The function Lixn measures dynamic interaction between two animals following
the methods outlined by Minta (1992).
Lixn(traj1, traj2, method = "spatial", tc = 0, hr1, hr2, OZ = NULL)This function returns a list of objects representing the calculated statistical values and associated p-values from the Chi-squared test.
pTable -- contingency table showing marginal probabilities of expected use
based on the selection of the method parameter.
nTable -- contingency table showing observed frequency of use of the shared area based on simultaneous fixes.
oTable -- the odds for each cell in the contingency table.
Laa -- the calculated value of the \(L_{AA}\) statistic
p.AA -- the associated p-value
Lbb -- the calculated value of the \(L_{BB}\) statistic
p.BB -- the associated p-value
Lixn -- the calculated value of the \(L_{ixn}\) statistic
p.IXN -- the associated p-value
an object of the class ltraj which contains the time-stamped
movement fixes of the first object. Note this object must be a type II
ltraj object. For more information on objects of this type see help(ltraj).
same as traj1.
method for computing the marginal distribution from which expected
values are computed. If method = "spatial", the marginal values are calculated based on areas
of the shared and unshared portions of the home ranges. If method = "frequency", the marginal
values are calculated based on the number of all fixes within the shared and unshared portions of
the home ranges -- see Details.
time threshold for determining simultaneous fixes -- see function: GetSimultaneous.
(-- required if method = 'spatial') home range polygon associated with traj1. Must
be a sf polygon object.
(-- required if method = 'spatial') same as hr1, but for traj2.
(-- required if method = 'frequency') shared area polygon associated with spatial use overlap
between traj1 and traj2. Must be a sf polygon object.
The function Lixn can be used to calculate the Minta (1992) measures of dynamic
interaction between two animals. The Minta statistic tests how the two animals simultaneously utilize
an area shared between the two individuals. Three coefficients are produced \(L_{AA}\), \(L_{BB}\),
and \(L_{ixn}\). Each of these statistics are based on a contingency table that compares the observed
frequency of those fixes that are simultaneous and within/outside the shared area to expectations based on
area overlap proportions (if method="spatial") or expectations derived from all fixes (if
method="frequency") -- see Minta (1992) for more details. A Chi-squared statistic can then
be used to examine the significance between the observed and expected use of the shared area.
Minta (1992) suggests the following interpretations of the coefficients. When \(L_{AA}\)
is near 0, the first animal's use of the shared area is random (or as expected). When
\(L_{AA} > 0\) it signifies spatial attraction to the shared area, or greater than
expected use. When \(L_{AA} < 0\) it signifies spatial avoidance of the shared area, or
less than expected use. Interpretation of \(L_{BB}\) is the same as for \(L_{AA}\) with
respect to the second animal. \(L_{ixn}\) tells us far more about the nature of the
interaction between the two individuals. As \(L_{ixn}\) nears 0, both animals use the
shared area randomly, with regards to the other animal. If \(L_{ixn} > 0\) the animals
use the shared area more simultaneously, whereas if \(L_{ixn} < 0\) it is an
indication of solitary use, or avoidance. This is why \(L_{ixn}\) is termed the temporal
interaction coefficient. A Chi-squared test can be used to identify the significance
of the \(L_{AA}\), \(L_{BB}\), and \(L_{ixn}\) values.
NOTEs:
1. With modern telemetry datasets, where home ranges are readily estimated, choosing method = 'spatial'
is most appropriate.
2. When the home ranges do not overlap the Lixn statistic is not defined and the function returns a
string of NA's.
3. When one home range completely encloses another the Lixn statistic is not defined and the function returns
a string of NA's and 'ContainsB' (or 'ContainsB') under the p.IXN result.
4. Further to points 2 and 3, the Lixn statistic is not appropriate in situations where the overlap area is
either very large or very small relative to either home range (i.e., a situation with almost complete enclosure
or virtually no overlap). Thus, it is advised that Lixn be used only in situations where there are
suitable marginal areas for areaA, areaB, and areaAB -- see Minta (1992).
Minta, S.C. (1992) Tests of spatial and temporal interaction among animals. Ecological Applications, 2: 178-188
GetSimultaneous
if (FALSE) {
data(deer)
deer37 <- deer[1]
deer38 <- deer[2]
library(sf)
#use minimum convex polygon for demonstration...
hr37 <- deer37 |>
ltraj2sf() |>
st_union () |>
st_convex_hull()
hr38 <- deer38 |>
ltraj2sf() |>
st_union () |>
st_convex_hull()
#tc = 7.5 minutes, dc = 50 meters
Lixn(deer37, deer38, method='spatial', tc=7.5*60, hr1=hr37, hr2=hr38)
}
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