Estimating animal densities and home range in regions with irregular boundaries and holes: A lattice-based alternative to the kernel density estimator

Density estimates based on point processes are often restrained to regions with irregular boundaries or holes. We propose a density estimator, the lattice-based density estimator, which produces reasonable density estimates under these circumstances. The estimation process starts with overlaying the region with nodes, linking these together in a lattice and then computing the density of random walks of length k on the lattice. We use an approximation to the unbiased crossvalidation criterion to find the optimal walk length k. The technique is illustrated using walleye (Sander vitreus) radiotelemetry relocations in Lake Monroe, Indiana. We also use simulation to compare the technique to the traditional kernel density estimate in the situation where there are no significant boundary effects.

► Lattice-based approach to two-dimensional density estimation.
► Adjusts densities in the presence of boundaries and holes.
► Works similarly to kernel density estimation in absence of boundaries.
► Method is implemented as an R package.
► Illustrated by mapping walleye densities and delineating the home range.