Estimation of animal location from radio telemetry data with temporal dependencies

We evaluate the performance of several estimators of animal location when data arise from radio telemetry studies. We assume that error-prone bearings are taken at regular time intervals from known locations, that observations may be frequent enough to introduce temporal dependencies, and that animals remain within well-defined home ranges. We simulated data to examine several factors including home range shape, dependency between successive locations, sample size and strategy, and bearing error. Simulated data, supplemented by data based on actual paths for Rocky Mountain elk (Cervus elaphus nelsoni), were used to evaluate alternative location estimators: Lenth’s maximum likelihood estimator (MLE) that assumes independence; Pace’s moving average version of the MLE that introduces a post hoc dependence in the data; and three estimators from state-space models that explicitly model animal movement and dependencies. The state-space models differed in the assumed model of animal movement and included a simple normal random walk, a variation of the random walk that includes a centralizing parameter, and a discretetime version of the Ornstein-Uhlenbeck model for movement within an elliptical home range. Estimates were evaluated in terms of location error and estimator precision. The independent MLE had the poorest performance under most scenarios, particularly when actual locations were dependent. The centrally biased random walk estimator generally had smallest location errors and best precision, whether or not data displayed dependencies. Rather than assuming independence or discarding observations to achieve independence, estimation of location would be served better by accounting for potential dependencies. Methods based on simple models of animal movement may vastly improve estimates, and models that recognize an animal’s sense of home territory are preferred.     

Imputation Approaches for Animal Movement Modeling

The analysis of telemetry data is common in animal ecological studies. While the collection of telemetry data for individual animals has improved dramatically, the methods to properly account for inherent uncertainties (e.g., measurement error, dependence, barriers to movement) have lagged behind. Still, many new statistical approaches have been developed to infer unknown quantities affecting animal movement or predict movement based on telemetry data. Hierarchical statistical models are useful to account for some of the aforementioned uncertainties, as well as provide population-level inference, but they often come with an increased computational burden. For certain types of statistical models, it is straightforward to provide inference if the latent true animal trajectory is known, but challenging otherwise. In these cases, approaches related to multiple imputation have been employed to account for the uncertainty associated with our knowledge of the latent trajectory. Despite the increasing use of imputation approaches for modeling animal movement, the general sensitivity and accuracy of these methods have not been explored in detail. We provide an introduction to animal movement modeling and describe how imputation approaches may be helpful for certain types of models. We also assess the performance of imputation approaches in two simulation studies. Our simulation studies suggests that inference for model parameters directly related to the location of an individual may be more accurate than inference for parameters associated with higher-order processes such as velocity or acceleration. Finally, we apply these methods to analyze a telemetry data set involving northern fur seals (Callorhinus ursinus) in the Bering Sea. Supplementary materials accompanying this paper appear online.     

Influence of roads on the endangered Stephens' kangaroo rat (Dipodomys stephensi): are dirt and gravel roads different?

Roads can have major impacts on animal distribution and movement patterns by destroying or creating habitat, and by acting as both barriers and corridors for movement. Using a combination of live trapping and spool and line tracking, we compare the relative abundance, mass, and demographic turnover of the endangered Stephens' kangaroo rat (Dipodomys stephensi) on dirt and gravel roads in comparison with adjacent grassland habitat. D. stephensi was more active on dirt roads, and less so on gravel roads, relative to adjacent grassland habitat. Dirt roads were used extensively, and animals tended to move greater distances along dirt roads than in surrounding grasslands. In contrast, gravel roads were used much less extensively than adjacent grasslands. Animals using dirt roads were significantly lighter in mass than those on gravel roads and in adjacent grassland, suggesting greater use by juvenile animals. Dirt roads also had lower rates of recapture and higher rates of new arrivals than did adjacent habitat. These findings suggest that dirt roads provide potentially important landscape linkages for D. stephensi, whereas that gravel roads may act as movement barriers.     

