A comprehensive analysis of autocorrelation and bias in home range estimation

Abstract

Home range estimation is routine practice in ecological research. While advances in animal tracking technology have increased our capacity to collect data to support home range analysis, these same advances have also resulted in increasingly autocorrelated data. Consequently, the question of which home range estimator to use on modern, highly autocorrelated tracking data remains open. This question is particularly relevant given that most estimators assume independently sampled data. Here, we provide a comprehensive evaluation of the effects of autocorrelation on home range estimation. We base our study on an extensive data set of GPS locations from 369 individuals representing 27 species distributed across five continents. We first assemble a broad array of home range estimators, including Kernel Density Estimation (KDE) with four bandwidth optimizers (Gaussian reference function, autocorrelated‐Gaussian reference function [AKDE], Silverman's rule of thumb, and least squares cross‐validation), Minimum Convex Polygon, and Local Convex Hull methods. Notably, all of these estimators except AKDE assume independent and identically distributed (IID) data. We then employ half‐sample cross‐validation to objectively quantify estimator performance, and the recently introduced effective sample size for home range area estimation (normalNfalse^area) to quantify the information content of each data set. We found that AKDE 95% area estimates were larger than conventional IID‐based estimates by a mean factor of 2. The median number of cross‐validated locations included in the hold‐out sets by AKDE 95% (or 50%) estimates was 95.3% (or 50.1%), confirming the larger AKDE ranges were appropriately selective at the specified quantile. Conversely, conventional estimates exhibited negative bias that increased with decreasing normalNfalse^area. To contextualize our empirical results, we performed a detailed simulation study to tease apart how sampling frequency, sampling duration, and the focal animal's movement conspire to affect range estimates. Paralleling our empirical results, the simulation study demonstrated that AKDE was generally more accurate than conventional methods, particularly for small normalNfalse^area. While 72% of the 369 empirical data sets had >1,000 total observations, only 4% had an normalNfalse^area >1,000, where 30% had an normalNfalse^area <30. In this frequently encountered scenario of small normalNfalse^area, AKDE was the only estimator capable of producing an accurate home range estimate on autocorrelated data.

Movement ecology of Afrotropical birds: Functional traits provide complementary insights to species identity

“…Individual home‐range sizes were estimated using autocorrelated kernel density estimation (AKDE) in the ctmm R package (Fleming & Calabrese, 2017b) for 95%, 75%, and 50% levels. The AKDE method was chosen as it corrects for temporal autocorrelation bias and is more accurate than the conventional kernel density estimation (KDE) with frequent fixes (here 10 min interval; Fleming and Calabrese, 2017a, 2017b, Noonan et al., ). Therefore, continuous time movement models (ctmm) were used to separate the continuous‐time movement process of an individual from the discrete‐time sampling process (Fleming et al., ).…”

“…with frequent fixes (here 10 min interval;Fleming and Calabrese, 2017a, 2017b, Noonan et al, 2019. Therefore, continuous time TA B L E 1 Ecological classification of the nine study species.…”

Population structure and spatial ecology of Kordofan giraffe in Garamba National Park, Democratic Republic of Congo

“…Modeling has a number of attractive features common to analyses of animal movement data, including the incorporating of irregular sampling intervals and complex autocorrelation structures (Fleming et al, 2014a(Fleming et al, , 2014b, both of which have been shown to severely bias results if not handled properly (Noonan et al, 2018). Importantly, CTMM results are also displayed with appropriate confidence intervals, providing an important measure of the precision of parameter estimates.…”

Post‐stocking movement and survival of hatchery‐reared bloater (Coregonus hoyi) reintroduced to Lake Ontario

“…We chose to use AKDEs as opposed to conventional kernel density estimation (KDE), which explicitly assumes that location data are independent and identically distributed and often results in KDEs that underestimate activity space areas (Fleming & Calabrese, 2017;Fleming et al, 2015;Noonan et al, 2019). AKDE estimates the correlation structure in the data by fitting continuous-time movement models and selecting the best fitting model based on the approximate small sample size corrected Akaike information criterion to address the stronger autocorrelation that is associated with the ever-finer sampling of movement paths (Kays, Crofoot, Jetz, & Wikelski, 2015;Noonan et al, 2019). The number of days detected and the number of COAs were highly TA B L E 1 Summary of bloater tagged and released into eastern Lake Ontario over four periods in autumn 2016, spring 2017, autumn 2017, and autumn 2018 Mean ± SD (range) are shown for mass (g) and fork length (mm) and refers to tagged individuals.…”