Movement-based kernel density estimates (MKDEs) in 2 or 3 spatial dimensions.

Description

The mkde package enables animal space use to be estimated in three dimensions (3D) using data collected from biotelemetry tracking devices. This package addresses a recognized need in modeling animal space use (Belant et al. 2012) wherein researchers have been limited by the lack of 3D home range estimators. Animal space use can be characterized by the (x, y) spatial dimensions as well as a third z-dimension representing altitude, elevation, or depth for flying, terrestrial, or aquatic species, respectively. Although many biotelemetry devices record 3D location data with x, y, and z coordinates from tracked animals, the third z coordinate is typically not integrated into studies of animal spatial use. The mkde package enables users to visually explore the 3D MKDE volumes of animals to more intuitively understand how they are spatially related to the environmental covariates and bounding layers within their ranges, such as bathymetry or topography.

The mkde package builds on previous work on the Brownian bridge approach for estimating animal utilization distributions (Horne et al. 2007). This method, in contrast to location-based KDEs, integrates kernels over time along a movement path interpolated between observed locations. Benhamou distinguished location-based kernel density estimators (LKDE) from movement-based kernel density estimators (MKDE), which includes Brownian bridge and biased random walk models. MKDEs account for time between consecutively observations in the estimator, do not requiring independent samples from the UD, and thus more realistically represent the space used by an animal.

The user inputs animal location data typically obtained by a Global Positioning System (GPS) or Very High Frequency (VHF) device in which each observation includes an x-coordinate, a y-coordinate,a z-coordinate, and time. The observed locations are assumed to be subject to observation error and are normal random variables. The observation error variances are either provided by the manufacturers of the telemetry equipment or estimated from field trials, e.g., Hansen and Riggs (2008). Often, an animal's movement is limited in the z-dimension. For example, avian species are generally bounded below by the earth's surface, whereas marine animals are bounded below by the sea floor and above by the water's surface. Package functions allow the mkde user to bound the density in the z-dimension by a(x,y) and b(x,y) with a constant or a 2D raster.

The mkde package provides a 2.5D approach for computing home range area that essentially uses a 2D MKDE draped over a 2D elevation raster. The bias is corrected by calculating and summing the surface area of each cell of the elevation raster that falls within a desired probability contour of the 2D MKDE. An algorithm developed by Jenness (2004, 2014) is used to compute the surface area of each raster cell. This method uses the cell center coordinates and elevations of the focal cell and its eight neighboring cells to construct eight triangular facets within the focal cell. The area of each facet is calculated using Heron's formula and then summed to obtain the surface area for the focal cell.

Numerous functions are provided to write output files in various formats (VTK, XDMF, ASCII) for use in other GIS and 3D Visualization applications.

Details

Author(s)

Jeff A. Tracey (US Geological Survey, San Diego Field Station, Western Ecological Research Center)
James Sheppard (San Diego Zoo Institute for Conservation Research)
Jun Zhu (Department of Statistics and Department of Entomology, University of Wisconsin – Madison)
Robert Sinkovits (San Diego Supercomputer Center)
Amit Chourasia (San Diego Supercomputer Center)
Glenn Lockwood (San Diego Supercomputer Center)
Maintainer: Jeff A. Tracey <jatracey@usgs.gov, jeff.a.tracey@gmail.com>

References

Tracey, J. A., Sheppard, J., Zhu, J., Wei, F., Swaisgood, R. R. and Fisher, R. N. (2014) Movement-Based Estimation and Visualization of Space Use in 3D for Wildlife Ecology and Conservation. PLoS ONE 9(7): e101205. doi: 10.1371/journal.pone.0101205
Tracy, J. A., Sheppard, J. Lockwood, G., Chourasia, A., Tatineni, M., Fisher, R. N., and Sinkovits, R. (2014) Efficient 3D Movement-Based Kernel Density Estimator and Application to Wildlife Ecology. XSEDE 14 Conference Proceedings, Article No. 14. doi: 10.1145/2616498.2616522
Belant, J. L., Millspaugh, J. J., Martin, J. A. & Gitzen, R. A. (2012). Multi-dimensional space use: the final frontier. Frontiers in Ecology & Environment 10, 11-12.
Benhamou, S. (2011). Dynamic Approach to Space and Habitat Use Based on biased random bridges. PLoS ONE 6.
Hansen, M. C., & Riggs, R. A. (2008). Accuracy, precision, and observation rates of global positioning system telemetry collars. The Journal of Wildlife Management, 72(2), 518-526.
Horne, J. S., Garton, E. O., Krone, S. M., Lewis, J. S. (2007). Analyzing animal movements using Brownian bridges. Ecology 88, 2354-2363.
Jenness J. S. (2004) Calculating landscape surface area from digital elevation models. Wildlife Society Bulletin 32: 829-839.
Jenness, J. S. (2014) Calculating landscape surface area from unprojected digital elevation models. In preparation.

Calculate cell areas from elevation raster.

Description

A lower-level function for calculating a cell area matrix (2D array) from an elevation matrix. The area is based on the surface area of the terrain in the cell. The area matrix is then used in calculating areas of 2.5D MKDES.

Usage

computeAreaRaster(RelevMatrix, RcellSize)	

Arguments

Details

This is a wrapper function for C++ function that calculates the surface area of each raster cell given the cell elevations. It is not intended to be used directly; instead, the user should call initializeAreaRaster on an MKDE object.

Value

A 2D matrix of cell surface areas.

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

References

Jenness J.S. (2004) Calculating landscape surface area from digital elevation models. Wildlife Society Bulletin 32: 829-839.
Jenness, J.S. (2014) Calculating landscape surface area from unprojected digital elevation models. In preparation.

