80
R O G E R A . P O W E L L
95 percent of the data points that form the smallest polygon, but this does not
avoid the flaws inherent in the method other than the problem with extreme
data points. To construct a minimum convex polygon, a researcher discards 90
percent of the data he or she worked so hard to collect and keeps only the
extreme data points. This method, more than any other, emphasizes only the
unstable, boundary properties of a home range and ignores the internal structures of home ranges and central tendencies, which are more stable and are
important for most critical questions about animals.
CIRCLE AND ELLIPSE APPROACHES
Hayne (1949) suggested that to estimate an animal’s home range from point
location data one should use a circle; Jennrich and Turner (1969) and Dunn
and Gipson (1977) generalized the circle to an ellipse. Circle and ellipse approaches assume that animals use space in a fashion conforming to an underlying bivariate normal distribution. Using a circle to represent an animal’s
home range assumes that each animal has a single center of activity that is the
very center, or the two-dimensional arithmetic mean, of all locations. Using an
ellipse assumes that each animal has two such centers of activity that are the
foci of the ellipse. An ellipse can be drawn around the two centers of activity
for an animal such that it contains 95 percent of the location data. This 95
percent ellipse can also be used as an estimate of the animal’s home range.
Dunn and Gipson’s (1977) approach incorporates time data for animal location estimates but time data must conform to a highly restrictive pattern,
which is usually impossible for field research. Because animals do not use space
in a bivariate normal fashion, any estimator of animal home ranges that
assumes such use will estimate utility distributions poorly. de Haan and
Resnick (1994) recently developed a home range estimator based on polar
coordinates that incorporates the time sequential aspect of location data.
However, their estimator appears not to be broadly applicable to real animal
location data because data must be of a restricted type and outliers (sampling
errors) must be identifiable. All ellipse estimators include within an estimated
home range many areas not actually used by an animal.
FOURIER SERIES
In statistics, Fourier series are often used to smooth data, so Anderson (1982)
developed a home range estimator based on the bivariate Fourier series. Each
animal location estimate is treated as a spike in the third dimension above an
R O G E R A . P O W E L L
95 percent of the data points that form the smallest polygon, but this does not
avoid the flaws inherent in the method other than the problem with extreme
data points. To construct a minimum convex polygon, a researcher discards 90
percent of the data he or she worked so hard to collect and keeps only the
extreme data points. This method, more than any other, emphasizes only the
unstable, boundary properties of a home range and ignores the internal structures of home ranges and central tendencies, which are more stable and are
important for most critical questions about animals.
CIRCLE AND ELLIPSE APPROACHES
Hayne (1949) suggested that to estimate an animal’s home range from point
location data one should use a circle; Jennrich and Turner (1969) and Dunn
and Gipson (1977) generalized the circle to an ellipse. Circle and ellipse approaches assume that animals use space in a fashion conforming to an underlying bivariate normal distribution. Using a circle to represent an animal’s
home range assumes that each animal has a single center of activity that is the
very center, or the two-dimensional arithmetic mean, of all locations. Using an
ellipse assumes that each animal has two such centers of activity that are the
foci of the ellipse. An ellipse can be drawn around the two centers of activity
for an animal such that it contains 95 percent of the location data. This 95
percent ellipse can also be used as an estimate of the animal’s home range.
Dunn and Gipson’s (1977) approach incorporates time data for animal location estimates but time data must conform to a highly restrictive pattern,
which is usually impossible for field research. Because animals do not use space
in a bivariate normal fashion, any estimator of animal home ranges that
assumes such use will estimate utility distributions poorly. de Haan and
Resnick (1994) recently developed a home range estimator based on polar
coordinates that incorporates the time sequential aspect of location data.
However, their estimator appears not to be broadly applicable to real animal
location data because data must be of a restricted type and outliers (sampling
errors) must be identifiable. All ellipse estimators include within an estimated
home range many areas not actually used by an animal.
FOURIER SERIES
In statistics, Fourier series are often used to smooth data, so Anderson (1982)
developed a home range estimator based on the bivariate Fourier series. Each
animal location estimate is treated as a spike in the third dimension above an