John Fieberg

QUANTIFYING HOME-RANGE OVERLAP: THE IMPORTANCE OF THE UTILIZATION DISTRIBUTION

Abstract The concept of an animals home range has evolved over time, as have methods for estimating home-range size and shape. Recently, home-range estimation methods have focused on estimating an animals utilization distribution (UD; i.e., the probability distribution defining the animals use of space). We illustrate the importance of the utilization distribution in characterizing the degree of overlap between home ranges (e.g., when assessing site fidelity or space-use sharing among individuals). We compare several different statistics for their ability to accurately rank paired examples in terms of their degree of overlap. These examples illustrate limitations of indices commonly used to quantify home-range overlap and suggest that new overlap indices that are a function of the UD are likely to be more informative. We suggest 2 new statistics for measuring home-range overlap: (1) for a measure of space-use sharing, we suggest a generalization of Hurlberts (1978) E/Euniform statistic, which we term the utilization distribution overlap index (UDOI), and (2) for a general measure of similarity between UD estimates, we suggest Bhattacharyyas affinity (BA; Bhattacharyya 1943). Using a short simulation study, we found that overlap indices can accurately rank pairs of UDs in terms of the extent of overlap, but estimates of overlap indices are likely to be biased. The extent of the bias depended on sample size and the degree of overlap (UDs with a high degree of overlap resulted in statistics that were more biased [low]), suggesting that comparisons across studies may be problematic. We illustrate the use of overlap indices to quantify the degree of similarity among UD estimates obtained using 2 different data collection methods (Global Positioning Systems [GPS] and very high frequency [VHF] radiotelemetry) for an adult female northern white-tailed deer (Odocoileus virginianus) in north-central Minnesota.

The home-range concept: are traditional estimators still relevant with modern telemetry technology?

Recent advances in animal tracking and telemetry technology have allowed the collection of location data at an ever-increasing rate and accuracy, and these advances have been accompanied by the development of new methods of data analysis for portraying space use, home ranges and utilization distributions. New statistical approaches include data-intensive techniques such as kriging and nonlinear generalized regression models for habitat use. In addition, mechanistic home-range models, derived from models of animal movement behaviour, promise to offer new insights into how home ranges emerge as the result of specific patterns of movements by individuals in response to their environment. Traditional methods such as kernel density estimators are likely to remain popular because of their ease of use. Large datasets make it possible to apply these methods over relatively short periods of time such as weeks or months, and these estimates may be analysed using mixed effects models, offering another approach to studying temporal variation in space-use patterns. Although new technologies open new avenues in ecological research, our knowledge of why animals use space in the ways we observe will only advance by researchers using these new technologies and asking new and innovative questions about the empirical patterns they observe.

Resolving issues of imprecise and habitat-biased locations in ecological analyses using GPS telemetry data

Global positioning system (GPS) technologies collect unprecedented volumes of animal location data, providing ever greater insight into animal behaviour. Despite a certain degree of inherent imprecision and bias in GPS locations, little synthesis regarding the predominant causes of these errors, their implications for ecological analysis or solutions exists. Terrestrial deployments report 37 per cent or less non-random data loss and location precision 30 m or less on average, with canopy closure having the predominant effect, and animal behaviour interacting with local habitat conditions to affect errors in unpredictable ways. Home-range estimates appear generally robust to contemporary levels of location imprecision and bias, whereas movement paths and inferences of habitat selection may readily become misleading. There is a critical need for greater understanding of the additive or compounding effects of location imprecision, fix-rate bias, and, in the case of resource selection, map error on ecological insights. Technological advances will help, but at present analysts have a suite of ad hoc statistical corrections and modelling approaches available—tools that vary greatly in analytical complexity and utility. The success of these solutions depends critically on understanding the error-inducing mechanisms, and the biggest gap in our current understanding involves species-specific behavioural effects on GPS performance.

WHEN IS IT MEANINGFUL TO ESTIMATE AN EXTINCTION PROBABILITY

Recently Don Ludwig has shown that calculations of extinction probabilities based on currently available data are often meaningless due to the large uncertainty accompanying the estimates. Here we address two questions posed by his findings. Can one ever calculate extinction probabilities accurately? If so, how much data would be necessary? Our analysis indicates that reliable predictions of long-term extinction probabilities are likely to require unattainable amounts of data. Analytic calculations based on diffusion approximations indicate that reliable predictions of extinction probabilities can be made only for short-term time horizons (10% to 20% as long as the period over which the population has been monitored). Simulation results for unstructured and structured populations (three stage classes) agree with these calculations.

