Animal space use: distinguishing a two‐level superposition of scale‐specific walks from scale‐free Lévy walk

How to differentiate between scale‐free space use like Lévy walk and a two‐level scale‐specific process like composite random walk (mixture of intra‐ and inter‐patch habitat movement) is surrounded by controversy. Composite random walk may under some parameter conditions appear Lévy walk‐like from the perspective of the path’s distribution of step lengths due to superabundance of very long steps relative to the expectation from a classic (single‐level) random walk. However, a more explicit focus on the qualitative differences between studying movement at a high resolution mechanistic (behavioral) level and the more coarse‐grained statistical mechanical level may contribute to resolving both this and other issues related to scaling complexity. Specifically, a re‐sampling of a composite random walk at larger time lags than the micro‐level unit time step for the simulation makes a Lévy‐look‐alike step length distribution re‐shaping towards a Brownian motion‐like pattern. Conversely, a true Levy walk maintains its scaling characteristics upon re‐sampling. This result illustrates how a confusing pattern at the mechanistic level may be resolved by changing observational scale from the micro level to the coarser statistical mechanical meso‐ or macro‐scale. The instability of the composite random walk pattern under rescaling is a consequence of influence of the central limit theorem. I propose that a coarse‐graining test – studying simulated animal paths at a coarsened temporal scale by re‐sampling a series – should be routinely performed prior to comparing theoretical results with those patterns generated from GPS data describing animal movement paths. Fixes from terrestrial mammals are often collected at hourly intervals or larger, and such a priori coarse‐grained series may thus comply better with the statistical mechanical meso‐ or macro‐level of analysis than the behavioral mechanics observed at finer resolutions typically in the range of seconds and minutes. If fixes of real animals are collected at this high frequency, coarse graining both the simulated and real series is advised in order to bring the analysis into a temporal scale domain where analytical methods from statistical mechanics can be applied.     

The home range fractal: From random walk to memory-dependent space use

We present theoretical developments of the multi-scaled random walk (MRW) model for cognitive map-influenced space use by animals. The extensions include a unified space–time scaling function, and further details with respect to statistical properties of the spatial distribution of a set of locations. Supported by numeric simulations we show how memory effects may open for a complex, multi-scaled and self-organized – i.e., intrinsically driven – habitat utilization pattern with fractal dimensional properties. These properties allow for testing for MRW compliance by using parameters from classic movement models like Brownian motion, correlated random walk and Levy walks as null models. In terms of applied ecology, empirical confirmation of memory-influenced space use by individuals will have consequences for interpretation and statistical analyses of habitat utilization. For example, under memory map influence, re-visits to intra-home range locations do not represent independent events. Further, the MRW formulation specifically implies home range movements over a continuum of process rates, spanning a range of spatio-temporal scales in parallel, in violation of the traditional low order Markovian (scale-specific) model architecture. The MRW approach requires an extension of classic Boltzmann–Gibbs statistical mechanics, which rests on the premise that spatio-temporal memory effects are averaged out beyond micro-scales. We suggest that the emergent coherence between spatial and temporal scaling from the MRW approach may open for a more realistic statistical mechanics theory for population processes under terms of memory-influenced space use by individuals.     

Fix Success and Accuracy of Global Positioning System Collars in Old-Growth Temperate Coniferous Forests

Abstract: Global Positioning System (GPS) telemetry is used extensively to study animal distribution and resource selection patterns but is susceptible to biases resulting from data omission and spatial inaccuracies. These data errors may cause misinterpretation of wildlife habitat selection or spatial use patterns. We used both stationary test collars and collared free-ranging American black bears (Ursus americanus) to quantify systemic data loss and location error of GPS telemetry in mountainous, old-growth temperate forests of Olympic National Park, Washington, USA. We developed predictive models of environmental factors that influence the probability of obtaining GPS locations and evaluated the ability of weighting factors derived from these models to mitigate data omission biases from collared bears. We also examined the effects of microhabitat on collar fix success rate and examined collar accuracy as related to elevation changes between successive fixes. The probability of collars successfully obtaining location fixes was positively associated with elevation and unobstructed satellite view and was negatively affected by the interaction of overstory canopy and satellite view. Test collars were 33% more successful at acquiring fixes than those on bears. Fix success rates of collared bears varied seasonally and diurnally. Application of weighting factors to individual collared bear fixes recouped only 6% of lost data and failed to reduce seasonal or diurnal variation in fix success, suggesting that variables not included in our model contributed to data loss. Test collars placed to mimic bear bedding sites received 16% fewer fixes than randomly placed collars, indicating that microhabitat selection may contribute to data loss for wildlife equipped with GPS collars. Horizontal collar errors of >800 m occurred when elevation changes between successive fixes were >400 m. We conclude that significant limitations remain in accounting for data loss and error inherent in using GPS telemetry in coniferous forest ecosystems and that, at present, resource selection patterns of large mammals derived from GPS telemetry should be interpreted cautiously.     

