Species specific connectivity in reserve-network design using graphs

Systematic conservation planning applications based solely on the presence/absence of a large number of species are not sufficient to guarantee their persistence in highly fragmented landscapes. Recent developments have thus incorporated much desired spatial design considerations, and reserve-network connectivity has received increased attention. Nonetheless, connectivity is often determined without regard to species-specific responses to habitat fragmentation. But species differ in their dispersal ability and habitat requirements, making proximate priority areas necessary for some species, while undesirable for others. We present a novel approach that incorporates species-specific connectivity needs in reserve-network design. Importantly, our method differs from previous approaches in that connectivity is not part of the objective function, but part of the constraints, thus avoiding typical undesirable trade-off that may result in high connectivity for some species but null connectivity for others. We use graphs to describe the dispersal pattern of each species and our goal is to identify minimum sets of reserves with connected sites for each of the species. This is not a trivial problem and we present three algorithms, one heuristic and two integer cutting algorithms that guarantee optimality, based on different 0-1 linear programming formulations. Applications to simulated data show that one of the algorithms that guarantee optimality is superior to the other, although both have limited application due to the number of sites and species they can manage. Remarkably, the heuristic can obtain very satisfactory solutions in short computational times, surpassing the limitations of the exact algorithms.