Movement-based estimation and visualization of space use in 3D for wildlife ecology and conservation

Abstract

Advances in digital biotelemetry technologies are enabling the collection of bigger and more accurate data on the movements of free-ranging wildlife in space and time. 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. Disregarding the vertical component may seriously limit understanding of animal habitat use and niche separation. We present novel movement-based kernel density estimators and computer visualization tools for generating and exploring 3D home ranges based on location data. We use case studies of three wildlife species--giant panda, dugong, and California condor--to demonstrate the ecological insights and conservation management benefits provided by 3D home range estimation and visualization for terrestrial, aquatic, and avian wildlife research.

Figure 1. Example avian, terrestrial, and aquatic animal biotelemetry data sets and their spatial domains.

Left: California condor with a GPS biologger attached to its patagium. Center: A giant panda telemetered with a GPS collar. Right: A dugong fitted with a tail mounted GPS biologger.

Figure 2. An example of a 2.5D MKDE for a giant panda in rugged terrain.

In A, giant panda GPS locations in its summer (red points) and winter (blue points) ranges are shown in relation to a digital elevation model (DEM). Using the DEM, the surface area of each raster cell is calculated (B). The surface area increases as the color gradient changes from green to red. In C, the observed summer range locations and interpolated move paths (red points and lines) are shown against 2D MKDE contours draped over the DEM. In D, the observed winter range locations and interpolated move paths (blue points and lines) are shown against 2D MKDE contours draped over the DEM. 2D MKDE 99%, 95%, 75%, 50% contours are shown with colors ranging from light to dark green.

Figure 3. An illustration of the steps in generating a 3D MKDE for a California condor.

The 3D MKDE is constructed from observed 3D locations and a digital elevation model that sets the lower bound on the MKDE. The expected location (gray points) at each unobserved time is determined by linear interpolation (white lines) between the observations (A). The 3D MKDE is then constructed by integrating a trivariate normal distribution, possibly constrained above or below in the z-dimension, over time along the interpolated movement path (B). The variance of the kernel increases as it moves further from the times of the observed locations. The contours of the final 3D MKDE is shown in C. In B and C, the 99%, 95%, and 50% 3D MKDE volumes are shown in transparent white, orange, and red, respectively.

Figure 4. 3D MKDEs for a breeding pair of California condors.

First we illustrate the 99% contours for the female (orange) and male (yellow), shown as a profile view (A) and an overhead view (B). The MKDEs overlap considerably, but the male appears to spend more time at lower elevations when the pair moves into lower elevation areas. The contours for the voxels that contribute 75% and 50% of the total spatio-temporal interaction of the pair are shown in medium and deep purple (B, C). These areas correspond to the reintroduction site where condors were provisioned with carcasses following reintroduction and the nesting site for the pair. When the 99% (white) and 95% (light purple) contours shown, several other areas are included which may also be of ecological interest.

Figure 5. 3D MKDEs may help better identify threats to species.

In 2007, a subadult female condor made an exploratory movement through a proposed wind energy development (A). The proposed wind turbine locations are shown in yellow, and the 99% contour for the condor is shown in red. When approximating the condor's move path by linearly interpolating between observed locations (red lines, A–E), the path passes through the proposed locations of the wind turbines (B). The 3D models of 120 wind turbines are shown (B) in their proposed locations and size (Vestas V112-3.3 turbines with a 84 meter hub height and a 56 meter rotor radius). Using 2D and 3D MKDEs, we estimated the probability that the condor would have passed through cells (54 meters square, C) and voxels (54 meters cubed, D–E) intersecting each turbine. The 99%, 95%,75%,and 50% contours are shown for the 2D MKDE, and the height of blue 3D bars at each turbine location indicate the probability that the condor passed through cells intersected by the turbines (C). The 95%, 75%,and 50% contour volumes are shown for the 3D MKDE (D, the 99% contour was omitted because it covered most of the topography). For comparison to (C), the 99%, 95%,75%,and 50% contours for the three levels of voxels closest to the ground (the approximate height of the turbines) are shown, and red 3D bars at each turbine location indicate the probability that the condor passed through voxels intersected by the turbines (E). The height of the bars in (C) and (E) are on the same relative scale. In general, the probabilities based on the 3D MKDE are lower and more closely related to the observed altitudes of the condor, the possible altitudes it may be at when it is not observed, and the terrain.

Figure 6. 3D MKDE Voxel Probabilities and 3D Covariates.

Like 2D utilization distributions (UDs), 3D UDs can be related to 2D and 3D habitat covariates. In A, we show the 99% and 95% contour volumes for an adult female condor during the month of November, 2009. In B, we show a volume rendering for predicted mean wind speed (meters/second) for November 2009 in voxels 250 m by 250 m by 10 m (x, y, z, respectively) for 0 to 150 m above the ground. Wind speed increases as the color transitions from pale yellow to red. In C, we relate the probability of the condor being in a voxel to the predicted voxel wind speed for each voxel within 150 meters of the Earth's surface. Rug plots (in red) show the marginal distribution of each variable.

Figure 7. Examples of a 3D MKDE for a dugong in a marine environment.

Dugong 3D MKDE density is visualized in relation to bathymetry (A). The 99% contour volumes for 3D MKDEs based on locations when tidal heights ranged from 0.5–1.0 (red), 1.0–1.5 (orange), 1.5–2.0 (yellow), 2.0–2.5 (light green), and 2.5–3.0 (green) meters are shown. Based on the 3D MKDEs for each tidal height category, we computed the probability that the dugong would have been at different water depths, grouped in 0.5 meter bins (B). The value on the y-axis is the upper depth value for each 0.5 meter bin (i.e. 0 indicates 0.0–0.5 m depth).