Multi-scale Modeling of Animal Movement and General Behavior Data Using Hidden Markov Models with Hierarchical Structures

Hidden Markov models (HMMs) are commonly used to model animal movement data and infer aspects of animal behavior. An HMM assumes that each data point from a time series of observations stems from one of N possible states. The states are loosely connected to behavioral modes that manifest themselves at the temporal resolution at which observations are made. Due to advances in tag technology and tracking with digital video recordings, data can be collected at increasingly fine temporal resolutions. Yet, inferences at time scales cruder than those at which data are collected and, which correspond to larger-scale behavioral processes, are not yet answered via HMMs. We include additional hierarchical structures to the basic HMM framework, incorporating multiple Markov chains at various time scales. The hierarchically structured HMMs allow for behavioral inferences at multiple time scales and can also serve as a means to avoid coarsening data. Our proposed framework is one of the first that models animal behavior simultaneously at multiple time scales, opening new possibilities in the area of animal movement and behavior modeling. We illustrate the application of hierarchically structured HMMs in two real-data examples: (i) vertical movements of harbor porpoises observed in the field, and (ii) garter snake movement data collected as part of an experimental design. Supplementary materials accompanying this paper appear online.     

Reflected Stochastic Differential Equation Models for Constrained Animal Movement

Movement for many animal species is constrained in space by barriers such as rivers, shorelines, or impassable cliffs. We develop an approach for modeling animal movement constrained in space by considering a class of constrained stochastic processes, reflected stochastic differential equations. Our approach generalizes existing methods for modeling unconstrained animal movement. We present methods for simulation and inference based on augmenting the constrained movement path with a latent unconstrained path and illustrate this augmentation with a simulation example and an analysis of telemetry data from a Steller sea lion (Eumatopias jubatus) in southeast Alaska.     

Explaining movement decisions of forest rodents in fragmented landscapes

Functional connectivity is a measure of the interaction of landscape structure and a species’ dispersal ability to determine the degree to which a landscape facilitates movement among patches. Dispersal through an inhospitable matrix requires that a species is willing to enter the matrix and can successfully colonize another habitat patch. Many connectivity indices have been developed which incorporate various attributes of the landscape, but little empirical evidence of the accuracy of these indices is available. We studied the ability of white-footed mice (Peromyscus leucopus), eastern chipmunks (Tamias striatus), and southern flying squirrels (Glaucomys volans) to move through agricultural fields in west-central Indiana. Radio-collared animals were translocated into corridors that either were connected to or unconnected from an associated forest patch to determine their willingness to enter the matrix. Animals also were translocated into fields to determine how motivation to find resources influences movement through the matrix. All species demonstrated a strong motivation to find the forest. Animals were capable of moving through the matrix successfully, however, we were unable to determine whether they would do so willingly. Initial bearing was an important predictor for successfully reaching a forest patch, which has implications for modeling dispersal. Additionally, abiotic variables, such as temperature and precipitation, had a strong effect on latency to move from the release site. Although weather often correlates with seasonal migration, our study emphasizes the importance of weather in influencing short-term decisions on timing of movement.     

Using behavioral landscape ecology to predict species’ responses to land-use and climate change

Climate change and habitat destruction are widely recognized as major threats to species’ survival. As a result of these anthropogenic impacts, species are often forced into novel landscapes where their persistence is difficult to predict. Knowledge of how individuals move or disperse through the landscape, choose habitat in which to settle, and produce offspring which survive to repeat the process can greatly improve our ability to predict species’ persistence. The field of behavioral landscape ecology uses a strong theoretical base to explore, often experimentally, how the behavior of a particular species is affected by heterogeneous and rapidly changing landscapes and can offer valuable insight for managing species in the face of human-induced environmental changes. When interpreted by modelers, results of landscape-level behavioral experiments can be quantified for use in predictive models. To this end, we summarize the methods and results of research using direct experimental manipulation techniques broken into the following categories: translocations, playback experiments, food resource manipulations, manipulations of reproductive success, direct manipulations of the landscape, and manipulations of predation risk. We review and place in a theoretical framework the results from this emerging body of research regarding how organisms move in and respond to different types of landscapes, both natural and human-altered. We go onto highlight the potential of each experimental method to quantify different processes, which may be useful when interpreted by modelers attempting to parameterize predictive models. Finally, we suggest future directions for experimental research that will allow for greater integration of behavioral landscape ecology and predictive modeling.     

Modeling the Diving Behavior of Whales: A Latent-Variable Approach with Feedback and Semi-Markovian Components

Recent years have seen a fast-growing body of literature concerned with the statistical modeling of animal movement in the two horizontal dimensions. On the other hand, there is very little statistical work that deals with animal movement in the vertical dimension. We present an approach that provides an important step in analyzing such data. In particular, we introduce a hidden Markov-type modeling approach for time series comprising the depths of a diving marine mammal, thus modeling movement in the water column. We first develop a baseline Markov-switching model, which is then extended to incorporate feedback and semi-Markovian components, motivated by the observations made for a particular species, Blainville’s beaked whale (Mesoplodon densirostris). The application of the proposed model to the beaked whale data reveals both strengths and weaknesses of the suggested modeling framework. The framework is general enough that we anticipate that it can be used for many other species given minor changes in the model structure.     

