Voting power and target-based site prioritization

Indices for site prioritization are widely used to address the question: which sites are most important for conservation of biodiversity? We investigate the theoretical underpinnings of target-based prioritization, which measures sites' contribution to achieving predetermined conservation targets. We show a strong connection between site prioritization and the mathematical theory of voting power. Current site prioritization indices are afflicted by well-known paradoxes of voting power: a site can have zero priority despite having non-zero habitat (the paradox of dummies) and discovery of habitat in a new site can raise the priority of existing sites (the paradox of new members). These paradoxes arise because of the razor's edge nature of voting, and therefore we seek a new index that is not strictly based on voting. By negating such paradoxes, we develop a set of intuitive axioms that an index should obey. We introduce a simple new index, "fraction-of-spare," that satisfies all the axioms. For single-species site prioritization, the fraction- of-spare(s) of a site s equals zero if s has no habitat for the species and one if s is essential for meeting the target area for the species. In-between those limits it is linearly interpolated, and equals area(s)/(total area - target). In an evaluation involving multi-year scheduling of site acquisitions for conservation of forest types in New South Wales under specified clearing rates, fraction-of-spare outperforms 58 existing prioritization indices. We also compute the optimal schedule of acquisitions for each of three evaluation measures (under the assumed clearing rates) using integer programming, which indicates that there is still potential for improvement in site prioritization for conservation scheduling.