• bootstrap;
  • cross-validation;
  • Crotalus horridus;
  • Geographic Information System;
  • GIS;
  • habitat model;
  • hibernacula;
  • partitioned Mahalanobis distance;
  • radiotelemetry

Abstract: Mahalanobis Distance (D2) Statistic is a multivariate statistical method that has been used to model habitats occupied by wildlife and plant species. The output, whether standardized squared distance or probability values, represents the similarity of a given set of values with those of an optimum habitat configuration defined exclusively by sites where the species of interest is known to occur. Typically, all principal components with nonzero eigenvalues are used to calculate D2 values. We partitioned D2 into contributions from individual principal components (PCs) and selected PCs corresponding to relatively invariant aspects of the environment across all use sites to formulate D2(k). Partitioned Mahalanobis D2(k) represents the similarity of a given set of values with those of “minimum” habitat requirements of the species as defined by occupied sites using the k subset of principal components. We created a GIS-based model of the habitat surrounding 39 confirmed timber rattlesnake hibernacula on the Madison County Wildlife Management Area in northwest Arkansas, USA, using slope, aspect, elevation, and 11 physical soil attributes. We retained 4 of 15 principal components in D2(k = 4) calculations, and minimum habitat requirements corresponded to a combination of moderate slope, south to southwest facing slopes, and medium to high elevations. We used bootstrap and cross-validation techniques to examine the stability of the correlation matrix and the effect of each site on overall D2(k) values. The D2(k = 4) model specifically highlighted habitats similar to known rattlesnake hibernacula. We present a method to translate the probability surface into a qualitative data layer useful in making management decisions by examining the cumulative distributions of the percentages of (1) hibernacula correctly classified and (2) the study area predicted. We selected the probability threshold that maximized the predictive gain by including the greatest number of hibernacula in the smallest area. The probability threshold 0.2 captured 82% of the known hibernacula in 25% of the 5,666-ha study area. Partitioned Mahalanobis D2(k) requires only data for where species are known to occur, thus circumventing costly errors in misclassifying habitat use with commonly used classification algorithms that require dichotomous data sets.