Lixn: Minta's Spatial-temporal interaction statistics
In wildlifeDI: Calculate Indices of Dynamic Interaction for Wildlife Tracking Data

Description Usage Arguments Details Value References See Also Examples

The function Lixn measures dynamic interaction between two animals following the methods outlined by Minta (1992).

1	Lixn(traj1, traj2, method = "spatial", tc = 0, hr1, hr2, OZ = NULL)

`traj1`	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)`.
`traj2`	same as `traj1`.
`method`	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.
`tc`	time threshold for determining simultaneous fixes – see function: `GetSimultaneous`.
`hr1`	(– required if method = 'spatial') home range polygon associated with `traj1`. Must be an object that coerces to class `SpatialPolygons*`.
`hr2`	(– required if method = 'spatial') same as `hr1`, but for `traj2`.
`OZ`	(– required if method = 'frequency') shared area polygon associated with spatial use overlap between `traj1` and `traj2`. Must be an object that coerces to class `SpatialPolygons*`.

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).

This function returns a list of objects representing the calculated values from the Minta statistic 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

Minta, S.C. (1992) Tests of spatial and temporal interaction among animals. Ecological Applications, 2: 178-188

GetSimultaneous

## Not run: 
data(deer)
deer37 <- deer[1]
deer38 <- deer[2]
library(adehabitatHR)
library(sp)
#use minimum convex polygon for demonstration...
hr37 <- mcp(SpatialPoints(ld(deer37)[,1:2]))
hr38 <- mcp(SpatialPoints(ld(deer38)[,1:2]))
#tc = 7.5 minutes, dc = 50 meters
Lixn(deer37, deer38,  method='spatial', tc=7.5*60, hr1=hr37, hr2=hr38)

## End(Not run)