Abstract:
Parametric kernel methods currently dominate the literature regarding the construction of animal home ranges (HRs) and
utilization distributions (UDs). These methods frequently fail to capture the kinds of hard boundaries common to many natural
systems. Recently a local convex hull (LoCoH) nonparametric kernel method, which generalizes the minimum convex polygon
(MCP) method, was shown to be more appropriate than parametric kernel methods for constructing HRs and UDs, because of
its ability to identify hard boundaries (e.g., rivers, cliff edges) and convergence to the true distribution as sample size increases.
Here we extend the LoCoH in two ways: ‘‘fixed sphere-of-influence,’’ or r-LoCoH (kernels constructed from all points within
a fixed radius r of each reference point), and an ‘‘adaptive sphere-of-influence,’’ or a-LoCoH (kernels constructed from all points
within a radius a such that the distances of all points within the radius to the reference point sum to a value less than or equal
to a), and compare them to the original ‘‘fixed-number-of-points,’’ or k-LoCoH (all kernels constructed from k-1 nearest
neighbors of root points). We also compare these nonparametric LoCoH to parametric kernel methods using manufactured
data and data collected from GPS collars on African buffalo in the Kruger National Park, South Africa. Our results demonstrate
that LoCoH methods are superior to parametric kernel methods in estimating areas used by animals, excluding unused areas
(holes) and, generally, in constructing UDs and HRs arising from the movement of animals influenced by hard boundaries and
irregular structures (e.g., rocky outcrops). We also demonstrate that a-LoCoH is generally superior to k- and r-LoCoH (with
software for all three methods available at http://locoh.cnr.berkeley.edu).
