Kernel density, convex hull, and hypervolume estimates
Two-dimensional kernel density estimates (KDEs) were generated using thekde2d function in R’s MASS library (Venables & Ripley 2002). Default settings were used, so the smoothing kernel was Gaussian and the bandwidth was determined by the normal reference method. Note that a large number of kernel functions exist as alternatives, as with bandwidth methods, and that these choices have a non-trivial influence on the results. However, the point here is to see what would happen if a researcher took the path of least resistance and used the most popular approach.
By convention, KDEs are used by wildlife ecologists to estimate home ranges by taking 95% confidence intervals (Powell & Mitchell 2012). Likewise, the ”core area” of a range is defined as the 50% confidence interval. The 95% criterion is arbitrary and has come under criticism (Powell & Mitchell 2012). However, 95% KDEs will be considered in this paper because they are so widely used in the literature.
Convex hull areas were computed using the chull function in thegrDevices R package (R Core Team 2020) plus the st_areafunction in the sf package (Pebesma 2018), after preparing the hulls using st_polygon and st_sfc .
Hypervolumes were calculated using the hypervolume_gaussianfunction in the R library hypervolume (Blonder 2019). Again, default settings were used. This meant using Gaussian kernel density estimation, a prespecified formula for calculating the number of random samples per point, a default method for estimating the KDE bandwidth, a standard deviation count of three (which is important for fixing the actual area), and a fixed quantile value of 0.95 (likewise). As with other complex methods, the ability to vary numerous flexible parameters clouds the outcome. The mosaic area method has no flexible parameters.