Estimating space-use and habitat preference from wildlife telemetry data

Management and conservation of populations of animals requires information on where they are, why they are there, and where else they could be. These objectives are typically approached by collecting data on the animals' use of space, relating these positional data to prevailing environmental conditions and employing the resulting statistical models to predict usage at other geographical regions. Technical advances in wildlife telemetry have accomplished manifold increases in the amount and quality of available data, creating the need for a statistical framework that can use them to make population‐level inferences for habitat preference and space‐use. This has been slow‐in‐coming because wildlife telemetry data are spatio‐temporally autocorrelated, often unbalanced, presence‐only observations of behaviourally complex animals, responding to a multitude of cross‐correlated environmental variables. We review the evolution of regression models for the analysis of space‐use and habitat preference and outline the essential features of a framework that emerges naturally from these foundations. This allows us to derive a relationship between usage of points in geographical space and preference of habitats in environmental space. Within this framework, we discuss eight challenges, inherent in the spatial analysis of telemetry data and, for each, we propose solutions that can work in tandem. Specifically, we propose a logistic, mixed‐effects approach that uses generalized additive transformations of the environmental covariates and is fitted to a response data‐set comprising the telemetry and simulated observations, under a case‐control design. We apply this framework to a non‐trivial case‐study using satellite‐tagged grey seals Halichoerus grypus from the east coast of Scotland. We perform model selection by cross‐validation and confront our final model's predictions with telemetry data from the same, as well as different, geographical regions. We conclude that, despite the complex behaviour of the study species, flexible empirical models can capture the environmental relationships that shape population distributions.     

Effects of Species Behavior on Global Positioning System Collar Fix Rates

ABSTRACT Use of Global Positioning System (GPS) telemetry is increasing in wildlife studies and has provided researchers and managers with new insight into animal behavior. However, performance of GPS collars varies and a major concern is the cause of unsuccessful fixes. We examined possible factors causing missed fixes in GPS collars on sympatric free-ranging Eurasian lynx (Lynx lynx) and wolverines (Gulo gulo) in northern Sweden. We tested for effects of species, activity, habitat, individual, and collar on fix rate. Species was the most important factor affecting fix rate. Fix rate of GPS collars on lynx (80%) was almost twice as high as on wolverines (46%). Fix rate decreased during periods of low activity (day beds) for both species. Fix rate also decreased for females (both lynx and wolverine) for a period after they gave birth. We found no effect of proportion of forest within individual home range on fix rate. We conclude that species behavior, characteristics, and activity pattern are important factors affecting fix rate that we recommend be taken into consideration prior to analyzing GPS location data.     

Factors influencing soay sheep survival: a Bayesian analysis

This article presents a Bayesian analysis of mark-recapture-recovery data on Soay sheep. A reversible jump Markov chain Monte Carlo technique is used to determine age classes of common survival, and to model the survival probabilities in those classes using logistic regression. This involves environmental and individual covariates, as well as random effects. Auxiliary variables are used to impute missing covariates measured on individual sheep. The Bayesian approach suggests different models from those previously obtained using classical statistical methods. Following model averaging, features that were not previously detected, and which are of ecological importance, are identified.     

Density of Wild Prey Modulates Lynx Kill Rates on Free-Ranging Domestic Sheep

Understanding the factors shaping the dynamics of carnivore–livestock conflicts is vital to facilitate large carnivore conservation in multi-use landscapes. We investigated how the density of their main wild prey, roe deer Capreolus capreolus, modulates individual Eurasian lynx Lynx lynx kill rates on free-ranging domestic sheep Ovis aries across a range of sheep and roe deer densities. Lynx kill rates on free-ranging domestic sheep were collected in south-eastern Norway from 1995 to 2011 along a gradient of different livestock and wild prey densities using VHF and GPS telemetry. We used zero-inflated negative binomial (ZINB) models including lynx sex, sheep density and an index of roe deer density as explanatory variables to model observed kill rates on sheep, and ranked the models based on their AICc values. The model including the effects of lynx sex and sheep density in the zero-inflation model and the effect of lynx sex and roe deer density in the negative binomial part received most support. Irrespective of sheep density and sex, we found the lowest sheep kill rates in areas with high densities of roe deer. As roe deer density decreased, males killed sheep at higher rates, and this pattern held for both high and low sheep densities. Similarly, females killed sheep at higher rates in areas with high densities of sheep and low densities of roe deer. However, when sheep densities were low females rarely killed sheep irrespective of roe deer density. Our quantification of depredation rates can be the first step towards establishing fairer compensation systems based on more accurate and area specific estimation of losses. This study demonstrates how we can use ecological theory to predict where losses of sheep will be greatest, and can be used to identify areas where mitigation measures are most likely to be needed.     

