A Bivariate Normal Test for Elliptical Home-Range Models: Biological Implications and Recommendations

Abstract

I propose a goodness-of-fit test to evaluate compliance of the spatial distribution of activity with bivariate normality. Home-range data for 2 Columbian white-tailed deer fawns (Odocoileus virginianus leucurus) were subjected to this test. The distribution for 1 fawn departed significantly from the expected; the distribution of the other fawn did not. J. WILDL. MANAGE. 47(3):613-619 The study of home ranges and territories (Burt 1943) has become an increasingly prominent approach for elucidating intraand interspecific ecological phenomena among terrestrial vertebrates, notably rodents (Randolph 1977, O'Farrell 1978), insectivores (Hawes 1977), cervids (Robinette 1966, Martinka 1969, Miller 1970, Phillips et al. 1973, Inglis et al. 1979), canids (Ables 1968, Fuller 1978, Andelt and Gipson 1979, Fuller and Keith 1980), felids (Hornocker 1969, Bailey 1975), ursids (Pearson 1975, Landers et al. 1979), mustelids (Mitchell 1961, Shirer and Fitch 1970, Storm 1972), procyonids (Shirer and Fitch 1970, Urban 1970), didelphids (Verts 1963, Shirer and Fitch 1970), leporids (Rongstad and Tester 1971, Trent and Rongstad 1974), fringillids (Wasserman 1980), parulids (Zach and Falls 1978), and iguanids (Waldschmidt 1979). Generally, 2 methods of evaluating home areas (home range or territory size) have been used: nonstatistical (polygon) techniques and statistical models that calculate home areas with the assumption that the locational data follow some probabilistic distribution (Stickel 1954). The elliptical home-range models proposed by Jennrich and Turner (1969) and Koeppl et al. (1975) have gained general acceptance (Hawes 1977, Randolph 1977, O'Farrell 1978, Zach and Falls 1978, Gavin 1979, Inglis et al. 1979, Waldschmidt 1979, Danner and Smith 1980, Wasserman 1980). These models use similar algorithms that are dependent upon the assumption that the locational data follow a bivariate normal distribution. The G, and G2 statistics (Sokal and Rohlf 1969:113) were used to evaluate conformance of locational data to the bivariate normal distribution (Zach and Falls 1978, Waldschmidt 1979). However, skewness (GI) and kurtosis (G2) represent properties of the marginal (univariate) distributions and the accordance of marginal distributions to univariate normality does not generally imply joint conformance to the bivariate normal distribution (Neter and Wasserman 1974:395). This paper presents a technique for evaluating the compliance of locational data to a bivariate normal distribution. In addition to a description of the method and its application, 2 example sets of locational data obtained from telemetrymediated direct observations of marked Columbian white-tailed deer are evaluated. Moore and Stubblebine (1981) described the theoretical basis for a chisquare test of multivariate normality with applications in economics. Here I present a technique, derived from the Moore and IPresent address: Department of Biological Sciences, Southeastern Louisiana University, Hammond, LA 70402. J. Wildl. Manage. 47(3):1983 613 This content downloaded from 157.55.39.111 on Sat, 17 Sep 2016 05:33:05 UTC All use subject to http://about.jstor.org/terms 614 A TEST FOR HOME RANGE MODELS * Smith