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the harmonic mean estimate. Boulanger and White (1990) used Monte Carlo
simulations and tested the performance of the harmonic mean estimator
against the other estimators just discussed. Despite its problems, the harmonic
mean estimator was the best of the lot. Luckily, better estimators have since
been developed.
One set of home range estimators, kernel estimators, appears best suited
for estimating animals' utility distributions, and hence home ranges. Another
set, fractal estimators, may have promise.
FRACTAL ESTIMATORS
Bascompte and Vilà (1997), Gautestad and Mysterud (1993, 1995), and
Loehle (1990) modeled animal movements as multiscale random walks and
analyzed the patterns of locations as fractals. Bascompte and Vilà (1997)
explained that
D
, the fractal dimension, can be estimated as
lo
g
)
(
d/L
}
(
n
D
=
log(
n
)
+
l
o
g
where
n
is the number of steps along a trace of an animal's movements (1 less
than the number of locations),
L
is the sum of the lengths of all steps (total
length of the movement), and
d
is the planar diameter, which can be estimated
as the greatest distance between two locations. For a movement that is a
straight line,
d
=
L
, so
D
= 1; a line has one dimension. For a random walk,
D
= 2; a random walk spreads over a plane and has two dimensions.
For the animals studied by Bascompte and Vilà (1997) and Gautestad and
Mysterud (1993, 1995), the fractal dimensions,
D
, for movements averaged
less than 2. Finding
D
< 2 means that as they scrutinized their animal location
data on smaller and smaller scales, they found clumps of locations within
clumps within clumps ad infinitum. The movements of the animals did not
spread randomly across the landscape. Gautestad and Mysterud (1993, 1995)
argued, therefore, that animals use their home ranges in a multiscale manner,
which makes ultimate sense. Optimality modeling (giving up time) and
empirical data show that animals who forage in patchy environments are pre-
dicted to and, indeed, do change their movements dependent on both fine-
scale and large-scale characteristics of food availability (Curio 1976; Krebs and
Kacelnik 1991). Thus an animal's decision to remain in or to leave a food
patch depends not just on the availability of food within the patch but also on