Correlation and studies of habitat selection: problem, red herring or opportunity?

With the advent of new technologies, animal locations are being collected at ever finer spatio-temporal scales. We review analytical methods for dealing with correlated data in the context of resource selection, including post hoc variance inflation techniques, ‘two-stage’ approaches based on models fit to each individual, generalized estimating equations and hierarchical mixed-effects models. These methods are applicable to a wide range of correlated data problems, but can be difficult to apply and remain especially challenging for use–availability sampling designs because the correlation structure for combinations of used and available points are not likely to follow common parametric forms. We also review emerging approaches to studying habitat selection that use fine-scale temporal data to arrive at biologically based definitions of available habitat, while naturally accounting for autocorrelation by modelling animal movement between telemetry locations. Sophisticated analyses that explicitly model correlation rather than consider it a nuisance, like mixed effects and state-space models, offer potentially novel insights into the process of resource selection, but additional work is needed to make them more generally applicable to large datasets based on the use–availability designs. Until then, variance inflation techniques and two-stage approaches should offer pragmatic and flexible approaches to modelling correlated data.

Kernel density estimators of home range : Smoothing and the autocorrelation red herring

Two oft-cited drawbacks of kernel density estimators (KDEs) of home range are their sensitivity to the choice of smoothing parameter(s) and their need for independent data. Several simulation studies have been conducted to compare the performance of objective, data-based methods of choosing optimal smoothing parameters in the context of home range and utilization distribution (UD) estimation. Lost in this discussion of choice of smoothing parameters is the general role of smoothing in data analysis, namely, that smoothing serves to increase precision at the cost of increased bias. A primary goal of this paper is to illustrate this bias-variance trade-off by applying KDEs to sampled locations from simulated movement paths. These simulations will also be used to explore the role of autocorrelation in estimating UDs. Autocorrelation can be reduced (1) by increasing study duration (for a fixed sample size) or (2) by decreasing the sampling rate. While the first option will often be reasonable, for a fixed study duration higher sampling rates should always result in improved estimates of space use. Further, KDEs with typical data-based methods of choosing smoothing parameters should provide competitive estimates of space use for fixed study periods unless autocorrelation substantially alters the optimal level of smoothing.

Could you please phrase “home range” as a question?

Abstract Statisticians frequently voice concern that their interactions with applied researchers start only after data have been collected. The same can be said for our experience with home-range studies. Too often, conversations about home range begin with questions concerning estimation methods, smoothing parameters, or the nature of autocorrelation. More productive efforts start by asking good (and interesting) research questions; once these questions are defined, it becomes possible to ask how various design and analysis strategies influence ones ability to answer these questions. With this process in mind, we address key sample-design and data-analysis issues related to the topic of home range. The impact of choosing a particular home-range estimator (e.g., minimum convex polygon, kernel density estimator, or local convex hull) will be question dependent, and for some problems other movement or use-based metrics (e.g., mean step lengths or time spent in particular areas) may be worthy of consideration. Thus, we argue the need for more question-driven and focused research and for clearly distinguishing the biological concept of an animals home range from the statistical quantities one uses to investigate this concept. For comparative studies, it is important to standardize sampling regimes and estimation methods as much as possible, and to pay close attention to missing data issues. More attention should also be given to temporally changing space-use patterns, with biologically meaningful time periods (e.g., life-history stages) used to define sampling periods. Last, we argue the need for closer connections between theoretical and empirical researchers. Advances in ecological theory, and its application to natural resources management, will require carefully designed research studies to test theoretical predictions from more mechanistic modeling approaches.

