Optimal design of compact and connected nature reserves for multiple species.

When designing a conservation reserve system for multiple species, spatial attributes of the reserves must be taken into account at species level. The existing optimal reserve design literature considers either one spatial attribute or when multiple attributes are considered the analysis is restricted only to one species. We built a linear integer programing model that incorporates compactness and connectivity of the landscape reserved for multiple species. The model identifies multiple reserves that each serve a subset of target species with a specified coverage probability threshold to ensure the species' long-term survival in the reserve, and each target species is covered (protected) with another probability threshold at the reserve system level. We modeled compactness by minimizing the total distance between selected sites and central sites, and we modeled connectivity of a selected site to its designated central site by selecting at least one of its adjacent sites that has a nearer distance to the central site. We considered structural distance and functional distances that incorporated site quality between sites. We tested the model using randomly generated data on 2 species, one ground species that required structural connectivity and the other an avian species that required functional connectivity. We applied the model to 10 bird species listed as endangered by the state of Illinois (U.S.A.). Spatial coherence and selection cost of the reserves differed substantially depending on the weights assigned to these 2 criteria. The model can be used to design a reserve system for multiple species, especially species whose habitats are far apart in which case multiple disjunct but compact and connected reserves are advantageous. The model can be modified to increase or decrease the distance between reserves to reduce or promote population connectivity.