Examples

library(terra)
fpath <- system.file("extdata", "condordem.RDS", package="mkde")
condordem <- terra::readRDS(fpath)
cell.sz <- mean(res(condordem))
area.rast <- computeAreaRaster(as.matrix(condordem, wide=TRUE), cell.sz)

Find thresholds for contour intervals

Description

Find the cell or voxel probabilities that correspond to user-specified probability contours

Usage

computeContourValues(mkde.obj, prob)	

Arguments

Details

This function computes threshold cell or voxel probability values corresponding to contours for specified proportions of the utilization distribution. Note that the arugment prob specifies the cumulative probability of the cells or voxels within the contour corresponding to the cell or voxel threshold probability. The cell or voxel threshold probabilities may be orders of magnitude smaller than the cumulative probabilities provided in the prob argument.

Value

A data frame with the probabilities given in the prob argument and corresponding thresholds in the MKDE

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

Examples

data(condor)

# Find min/max coordinates and add buffer
xmax = max(condor$x) + 1000
xmin = min(condor$x) - 1000
ymax = max(condor$y) + 1000
ymin = min(condor$y) - 1000

# Calculate grid dimensions
xrange <- xmax - xmin
yrange <- ymax - ymin
cell.sz = 150
nx <- as.integer(xrange/cell.sz)
ny <- as.integer(yrange/cell.sz)

mv.dat <- initializeMovementData(condor$t, condor$x, condor$y, sig2obs=25.0, t.max=185.0)
mkde.obj <- initializeMKDE2D(xmin, cell.sz, nx, ymin, cell.sz, ny)
dens.res <- initializeDensity(mkde.obj, mv.dat)

mkde.obj <- dens.res$mkde.obj
mv.dat <- dens.res$move.dat
my.quantiles <- c(0.95, 0.75, 0.50)
res <- computeContourValues(mkde.obj, my.quantiles)
print(res)

Compute the area or volume of an MKDE.

Description

For 2D MKDEs, this function computes the area. For a 2.5D MKDE it computes the area based on the cell areas computed from an elevation raster. For a 3D MKDE, it computes the volume.

Usage

computeSizeMKDE(mkde.obj, prob)	

Arguments

Details

For a 2D or 2.5D MKDE list object, areas within the contours specified by quant are calculated. For a 3D MKDE, the volumes within the contours are calculated.

Value

A vector with the areas or volumes is returned.

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

Examples

library(terra)
data(condor)

condor <- condor[1:20,] # simply to make example run more quickly
mv.dat <- initializeMovementData(condor$time, condor$x, condor$y, 
z.obs=condor$z, sig2obs=25.0, sig2obs.z=81.0, t.max=65.0)

fpath <- system.file("extdata", "condordem120.RDS", package="mkde")
condordem120 <- terra::readRDS(fpath)
cell.sz <- mean(res(condordem120))
ext <- ext(condordem120)
nx <- ncol(condordem120)
ny <- nrow(condordem120)
mkde.obj <- initializeMKDE3D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz,
ny, min(values(condordem120), na.rm=TRUE), cell.sz, 25)

# note: we use a raster coarse integration time step so the
# example runs faster
dens.res <- initializeDensity(mkde.obj, mv.dat, integration.step=10.0)
mkde.obj <- dens.res$mkde.obj
mv.dat <- dens.res$move.dat

my.quantiles <- c(0.95, 0.75, 0.50)
res <- computeContourValues(mkde.obj, my.quantiles)
res$volume <- computeSizeMKDE(mkde.obj, my.quantiles)
print(res)

California condor locations

Description

A data frame containing California condor location data

Usage

data(condor)

Format

A data frame with 421 observations on the following 4 variables.

time

Elapsed time in minutes

x

x-coordinate (UTM easting in meters)

y

y-coordinate (UTM northing in meters)

z

z-coordinate (height above sea level in meters)

Details

GPS location data acquired from a wild California condor (Gymnogyps californianus) tracked by San Diego Zoo Global around its reintroduction site in Baja California, Mexico during November 2012 (Sheppard et al. 2013).

Source

James Sheppard, San Diego Zoo Institute for Conservation Research

References

Sheppard, J.K., Walenski, M., Wallace, M.P., Velazco, J.J.V., Porras, C., & Swaisgood, R.R. (2013). Hierarchical dominance structure in reintroduced California condors: correlates, consequences, and dynamics. Behavioral Ecology and Sociobiology. 67: 1-12.

Examples

data(condor)
head(condor, 30)

A RasterLayer containing a digital elevation model (DEM) for the condor data

Description

Digital elevation model of the terrain within the condor's range with a cell resolution of 30 meters (ASTER GDEM version 2, Tachikawa et. al. 2011).

Format

A raster package RasterLayer object with 749 rows, 623 columns, and a cell size of 30 by 30 meters. Each cell contains an elevation in meters.

Source

URL: http://asterweb.jpl.nasa.gov/gdem.asp

References

Tachikawa, T., Hato, M., Kaku, M. & Iwasaki, A. (2011). The characteristics of ASTER GDEM version 2, IGARSS.

Examples

library(terra)
fpath <- system.file("extdata", "condordem.RDS", package="mkde")
condordem <- terra::readRDS(fpath)
plot(condordem)

A RasterLayer containing a digital elevation model (DEM) for the condor data

Description

Digital elevation model of the terrain within the condor's range with a cell resolution of 120 meters (ASTER GDEM version 2, Tachikawa et. al. 2011).

Format

A raster package RasterLayer object with 188 rows, 156 columns, and a cell size of 120 by 120 meters. Each cell contains an elevation in meters.

