A sequential approach to reserve design with compactness and contiguity considerations

Biological conservation depends increasingly on the establishment of protected areas that include as many species as possible, and are extensive, compact, and connected. Various optimization models have been developed to address one or more of these goals; this article develops a set of models that can be used sequentially or separately to promote all four. Assuming that species are mapped across a rectangular grid, we first identify core areas that are extensive and compact by maximizing the density of the graph associated with the reserve. This minimizes the number of boundary edges (suitably normalized) and thus reduces opportunities for organisms to leave the core areas, and external threats to enter. We then identify contiguous corridors between these compact areas based on costs and species conservation goals, allowing the judicious replacement of core elements where possible. This suite of optimization models can assist in designing an efficient and effective system of compact protected areas along with connecting corridors.