# An axiomatic theory of target-based site prioritization produces a simple and effective new index

#### by Steven Phillips, AT and T Labs

Institution: AT and T Labs
Date: Fri 20th February 2009
Time: 1:15 PM
Location: Room 213, Richard Berry Bldg, The University of Melbourne

Abstract: Indices for site prioritization are widely used as a means of addressing the question: which sites are the most important for conservation of biodiversity? Here we investigate the theoretical underpinnings of target-based prioritization indices, which prioritize sites according to the degree to which they contribute to achieving a set of predetermined conservation targets. We show a strong connection between existing work on site prioritization and the mathematical theory of voting power. Some well-known paradoxes of voting power afflict commonly-used site prioritization indices; by negating such paradoxes, we develop a set of intuitive axioms that we would like a single-species site prioritization index to obey. We introduce an extremely simple new index, called fraction-of-spare,'' that satisfies all the axioms. As an experimental evaluation, we study the multi-year scheduling of site acquisitions for conservation of forest types in New South Wales, under specific assumptions about clearing rates. We find that for this application, the fraction-of-spare index outperforms 52 existing prioritization indices.
We are also able to compute the optimal schedule of acquisitions (under the assumed clearing rates) using mathematical programming techniques, which allows us to conclude that there is still further potential for improvement in the use of site prioritization indices for conservation scheduling.