Robert A. Gitzen

Effects of sample size on KERNEL home range estimates

Kernel methods for estimating home range are being used increasingly in wildlife research, but the effect of sample size on their accuracy is not known. We used computer simulations of 10-200 points/ home range and compared accuracy of home range estimates produced by fixed and adaptive kernels with the reference (REF) and least-squares cross-validation (LSCV) methods for determining the amount of smoothing. Simulated home ranges varied from simple to complex shapes created by mixing bivariate normal distributions. We used the size of the 95% home range area and the relative mean squared error of the surface fit to assess the accuracy of the kernel home range estimates. For both measures, the bias and variance approached an asymptote at about 50 observations/home range. The fixed kernel with smoothing selected by LSCV provided the least-biased estimates of the 95% home range area. All kernel methods produced similar surface fit for most simulations, but the fixed kernel with LSCV had the lowest frequency and magnitude of very poor estimates. We reviewed 101 papers published in The Journal of Wildlife Management (JWM) between 1980 and 1997 that estimated animal home ranges. A minority of these papers used nonparametric utilization distribution (UD) estimators, and most did not adequately report sample sizes. We recommend that home range studies using kernel estimates use LSCV to determine the amount of smoothing, obtain a minimum of 30 observations per animal (but preferably >50), and report sample sizes in published results.

Analysis of Animal Space Use and Movements

Publisher Summary Animal space use and movements are best understood through direct observation. This chapter describes a variety of techniques used to analyze animal space use, including home range estimation, analysis of site fidelity, and animal interactions. It also provides limitations of using many traditional techniques. The chapter provides a discussion of modeling animal movements using a combination of advanced descriptive and visualization approaches, general movement models, and biological models. The importance of sample size and autocorrelation of data in estimating home ranges and animal movements cannot be overemphasized. When considering tradeoffs between sample size and independence, obtaining an adequate sample size is more important than independence between data points. Any analysis of radiotelemetry data must consider the full range of biological and environmental factors that may impact the results. Home range estimation and animal movement analyses must answer difficult questions regarding the internal anatomy of home range boundaries and movement pathways through the judicious use of biological and environmental information. Also, radiotelemetry studies should go beyond simple, general descriptions and use a model-driven approach to examine the key factors determining why and how an animal uses space.

Bandwidth Selection for Fixed-Kernel Analysis of Animal Utilization Distributions

Abstract In studies of animal space use, researchers often use kernel-based techniques for estimating the size of an animals home range and its utilization distribution from radiotracking data. However, the kernel estimator is highly sensitive to the bandwidth value used. Previous ecological studies recommended least-squares cross-validation (LSCV) as the default bandwidth selection method, but some statisticians consider this technique inferior to newer methods. We used simulations to compare the performance of the scaling LSCV and reference approaches to plug-in and solve-the-equation (STE) bandwidth methods. We generated samples of 20, 50, and 150 points from mixtures of 2, 4, and 16 bivariate normal distributions. We selected the ranges of potential variances for these distributions to create 4 distribution types with varied levels of clumping to simulate the diversity of location patterns expected from radiotracking data. For most distribution types, plug-in and STE methods performed as well or better than LSCV in % absolute error of home-range size estimates and overlap of estimated and true utilization distributions. Although the relative differences usually were small, the plug-in and STE approaches provide good alternatives to LSCV. However, LSCV performed better with distribution types composed entirely of tight clumps of points. The reference bandwidth performed poorly for most distributions. Surprisingly, it often had the lowest absolute error at outer contours for distributions consisting of a single very tight cluster surrounded by more dispersed points. Although our results demonstrate the utility of plug-in and STE approaches, no method was best across all distributions. Rather, choice of a bandwidth selection method may vary depending on the study goals, sample size, and patterns of space use by the study species. In general, we recommend plug-in and STE approaches for estimating relatively smooth outer contours. The LSCV approach is better at identifying tight clumps, including areas of peak use, although risk of LSCV failure also increases when a distribution has a very tight cluster of points. When planning to use kernel methods, researchers should consider these factors to make preliminary decisions about the bandwidth method expected to be most appropriate in their study.