Space use and social association in a gregarious ungulate: Testing the conspecific attraction and resource dispersion hypotheses

Animals use a variety of proximate cues to assess habitat quality when resources vary spatiotemporally. Two nonmutually exclusive strategies to assess habitat quality involve either direct assessment of landscape features or observation of social cues from conspecifics as a form of information transfer about forage resources. The conspecific attraction hypothesis proposes that individual space use is dependent on the distribution of conspecifics rather than the location of resource patches, whereas the resource dispersion hypothesis proposes that individual space use and social association are driven by the abundance and distribution of resources. We tested the conspecific attraction and the resource dispersion hypotheses as two nonmutually exclusive hypotheses explaining social association and of adult female caribou (Rangifer tarandus). We used location data from GPS collars to estimate interannual site fidelity and networks representing home range overlap and social associations among individual caribou. We found that home range overlap and social associations were correlated with resource distribution in summer and conspecific attraction in winter. In summer, when resources were distributed relatively homogeneously, interannual site fidelity was high and home range overlap and social associations were low. Conversely, in winter when resources were distributed relatively heterogeneously, interannual site fidelity was low and home range overlap and social associations were high. As access to resources changes across seasons, caribou appear to alter social behavior and space use. In summer, caribou may use cues associated with the distribution of forage, and in winter caribou may use cues from conspecifics to access forage. Our results have broad implications for our understanding of caribou socioecology, suggesting that caribou use season‐specific strategies to locate forage. Caribou populations continue to decline globally, and our finding that conspecific attraction is likely related to access to forage suggests that further fragmentation of caribou habitat could limit social association among caribou, particularly in winter when access to resources may be limited.     

Effects of Telemetry Location Error on Space-Use Estimates Using a Fixed-Kernel Density Estimator

ABSTRACT Fixed-kernel density estimates using radiotelemetry locations are frequently used to quantify home ranges of animals, interactions, and resource selection. However, all telemetry data have location error and no studies have reported the effects of error on utilization distribution and area estimates using fixed-kernel density estimators. We simulated different home range sizes and shapes by mixing bivariate-normal distributions and then drawing random samples of various sizes from these distributions. We compared fixed-kernel density estimates with and without error to the true underlying distributions. The effects of telemetry error on fixed-kernel density estimates were related to sample size, distribution complexity, and ratio of median Circular Error Probable to home range size. We suggest a metric to assess the adequacy of the telemetry system being used to estimate an animal's space use before a study is undertaken. Telemetry location error is unlikely to significantly affect fixed-kernel density estimates for most wildlife telemetry studies with adequate sample sizes.     

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.     

A model for dispersion experiments

Summary A new model is proposed for the dispersion of animals and other organisms and its use is discussed for the analysis of the data from experiments on dispersion. The model is a generalisation of the random walk model, but because of its flexibility it should be much more widely applicable than the random walk model.The new model has been found to fit the results of many dispersion experiments and examples are given of its use with data for millipedes and Drosophila.     

A Non-Lévy Random Walk in Chacma Baboons: What Does It Mean?

The Lévy walk is found from amoebas to humans and has been described as the optimal strategy for food research. Recent results, however, have generated controversy about this conclusion since animals also display alternatives to the Lévy walk such as the Brownian walk or mental maps and because movement patterns found in some species only seem to depend on food patches distribution. Here I show that movement patterns of chacma baboons do not follow a Lévy walk but a Brownian process. Moreover this Brownian walk is not the main process responsible for movement patterns of baboons. Findings about their speed and trajectories show that baboons use metal maps and memory to find resources. Thus the Brownian process found in this species appears to be more dependent on the environment or might be an alternative when known food patches are depleted and when animals have to find new resources.     

