To maintain the long-term well-being of the global population, management of the world's natural resources must emphasize conservation and renewal over depletion and spending. Natural resource management is a broad topic with both national and international policy implications. This workshop will investigate challenges for the mathematical sciences including models that describe processes affecting water, forests, and food supplies. They involve complex adaptive systems that interconnect natural systems with human ones, thus calling for understanding of both types of systems.
Water: The quality of water in our lakes, rivers, streams, and oceans is critical to sustaining life. Locating sensors to monitor the water supply provides a variety of mathematical sciences challenges. Water and food production are critically linked and often modeled by economic-ecological models on lake eutrophication from agricultural runoff. Climate change challenges mathematical scientists to predict areas of future shortage. Large-scale computational models are required to better understand long-term and short-term carbon cycling in the oceans. The field of ocean science relies on sophisticated numerical analysis methods to model the interconnection of oceans and climate, but models such as those predicting temporal change of pH in oceans carry great uncertainty and require new fundamental methods for uncertainty quantification. Hydro-economic models are needed to address water demand, supply and management questions.
Forests: Forests contribute to clean air and provide lumber and habitat for many species. Forests are complex adaptive systems, displaying features of self-organization, connectedness, and resilience to small-scale disturbances. Challenges for the mathematical sciences are to model spatial and temporal complexity of forests, the effect of human processes such as deforestation, and the effect of feedback processes such as reforestation. The latter includes complex issues: spatial and temporal distribution of reforestation efforts, the effect of diversity (as in tropical forests with 100s of tree species), changing economic demands for lumber, etc. Monitoring forest health, e.g., through the US national forest inventory, leads to a variety of statistical challenges, such as sampling intensity, metrics of diversity and sustainability, and interplay of such variables as tree diameter, height, and health, live/dead status, and understory vegetation. Critical statistical issues involve spatial interpolation methods and changepoint detection. Forest fire prevention is a central issue in forest management, requiring a process to decide which fires should be suppressed. Combinatorial optimization approaches can be found in, but stochastic models to aid in real-time decision making about fire suppression are needed as opposed to longer-term stochastic modeling. Finally, insect pests threaten forest health and call for serious new work on control problems.
Food: Food shortage is an international challenge, and food resource models (of fisheries, forest products, crops) can impact international policy. Model features can include multispecies, age structure, spatial heterogeneities, marine reserves and economic analysis. Mathematical models have guided fisheries management for over 50 years. Many such models aimed at determining the best strategy for obtaining the maximum sustainable yield for various fish stocks but sometimes led to unexpected conclusions. Tradable quotas addressed some of these issues but led to other questions such as determining effective pricing systems and understanding the impact of a pricing system on the economic system and on the ecology. The use of "no take" areas to protect breeding stocks could lead to greater fish catches in the long term, but need appropriate incentive systems to promote compliance. Other modeling questions arise in estimating the "optimal" age for capture. Finally, there are mathematical challenges in developing decision rules for enforcement.
Agricultural systems are coupled with environmental and human processes. For example, they account for 70% of water usage worldwide. Methods to achieve equitable allocation of resources to meet increasing world demand are needed, as are methods to assess policies in the face of uncertainty from environmental conditions and human response. Considerable work exists on management of agricultural systems and resulting impact on food availability, water resources, waste production, and greenhouse gas emission. For example, significant challenges to accurate prediction of greenhouse gas emission arise from spatial and temporal variation in agricultural practice.
Many mathematical science challenges cut across the applied areas of water, forests, and food, and these areas in turn overlap each other. We will devote part of each day to discussion of common features and overlapping mathematical issues. Discussion topics may include: sequential decisions under uncertainty; game theory in competition for resources; use of mathematical economics for pricing policy and incentives; control theory for management of resources; mathematical models of human and natural systems and their interactions; predictive methodologies for management of natural systems; spatio-temporal and network modeling for management of natural systems; spatially explicit modeling; computational biology as a modeling tool in management of natural systems; and ecologic inference.