Analysis of Resource Selection Using Utilization Distributions

Abstract Often resource selection functions (RSFs) are developed by comparing resource attributes of used sites to unused or available ones. We present alternative approaches to the analysis of resource selection based on the utilization distribution (UD). Our objectives are to describe the rationale for estimation of RSFs based on UDs, offer advice about computing UDs and RSFs, and illustrate their use in resource selection studies. We discuss the 3 main factors that should be considered when using kernel UD-based estimates of space use: selection of bandwidth values, sample size versus precision of estimates, and UD shape and complexity. We present 3 case studies that demonstrate use of UDs in resource selection modeling. The first example demonstrates the general case of RSF estimation that uses multiple regression adjusted for spatial autocorrelation to relate UD estimates (i.e., the probability density function) to resource attributes. A second example, involving Poisson regression with an offset term, is presented as an alternative for modeling the relative frequency, or probability of use, within defined habitat units. This procedure uses the relative frequency of locations within a habitat unit as a surrogate of the UD and requires relatively fewer user-defined options in the modeling of resource selection. Last, we illustrate how the UD can also be used to enhance univariate resource selection analyses, such as compositional analysis, in cases where animals use their range nonrandomly. The UD helps overcome several common shortcomings of some other analytical techniques by treating the animal as the primary sampling unit, summarizing use in a continuous and probabilistic manner, and relying on the pattern of animal space use rather than using individual sampling points. However, several drawbacks are apparent when using the UD in resource selection analyses. Choice of UD estimator is important and sensitive to sample size and user-defined options, such as bandwidth and software selection. Extensions to these procedures could consider behavioral-based approaches and alternative techniques to estimate the UD directly.

Comparability of three analytical techniques to assess joint space use

Abstract The degree of space-use overlap among adjacent individuals is a central focus of many wildlife investigations. We studied the comparability of minimum convex polygon and fixed-kernel home-range overlap indices and Volume of Intersection (VI) scores using simulated data. We simulated pairs of point patterns to represent telemetry locations of adjacent individuals and varied the amount of potential overlap in the simulation region (100%, 50%, and 10%) and the point distribution (random, loosely clumped, and tightly clumped). We created 1,000 pairs of point sets (60 points in each individual set) for each of the 9 potential overlap and point distribution combinations. In all 9 treatment combinations, VI scores were highest followed by kernel and then polygon estimates. Raw differences among estimates within a treatment were greatest when there was 50% potential overlap, and overlap indices decreased as the degree of clumping increased. The relative differences among overlap indices within a treatment were affected most by potential overlap; differences generally were greatest at 10% and least at 100%. Correlation between index values was lowest for random point patterns, and highest for loosely clumped and tightly clumped point patterns. Although the VI tended to indicate the most overlap and minimum convex polygon the least, there was no consistent correction factor among techniques because of the interacting effects of the overlap index, distribution pattern, and potential overlap. Interpretation of overlap measures requires careful consideration of assumptions and properties of animals under study.

Elk and hunter space-use sharing in South Dakota.

Documenting space-use patterns of elk (Cervus elaphus) and hunters is important for determining whether disturbance by hunters affects elk movements and resource use. We compared utilization distributions of elk and hunters during 4 hunting seasons (early archery, trophy rifle, antlerless rifle, and late archery) from 1993 to 1996 in the southern Black Hills, South Dakota, using the Volume of Intersection Index statistic. Volume of Intersection Indices were used as the response variable in a general linear regression model analysis to determine if environmental features were correlated with measures of space-use sharing. Space-use sharing for cow elk and hunters was lowest during the late archery hunt and highest during the trophy rifle and early archery seasons. Space-use sharing was lowest for bull elk and hunters during the trophy rifle hunt and highest during the early archery season. Hunter density, secondary road use, and tertiary road density were negatively correlated with space-use sharing. In contrast, vegetative cover was positively correlated with space-use sharing. Subherds occupying areas dominated by overstory-killed habitat exhibited less overlap with hunters than subherds residing in more heavily forested habitats. These results suggested that control of hunter density, including limitation of road access, in areas which lack vegetative cover may help mitigate hunter disturbance of elk. Variation in elk movements and environmental features correlated with overlap measures indicated that elk response to hunters was adaptive and short-lived.

