Animal Home Ranges and Territories
97
pairwise overlap when testing for differences among sites, among years, or
among populations of different species.
These indices of overlap and similar indices (Hurlbert 1978) can be used to
compare overlap among sites, to compare changes in overlap with changes in
food or other limiting resources, or to deduce territorial behavior when active
defense, scent marks, or calls have not been documented.
DYNAMIC INTERACTIONS
Several approaches can be used to quantify and test whether two individuals
affect the behavior of each other. The indices test predominantly for attraction
or avoidance.
Doncaster (1990), Horner and Powell (1990, citing Minta’s work in preparation) and Minta (1992) used chi-square and G tests to explore whether two
animals located at the same time (approximately) tended to be found together.
In a 2 × 2 contingency table, paired and unpaired distances can be labeled as
near (animals together or associated) or far (not together or not associated).
Doncaster labeled the foxes he studied as near when they were close enough to
detect each other; Horner and Powell labeled black bears as near when they
were closer than the median distance of telemetry error. Other objective criteria might be based on the animals being within an area of overlap at the same
time (Minta 1992). The N paired locations are a sample estimating how often
the two animals are close together. By taking each location for each animal and
calculating the distance to the N – 1 locations of the other animal not taken at
the same time, one obtains a sample of N 2 – N distances that can also be
divided into near and far and estimate how often the animals would be found
near each other if the movements of each were unaffected by the other. A significant chi-square or G value indicates that the animals attract or avoid each
other. Minta (1992) noted that chi-square statistics behave better than G with
small sample sizes.
My coworkers and I used fixed kernel estimates of utility distributions to
estimate the probabilities that two animals would be in their area of overlap
simultaneously (Powell et al. 1987). Because p ki is the probability that at any
given time individual i will be found in cell k, L p is the probability that two
animals are in their area of home range overlap at the same time if each uses the
area without regard to use by the other. L p can be tested against the actual proportion of time (proportion of location estimates) that either animal spends in
the area of overlap with the other. Because the two animals are unlikely to be
located the same number of times, but must be in the overlap together the
97
pairwise overlap when testing for differences among sites, among years, or
among populations of different species.
These indices of overlap and similar indices (Hurlbert 1978) can be used to
compare overlap among sites, to compare changes in overlap with changes in
food or other limiting resources, or to deduce territorial behavior when active
defense, scent marks, or calls have not been documented.
DYNAMIC INTERACTIONS
Several approaches can be used to quantify and test whether two individuals
affect the behavior of each other. The indices test predominantly for attraction
or avoidance.
Doncaster (1990), Horner and Powell (1990, citing Minta’s work in preparation) and Minta (1992) used chi-square and G tests to explore whether two
animals located at the same time (approximately) tended to be found together.
In a 2 × 2 contingency table, paired and unpaired distances can be labeled as
near (animals together or associated) or far (not together or not associated).
Doncaster labeled the foxes he studied as near when they were close enough to
detect each other; Horner and Powell labeled black bears as near when they
were closer than the median distance of telemetry error. Other objective criteria might be based on the animals being within an area of overlap at the same
time (Minta 1992). The N paired locations are a sample estimating how often
the two animals are close together. By taking each location for each animal and
calculating the distance to the N – 1 locations of the other animal not taken at
the same time, one obtains a sample of N 2 – N distances that can also be
divided into near and far and estimate how often the animals would be found
near each other if the movements of each were unaffected by the other. A significant chi-square or G value indicates that the animals attract or avoid each
other. Minta (1992) noted that chi-square statistics behave better than G with
small sample sizes.
My coworkers and I used fixed kernel estimates of utility distributions to
estimate the probabilities that two animals would be in their area of overlap
simultaneously (Powell et al. 1987). Because p ki is the probability that at any
given time individual i will be found in cell k, L p is the probability that two
animals are in their area of home range overlap at the same time if each uses the
area without regard to use by the other. L p can be tested against the actual proportion of time (proportion of location estimates) that either animal spends in
the area of overlap with the other. Because the two animals are unlikely to be
located the same number of times, but must be in the overlap together the