Clustering and compactness in reserve site selection: an extension of the Biodiversity Management Area Selection model

Over the last 15 yr, a number of formal mathematical models and heuristics have been developed for the purpose of selecting sites for biodiversity conservation. One of these models, the Biodiversity Management Area Selection (BMAS) model, places a major emphasis on protecting at least a certain area for each biodiversity element. Viewed spatially, solutions from this model tend to be a combination of isolated planning units and, sometimes, small clusters. One method to identify solutions with potentially less fragmentation is to add an objective to minimize the outside perimeter of selected areas. Outside perimeter only counts those edges of a planning unit that are not shared in common with another selected planning unit in a cluster, and, therefore, compact clustering is encouraged. This article presents a new math programming model that incorporates this perimeter objective into the BMAS model. We present an application using data from the USDA Forest Service-funded Sierra Nevada Ecosystem Project and show that the model can be solved optimally by off-the-shelf software. Our tests indicated that the model can produce dramatic reductions in perimeter of the reserve system (increasing clustering and compactness) at the expense of relatively small decreases in performance against area and suitability measures.