Nature Reserve Site Selection to Maximize Expected Species Covered

We analyze the problem of maximizing the expected number of species in a nature reserve network, subject to a constraint on the number of sites in the network, given probabilistic information about species occurrences. The problem is a nonlinear binary integer program that is NP-hard. We develop a linear integer programming approximation that may be solved with standard integer programming software. We compare the approximation with two other approaches, an expected greedy approach and a probability hurdle approach, using probabilistic data on occurrences of terrestrial vertebrates in the state of Oregon. Results of the approximation and an exact algorithm are compared by using samples from the North American Breeding Bird Survey.