A rule-based ad hoc method for selecting a bandwidth in kernel home-range analyses

Abstract

Background: An important issue in conducting kernel home-range analyses is the choice of bandwidth or smoothing parameter. To examine the effects of this choice, telemetry data were collected at high sampling rates (843 to 5,069 locations) on 20 North American elk, Cervus elaphus, in northeastern Oregon, USA, during 2000, 2002, and 2003. The elk had their collars replaced annually, hence none were monitored for more than a single year. True home ranges were defined by buffering the actual paths of individuals. Fixed-kernel and adaptive-kernel estimates were then determined with reference bandwidths (h ref), least-squares cross-validation bandwidths (h lscv), and rule-based ad hoc bandwidths designed to prevent under-smoothing (h ad hoc). Both raw data and sub-sampled sparse datasets (1, 2, 4, 6, 12, and 24 locations/elk/day) were used. Results: With fixed-kernel and adaptive-kernel analyses, reference bandwidths were positively biased (including areas not part of an animal's home range) but performed better (lower bias, closer match between estimated and true home ranges) with increasing sample size. Least-squares cross-validation bandwidths were positively biased with very small sample sizes, but quickly became negatively biased with increasing sample size, as home-range estimates broke up into disjoint polygons. Ad hoc bandwidths outperformed reference and least-squares cross-validation bandwidths, exhibited only moderate positive bias, were relatively unaffected by sample size, and were characterized by lower Type I errors (falsely including areas not part of the true home range). Ad hoc bandwidths also exhibited lower Type II errors (failure to include portions of the true home range) than did least-squares cross-validation bandwidths, although reference bandwidths resulted in lowest Type II error rates. Auto-correlation indices increased to about 150 to 200 locations per elk, and then stabilized. Bias of fixed-kernel analyses with ad hoc bandwidths was not affected by auto-correlation, but did increase with irregularly shaped home ranges with high fractal dimensions. Conclusions: The rule-based ad hoc bandwidths, specifically designed to prevent fragmentation of estimated home ranges, outperformed both h ref and h lscv, and gave the smallest value for h consistent with a contiguous home-range estimate. The protocol for choosing the ad hoc bandwidth was shown to be consistent and repeatable.