Source

URL: http://asterweb.jpl.nasa.gov/gdem.asp

References

Tachikawa, T., Hato, M., Kaku, M. & Iwasaki, A. (2011). The characteristics of ASTER GDEM version 2, IGARSS.

Examples

library(terra)
fpath <- system.file("extdata", "condordem120.RDS", package="mkde")
condordem120 <- terra::readRDS(fpath)
plot(condordem120)

Flag 3D locations with out-of-bounds z-coordinates

Description

For a 3D MKDE object and 3D location data, the z-coordinates in the location data are checked to make sure they are within the lower and upper bounds specified in the MKDE list object.

Usage

deselectLocationsOutsideBounds(move.dat, mkde.obj) 	

Arguments

Details

If a 2D or 2.5D MDKE object is passed as an argument, no change is made to the movement data list object. If a 3D MKDE list object is passed as an argument, the z-coordinates in the movement data are checked to determine if they are in range. If they are not, the corresponding value in move.dat$use.obs is set to FALSE. Note that this function is not called within initialzeDensity. If you want to exclude locations because they are outside of the allowed range in the z-dimension, this function must be used before computing the density.

Value

An updated move data list object is returned.

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

Examples

library(terra)
data(condor)
mv.dat <- initializeMovementData(condor$time, condor$x, condor$y, 
z.obs=condor$z, sig2obs=25.0, sig2obs.z=81.0, t.max=65.0)

fpath <- system.file("extdata", "condordem.RDS", package="mkde")
condordem <- terra::readRDS(fpath)

cell.sz <- mean(res(condordem))
ext <- ext(condordem)
nx <- ncol(condordem)
ny <- nrow(condordem)
mkde.obj <- initializeMKDE3D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz,
ny, min(values(condordem), na.rm=TRUE), 30.0, 100)
mkde.obj <- setMinimumZfromRaster(mkde.obj, condordem)
mv.dat <- deselectLocationsOutsideBounds(mv.dat, mkde.obj)

Flag non-movements so they are excluded from MKDE estimation

Description

This function deselects move steps where the probability that the initial and final location are the same location is greater than or equal to a user-defined threshold probability

Usage

deselectNonMovementSteps(move.dat, p) 	

Arguments

Details

If the probability that the initial and final location are the same location is greater than or equal to a user-defined threshold probability, the corresponding value in move.dat$use.obs is set to FALSE. Note that this function is not called within initialzeDensity. If you want to exclude locations because they the initial location in a non-movement step, this function must be used before computing the density.

Value

An updated move data list object is returned.

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

Examples

data(condor)
mv.dat <- initializeMovementData(condor$time, condor$x, condor$y, 
z.obs=condor$z, sig2obs=25.0, sig2obs.z=81.0, t.max=65.0)

mv.dat <- deselectNonMovementSteps(mv.dat, 0.05)

Dugong locations

Description

A data frame containing dugong location data

Usage

data(dugong)

Format

A data frame with 426 observations on the following 4 variables.

time

Elapsed time in minutes

x

x-coordinate (UTM easting in meters)

y

y-coordinate (UTM northing in meters)

z

z-coordinate (Depth in meters)

Details

GPS location data acquired from a wild dugong (Dugong dugon) tracked by James Cook University in Hervey Bay, Australia during August 2004 (Sheppard et. al. 2010)

Source

James Sheppard, San Diego Zoo Institute for Conservation Research

References

Sheppard, J. Marsh, H., Jones, R.E., & Lawler, I.R. (2010). Dugong habitat use in relation to seagrass nutrients, tides, and diel cycles. Marine Mammal Science 26, 855-879.

Examples

data(dugong)
head(dugong, 30)

A RasterLayer containing bathymetry for the dugong data

Description

A 10-meter resolution bathymetric surface of the core seagrass habitat in depth below the mean sea level within the dugong's range (Sheppard et. al. 2007).

Format

A raster package RasterLayer object with 220 rows, 485 columns, and a cell size of 10 by 10 meters. Each cell contains a depth at low tide in meters.

Source

James Sheppard, San Diego Zoo Institute for Conservation Research

References

Sheppard, J. K., Lawler, I. R., & Marsh, H. (2007). Seagrass as pasture for seacows: Landscape-level dugong habitat evaluation. Estuarine, Coastal and Shelf Science, 71(1), 117-132.

Examples

library(terra)
fpath <- system.file("extdata", "dugongdem.RDS", package="mkde")
dugongdem <- terra::readRDS(fpath)
plot(dugongdem)

Estimate move variances for 3D MKDE.

Description

Estimates the move variance for the (x, y) and z dimensions and altitude for a Brownian bridge MKDE.

Usage

estVarMKDE(move.dat)	

Arguments

Details

Computes maximum-likelihood estimates for move variances. If the MKDE is 2D or 2.5D, only the variance for the xy-dimension is estimated. If the MKDE is 3D, a separate move variance for the z-dimension is also estimated.

Value

A move data object updated with move variances

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

Examples

data(condor)
mv.dat <- initializeMovementData(condor$time, condor$x, condor$y, 
z.obs=condor$z, sig2obs=25.0, sig2obs.z=81.0, t.max=65.0)

mv.dat <- estVarMKDE(mv.dat)
cat(paste("Move variance in xy-dimensions = ",
mv.dat$sig2xy[1], "\n", sep=""))
cat(paste("Move variance in z-dimension = ",
mv.dat$sig2z[1], "\n", sep=""))

Initialize an area raster for a 2.5D MKDE.

Description

Initialize the surface area for a 2.5D MKDE.

Usage

initializeAreaRaster(mkde.obj)	

Arguments

Details

After creating the MKDE object and setting the lower bounds in the z-dimension using setMinimumZfromRaster, this function computes the surface area of each raster cell and sets the dimension of the MKDE object to 2.5.

