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the radius of an animal's perception, and other pertinent information. Luckily,
kernel shape has little effect on the output of the kernel estimators, as long as
the kernel is hill-shaped and rounded on top (Silverman 1986), not sharply
peaked (deduced from criticisms by Gautestad and Mysterud, personal com-
munication). Although no objective method exists at present to tie band width
to biology or to location error, except that band width should be greater than
location error (Silverman 1986), objective methods do exist for choosing a
band width that is consistent with statistical properties of the data on animal
locations. Band width can be held constant for a data set (fixed kernel). Or
band width can be varied (adaptive kernel) such that data points are covered
with kernels of different widths ranging from low, broad kernels for widely
spaced points to sharply peaked, narrow kernels for tightly packed points.
Although adaptive kernel density estimators have been expected, intuitively, to
perform better than fixed kernel estimators (Silverman 1986), this has not
been the case (Seaman 1993; Seaman et al. 1999; Seaman and Powell 1996).
The utility distribution is a surface resulting from the mean at each point of
the values at that point for all kernels. In practice, a grid is superimposed on
the data and the density is estimated at each grid intersection as the mean at
that point of all kernels. The probability density function is calculated by mul-
tiplying the mean kernel value for each cell by the area of each cell.
Choosing band width is one of the most important and yet the most diffi-
cult aspects of developing a kernel estimator for animal home ranges (Silver-
man 1986). Narrow kernels reveal small-scale details in the data, and, conse-
quently, tend also to highlight measurement error (telemetry error or trap
placement, for example). Wide kernels smooth out sampling error but also
hide local detail. The optimal band width is known for data that are approxi-
mately normal but, unfortunately, animal location data seldom approximate
bivariate, normal distributions (Horner and Powell 1990; Seaman and Powell
1996). For distributions that are not normal, a band width more appropriate
than that for a normal distribution can be chosen using least squares cross val-
idation. This process chooses various band widths and selects the one that pro-
vides the minimum estimated error. Seaman (1993; Seaman and Powell 1996)
found that cross-validation chooses band widths that estimate known utility
distributions better than do band widths appropriate for bivariate normal
distributions.
Using computer simulations and telemetry data for bears, Seaman (Sea-
man 1993; Seaman et al. 1999; Seaman and Powell 1996) explored the accu-
racy of both fixed and adaptive kernel home range estimators and compared
their accuracies to the harmonic mean estimator. He used simulated home
ranges that looked much like real home ranges but he knew the utility distri-
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