A General Approach to Model Movement in (Highly) Fragmented Patch Networks

Landscape heterogeneity can often be represented as a series of discrete habitat or resource patches surrounded by a matrix of non-habitat. Understanding how animals move in such networks of patches is important for many theoretical and applied questions. The probability of going from one patch to another is affected in a non-trivial way by the characteristics and location of other patches in the network. Nearby patches can compete as possible destinations, and a particular patch can be shadowed by neighboring patches. We present a way to account for the effects of the spatial configuration of patches in models of space use where individuals alternate between spending time in a patch and moving to other patches in the network. The approach is based on the original derivation of Ovaskainen and Cornell (J Appl Probab 40:557–580, 2003) for a diffusion model that considered all possible ways in which an individual leaving a particular patch can eventually reach another patch before dying or leaving the patch network. By replacing the theoretical results of Ovaskainen and Cornell by other appropriate functions, we provide generality and thus make their approach useful in contexts where diffusion is not a good approximation of movement. Furthermore, we provide ways to estimate time spent in the non-habitat matrix when going from patch to patch and implement a method to incorporate the effect of the history of previous visits on future patch use. We present an MCMC way to fit these models to data and illustrate the approach with both simulated data and data from sheep moving among seasonally flooded meadows in northern Patagonia.Supplementary materials accompanying this paper appear online.     

Restoring habitat permeability to roaded landscapes with isometrically-scaled wildlife crossings

Globally, human activities impact from one-third to one-half of the earth’s land surface; a major component of development involves the construction of roads. In the US and Europe, road networks fragment normal animal movement patterns, reduce landscape permeability, and increase wildlife-vehicle collisions, often with serious wildlife population and human health consequences. Critically, the placement of wildlife crossing structures to restore landscape connectivity and reduce the number of wildlife-vehicle collisions has been a hit-or-miss proposition with little ecological underpinning, however recent important developments in allometric scaling laws can be used to guide their placement. In this paper, we used cluster analysis to develop domains of scale for mammalian species groups having similar vagility and developed metrics that reflect realistic species movement dynamics. We identified six home range area domains; three quarters of 102 species clustered in the three smallest domains. We used HR^0.5 to represent a daily movement metric; when individual species movements were plotted against road mile markers, 71.2% of 72 species found in North America were included at distances of ?1 mi. The placement of wildlife crossings based on the HR^0.5 metric, along with appropriate auxiliary mitigation, will re-establish landscape permeability by facilitating wildlife movement across the roaded landscape and significantly improve road safety by reducing wildlife vehicle collisions.     

Surface Armour and Erosion – Impacts on Long‐term Landscape Evolution

The parameterisation of landscape evolution models is key to their reliable use. To determine reliable parameter sets, data collected from many events over a number of years are required. However, for many recently disturbed, degraded and/or rehabilitated sites, this data may not represent the long‐term behaviour of the surface as armouring, weathering, together with vegetation establishment change the erodibility of the surface. Here, we evaluate a new armouring sub‐model within the SIBERIA landscape evolution model. The calibration of the armour model is conducted using 6 years of field data from four plots, each composed of different surface materials and vegetation characteristics. The calibrated model is then tested on an area of the proposed rehabilitated landform of the Ranger Uranium Mine in the Northern Territory, Australia. The SIBERIA model was then run for a simulated period of 100,000 years using parameters representing (i) a surface constructed of fresh waste rock; (ii) a vegetated surface; and (iii) the calibrated armour sub‐model. The results demonstrate that the different parameter sets produce catchments that are unique despite the same starting surface. Surface material properties exert a first‐order control on landscape evolution. Therefore making predictions for the evolution of a landscape requires a reliable understanding of the material properties. This requires a knowledge of what material will be placed where in the catchment. Copyright © 2017 John Wiley & Sons, Ltd.     

