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and j will be in their area of home range overlap at the same time were they to
move independently of each other. Of course, most animals do not move with-
out respect to the movements of other animals. Consequently, static interac-
tions should be studied in conjunction with dynamic interactions.
A similar index, I L , is Lloyd's (1967) * index of mean crowding, which
Hurlbert (1978) identified as probably the least biased overlap index:
k
* = N ·
P ki · P kj
where N is the number of cells in which animal i or animal j (or both) has
nonzero probability of use. The mean crowding index standardizes overlap by
the probability of both animals being in the same cell at the same time were
each to use all cells in the combined home ranges evenly and without respect
to use by the other.
Seaman (1993; Seaman et al. 1999; Seaman and Powell 1996) indexed the
abilities of different home range estimators to reconstruct a known utility dis-
tribution by calculating the summed squared differences between predicted
and known values for each cell. This index can be used to index overlap of two
home ranges as
å
( p ki - p kj ) 2 , where p ki and p kj are defined as above, and
emphasizes differences where probability of use is high. The behavior of this
index has not been explored.
Doncaster (1990) indexed overlap using Spearman's coefficient of rank
correlation. Spearman's r is calculated for the utility distributions of two ani-
mals with overlapping home ranges, or for the frequencies of use of cells in a
grid. Doncaster showed that the index behaves well and that nonlinear
responses of the index outside of the area of overlap (where one individual has
probability of use equal to 0) do not affect the overall usefulness of the index.
This appears to be a robust index that can be used broadly to index overlap of
home ranges.
I index pairwise overlap only for animals whose home ranges overlap, or are
adjacent, in the same year, that is, animals for which I p > 0. This criterion
sometimes excludes from analyses two home ranges that are adjacent but do
not overlap, possibly because of sampling error. An objective method of choos-
ing nearest neighbors is needed. Because an animal's home range can overlap
with the home ranges of several other animals, all pairwise index values within
a study site are not strictly independent. Similarly, for studies that follow some
individuals for more than 1 year, index values for different years may not be
independent. Statistical tests must be controlled for both individuals in each
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