Value

Returns a 2.5 MKDE object with an initialized area raster.

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

Examples

library(terra)
fpath <- system.file("extdata", "pandadem.RDS", package="mkde")
pandadem <- terra::readRDS(fpath)
cell.sz <- mean(res(pandadem))
ext <- ext(pandadem)
nx <- ncol(pandadem)
ny <- nrow(pandadem)
mkde.obj <- initializeMKDE2D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz, ny)

mkde.obj <- setMinimumZfromRaster(mkde.obj, pandadem)
mkde.obj <- initializeAreaRaster(mkde.obj)

Calculate raster of density values for MKDE.

Description

Given a movement data object (list) and MKDE object (list), estimate the movement variance parameters and update them in the movement data object and then compute the density for a 2D, 2.5D, or 3D MKDE.

Usage

initializeDensity(mkde.obj, move.dat, integration.step, d.thresh=1e-25) 	

Arguments

Details

This function computes the density for a 2D, 2.5D, or 3D MKDE. If the move variance parameters have not been estimated, they will be prior to computing the density. The integration time step should be much less than the maximum time step allowed between observed animal locations. For a 2.5D MKDE, if the area has been calculated with initializeAreaRaster, then the cell probabilities are weighted by the proportion of the total surface area represented by the cell.

Value

A list is returned with two elements: move.dat and mkde.obj. The first is an updated move data object and the second is an updated MKDE object.

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
Robert Sinkovits, PhD
San Diego Supercomputer Center
sinkovit@sdsc.edu
Glenn Lockwood, PhD
San Diego Supercomputer Center
glock@sdsc.edu

Examples

library(terra)
data(condor)
condor <- condor[1:20,] # simply to make example run more quickly
mv.dat <- initializeMovementData(condor$time, condor$x, condor$y, 
z.obs=condor$z, sig2obs=25.0, sig2obs.z=81.0, t.max=65.0)

fpath <- system.file("extdata", "condordem120.RDS", package="mkde")
condordem120 <- terra::readRDS(fpath)
cell.sz <- mean(res(condordem120))
ext <- ext(condordem120)
nx <- ncol(condordem120)
ny <- nrow(condordem120)
mkde.obj <- initializeMKDE3D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz,
ny, min(values(condordem120), na.rm=TRUE), cell.sz, 25)

# note: we use a raster coarse integration time step so the
# example runs faster
dens.res <- initializeDensity(mkde.obj, mv.dat, integration.step=10.0)
mkde.obj <- dens.res$mkde.obj
mv.dat <- dens.res$move.dat

Set up a 2D MKDE object.

Description

Define the spatial extent and resolution of a 2D MKDE and create an 2D MKDE list object for use in other functions in the package.

Usage

initializeMKDE2D(xLL, xCellSize, nX, yLL, yCellSize, nY)	

Arguments

Details

It is strongly recommended that the same value is used for xCellSize and yCellSize. The grid should be defined so that it covers the area that the animal used, plus a sufficient buffer so that the density is negligable beyond the grid.

Value

A list representing an MKDE object is returned with the following elements:

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

Examples

library(terra)
fpath <- system.file("extdata", "pandadem.RDS", package="mkde")
pandadem <- terra::readRDS(fpath)
cell.sz <- mean(res(pandadem))
ext <- ext(pandadem)
nx <- ncol(pandadem)
ny <- nrow(pandadem)
mkde.obj <- initializeMKDE2D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz, ny)

Set up a 3D MKDE object.

Description

Define the spatial extent and resolution of a 3D MKDE and create an 3D MKDE list object for use in other functions in the package.

Usage

initializeMKDE3D(xLL, xCellSize, nX, yLL, yCellSize, nY,
zLL, zCellSize, nZ)	

Arguments

Details

It is strongly recommended that the same value is used for xCellSize and yCellSize. The grid should be defined so that it covers the volume that the animal used, plus a sufficient buffer so that the density is negligable beyond the grid.

Value

A list representing an MKDE object is returned with the following elements:

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

Examples

library(terra)
fpath <- system.file("extdata", "condordem.RDS", package="mkde")
condordem <- terra::readRDS(fpath)
cell.sz <- mean(res(condordem))
ext <- ext(condordem)
nx <- ncol(condordem)
ny <- nrow(condordem)
zmin <- min(values(condordem), na.rm=TRUE)
nz <- 30
mkde.obj <- initializeMKDE3D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz,
ny, zmin, cell.sz, nz)

Initialize a movement data list

Description

This function sets up the movement data for use in other functions in the package.

Usage

initializeMovementData(t.obs, x.obs, y.obs, z.obs=NULL, sig2obs=0.0,
sig2obs.z=NA, t.max=max(diff(t.obs), na.rm=TRUE))

Arguments

Details

If only 2D or 2.5D MKDEs are to be calculated, then z.obs and sig2obs.z do not have to be provided.

Value

A move data object, in the form of a list, is returned.

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

Examples

data(condor)
mv.dat <- initializeMovementData(condor$time, condor$x,
condor$y, z.obs=condor$z, 65.0, 25.0, sig2obs.z=81.0)

Movement-based kernel density estimate (MKDE) in 2D using Rcpp

Description

Provides a function for 2-dimensional MKDEs.

Usage

mkde2Dgrid(mkde.obj, move.dat, t.step, d.thresh)	

Arguments

Details

This is lower-level function that call the C++ function. for estimating the movement-based density in 2D. In practice, users should call initializeDensity.
The argument d.thresh is a univariate probability density beyond which the kernel contribution to the overall MKDE is assumed to be negligible. Usually this is set at a very small value and is used to prevent calculations from being performed in cells to which the kernel makes a negligible contribution.

