematical Bioeconomics. These approaches have proved extremely useful, but for the most part have focused on single species questions. Extending these ideas to questions that are larger in scope in terms of more species and including spatial heterogeneity is a real mathematical challenge. Optimal control theory provides one potential framework for evaluating EBM, but the complexities of spatially distributed, age structured, and/or stochastic population models will push the frontier of analytical and numerical analysis. Answering the many questions surrounding the implementation and effects of EBM also requires developing mathematical tools and methods for understanding complex coupled natural-human systems, that is, the interaction between ecosystem dynamics and human community dynamics.
Mathematical models for EBM need to take into account both the dynamics of coupled ecological and economic systems and the game theoretic issues arising from the differing interests and values of different stakeholders. Some mathematical approaches to those issues have been developed in both ecology and economics. On the ecological side there are ideas such as the theory of adaptive dynamics. On the economic side there is the theory of differential games, where the single control parameter that can be used for optimization in traditional control theory is replaced by a collection of controls, and where different controls are in the hands of different stakeholders who may want to optimize different things. What is needed for scientific progress is a high level synthesis of these and other ideas, which can occur only if experts on modeling in both ecology and economics collaborate with each other and with experts in mathematical sub-disciplines that are likely to be relevant, including game theory, control theory, dynamical systems, and stochastic processes.
An important goal of the mathematical modeling is to analyze the likely consequences of policy choices proposed by Congress, government agencies, or eco-system managers. These choices will have important consequences not only for ecological systems, but also for the health and economic well being of human communities. Therefore, this workshop will have a public policy component, and representatives of policy makers and fellows of public policy institutes will be invited. At least two afternoons will be devoted to case studies which will develop new research directions, rather than lectures.