Ranking mahalanobis distance models for predictions of occupancy from presence-only data

The Mahalanobis distance statistic (D²) has emerged as an effective tool to identify suitable habitat from presence data alone, but there has been no mechanism to select among potential habitat covariates. We propose that the best combination of explanatory variables for a D² model can be identified by ranking potential models based on the proportion of the entire study area that is classified as potentially suitable habitat given that a predetermined proportion of occupied locations are correctly classified. In effect, our approach seeks to minimize errors of commission, or maximize specificity, while holding the omission error rate constant. We used this approach to identify potentially suitable habitat for the Olympic marmot (Marmota olympus), a declining species endemic to Olympic National Park, Washington, USA. We compared models built with all combinations of 11 habitat variables. A 7-variable model identified 21,143 ha within the park as potentially suitable for marmots, correctly classifying 80 of occupied locations. Additional refinements to the 7-variable model (e.g., eliminating small patches) further reduced the predicted area to 18,579 ha with little reduction in predictive power. Although we sought a model that would allow field workers to find 80 of Olympic marmot locations, in fact, <3 of 376 occupied locations and <9 of abandoned locations were >100 m from habitat predicted by the final model, suggesting that >90 of occupied marmot habitat could be found by observant workers surveying predicted habitat. The model comparison procedure allowed us to identify the suite of covariates that maximized specificity of our model and, thus, limited the amount of less favorable habitat included in the final prediction area. We expect that by maximizing specificity of models built from presence-only data, our model comparison procedure will be useful to conservation practitioners planning reintroductions, searching for rare species, or identifying habitat for protection.