Value

An array whose elements are the estimated utilization probabilities for each cell.

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
Robert Sinkovits, PhD
San Diego Supercomputer Center
sinkovit@sdsc.edu
Glenn Lockwood, PhD
San Diego Supercomputer Center
glock@sdsc.edu
Jun Zhu, PhD
University of Wisconsin-Madison
jzhu@stat.wisc.edu

Examples

data(panda)

# Find min/max coordinates and add buffer
xmax = max(panda$x) + 100
xmin = min(panda$x) - 100
ymax = max(panda$y) + 100
ymin = min(panda$y) - 100

# Calculate grid dimensions
xrange <- xmax - xmin
yrange <- ymax - ymin
cell.sz = 30
nx <- as.integer(xrange/cell.sz)
ny <- as.integer(yrange/cell.sz)

mv.dat <- initializeMovementData(panda$time, panda$x, panda$y, t.max=185.0, sig2obs=25.0)
if (all(is.na(mv.dat$sig2xy))) {
  mv.dat <- estVarMKDE(mv.dat)
}

mkde.obj <- initializeMKDE2D(xmin, cell.sz, nx, ymin, cell.sz, ny)
res <- mkde2Dgrid(mkde.obj, mv.dat, 10.0, 1e-20)

Probability of 2D spatial-temporal interaction.

Description

Probability of 2D spatial-temporal interaction.

Usage

mkde2Dinteraction(mkde.obj, move.dat0, move.dat1, t.step, d.thresh)	

Arguments

Details

This function assumes that the two individual animals were observed at the same times. The cell values returned in the mkde.obj can be summed to obtain a global measure of spatio-temporal interaction.

Value

Returns a list with the following elements:

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

library(terra)
data(panda)
mv.dat0 <- initializeMovementData(panda$time, panda$x, panda$y, 
sig2obs=25.0, t.max=185.0)

n <- nrow(panda)
v <- 20.0 # increase from 0 to increase difference
mv.dat1 <- initializeMovementData(panda$time, panda$x+rnorm(n, 0, v), 
panda$y+rnorm(n, 0, v), sig2obs=25.0, t.max=185.0)

fpath <- system.file("extdata", "pandadem.RDS", package="mkde")
pandadem <- terra::readRDS(fpath)
cell.sz <- mean(res(pandadem))
ext <- ext(pandadem)
nx <- ncol(pandadem)
ny <- nrow(pandadem)
mkde.obj <- initializeMKDE2D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz,
ny)

res <- mkde2Dinteraction(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

Movement-based kernel density estimate (MKDE) in 3D using Rcpp

Description

Provides a function for 3-dimensional MKDEs.

Usage

mkde3Dgrid(mkde.obj, move.dat, t.step, d.thresh)	

Arguments

Details

This is lower-level function that call the C++ function. for estimating the movement-based density in 3D. In practice, users should call initializeDensity.
The argument d.thresh is a univariate probability density beyond which the kernel contribution to the overall MKDE is assumed to be negligible. Usually this is set at a very small value and is used to prevent calculations from being performed in cells to which the kernel makes a negligible contribution.

Value

An array whose elements are the estimated utilization probabilities for each voxel.

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
Robert Sinkovits, PhD
San Diego Supercomputer Center
sinkovit@sdsc.edu
Glenn Lockwood, PhD
San Diego Supercomputer Center
glock@sdsc.edu
Jun Zhu, PhD
University of Wisconsin-Madison
jzhu@stat.wisc.edu

Examples

data(condor)

# Find min/max coordinates and add buffer
xmax = max(condor$x) + 1000
xmin = min(condor$x) - 1000
ymax = max(condor$y) + 1000
ymin = min(condor$y) - 1000

# Calculate grid dimensions
xrange <- xmax - xmin
yrange <- ymax - ymin
cell.sz = 600
nx <- as.integer(xrange/cell.sz)
ny <- as.integer(yrange/cell.sz)
nz <- ceiling(3000.0/cell.sz)

mv.dat <- initializeMovementData(condor$time, condor$x, condor$y, z.obs=condor$z, t.max=185.0,
sig2obs=25.0, sig2obs.z=81.0)
if (all(is.na(mv.dat$sig2xy))) {
  mv.dat <- estVarMKDE(mv.dat)
}

mkde.obj <- initializeMKDE3D(xmin, cell.sz, nx, ymin, cell.sz, ny, 0.0, cell.sz, nz)
res <- mkde3Dgrid(mkde.obj, mv.dat, 5.0, 1e-20)

Probability of 3D spatial-temporal interaction.

Description

Metric of 3D spatial-temporal interaction.

Usage

mkde3Dinteraction(mkde.obj, move.dat0, move.dat1, t.step, d.thresh)	

Arguments

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.

Value

Returns a list with the following elements:

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

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

MKDE to RasterLayer or RasterStack

Description

Converts an MKDE into a RasterLayer or RasterStack so that raster package functions can be used.

Usage

mkdeToTerra(mkde.obj)	

Arguments

Details

This method converts the density array in the MKDE oject to an object of a class from the raster package. This allows the functions in the raster package to be used with the MKDEs.

Value

If the MKDE is 2D or 2.5D, a RasterLayer object is returned. If the MKDE is 3D, a RasterStack is returned with one layer in the stack per level.

