An integer optimization approach to a probabilistic reserve site selection problem

Interest in protecting natural areas is increasing as development pressures and conflicting land uses threaten and fragment ecosystems. A variety of quantitative approaches have been developed to help managers select sites for biodiversity protection. The problem is often formulated to select the set of reserve sites that maximizes the number of species or ecological communities that are represented, subject to an upper bound on the number or area of selected sites. Most formulations assume that information about the presence or absence of species in the candidate sites is known with certainty. Because complete information typically is lacking, we developed a reserve selection formulation that incorporates probabilistic presence–absence data. The formulation was a discrete 0/1 optimization model that maximized the number of represented vegetation communities subject to a budget constraint, where a community was considered represented if its probability of occurrence in the set of selected sites exceeded a specified minimum reliability threshold. Although the formulation was nonlinear, a log transformation allowed us to represent the problem in a linear format that could be solved using exact optimization methods. The formulation was tested using a moderately sized reserve selection problem based on data from the Superior National Forest in Minnesota.