Geoscience Reference
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sidered as
A
and 1/
C
=
n
1/2
/
A
. Now divide the single cell into four equal cells
and calculate 1/
C
for each cell, letting
A
be the area of each new cell and
n
the
number of locations in each new cell. The cells can be divided again each into
four equal cells and the new 1/
C
calculated for each. In either of these
approaches, a utility distribution can be calculated on different scales appro-
priate for different questions.
Gautestad and Mysterud (1993:526) also argued that the fractal approach
to animal movements shows that “it is just as meaningless to calculate [home
range] areas or perimeters as it is to calculate specific lengths of a rugged coast-
line.” They concluded that home range areas cannot be measured because the
number of data points needed for an accurate estimate exceeds the number
that can be collected on most studies. Unfortunately, Gautestad and Mysterud
overstate their point. Clearly, home range boundaries and areas are simple and
usually poor measures of animals' home ranges. The important aspects an ani-
mal's home range relate to the intensity of use and the importance of areas on
the
interior
of the home range (Horner and Powell 1990). So Gautestad and
Mysterud are correct in playing down the importance of boundaries and areas.
Nonetheless, boundaries and areas can be estimated. Animals' home ranges
have indistinct boundaries, just as the coastline of an island becomes indistinct
when viewed using several different scales. But an island whose perimeter can-
not be measured accurately nonetheless has a finite limit to its area, and that
limit can be estimated. Likewise, animals who confine their movements to
local areas (exhibit site fidelity) do have home ranges whose areas can be esti-
mated, even if those areas must be estimated as a range between upper and
lower limits, and even if the home range boundaries may never be known pre-
cisely. In addition, a useful estimate of the internal structure of a home range
may be estimated with fewer data than needed to obtain reasonable estimates
of the home range boundary or area.
In fact, during a finite period of time, an animal
must
confine its movements
to a finite area and limits to that area can be estimated. The black bears I have
studied do confine their movements to finite areas. Fixed kernel estimates of the
areas of the annual home ranges of all bears located more than 300 times
reached asymptotes after at most 300 chronological locations (131 ± 90, mean
±SD,
n
= 7; Powell, unpublished data; asymptote at 300 for a bear located more
than 450 times, 95 percent home ranges). However, equation 3.1 states that the
estimated home range area must increase infinitely as the number of location
data points used to estimate the home range increases. Clearly, this is a contra-
diction. The solution to the contradiction lies, I believe, with whether one
includes unused areas within an animal's home range and whether one uses sta-
