Statistical inference for home range overlap. Issue 7 (8th June 2018) - Winner, Kevin; Noonan, Michael J.; Fleming, Christen H.; Olson, Kirk A.; Mueller, Thomas; Sheldon, Daniel; Calabrese, Justin M.
Abstract: Despite the routine nature of estimating overlapping space use in ecological research, to date no formal inferential framework for home range overlap has been available to ecologists. Part of this issue is due to the inherent difficulty of comparing the estimated home ranges that underpin overlap across individuals, studies, sites, species, and times. As overlap is calculated conditionally on a pair of home range estimates, biases in these estimates will propagate into biases in overlap estimates. Further compounding the issue of comparability in home range estimators is the historical lack of confidence intervals on overlap estimates. This means that it is not currently possible to determine if a set of overlap values is statistically different from one another. As a solution, we develop the first rigorous inferential framework for home range overlap. Our framework is based on the autocorrelated‐Kernel density estimation (AKDE) family of home range estimators, which correct for biases due to autocorrelation, small effective sample size, and irregular sampling in time. Collectively, these advances allow AKDE estimates to validly be compared even when sampling strategies differ. We then couple the AKDE estimates with a novel bias‐corrected Bhattacharyya coefficient (BC) to quantify overlap. Finally, we propagate uncertainty in the AKDE estimates through to overlap and thus are able to put confidence intervals on the BC point estimate. Using simulated data, we demonstrate how our inferential framework provides accurate overlap estimates, and reasonable coverage of the true overlap, even at small sample sizes. When applied to empirical data, we found that building an interaction network for Mongolian gazelles Procapra gutturosa based on all possible ties, vs. only those ties with statistical support, substantially influenced the network's properties and any potential biological inferences derived from it. Our inferential framework permits researchers to calculate overlap estimates that can validly be compared across studies, sites, species, and times, and test whether observed differences are statistically meaningful. This method is available via the R package ctmm .