Rigorous home range estimation with movement data: a new autocorrelated kernel density estimator

Abstract

Abstract. Quantifying animals' home ranges is a key problem in ecology and has important conservation and wildlife management applications. Kernel density estimation (KDE) is a workhorse technique for range delineation problems that is both statistically efficient and nonparametric. KDE assumes that the data are independent and identically distributed (IID). However, animal tracking data, which are routinely used as inputs to KDEs, are inherently autocorrelated and violate this key assumption. As we demonstrate, using realistically autocorrelated data in conventional KDEs results in grossly underestimated home ranges. We further show that the performance of conventional KDEs actually degrades as data quality improves, because autocorrelation strength increases as movement paths become more finely resolved. To remedy these flaws with the traditional KDE method, we derive an autocorrelated KDE (AKDE) from first principles to use autocorrelated data, making it perfectly suited for movement data sets. We illustrate the vastly improved performance of AKDE using analytical arguments, relocation data from Mongolian gazelles, and simulations based upon the gazelle's observed movement process. By yielding better minimum area estimates for threatened wildlife populations, we believe that future widespread use of AKDE will have significant impact on ecology and conservation biology.

Space Use and Movement of a Neotropical Top Predator: The Endangered Jaguar

“…Understanding animal movement and space use across dynamic landscapes is critical for the establishment of effective conservation strategies [7], including the creation/maintenance of ecological corridors designed to guarantee the movement of focal species, improving the connectivity of habitat patches within fragmented landscapes [8], and identifying priority areas for conservation [9]. Accurately estimating home ranges and understanding animal movement behavior provide information on ecological processes that can impact species conservation [10,11]. …”

“…Nevertheless, no study has accounted for the inherent autocorrelation structure of the movement data when calculating jaguar home range estimates. Resulting home ranges are likely underestimated [11]. Moreover, former studies lacked an empirical way to characterize range residency.…”

“…The minimum convex polygon (MCP) and kernel density estimators (KDE) are the most commonly used tools to estimate animal home ranges [11]. Both tools have limitations that are often not acknowledged.…”

“…Both tools have limitations that are often not acknowledged. MCPs, for example, lack any underlying probabilistic model while KDEs are derived under the assumption of independent and identically distributed data (IID), a process that assumes uncorrelated positions and velocities and which cannot be recognized as a movement model [11,25]. Incorporating autocorrelated data in conventional KDE frameworks has the potential to underestimate the size of animal home ranges, especially as the temporal frequency of positions collected increases [11]—a situation common with modern GPS tracking devices.…”

Individual-level Variation and Higher-level Interpretations of Space Use in Wide-ranging Species: An Albatross Case Study of Sampling Effects

“…When applied to tracking data, the result of a KDE analysis is the creation of contours representing densities or intensities of space use, often called a Kernel Density Estimate (herein we use "KDE" interchangeably to refer to both the analytical approach and output of the analysis). There has been much discussion over best practices in implementing and reporting for KDE and other similar approaches, and these have been thoroughly reviewed elsewhere (e.g., Laver and Kelly, 2008;Kie et al, 2010;Fieberg and Börger, 2012;Fleming et al, 2015;Signer et al, 2015). Despite shifting baselines in execution, KDE continues to endure among ecologists as a relatively simple and accessible tool for describing space use.…”