Society faces rapidly accelerating environmental change and uncertainty about the consequences of this change. Society must thus develop mechanisms to navigate disturbances and change in the environment. There are many examples of both long-lived societies which have successfully faced such challenges, and have failed. These examples may provide important guiding principles for policy design under uncertainty. By exploiting data on a set of relatively simple societies relating to their responses to changes in particular classes of environmental risks, this project will build and analyze set of models of social change. These results will be combined with qualitative analysis of the case studies to deepen our understanding of the characteristics of social-ecological systems that confer robustness to particular disturbances. This analysis will help us predict when alternative responses to disturbance and environmental change will succeed and how they will most likely fail.

The intellectual merit of the proposed activity is the development of a new, integrated approach to study how societies deal with uncertainty, disturbance and change. By applying a range of complementary quantitative approaches to models developed based on a large set of case studies, we will develop tools able to cope with more complexity than traditional approaches in resource economics. At the same time, we will keep the models simple enough to exploit powerful tools developed in mathematics and engineering to obtain general results. Our research is targeted between the extremes of simple bioeconomic models typically employed in resource economics and extremely complex, difficult to analyze simulation models used in environmental science. Further, the project is not only innovative in its approach, but in the questions it asks. It is an attempt to move beyond traditional approaches and focus on a fundamentally different, and arguably more important question: what robustness and vulnerability trade-offs do societies face in dealing with ecological and social complexity, uncertainty and change?

The broader impacts of the proposed activity will be felt in areas of resource management and mathematical education. Management practitioners are faced with such uncertainty that "optimal" management policies are of little use. Adaptive management emerged in the 1970's in response to the inadequacy of traditional approaches. However, adaptive management with its own challenges of replicating large scale experiments has produced few successes. Resource managers need "design principles" for robust institutions that perform well in the face of both social and environmental disturbances. This research project will develop such design principles. The product of this project will be channeled to practitioners and resource managers through the activity of the Resilience Alliance (http://www.resalliance.org) of which 3 members of the research team are members. The Resilience Alliance, produces research, educational materials and practical management tools for resource managers and is presently developing a Practitioners Workbook to which research results from this project will contribute, and make a difference in management practices. Second, our education program will help address our nation's challenges with low mathematical literacy. The NSF, NIH, and National Academies all recognize the need to increase numeracy to remain a leader in new knowledge production. Providing opportunities for students to learn mathematics in context is a critical component of any program aimed at improving numeracy. The educational component of this project, combined with ongoing activities at ASU will immerse students in research at the boundary of natural and social sciences involving mathematics through one-on-one mentoring and targeted summer workshops. Thus, our project will contribute to a critical need in the United States to increase numeracy and maintain global leadership in new knowledge production.