# Probability of 3D spatial-temporal interaction. Metric of 3D spatial-temporal interaction. ```r mkde3Dinteraction(mkde.obj, move.dat0, move.dat1, t.step, d.thresh) ``` ## Arguments - `mkde.obj`: An MKDE object created with `initialize3DMKDE` - `move.dat0`: A move data object for the first individual created with `initializeMovementData` - `move.dat1`: A move data object for the second individual created with `initializeMovementData` - `t.step`: A time step used for numerical integration over the movement trajectory - `d.thresh`: The value of the kernel below which its contibrution to the overal density is considered negligible ## Details This function assumes that the two individual animals were observed at the same times. The voxel values returned in the mkde.obj can be summed to obtain a global measure of spatio-temporal interaction. ## Returns Returns a list with the following elements: - **mkde.obj**: An updated MKDE object containing the voxel-level Bhattacharyya coefficients - **move.dat0**: A move data object for the first individuals with updated variance parameters - **move.dat1**: A move data object for the second individuals with updated variance parameters ## Author(s) Jeff A. Tracey, PhD USGS Western Ecological Research Center, San Diego Field Station jatracey@usgs.gov James Sheppard, PhD San Diego Zoo Institute for Conservation Research jsheppard@sandiegozoo.org Jun Zhu, PhD University of Wisconsin-Madison jzhu@stat.wisc.edu ## Examples ```r library(terra) data(condor) condor <- condor[1:4,] # simply to make example run more quickly mv.dat0 <- initializeMovementData(condor$time, condor$x, condor$y, z.obs=condor$z, sig2obs=25.0, sig2obs.z=81.0, t.max=65.0) n <- nrow(condor) v <- 20.0 # increase from 0 to increase difference between move trajectories vz <- 5.0 mv.dat1 <- initializeMovementData(condor$time, condor$x+rnorm(n, 0, v), condor$y+rnorm(n, 0, v), z.obs=condor$z+rnorm(n, 0, vz), sig2obs=25.0, sig2obs.z=81.0, t.max=65.0) fpath <- system.file("extdata", "condordem120.RDS", package="mkde") condordem120 <- terra::readRDS(fpath) # next two lines reduce extent of 2D space to speed execution of example tmp <- ext(c(range(condor$x) + c(-100, 100), range(condor$y) + c(-100, 100))) condordem120 <- crop(condordem120, tmp) cell.sz <- mean(res(condordem120)) ext <- ext(condordem120) nx <- ncol(condordem120) ny <- nrow(condordem120) nz <- ceiling(3000.0/cell.sz) mkde.obj <- initializeMKDE3D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz, ny, 0.0, cell.sz, nz) res <- mkde3Dinteraction(mkde.obj, mv.dat0, mv.dat1, 10.0, 1e-20) mkde.obj <- res$mkde.obj mv.dat0 <- res$move.dat0 mv.dat1 <- res$move.dat1 ```

mkde3Dinteraction function