PARENT SESSION
Symposium #14: Spatial control of natural and managed systems: theory and applications.
Sponsored by ESA Theoretical Ecology Section
Organized by: L. Gross.
Wednesday, August 8, 2001. 8:00 AM to 12:00 PM. Madison Ballroom A
Spatial optimization in ecological applications.
Hof, John1, Bevers, Michael1, 1
ABSTRACT- As applications of mathematical programming in natural resource management have evolved past commercial forestry problems, capturing ecological functions and relationships has been the central challenge. In meeting this challenge, most researchers have resorted to nonlinear and integer programming methods. In fact, in our previous book, "Spatial Optimization for Managed Ecosystems," we used nonlinear and integer formulations in all but two of our chapters. These models, however, are difficult to solve, thus limiting the size of the application and limiting the confidence that the analyst has in actually obtaining an optimal or near-optimal solution. In this presentation, we will explore formulations that capture highly nonlinear ecological relationships with linear programs that can be solved with simplex algorithms. This makes it possible to include many thousands of choice variables and many thousands of constraints and still be quite confident of global optimality in solution. The seemingly impossible feat of capturing nonlinearities in linear programs is accomplished with a variety of formulation methods, but they all boil down to discretizing the problem so that the difference equations that relate one discrete time period to another or one discrete land area to another are linear (at least as first order approximations). The presentation will cover simple proximity relationships, reaction-diffusion models, population control problems, and using optimization to develop hypotheses about ecosystems.
KEY WORDS: linear programming, reaction-diffusion models, spatial control, proximity relationships