Bandwidth Selection for Fixed-Kernel Analysis of Animal Utilization Distributions

Abstract

In studies of animal space use, researchers often use kernel-based techniques for estimating the size of an animal's home range and its utilization distribution from radiotracking data. However, the kernel estimator is highly sensitive to the bandwidth value used. Previous ecological studies recommended least-squares cross-validation (LSCV) as the default bandwidth selection method, but some statisticians consider this technique inferior to newer methods. We used simulations to compare the performance of the scaling LSCV and reference approaches to plug-in and solve-the-equation (STE) bandwidth methods. We generated samples of 20, 50, and 150 points from mixtures of 2, 4, and 16 bivariate normal distributions. We selected the ranges of potential variances for these distributions to create 4 distribution types with varied levels of clumping to simulate the diversity of location patterns expected from radiotracking data. For most distribution types, plug-in and STE methods performed as well or better than LSCV in % absolute error of home-range size estimates and overlap of estimated and true utilization distributions. Although the relative differences usually were small, the plug-in and STE approaches provide good alternatives to LSCV. However, LSCV performed better with distribution types composed entirely of tight clumps of points. The reference bandwidth performed poorly for most distributions. Surprisingly, it often had the lowest absolute error at outer contours for distributions consisting of a single very tight cluster surrounded by more dispersed points. Although our results demonstrate the utility of plug-in and STE approaches, no method was best across all distributions. Rather, choice of a bandwidth selection method may vary depending on the study goals, sample size, and patterns of space use by the study species. In general, we recommend plug-in and STE approaches for estimating relatively smooth outer contours. The LSCV approach is better at identifying tight clumps, including areas of peak use, although risk of LSCV failure also increases when a distribution has a very tight cluster of points. When planning to use kernel methods, researchers should consider these factors to make preliminary decisions about the bandwidth method expected to be most appropriate in their study.