Spatial optimization of wildlife populations with probabilistic habitat connections

Abstract

I consider a land area divided into cells and the problem that consists of determining the cells that must be harvested and the cells that must be left in old-growth to maximize the size of wildlife populations that depend on amounts of young- and old-growth forest. In each old-growth cell, the size of the old-growth-dependent population depends on the spatial arrangement of the old-growth cells, specifically of the probability that the cell is connected to at least one other old-growth cell. This problem suggested by Hof and Bevers can be easily formulated by a difficult nonlinear 0-1 program. These authors proposed a linear approximation of a special case of the pairwise connection probabilities. The aim of this article was to show that the problem can be solved simply and efficiently with any set of connection probabilities by using standard 0-1 linear programming software. The key feature to transform the nonlinear program into a linear program is an approximation of the logarithmic function curve by some of its tangents. Computational results on hypothetical grid forests with up to 900 cells are presented to illustrate potentialities of the approach. Near-optimal solutions guaranteed to be within 0.5% of the optimal solution are obtained in less than 10 minutes of computing time. © 2011 by the Society of American Foresters.