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.
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 <[email protected], jef[email protected]>
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:
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.
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