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

Examples

library(terra)

# set up MKDE object
fpath <- system.file("extdata", "pandadem.RDS", package="mkde")
pandadem <- terra::readRDS(fpath)
cell.sz <- mean(res(pandadem))
ext <- ext(pandadem)
nx <- ncol(pandadem)
ny <- nrow(pandadem)
mkde.obj <- initializeMKDE2D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz, ny)

# set up movement data
data(panda)
mv.dat <- initializeMovementData(panda$time, panda$x, panda$y, 
sig2obs=25.0, t.max=185.0)

# estimate density
dens.res <- initializeDensity(mkde.obj, mv.dat)
mkde.obj <- dens.res$mkde.obj
mv.dat <- dens.res$move.dat
mkde.rst <- mkdeToTerra(mkde.obj)
plot(mkde.rst)

Giant panda locations

Description

A data frame containing giant panda location data

Usage

data(panda)

Format

A data frame with 147 observations on the following 4 variables.

time

Elapsed time in minutes

x

x-coordinate (UTM easting in meters)

y

y-coordinate (UTM northing in meters)

z

z-coordinate (height above sea level in meters)

Details

GPS location data acquired from a wild giant panda (Ailuropoda melanoleuca) tracked by the Chinese Academy of Sciences and San Diego Zoo Global in Foping National Nature Reserve, China during August 2008 (Zhang et. al. 2012).

Source

Giant panda (Ailuropoda melanoleuca) biotelemetry data was collected by Fuwen Wei and others of the Key Laboratory of Animal Ecology and Conservation Biology, Institute of Zoology, Chinese Academy of Science, People's Republic of China in collaboration with the San Diego Zoo Institute for Conservation Research. Giant panda research was funded by the National Natural Science Foundation of China (31230011), Wildlife Experimental Platform of Chinese Academy of Sciences, and San Diego Zoo Global.

References

Zhang, Z., Sheppard, J.K., Swaisgood, R.R., Wang, G., Nie, Y., Wei, W., Zhao, N. & Wei, F. (2014). Ecological Scale and Seasonal Heterogeneity in the Spatial Behaviors of Giant Pandas. Integrative Zoology, 9: 46-60.

Examples

data(panda)
head(panda, 30)

A RasterLayer containing a digital elevation model (DEM) for the panda data

Description

Digital elevation model of the terrain within the panda's range with a cell resolution of 30 meters (ASTER GDEM version 2, Tachikawa et. al. 2011).

Format

A raster package RasterLayer object with 58 rows, 78 columns, and a cell size of 30 by 30 meters. Each cell contains an elevation in meters.

Source

URL: http://asterweb.jpl.nasa.gov/gdem.asp

References

Tachikawa, T., Hato, M., Kaku, M. & Iwasaki, A. (2011). The characteristics of ASTER GDEM version 2, IGARSS.

Examples

library(terra)
fpath <- system.file("extdata", "pandadem.RDS", package="mkde")
pandadem <- terra::readRDS(fpath)
plot(pandadem)

Make an image plot of an MKDE.

Description

Makes an image plot of an MKDE. If the MKDE is 3D, the contours will be based on the entire MKDE, but only one level indexed by z.index will be plotted.

Usage

plotMKDE(mkde.obj, z.index=1, probs=c(0.99, 0.95, 0.90, 0.75, 0.5, 0.0),
cmap=rev(rainbow(length(probs)-1)), add=FALSE, ...)	

Arguments

Details

A plot of the density for the specified level in the z-dimension (which should be 1, the defaul value, for a 2D or 2.5D MKDE) is generated.

Value

No value is returned.

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

Examples

library(terra)
fpath <- system.file("extdata", "pandadem.RDS", package="mkde")
pandadem <- terra::readRDS(fpath)
cell.sz <- 0.25*mean(res(pandadem))
ext <- ext(pandadem)
nx <- 4*ncol(pandadem)
ny <- 4*nrow(pandadem)
mkde.obj <- initializeMKDE2D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz, ny)

# set up movement data
data(panda)
mv.dat <- initializeMovementData(panda$time, panda$x, panda$y, 
sig2obs=25.0, t.max=185.0)

# estimate density
dens.res <- initializeDensity(mkde.obj, mv.dat)
mkde.obj <- dens.res$mkde.obj
mv.dat <- dens.res$move.dat
plotMKDE(mkde.obj)

Initialize maximum allowable z-axis coordinates to a constant value.

Description

Set the upper bounds in the z-dimension for each location in the x and y dimensions to a constant value.

Usage

setMaximumZfromConstant(mkde.obj, val)	

Arguments

Details

Obviously, the upper bound must be greater than the lower bound.

Value

An updated MKDE list object is returned.

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

Examples

library(terra)
fpath <- system.file("extdata", "dugongdem.RDS", package="mkde")
dugongdem <- terra::readRDS(fpath)
cell.sz <- mean(res(dugongdem))
ext <- ext(dugongdem)
nx <- ncol(dugongdem)
ny <- nrow(dugongdem)
mkde.obj <- initializeMKDE3D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz,
ny, min(values(dugongdem), na.rm=TRUE), 50.0, 15)
mkde.obj <- setMaximumZfromConstant(mkde.obj, 100.0)

Initialize maximum z-axis value from a raster

Description

Set the upper bounds in the z-dimension for each location in the x and y dimensions from a raster.

Usage

setMaximumZfromRaster(mkde.obj, spat.raster)

Arguments

Details

This function sets the upper bounds of the space the animal may occupy in the z-dimension. For example, the ascii.raster.filez argument may represent a raster for elevation for subterranean animals, or other surface.

Value

An updated MKDE list object is returned.