Computational and analytical framework for small RNA profiling by high-throughput sequencing

The advent of high-throughput sequencing (HTS) methods has enabled direct approaches to quantitatively profile small RNA populations. However, these methods have been limited by several factors, including representational artifacts and lack of established statistical methods of analysis. Furthermore, massive HTS data sets present new problems related to data processing and mapping to a reference genome. Here, we show that cluster-based sequencing-by-synthesis technology is highly reproducible as a quantitative profiling tool for several classes of small RNA from Arabidopsis thaliana. We introduce the use of synthetic RNA oligoribonucleotide standards to facilitate objective normalization between HTS data sets, and adapt microarray-type methods for statistical analysis of multiple samples. These methods were tested successfully using mutants with small RNA biogenesis (miRNA-defective dcl1 mutant and siRNA-defective dcl2 dcl3 dcl4 triple mutant) or effector protein (ago1 mutant) deficiencies. Computational methods were also developed to rapidly and accurately parse, quantify, and map small RNA data.     

Do fences constrain predator movements on an evolutionary scale? Home range, food intake and movement patterns of large predators reintroduced to Addo Elephant National Park, South Africa

Fencing conservation areas is ubiquitous in South Africa, however, the impact of these on predator ecology has not been tested. We used relationships between prey abundance and predator space use to create equations to predict the home range size of lions Panthera leo and leopards Panthera pardus. We then successfully tested these predictions using published data (Phinda, Makalali) and home range estimates from radio collared individuals reintroduced to Addo Elephant National Park. Spotted hyaena Crocuta crocuta ranges also seem food dependent. Lion home ranges in Addo (114 ± 5 km²) required 180 fixes to be accurately estimated, spotted hyaena ranges (91 ± 10 km²) required 200 fixes, and the solitary leopard had 295 fixes for a range of 38 km². There were no sexual differences in home range sizes of lions or hyaenas. The daily food intake rate of lions, measured during continuous follows, was 9.8 kg per female equivalent unit. Dominant male lions (14.3 km for 8.3 kg) traveled furthest but obtained the least amount of food per day compared to subordinate males (8.9 km for 16.0 kg) and females (5.8 km for 17.9 kg). Subordinate males traveled the fastest and during the day, to avoid competition and harassment from the dominant males. From an evolutionary viewpoint, the use of fences for conservation has not affected the natural behaviour of the predators as they still conform to predictions derived from unfenced reserves; that is, prey abundance is the key factor in determining space use of large predators.     

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

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.     

GPS telemetry of forest elephants in Central Africa: results of a preliminary study

Few data exist on the ranging behaviour of forest elephants. A feasibility study on the use of GPS telemetry as a tool to study ranging, seasonal movements and distribution was implemented in the Dzanga‐Sangha and Nouabalé‐Ndoki National Parks Complex of Central African Republic and Congo. The study consisted of two parts – a thorough hand‐held testing of an elephant GPS telemetry collar under tropical forest conditions and the deployment of collars on two elephants. During the feasibility study the system performance was satisfactory; GPS fix acquisition success rate, VHF and UHF collar–researcher communications were adequate. Two elephants, a mature bull and an adult female, were immobilized and fitted with GPS collars in October 1998. After deployment, the female's GPS collar performed well initially, but in less than a month the GPS within the collar stopped acquiring fixes. She was subsequently located using VHF tracking. The male was never relocated strongly suggesting complete failure of the collar. Despite these setbacks, the small amount of data retrieved provide an important first insight into forest elephant ranging and daily activity patterns, with significant conservation implications. When technical difficulties of reliability are overcome, GPS telemetry will provide an exceptionally useful tool in forest elephant research and management.     

Testing the consistency of wildlife data types before combining them: the case of camera traps and telemetry

Wildlife data gathered by different monitoring techniques are often combined to estimate animal density. However, methods to check whether different types of data provide consistent information (i.e., can information from one data type be used to predict responses in the other?) before combining them are lacking. We used generalized linear models and generalized linear mixed-effects models to relate camera trap probabilities for marked animals to independent space use from telemetry relocations using 2 years of data for fishers (Pekania pennanti) as a case study. We evaluated (1) camera trap efficacy by estimating how camera detection probabilities are related to nearby telemetry relocations and (2) whether home range utilization density estimated from telemetry data adequately predicts camera detection probabilities, which would indicate consistency of the two data types. The number of telemetry relocations within 250 and 500 m from camera traps predicted detection probability well. For the same number of relocations, females were more likely to be detected during the first year. During the second year, all fishers were more likely to be detected during the fall/winter season. Models predicting camera detection probability and photo counts solely from telemetry utilization density had the best or nearly best Akaike Information Criterion (AIC), suggesting that telemetry and camera traps provide consistent information on space use. Given the same utilization density, males were more likely to be photo-captured due to larger home ranges and higher movement rates. Although methods that combine data types (spatially explicit capture–recapture) make simple assumptions about home range shapes, it is reasonable to conclude that in our case, camera trap data do reflect space use in a manner consistent with telemetry data. However, differences between the 2 years of data suggest that camera efficacy is not fully consistent across ecological conditions and make the case for integrating other sources of space-use data.     

