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Accurately quantifying species' area requirements is a prerequisite for effective area-based conservation. This typically involves collecting tracking data on species of interest and then conducting home-range analyses. Problematically, autocorrelation in tracking data can result in space needs being severely underestimated. Based on the previous work, we hypothesized the magnitude of underestimation varies with body mass, a relationship that could have serious conservation implications. To evaluate this hypothesis for terrestrial mammals, we estimated home-range areas with global positioning system (GPS) locations from 757 individuals across 61 globally distributed mammalian species with body masses ranging from 0.4 to 4000 kg. We then applied block cross-validation to quantify bias in empirical home-range estimates. Area requirements of mammals 1, meaning the scaling of the relationship changed substantially at the upper end of the mass spectrum.

1. Home-range estimates are a common product of animal tracking data, as each range represents the area needed by a given individual. Population-level inference of home-range areas—where multiple individual home ranges are considered to be sampled from a population—is also important to evaluate changes over time, space or covariates such as habitat quality or fragmentation, and for comparative analyses of species averages. Population-level home-range parameters have traditionally been estimated by first assuming that the input tracking data were sampled independently when calculating home ranges via conventional kernel density estimation (KDE) or minimal convex polygon (MCP) methods, and then assuming that those individual home ranges were measured exactly when calculating the population-level estimates. This conventional approach does not account for the temporal autocorrelation that is inherent in modern tracking data, nor for the uncertainties of each individual home-range estimate, which are often large and heterogeneous. 2. Here, we introduce a statistically and computationally efficient framework for the population-level analysis of home-range areas, based on autocorrelated kernel density estimation (AKDE), that can account for variable temporal autocorrelation and estimation uncertainty. 3. We apply our method to empirical examples on lowland tapir Tapirus terrestris, kinkajou Potos flavus, white-nosed coati Nasua narica, white-faced capuchin monkey Cebus capucinus and spider monkey Ateles geoffroyi, and quantify differences between species, environments and sexes. 4. Our approach allows researchers to more accurately compare different populations with different movement behaviours or sampling schedules while retaining statistical precision and power when individual home-range uncertainties vary. Finally, we emphasize the estimation of effect sizes when comparing populations, rather than mere significance tests. [ABSTRACT FROM AUTHOR]

Technological advances have steadily increased the detail of animal tracking datasets, yet fundamental data limitations exist for many species that cause substantial biases in home‐range estimation. Specifically, the effective sample size of a range estimate is proportional to the number of observed range crossings, not the number of sampled locations. Currently, the most accurate home‐range estimators condition on an autocorrelation model, for which the standard estimation frame‐works are based on likelihood functions, even though these methods are known to underestimate variance—and therefore ranging area—when effective sample sizes are small.Residual maximum likelihood (REML) is a widely used method for reducing bias in maximum‐likelihood (ML) variance estimation at small sample sizes. Unfortunately, we find that REML is too unstable for practical application to continuous‐time movement models. When the effective sample size N is decreased to N ≤ O(10), which is common in tracking applications, REML undergoes a sudden divergence in variance estimation. To avoid this issue, while retaining REML's first‐order bias correction, we derive a family of estimators that leverage REML to make a perturbative correction to ML. We also derive AIC values for REML and our estimators, including cases where model structures differ, which is not generally understood to be possible.Using both simulated data and GPS data from lowland tapir (Tapirus terrestris), we show how our perturbative estimators are more accurate than traditional ML and REML methods. Specifically, when O(5) home‐range crossings are observed, REML is unreliable by orders of magnitude, ML home ranges are ~30% underestimated, and our perturbative estimators yield home ranges that are only ~10% underestimated. A parametric bootstrap can then reduce the ML and perturbative home‐range underestimation to ~10% and ~3%, respectively.Home‐range estimation is one of the primary reasons for collecting animal tracking data, and small effective sample sizes are a more common problem than is currently realized. The methods introduced here allow for more accurate movement‐model and home‐range estimation at small effective sample sizes, and thus fill an important role for animal movement analysis. Given REML's widespread use, our methods may also be useful in other contexts where effective sample sizes are small. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Kernel density estimators are widely applied to area-related problems in ecology, from estimating the home range of an individual to estimating the geographic range of a species. Currently, area estimates are obtained indirectly, by first estimating the location distribution from tracking (home range) or survey (geographic range) data and then estimating areas from that distribution. This indirect approach leads to biased area estimates and difficulty in deriving reasonable confidence intervals., We introduce a new kernel density estimator (and associated confidence intervals) focused specifically on area estimation that applies to both independently sampled survey data and autocorrelated tracking data. We test our methods against simulated movement data and demonstrate its use with African buffalo data., The area-corrected kernel density estimator produces much more accurate area estimates, particularly at small sample sizes, and the newly derived confidence intervals are more reliable than existing alternatives., This new method is the most efficient nonparametric home-range estimator for animal tracking data and should also be considered when calculating nonparametric range estimates from survey data. This estimator is now the default method in the ctmm r package. [ABSTRACT FROM AUTHOR]

Accurately estimating home range and understanding movement behavior can provide important information on ecological processes. Advances in data collection and analysis have improved our ability to estimate home range and movement parameters, both of which have the potential to impact species conservation. Fitting continuous-time movement model to data and incorporating the autocorrelated kernel density estimator (AKDE), we investigated range residency of forty-four jaguars fit with GPS collars across five biomes in Brazil and Argentina. We assessed home range and movement parameters of range resident animals and compared AKDE estimates with kernel density estimates (KDE). We accounted for differential space use and movement among individuals, sex, region, and habitat quality. Thirty-three (80%) of collared jaguars were range resident. Home range estimates using AKDE were 1.02 to 4.80 times larger than KDE estimates that did not consider autocorrelation. Males exhibited larger home ranges, more directional movement paths, and a trend towards larger distances traveled per day. Jaguars with the largest home ranges occupied the Atlantic Forest, a biome with high levels of deforestation and high human population density. Our results fill a gap in the knowledge of the species’ ecology with an aim towards better conservation of this endangered/critically endangered carnivore—the top predator in the Neotropics. [ABSTRACT FROM AUTHOR]