Average optimacity: An index to guide site prioritization for biodiversity conservation

We developed an index, called average optimacity, that can be used to guide site prioritization for biodiversity conservation. Our index has three desirable properties: (1) it indicates a site's potential contribution to an efficient representative reserve system; (2) it equals zero if and only if a site contains no elements of biodiversity; and (3) it accommodates multiple sets of representation targets. The index is calculated with an optimization algorithm - simulated annealing as implemented in the computer program Marxan. We ran Marxan with 10 different representation target sets and averaged the results. The 10 target sets approximated equal increments in conservation value. Data from the Willamette Valley-Puget Sound-Georgia Basin Ecoregion were used to evaluate the index. To help conservation planners understand average optimacity we: (1) compared it to an average of irreplaceability, a well-known index of conservation value, and (2) used logistic regression models to relate average optimacity to other measures of conservation value (e.g., rarity, richness). Average optimacity and average irreplaceability were highly correlated (Spearman rank correlation = 0.90), suggesting substantial agreement in site prioritization. However, there were clear differences in the rankings of highly valued sites, demonstrating that these two indices provide different perspectives on priorities. Simple regression models showed that average optimacity was strongly associated with maximum representation and maximum rarity. Two of the top multiple regression models for average optimacity exhibited a moderate increase in explanatory power relative to the best simple regression model and had three independent variables, which reflects the multi-dimensional nature of this index. The average optimacity index may be preferable to an irreplaceability index when efficiency is considered an important dimension for site prioritization.