Home Range: A Weighted Normal Estimate and Tests of Underlying Assumptions

Abstract

A robust estimation procedure is proposed to identify and reduce the influence of extreme locations for the bivariate normal home-range method. Tests are proposed for validating the underlying probability distribution from observed animal locations. Location data from a black bear (Ursus americanus) are used to demonstrate the effect of outliers on size and orientation of home-range estimates and to illustrate the goodness-of-fit tests. J. WILDL. MANAGE. 49(2):513-519 Burt (1943:351) defined the home range as area traversed by the individual in its normal activities of food gathering, mating, and caring for young. He believed that occasional sallies and exploratory moves outside the area should not be included as part of the home range. However, a lack of standard conventions for identifying such extreme locations has resulted in potentially arbitrary home-range estimates (Schoener 1981). Hayne (1949) recognized that biological understanding of an animal's home range required information about the intensity of use within the area. Furthermore, he believed that knowledge of the use pattern was important to define the limit of the home range. This pattern of use has subsequently been termed the utilization distribution or UD (Jennrich and Turner 1969, Van Winkle 1975, Anderson 1982). When the observed UD matches a simple probability distribution, we can readily obtain estimates of home-range size, shape, and orientation. These parameters provide a basis for important behavioral and ecological interpretations. Three commonly used methods to estimate home range are the minimum convex polygon, circular bivariate normal, and general bivariate normal methods. These approaches and their underlying probability distributions are discussed by Metzgar (1973); their biological assumptions, sample size biases, and sensitivity to extreme locations have been criticized by several authors (Jennrich and Turner 1969, Dixon and Chapman 1980, MacDonald et al. 1980, Schoener 1981, Anderson 1982). Typically, home-range methods are applied without evaluating the fit of the assumed probability distribution to the observed data. The method selected seems to be based on tradition rather than underlying properties of the data. I this paper we describe a robust estimator t minimize the problems of outliers for the general bivariate normal method and propose procedures for testing the goodness-of-fit of the assumed probability distributions. Location data from a black bear are used to illustrate the good ess-of-fit test and to demonstrate the effect of outliers on size and orientation for bivariate normal and minimum convex polygon home ranges. We wish to thank R. K. Steinhorst for valuable assistance during the development of the statistical methods. Data for our example were provided by J. Unsworth and the Idaho Dep. of Fish and Game. L. J. Nelson, D. F. Stauffer, and D. H. Johnson provided comments on the manuscript. Computer time for this project was provided by the Computing Cent., Univ. of Idaho. This is Contrib. No. 270 from the For., Wildl. and Range Exp. Stn., Univ. of Idaho. This content downloaded from 157.55.39.132 on Thu, 15 Sep 2016 04:56:52 UTC All use subject to http://about.jstor.org/terms 514 HOME RANGE * Samuel and Garton J. Wildl. Manage. 49(2):1985 UNIFORM DISTRIBUTION Metzgar (1973) described the frequency distribution of locations for an animal with equal probability of occurrence per unit of area throughout its home range. This bivariate uniform distribution assumes that the animal has no area of highest activity (center of activity), although an arithmetic center exists. A uniform UD may be appropriate for animals that perceive the environment in a fine-grained fashion (Schoener 1981), whose home ranges are uniform, and that lack a center of activity. The minimum convex polygon (MCP) appears to be an appropriate method to represent the homerange boundary of a uniform UD. The MCP method defines a distinct boundary as Metzgar (1973) suggested for the uniform UD, and Stickel (1954) found that home ranges of uniform use were accurately represented by similar polygon methods. However, because the MCP method does not consider the distribution of use within the home range (Macdonald et al. 1980, Voigt and Tinline 1980), the calculation of potential interaction measures (Macdonald et al. 1980, Voigt and Tinline 1980) by proportional home-range overlap (Owings et al. 1977, Nelson and Mech 1981, Seegmiller and Ohmart 1981) assumes an underlying uniform use pattern and may produce dramatically different values from that of a bivariate normal (Macdonald et al. 1980).