Living on the Edge: Viability of Moose in Northeastern Minnesota

Abstract North temperate species on the southern edge of their distribution are especially at risk to climate-induced changes. One such species is the moose (Alces alces), whose continental United States distribution is restricted to northern states or northern portions of the Rocky Mountain cordillera. We used a series of matrix models to evaluate the demographic implications of estimated survival and reproduction schedules for a moose population in northeastern Minnesota, USA, between 2002 and 2008. We used data from a telemetry study to calculate adult survival rates and estimated calf survival and fertility of adult females by using results of helicopter surveys. Estimated age- and year-specific survival rates showed a sinusoidal temporal pattern during our study and were lower for younger and old-aged animals. Estimates of annual adult survival (when assumed to be constant for ages >1.7 yr old) ranged from 0.74 to 0.85. Annual calf survival averaged 0.40, and the annual ratio of calves born to radiocollared females averaged 0.78. Point estimates for the finite rate of increase (λ) from yearly matrices ranged from 0.67 to 0.98 during our 6-year study, indicative of a long-term declining population. Assuming each matrix to be equally likely to occur in the future, we estimated a long-term stochastic growth rate of 0.85. Even if heat stress is not responsible for current levels of survival, continuation of this growth rate will ultimately result in a northward shift of the southern edge of moose distribution. Population growth rate, and its uncertainty, was most sensitive to changes in estimated adult survival rates. The relative importance of adult survival to population viability has important implications for harvest of large herbivores and the collection of information on wildlife fertility.

A Long-Term Age-Specific Survival Analysis of Female White-Tailed Deer

Abstract We conducted a 13-year survival (i.e., time survived since birth) and cause-specific mortality study, divided into 2 phases (Phase I = years 1–6; Phase II = years 7–13), of 302 female white-tailed deer (Odocoileus virginianus) ≥0.6 years old at capture. The study spanned a period of extreme variability in winter severity (maximum winter severity indexes [WSI] of 45–195) and hunting pressure. Most studies of survival and cause-specific mortality of northern deer have assumed constant survival rates for adults of each sex (≥1.0 yr old pooled) and examined fawns (0.6 ≤ x ≤ 1.0 yr old) separately. We observed U-shaped hazard (i.e., instantaneous risk of death) curves for both phases of the study, indicating that risk of death is highest for younger and older individuals. The estimated hazard for Phase II was generally lower and relatively constant for adults 2–10 years old compared to Phase I, where the instantaneous risk of death began to increase at age 6 years. This difference likely reflected differences in winter severities, associated changes in magnitude of wolf (Canis lupus) predation, and changes in hunting pressure between the 2 phases. The age distribution of our study cohort was relatively stable over the study period. Subsequently, when we included 76 neonates (i.e., ≤0.6 yr old) in the study cohort, the descending arm of the all-causes hazard began its descent at a hazard rate of 2.3 (vs. 1.0 without neonates), clearly demonstrating that the greatest risk of mortality occurs in the first year of life. We compared cumulative survival estimates for these data using the generalized Kaplan–Meier (GKM) and the iterative Nelson estimator (INE), and we illustrate the potential for bias when applying the GKM to left-truncated data. Median age of survival for females was 0.83 years old (90% CI = 0.79–1.45 yr old) using the INE and 0.43 years old (90% CI = 0.17–0.78 yr old) using the GKM. Lastly, we used a simulation approach to examine the potential for bias resulting from pooling adults. These simulations suggest that models using the constructed discrete time variable give nearly unbiased survival estimates and provide support for researchers and managers applying age-specific hazards derived during study periods to determine the reliability of adult age-pooled survival estimates. As indicated by our data, it is important to consider environmental variation and its interactions with natural mortality forces (e.g., predation) and age distribution of the population when setting harvest goals.

Bears Show a Physiological but Limited Behavioral Response to Unmanned Aerial Vehicles

Unmanned aerial vehicles (UAVs) have the potential to revolutionize the way research is conducted in many scientific fields. UAVs can access remote or difficult terrain, collect large amounts of data for lower cost than traditional aerial methods, and facilitate observations of species that are wary of human presence. Currently, despite large regulatory hurdles, UAVs are being deployed by researchers and conservationists to monitor threats to biodiversity, collect frequent aerial imagery, estimate population abundance, and deter poaching. Studies have examined the behavioral responses of wildlife to aircraft (including UAVs), but with the widespread increase in UAV flights, it is critical to understand whether UAVs act as stressors to wildlife and to quantify that impact. Biologger technology allows for the remote monitoring of stress responses in free-roaming individuals, and when linked to locational information, it can be used to determine events or components of an animals environment that elicit a physiological response not apparent based on behavior alone. We assessed effects of UAV flights on movements and heart rate responses of free-roaming American black bears. We observed consistently strong physiological responses but infrequent behavioral changes. All bears, including an individual denned for hibernation, responded to UAV flights with elevated heart rates, rising as much as 123 beats per minute above the pre-flight baseline. It is important to consider the additional stress on wildlife from UAV flights when developing regulations and best scientific practices.