Temporal autocorrelation functions for movement rates from global positioning system radiotelemetry data

Autocorrelation has been viewed as a problem in telemetry studies because sequential observations are not independent in time or space, therefore violating assumptions for statistical inference. Yet nearly all ecological and behavioural data are autocorrelated in both space and time. We argue that there is much to learn about the structure of ecological and behavioural data from patterns of autocorrelation. Such patterns include periodicity in movement and patchiness in spatial data, which can be characterized by an autocorrelogram, semivariogram or spectrum. We illustrate the utility of temporal autocorrelation functions (ACFs) for analysing step-length data from GPS telemetry of wolves (Canis lupus), cougars (Puma concolor), grizzly bears (Ursus arctos) and elk (Cervus elaphus) in western Alberta. ACFs often differ by season, reflecting differences in foraging behaviour. In wilderness landscapes, step-length ACFs for predators decay slowly to apparently random patterns, but sometimes display strong daily rhythms in areas of human disturbance. In contrast, step lengths of elk are consistently periodic, reflecting crepuscular activity.     

Selecting Habitat to Survive: The Impact of Road Density on Survival in a Large Carnivore

Habitat selection studies generally assume that animals select habitat and food resources at multiple scales to maximise their fitness. However, animals sometimes prefer habitats of apparently low quality, especially when considering the costs associated with spatially heterogeneous human disturbance. We used spatial variation in human disturbance, and its consequences on lynx survival, a direct fitness component, to test the Hierarchical Habitat Selection hypothesis from a population of Eurasian lynx Lynx lynx in southern Norway. Data from 46 lynx monitored with telemetry indicated that a high proportion of forest strongly reduced the risk of mortality from legal hunting at the home range scale, while increasing road density strongly increased such risk at the finer scale within the home range. We found hierarchical effects of the impact of human disturbance, with a higher road density at a large scale reinforcing its negative impact at a fine scale. Conversely, we demonstrated that lynx shifted their habitat selection to avoid areas with the highest road densities within their home ranges, thus supporting a compensatory mechanism at fine scale enabling lynx to mitigate the impact of large-scale disturbance. Human impact, positively associated with high road accessibility, was thus a stronger driver of lynx space use at a finer scale, with home range characteristics nevertheless constraining habitat selection. Our study demonstrates the truly hierarchical nature of habitat selection, which aims at maximising fitness by selecting against limiting factors at multiple spatial scales, and indicates that scale-specific heterogeneity of the environment is driving individual spatial behaviour, by means of trade-offs across spatial scales.     

Patterns of Spatial use and movement of the Poóuli – a critically endangered Hawaiian honeycreeper

The Poóuli (Melamprosops phaeosoma) is a highly endangered Hawaiian honeycreeper endemic to Maui, and is currently one of the World's rarest birds. Only two wild individuals of this species are now known to exist, and they are restricted to the windward slopes of Haleakala volcano on east Maui. Studies of the more common honeycreepers on the Hawaiian islands describe a diverse array of spatial use and movement patterns, which vary according to specific ecological needs. In contrast, spatial use and movement of Poóuli are very poorly known, despite continuous field monitoring of all three individuals since 1997. We analyzed annual data by breeding season between 1995 and 2001 for three individuals, and eight days of telemetry data derived from the radio-tracking of one individual in 2002, using GIS and conventional methods, to estimate home range size, and to interpret these data alongside those for other honeycreepers. We estimated mean home range sizes of 8.43 hectares (ha) from annual re-sights using kernel analysis and 2.14 ha using minimum convex polygons, and 8.44 and 3.51 ha respectively from telemetry data. Our estimates conform to those derived for other insectivorous honeycreepers, but indicate that Poóuli may forage widely to support their diet of forest snails. Our home range size estimates are compatible with estimates of population density for Poóuli that were derived from field transects between 1975 and 1985, suggesting that such field methods may be a reliable density estimator for rare forest birds. Jim J. Groombridge and Bill Sparklin: Joint first author