https://web.stanford.edu/~hastie/Papers/GuisanEtAl_EcolModel-2003.pdf

Generalized linear and generalized additive models in studies of species distributions: setting the scene

Preface 1. Spatial concepts and notions 2. Ecological and spatial processes 3. Points, lines and graphs 4. Spatial analysis of complete point location data 5. Contiguous units analysis 6. Spatial analysis of sample data 7. Spatial relationship and multiscale analysis 8. Spatial autocorrelation and inferential tests 9. Spatial partitioning: spatial clusters and boundary detection 10. Spatial diversity analysis 11. Spatio-temporal analysis 12. Closing comments and future directions References Index.

Spatial Analysis A Guide for Ecologists

By studying animal movements, researchers can gain insight into many of the ecological characteristics and processes important for understanding population-level dynamics. We developed a Brownian bridge movement model (BBMM) for estimating the expected movement path of an animal, using discrete location data obtained at relatively short time intervals. The BBMM is based on the properties of a conditional random walk between successive pairs of locations, dependent on the time between locations, the distance between locations, and the Brownian motion variance that is related to the animal's mobility. We describe two critical developments that enable widespread use of the BBMM, including a derivation of the model when location data are measured with error and a maximum likelihood approach for estimating the Brownian motion variance. After the BBMM is fitted to location data, an estimate of the animal's probability of occurrence can be generated for an area during the time of observation. To illustrate potential applications, we provide three examples: estimating animal home ranges, estimating animal migration routes, and evaluating the influence of fine-scale resource selection on animal movement patterns.

https://www.webpages.uidaho.edu/population_ecology/Horne,%20Garton,%20Krone%20&%20Lewis%202007%20Ecology%20-%20BrownianBridge.pdf

Analyzing animal movements using Brownian bridges.

The concept of an animal's 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 animal's utilization distribution (UD; i.e., the probability distribution defining the animal's 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 Hurlbert's (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 Bhattacharyya's 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.

Quantifying home-range overlap: the importance of the utilization distribution

1. Although the home range is a fundamental ecological concept, there is considerable debate over how it is best measured. There is a substantial literature concerning the precision and accuracy of all commonly used home range estimation methods; however, there has been considerably less work concerning how estimates vary with sampling regime, and how this affects statistical inferences. 2. We propose a new procedure, based on a variance components analysis using generalized mixed effects models to examine how estimates vary with sampling regime. 3. To demonstrate the method we analyse data from one study of 32 individually marked roe deer and another study of 21 individually marked kestrels. We subsampled these data to simulate increasingly less intense sampling regimes, and compared the performance of two kernel density estimation (KDE) methods, of the minimum convex polygon (MCP) and of the bivariate ellipse methods. 4. Variation between individuals and study areas contributed most to the total variance in home range size. Contrary to recent concerns over reliability, both KDE methods were remarkably efficient, robust and unbiased: 10 fixes per month, if collected over a standardized number of days, were sufficient for accurate estimates of home range size. However, the commonly used 95% isopleth should be avoided; we recommend using isopleths between 90 and 50%. 5. Using the same number of fixes does not guarantee unbiased home range estimates: statistical inferences differ with the number of days sampled, even if using KDE methods. 6. The MCP method was highly inefficient and results were subject to considerable and unpredictable biases. The bivariate ellipse was not the most reliable method at low sample sizes. 7. We conclude that effort should be directed at marking more individuals monitored over long periods at the expense of the sampling rate per individual. Statistical results are reliable only if the whole sampling regime is standardized. We derive practical guidelines for field studies and data analysis.

https://besjournals.onlinelibrary.wiley.com/doi/epdf/10.1111/j.1365-2656.2006.01164.x

Effects of sampling regime on the mean and variance of home range size 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.

Effects of sample size on kernel home range estimates

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.

Analysis of Animal Space Use and Movements

In studies of animal space use, researchers often use kernel-based techniques for estimating the size of an animal's 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.

Bandwidth Selection for Fixed‐Kernel Analysis of Animal Utilization Distributions

The use of habitat suitability index (HSI) models is often criticized because of unreliable model performance; however, no consistent framework to validate these models exists. We offer a framework to evaluate the thoroughness of HSI model validation studies. We evaluated 17 studies that tested the reliability of 58 HSI models according to 7 criteria. The criteria included model components evaluated, input data variabi I ity, val idity of comparative test(s) used, scale, range of HSls, popu lation i ndex, and duration of population data collection. Guidelines that indexed the adequacy of study design were established for each criterion based on published information and past experience. All studies were deficient (maximum score was 4.05 out of 7.00 possible) according to adequacy guidelines. Most common deficiencies included inadequate consideration of input parameter variability, application of the models to inappropriate spatial scales, sampling too narrow a range of HSI values, and population data that were collected over too short a time frame.

https://www.jstor.org/stable/pdfplus/3783655.pdf

Evaluating reliability of habitat suitability index models

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.

Brian J. Kernohan

Papers

Effects of sample size on kernel home range estimates

Analysis of Animal Space Use and Movements

Bandwidth Selection for Fixed‐Kernel Analysis of Animal Utilization Distributions

Evaluating reliability of habitat suitability index models

Comparability of three analytical techniques to assess joint space use