Design and analysis of long-term ecological monitoring studies

List of contributors Foreword Preface Acknowledgements Part I. Overview: 1. Ecological monitoring: the heart of the matter Robert A. Gitzen and Joshua J. Millspaugh 2. An overview of statistical considerations in long-term monitoring Joel H. Reynolds 3. Monitoring (that) matters Douglas H. Johnson 4. Maximizing the utility of monitoring to the adaptive management of natural resources William L. Kendall and Clinton T. Moore Part II. Survey Design: 5. Spatial sampling designs for long-term ecological monitoring Trent McDonald 6. Spatially balanced survey designs for natural resources Anthony R. Olsen, Thomas M. Kincaid and Quinn Payton 7. The role of monitoring design in detecting trend in long-term ecological monitoring studies N. Scott Urquhart 8. Estimating variance components and related parameters when planning long-term monitoring programs John R. Skalski 9. Variance components estimation for continuous and discrete data, with emphasis on cross-classified sampling designs Brian R. Gray 10. Simulating future uncertainty to guide the selection of survey designs for long-term monitoring Steven L. Garman, E. William Schweiger and Daniel J. Manier Part III. Data Analysis: 11. Analysis options for estimating status and trends in long-term monitoring Jonathan Bart and Hawthorne L. Beyer 12. Analytical options for estimating ecological thresholds - statistical considerations Song S. Qian 13. The treatment of missing data in long-term monitoring programs Douglas H. Johnson and Michael B. Soma 14. Survey analysis in natural resource monitoring programs with a focus on cumulative distribution functions Thomas M. Kincaid and Anthony R. Olsen 15. Structural equation modeling and the analysis of long-term monitoring data James B. Grace, Jon E. Keeley, Darren J. Johnson and Kenneth A. Bollen Part IV. Advanced Issues and Applications: 16. GRTS and graphs: monitoring natural resources in urban landscapes Todd R. Lookingbill, John Paul Schmit and Shawn L. Carter 17. Incorporating predicted species distribution in adaptive and conventional sampling designs David R. Smith, Lei Yuancai, Christopher A. Walter and John A. Young 18. Study design and analysis options for demographic and species occurrence dynamics Darryl I. MacKenzie 19. Dealing with incomplete and variable detectability in multi-year, multi-site monitoring of ecological populations Sarah J. Converse and J. Andrew Royle 20. Optimal spatio-temporal monitoring designs for characterizing population trends Mevin B. Hooten, Beth E. Ross and Christopher K. Wikle 21. Use of citizen-science monitoring for pattern discovery and biological inference Wesley M. Hochachka, Daniel Fink and Benjamin Zuckerberg Part V. Conclusion: 22. Institutionalizing an effective long-term monitoring program in the US National Park Service Steven G. Fancy and Robert E. Bennetts 23. Choosing among long-term ecological monitoring programs and knowing when to stop Hugh P. Possingham, Richard A. Fuller and Liana N. Joseph References Index.

Herd organization of cow elk in Custer State Park, South Dakota

Abstract Understanding herd organization is important when considering management alternatives designed to benefit or manipulate elk (Cervus elaphus) populations. We studied the seasonal and annual herd organization of cow elk in Custer State Park, South Dakota from 1993–1997 by examining seasonal subherd range size, spatial arrangement, overlap, and site fidelity. Based on social interaction analyses, we combined locations of radiocol-lared cow elk to delineate subherds. We computed 95% kernel home ranges with least-squares cross validation for each subherd by season and year. Subherd overlap and fidelity by season and year were computed using the Volume of Intersection Index (VI) statistic. We identified 5 relatively discrete, resident cow–calf subherds. We observed little overlap in utilization distributions of adjacent subherds. The mean VI score across all subherds and time points (n=140) was 0.06 (SE=0.009), indicating an average 6% overlap in subherd area utilization. Subherd overlap between pairs was 0.08 in fall (SE= 0.021), 0.06 in winter (SE=0.018), 0.06 in spring (SE=0.2), and 0.05 in summer (SE= 0.016). Range sizes were not different between any pairs of seasons or years (F13,52=0.7, P=0.75). Subherd fidelity ranged from 0.41 (SE=0.033) to 0.60 (SE=0.018) overall, indicating differential use within the subherd boundary across years. The ability to distinguish discrete cow–calf subherd units is consistent with other studies and may aid elk management in Custer State Park. However, use patterns within subherd boundaries were inconsistent across years and may reflect human disturbances (e.g., hunting and logging activities), differences in our sampling approach, or changes in matriarchal leadership. Further evaluation into factors affecting space-use patterns is necessary to predict changes in range use within the subherd boundary.

