Optimal reserve site selection with distance requirements

The reserve set covering problem minimizes the total cost or area of sites needed to represent all species within a system of nature reserves, but does not address spatial characteristics such as distances between reserve sites. Inter-site distance, as a surrogate for connectivity, is likely to affect species persistence and other functional aspects of reserve systems. Two new 0-1 programming models that build upon the reserve set covering problem are formulated for controlling inter-site distance. Depending on the circumstances, longer or shorter inter-site distances may be desirable, and arguments for each case are discussed. The first model requires reserves to be at least a minimum separation distance apart. The second model requires at least two representations of each species and also requires the sites that represent a species to be no farther apart than a stated proximity distance. These models are applied to four demonstration problems in which both synthetic and real presence/absence data are used. Results and computational experience are discussed. The first model achieves site dispersal while the second model achieves site connectivity to the extent that each is compatible with set covering.