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

Examples

library(terra)
fpath <- system.file("extdata", "dugongdem.RDS", package="mkde")
dugongdem <- terra::readRDS(fpath)
cell.sz <- mean(res(dugongdem))
ext <- ext(dugongdem)
nx <- ncol(dugongdem)
ny <- nrow(dugongdem)
mkde.obj <- initializeMKDE3D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz,
ny, min(values(dugongdem), na.rm=TRUE), 50.0, 15)
mkde.obj <- setMaximumZfromRaster(mkde.obj, dugongdem)

Set minimum z-axis value to a constant.

Description

Set the lower bounds in the z-dimension for each location in the x and y dimensions to a constant value.

Usage

setMinimumZfromConstant(mkde.obj, val)	

Arguments

Details

Obviously, the lower bound must be less than the upper bound.

Value

An updated MKDE list object is returned.

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

Examples

library(terra)
fpath <- system.file("extdata", "dugongdem.RDS", package="mkde")
dugongdem <- terra::readRDS(fpath)
cell.sz <- mean(res(dugongdem))
ext <- ext(dugongdem)
nx <- ncol(dugongdem)
ny <- nrow(dugongdem)
mkde.obj <- initializeMKDE3D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz,
ny, min(values(dugongdem), na.rm=TRUE), 50.0, 15)
mkde.obj <- setMinimumZfromConstant(mkde.obj, -20.0)

Set minimum z-axis values from a raster

Description

Set the lower bounds in the z-dimension for each location in the x and y dimensions from a raster.

Usage

setMinimumZfromRaster(mkde.obj, spat.raster)

Arguments

Details

This function sets the lower bounds of the space the animal may occupy in the z-dimension. For example, the ascii.raster.file argument may represent a raster for elevation, depth of the sea floor, or other surface.

Value

An updated MKDE list object is returned.

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

Examples

library(terra)
fpath <- system.file("extdata", "dugongdem.RDS", package="mkde")
dugongdem <- terra::readRDS(fpath)
cell.sz <- mean(res(dugongdem))
ext <- ext(dugongdem)
nx <- ncol(dugongdem)
ny <- nrow(dugongdem)
mkde.obj <- initializeMKDE3D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz,
ny, min(values(dugongdem), na.rm=TRUE), 50.0, 15)
mkde.obj <- setMinimumZfromRaster(mkde.obj, dugongdem-20.0)

Write path to VTK.

Description

Write the interpolated move path to a VTK file.

Usage

writeInterpolatedPathVTK(move.dat, mkde.obj, description, filename, control)	

Arguments

Details

Writes 3D lines between observed locations for move steps. Move steps where the initial location i has a value of FALSE for move.dat$use.obs[i] are omitted. Currently, the list argument control only has three elements: (1) “method” with a default value of “linear”, (2) method.par which is a list of method parameters, and (3) z.scale used to scale the z-coordinates. Only the z.scale should be set by the user at this time.

Value

No value is returned

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

Examples

library(terra)
data(condor)
mv.dat <- initializeMovementData(condor$time, condor$x, condor$y, 
z.obs=condor$z, sig2obs=25.0, sig2obs.z=81.0, t.max=65.0)

fpath <- system.file("extdata", "condordem.RDS", package="mkde")
condordem <- terra::readRDS(fpath)
cell.sz <- mean(res(condordem))
ext <- ext(condordem)
nx <- ncol(condordem)
ny <- nrow(condordem)
mkde.obj <- initializeMKDE3D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz,
ny, min(values(condordem), na.rm=TRUE), 30.0, 100)

writeInterpolatedPathVTK(mv.dat, mkde.obj,
"Example California condor move steps", "condor_path.vtk")

# Clean up files
unlink("condor_path.vtk")

Write observed locations to VTK.

Description

Write the observed points to a VTK file.

Usage

writeObservedLocationVTK(move.dat, mkde.obj, description, filename, control)	

Arguments

Details

Writes 3D points for observed locations for move steps. Currently, the list argument control only has one element z.scale used to scale the z-coordinates.

Value

No value is returned

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

Examples

library(terra)
data(condor)
mv.dat <- initializeMovementData(condor$time, condor$x, condor$y, 
z.obs=condor$z, sig2obs=25.0, sig2obs.z=81.0, t.max=65.0)

fpath <- system.file("extdata", "condordem.RDS", package="mkde")
condordem <- terra::readRDS(fpath)
cell.sz <- mean(res(condordem))
ext <- ext(condordem)
nx <- ncol(condordem)
ny <- nrow(condordem)
mkde.obj <- initializeMKDE3D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz,
ny, min(values(condordem), na.rm=TRUE), 30.0, 100)

writeObservedLocationVTK(mv.dat, mkde.obj,
"Example California condor locations", "condor_locations.vtk")

# Clean up files
unlink("condor_locations.vtk")

Write a 2D raster to XDMF XML wrapper and binary data file.

Description

Write the raster to a XDMF files.

Usage

writeRasterToVTK(elev, r.rst, g.rst, b.rst, descr, fname)	

Arguments

Details

This function writes a raster to VTK format. The raster is colored according to the RGB values in r.rst, g.rst, and b.rst, respectively. The RGB balues must be an interger from 0 to 255.