Effects of Culling on Bison Demographics in Wind Cave National Park, South Dakota

Abstract We used a stochastic Leslie matrix model parameterized with demographic data from Wind Cave National Park to evaluate effects of four culling strategies on population growth rates and age and sex structure of bison (Bison bison Linnaeus). The four culling scenarios we modeled included removal of: (1) yearlings only; (2) calf/cow combination; (3) a herd-wide proportional cull (i.e., individuals taken in proportion to their availability); and (4) calves only. We also allowed either one, two, or three years to elapse between culls to mimic current management activities, and chose culling values for each scenario that would maintain a stable population (i.e., λ ≈ 1.00). In the absence of culling, our model projected a growth rate of 16% per year (λ= 1.16) (SD = 0.02) for the Wind Cave bison population. The modeled population was characterized by a unimodal age structure for bulls and cows and a 1:1 bull: cow ratio. Removal of 75% of the yearlings or 75% of the calves every year was needed to maintain abundance at current size. These culling strategies altered the age distribution from baseline conditions, resulting in nearly equal proportions of age classes 2–15. When yearling culling or calf removal was skipped one year or two consecutive years, the yearling or calf removal option resulted in positive population growth even in the presence of a 90% cull. Because these strategies nearly removed entire cohorts, corresponding gaps were introduced in the age structure. About 40% of calves and 20% of cows needed to be removed under the annual calf/cow cull to stabilize population growth, producing a unimodal age structure of cows. However, the proportion of bulls in the 2–16 age classes increased, and the proportion of males was nearly equal across the middle age classes. The proportional cull, regardless of time between culling operations, resulted in the most symmetric age structure for males and females. To achieve λ ≈ 1.00 under a proportional cull strategy, 16% of all animals would need to be removed annually, 33% every other year, or 50% once every three years. Sensitivity and elasticity analysis indicated that adult females (5–13 years old) were the most important group of bison affectingλ. These modeled effects, along with factors such as logistical constraints, costs, efficacy, viewing opportunities for tourists, genetics, behavior, and agency policies should be considered when managers choose among culling strategies. When considering historical predation and harvest by Native Americans, we hypothesize that the calf/cow combination cull would have most closely approximated natural bison demographics after the widespread availability of horses (Equus spp.) in the year 1735. Before 1735, we hypothesize that the proportional cull would most closely represent historic conditions, although even this option might not reproduce the variability inherent in historical bison dynamics. We discuss the possibility and management implications of variable culling that might more closely mimic historical influences on bison populations on the Northern Great Plains.

Modeling resource selection using polytomous logistic regression and kernel density estimates

Wildlife resource selection studies typically compare used to available resources; selection or avoidance occurs when use is disproportionately greater or less than availability. Comparing used to available resources is problematic because results are often greatly influenced by what is considered available to the animal. Moreover, placing relocation points within resource units is often difficult due to radiotelemetry and mapping errors. Given these problems, we suggest that an animal’s resource use be summarized at the scale of the home range (i.e., the spatial distribution of all point locations of an animal) rather than by individual points that are considered used or available. To account for differences in use-intensity throughout an animal’s home range, we model resource selection using kernel density estimates and polytomous logistic regression. We present a case study of elk (Cervus elaphus) resource selection in South Dakota to illustrate the procedure. There are several advantages of our proposed approach. First, resource availability goes undefined by the investigator, which is a difficult and often arbitrary decision. Instead, the technique compares the intensity of animal use throughout the home range. This technique also avoids problems with classifying locations rigidly as used or unused. Second, location coordinates do not need to be placed within mapped resource units, which is problematic given mapping and telemetry error. Finally, resource use is considered at an appropriate scale for management because most wildlife resource decisions are made at the level of the patch. Despite the advantages of this use-intensity procedure, future research should address spatial autocorrelation and develop spatial models for ordered categorical variables.