Assessment of alternative approaches for bioclimatic modeling with special emphasis on the Mahalanobis distance

We introduce the concept of the Mahalanobis distance to bioclimatic modeling. Specifically, we argue that climatic envelopes defined by the Mahalanobis distance produce more accurate predictions of species distribution than standard rectilinear envelopes (e.g. those produced by BIOCLIM). We base our hypothesis on three rationales: (1) the climatic envelope generated by the Mahalanobis distance is oblique, and therefore, may cope with correlations and interactions among the climatic variables; (2) the Mahalanobis envelope is elliptic, and therefore, better reflects the principle of central tendency as expressed by niche theory; (3) Mahalanobian predictions are based on the whole data rather than on the outermost observations, and are therefore, less sensitive to outliers. We test our hypothesis using data on the distribution of 192 species of woody plants in Israel. Validation tests based on four measures of accuracy (sensitivity, specificity, overall accuracy and the Kappa statistic) support our hypothesis, and suggest that Mahalanobis models produce predictions that are significantly more accurate than those produced by corresponding rectilinear models. Additional simulation experiments demonstrate that the superiority of Mahalanobian models cannot be related to their elliptic shape, or their ability to cope with correlations among the climatic variables. Accordingly, our conclusion is that the prime advantage of Mahalanobian models originates from the fact that their climatic envelopes are defined using all the observations, as opposed to rectilinear envelopes that are founded on the outermost observations.