Value

No value is returned

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
Amit Chourasia, MS
San Diego Supercomputer Center
amit@sdsc.edu

Examples

library(terra)
fpath <- system.file("extdata", "condordem120.RDS", package="mkde")
condordem120 <- terra::readRDS(fpath)
elev.val <- values(condordem120)
elev.min <- min(elev.val, na.rm=TRUE)
elev.max <- max(elev.val, na.rm=TRUE)

# make a color lookup table
cmap <- data.frame(value=c(0.0, 0.25, 0.5, 0.75, 1.0), 
  R=c(150, 179, 205, 192, 252), 
  G=c(224, 204, 205, 183, 243), 
  B=c(94, 147, 168, 147, 226))
                    
cmap$value <- cmap$value*(elev.max - elev.min) + elev.min
# red
f.R <- approxfun(cmap$value, cmap$R)
elev.r <- rast(condordem120)
values(elev.r) <- round(f.R(elev.val))
# green
f.G <- approxfun(cmap$value, cmap$G)
elev.g <- rast(condordem120)
values(elev.g) <- round(f.G(elev.val))
# blue
f.B <- approxfun(cmap$value, cmap$B)
elev.b <- rast(condordem120)
values(elev.b) <- round(f.B(elev.val))
writeRasterToVTK(condordem120, elev.r, elev.g, elev.b, "Elevation for
California condor Example", "condor_dem.vtk")

# Clean up files
unlink("condor_dem.vtk")

Write a 2D raster to XDMF XML wrapper and binary data file.

Description

Write the raster to a XDMF files.

Usage

writeRasterToXDMF(rast, fname, nodat="NA")	

Arguments

Details

This function writes XDMF XML wrapper and binary data file.

Value

No value is returned

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
Amit Chourasia, MS
San Diego Supercomputer Center
amit@sdsc.edu

Examples

library(terra)
fpath <- system.file("extdata", "condordem.RDS", package="mkde")
condordem <- terra::readRDS(fpath)

# Save as XDMF (notice no file extension in file name)
writeRasterToXDMF(condordem, "condor_dem")

# Clean up files
unlink("condor_dem.dat")
unlink("condor_dem.xdmf")

Write MKDE to a GRASS GIS 3D ASCII raster file.

Description

Write the MKDE to a VTK file.

Usage

writeToGRASS(mkde.obj, fname, nodat="NA", cumprob=FALSE)	

Arguments

Details

This function writes a GRASS GIS ASCII raster file that can be imported using the r3.in.ascii function.

Value

No value is returned

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

Examples

library(terra)
data(condor)
condor <- condor[1:20,] # simply to make example run more quickly
mv.dat <- initializeMovementData(condor$time, condor$x, condor$y, 
z.obs=condor$z, sig2obs=25.0, sig2obs.z=81.0, t.max=65.0)

fpath <- system.file("extdata", "condordem120.RDS", package="mkde")
condordem120 <- terra::readRDS(fpath)
cell.sz <- mean(res(condordem120))
ext <- ext(condordem120)
nx <- ncol(condordem120)
ny <- nrow(condordem120)
mkde.obj <- initializeMKDE3D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz,
ny, min(values(condordem120), na.rm=TRUE), cell.sz, 25)

# note: we use a raster coarse integration time step so the
# example runs faster
dens.res <- initializeDensity(mkde.obj, mv.dat, integration.step=10.0)
mkde.obj <- dens.res$mkde.obj
mv.dat <- dens.res$move.dat

# Write file
writeToGRASS(mkde.obj, "ascii3d.txt")

# Clean up files
unlink("ascii3d.txt")

Write MKDE to an ASCII Visualization Tool Kit (VTK) structured grid file.

Description

Write the MKDE to a VTK file.

Usage

writeToVTK(mkde.obj, fname, description="3D MKDE", cumprob=FALSE)

Arguments

Details

This function writes a VTK structured grid file for a 3D MKDE that can be used in 3D visualization tools such as MayaVI or ParaView

Value

No value is returned

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

Examples

library(terra)
data(condor)
condor <- condor[1:20,] # simply to make example run more quickly
mv.dat <- initializeMovementData(condor$time, condor$x, condor$y, 
z.obs=condor$z, 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)
mkde.obj <- initializeMKDE3D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz,
ny, min(values(condordem120), na.rm=TRUE), cell.sz, 25)

# note: we use a raster coarse integration time step so the
# example runs faster
dens.res <- initializeDensity(mkde.obj, mv.dat, integration.step=10.0)
mkde.obj <- dens.res$mkde.obj
mv.dat <- dens.res$move.dat

# Save as VTK file
writeToVTK(mkde.obj, "condor_3dMKDE.vtk",
description="Example California condor 3D MKDE")

# Clean up files
unlink("condor_3dMKDE.vtk")

Write 3D MKDE to XDMF XML wrapper and binary data file.

Description

Write the MKDE to a XDMF files.

Usage

writeToXDMF(mkde.obj, fname, nodat="NA", cumprob=FALSE)	

Arguments

Details

This function writes XDMF XML wrapper and binary data file.

Value

No value is returned

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
Amit Chourasia, MS
San Diego Supercomputer Center
amit@sdsc.edu

Examples

library(terra)
data(condor)
condor <- condor[1:20,] # simply to make example run more quickly
mv.dat <- initializeMovementData(condor$time, condor$x, condor$y, 
z.obs=condor$z, sig2obs=25.0, sig2obs.z=81.0, t.max=65.0)

fpath <- system.file("extdata", "condordem120.RDS", package="mkde")
condordem120 <- terra::readRDS(fpath)
cell.sz <- mean(res(condordem120))
ext <- ext(condordem120)
nx <- ncol(condordem120)
ny <- nrow(condordem120)
mkde.obj <- initializeMKDE3D(ext$xmin, cell.sz, nx, ext$ymin, cell.sz,
ny, min(values(condordem120), na.rm=TRUE), cell.sz, 25)

# note: we use a raster coarse integration time step so the
# example runs faster
dens.res <- initializeDensity(mkde.obj, mv.dat, integration.step=10.0)
mkde.obj <- dens.res$mkde.obj
mv.dat <- dens.res$move.dat

# Write file (note no file extension!)
writeToXDMF(mkde.obj, "condor_3dMKDE")

# Clean up files
unlink("condor_3dMKDE.dat")
unlink("condor_3dMKDE.xdmf")