QEIB: Spatially-distributed Population Models with External Forcing and Spatial Control

University Of Tennessee Knoxville, Knoxville TN

Investigators

Abstract

Gross 0110920 The investigators develop methods to carry out spatially explicit control to link natural and anthropogenic forces that influence the demand for biological resources with the dynamics of those resources. While there have been numerous alternative approaches taken to add spatial components to population models, few of these have attempted to deal with spatial control. The investigators evaluate extensions of optimal control methods for dynamical systems to spatial problems, with a focus on general mathematical and computational issues for spatial control linked with abiotic forcing of populations. The effort is motivated by two specific examples. The first concerns black bears in the southern Appalachians, a population with explicit environmental forcing associated with acorn mast production, which varies considerably in time and space. This interacts with hunting, which is spatially restricted. The second example involves an invasive exotic plant species, Lygodium microphyllum (Old World Climbing Fern), in the Everglades of South Florida. This species can completely cover the native tree islands of the region and spatial control of hydrology may be applied to limit its growth. Many of the current problems in regional management involve issues of spatial control -- what to do, where to do it and for what time periods. Examples include alternative plans for land use, forest harvesting, location of dams, and water control. A wide variety of the major environmental public policy issues in the US require scientific assessments of the impacts of alternative management. The investigators develop new mathematical and computational approaches that can aid managers and the public to compare alternative management plans of land and regional resources. The objective also is to allow for comparisons of alternative criteria, arising from different stakeholders, to judge the public utility of different spatial management plans. The project is supported by the Applied Mathematics, Computational Mathematics, and Population Biology programs and by the MPS Office of Multidisciplinary Activities.