**3. Bandwidth selection for kernel density estimation**

In KDE, a kernel distribution (i.e. a three-dimensional hill or kernel) is placed on each telemetry location. The height of the hill is determined by the bandwidth of the distribution, and many distributions and methods are available (e.g. fixed versus adaptive, univariate versus bivariate bandwidth; for a complete review see Worton 1989; Seaman & Powell 1996). The study extent is then gridded with evaluation points in which different kernels are summarized to produce a utilization distribution across the area of interest. The resulting utilization distribution is therefore sensitive to the resolution of the evaluation grid, and more importantly, to the bandwidth selection (i.e. smoothing parameter) of the kernels.

What Is the Proper Method to Delineate Home Range of an

Research Center, unpublished data; Fig. 3).

were collected.

successfully created.

Animal Using Today's Advanced GPS Telemetry Systems: The Initial Step 255

Florida, USA, had a 95% home range calculated with href that extended inland and into the Atlantic Ocean to areas locations were not even identified (J.W. Fischer, National Wildlife

Fig. 3. Home range (yellow polygon) of a migratory turkey vulture from South Carolina to Florida, USA as estimated using KDE with href bandwidth selection over-layed on actual GPS locations. Note that KDE occurs inland and into Atlantic Ocean where no GPS locations

An additional practical problem we encountered with href in adehabitat is that the extent of the generated home range polygon was truncated or not generated at all because a greater extent for evaluation points needed to be specified. To work around this issue, we created an evaluation grid of increased extent and iteratively re-estimated the home range until a large enough extent was specified and all isopleth (i.e. probability contour) polygons were

Both the least squares cross-validation (hlscv) and bias crossed validation (hbcv) have been suggested instead of href in attempts to prevent over-smoothing of KDE (Rodgers & Kie 2010). However, hlscv and hbcv have been minimally evaluated on GPS datasets because previous literature only evaluated datasets collected on VHF sampling protocols or simulated data that included at most 1,000 locations and did not represent actual animal distributions (Worton 1995; Gitzen et al., 2006; Lichti & Swihart 2011). Least-squares cross

**3.2 Least squares cross-validation bandwidth estimation** 

Because GPS data are autocorrelated, they can pose difficulties in estimating the bandwidth (Gitzen et al., 2006) and violate the assumption of independence of locations that is inherent to KDE (Worton 1989). Therefore, although previous research on principles of bandwidth selection and selection of software is suitable for some datasets (e.g. VHF sampling protocols; Seaman et al., 1999; Gitzen et al., 2006; Kie et al., 2010), GPS datasets present additional challenges that need to be addressed (Amstrup et al., 2004; Hemson et al., 2005; Getz et al., 2007).

Fig. 2. Multiple Universal Transverse Mercator zones traversed by a migratory American White Pelican in the U.S.
