A Three-Dimensional Home Range Model

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Abstract
Although the movements of many animals are in three spatial dimensions, a three-dimensional home range model has not been developed. We present a three-dimensional home range model based on an ellipsoid of a particular size (volume of the 95 percent confidence ellipsoid), shape (eigenvalues expressed as percent of trace), and orientation (position of orthogonal axes) in space. Equations to determine Cartesian coordinates for points on the confidence ellipsoid of the trivariate mean and cloud of points are developed, and a formula for determining the standardized distance for use in conjunction with behavioral data is presented. Because our model depends on trivariate normality of the data, it may be best applied in the analysis of locational data of animals which move through relatively homogeneous media, concentrating their activities in a central place. The model may also be applied to locational data partitioned according to spatial, behavioral, or chronological criteria, as a way of examining separate components of home range.

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