Bayesian Inference for Multistate ‘Step and Turn’ Animal Movement in Continuous Time

Mechanistic modelling of animal movement is often formulated in discrete time despite problems with scale invariance, such as handling irregularly timed observations. A natural solution is to formulate in continuous time, yet uptake of this has been slow. This lack of implementation is often excused by a difficulty in interpretation. Here we aim to bolster usage by developing a continuous-time model with interpretable parameters, similar to those of popular discrete-time models that use turning angles and step lengths. Movement is defined by a joint bearing and speed process, with parameters dependent on a continuous-time behavioural switching process, creating a flexible class of movement models. Methodology is presented for Markov chain Monte Carlo inference given irregular observations, involving augmenting observed locations with a reconstruction of the underlying movement process. This is applied to well-known GPS data from elk (Cervus elaphus), which have previously been modelled in discrete time. We demonstrate the interpretable nature of the continuous-time model, finding clear differences in behaviour over time and insights into short-term behaviour that could not have been obtained in discrete time.     

Habitat models and habitat connectivity analysis for butterflies and burnet moths - The example of Zygaena carniolica and Coenonympha arcania

In this paper, habitat models were used to predict potential habitat for endangered species, which is an important question in landscape and conservation planning. Based on logistic regression, we developed habitat distribution models for the burnet moth Zygaena carniolica and the nymphalid butterfly Coenonympha arcania in Northern Bavaria, Germany. The relation between adult occurrence and habitat parameters, including the influence of landscape context, was analyzed on 118 sites. Habitat connectivity analyses were carried out on the basis of (1) habitat suitability maps generated from these models and (2) dispersal data from mark recapture studies. Our results showed that (1) the presence of the burnet depended mainly on the presence of nectar plants and of nutrient-poor dry grasslands in direct vicinity, that of the nymphalid on larger areas of extensively used dry grasslands within 100 m vicinity in combination with small patches of higher shrubs and bushes. (2) Internal as well as external validation indicated the robustness and general applicability of the models. Transferability in time and space indicated their high potential relevance for applications in nature conservation, such as predicting possible effects of land use changes. (3) Habitat connectivity analyses revealed a high degree of habitat connectivity within the study area. Thus, we could show no effects of isolation or habitat size for both species.     

Spatial Variability of Corn Yield and Yield Response to Fertilizer Nitrogen: Role of Organic Carbon

Utility of organic carbon (OC) content as an indicator of corn (Zea maize L.) grain yield and yield response to nitrogen (N) across a broad range of conditions was assessed using data from two studies (the first on a variable landscape at Elora Research Station and the second on 19 landscapes in private farms) conducted from 1998 to 2003 in southern Ontario. Zero and 140/150 kg N ha^?1 were applied in all studies. Yields generally increased linearly or quadratically with increasing OC. Regression models indicated 42% of the data sets had no response to fertilizer N and in only two data sets in Elora and no data sets in private farms were yield responses to N dependent on OC. When yield increased with fertilizer addition, it was similar for all OC contents in a landscape. We concluded that OC content cannot be used to identify N-management units in southern Ontario.     

Identifying, understanding, and describing spatial processes in agricultural landscapes — four case studies

To evaluate the quality of the ecosystem and for making resources and land management decisions landscapes have to be assessed quantitatively. For a better understanding of landscape processes and their characterization, the analysis of the inherent variability is a major factor. Four case studies in which problems associated with landscape analysis are discussed. Spatial processes remain a main focus, as their analysis provides information on the relation between relevant state variables in agricultural landscapes. Variogram analysis showed that mineral soil nitrogen (N_min) sampled in a field at different scales, domains, and times is an instationary spatial process. Spatial association of grain yield, soil index and remotely sensed vegetation index may not be identifiable from kriged contour maps as local coincidence may be obscured behind classified areas. Crop yield in subsequent years and remotely sensed information are not related if a unique response is assumed. An alternative data stratification procedure is described here for the identification of different response functions in agricultural ecosystems. Processes of crop yield and underlying variables are described in autoregressive state-space models. This technique incorporates both deterministic and stochastic relations between different variables and is based on relative changes in space.     

Birds in eucalypt and pine forests: landscape alteration and its implications for research models of faunal habitat use

Most studies of faunal habitat fragmentation are based on a human perspective of the landscape in which landscape elements are classified as habitat and non-habitat. Moreover, many landscape models that define “habitat patches” assume that the same set of patches will be suitable for all taxa or a broad range of taxa. McIntyre and Hobbs [Conservation Biology 13 (1999) 1282] recently proposed a model in which landscapes can be classified according to the amount of habitat remaining and in which the remaining habitat can correspond to a continuum or gradient of modification. The perception of a landscape as being intact, variegated, fragmented or relictual [sensu Conservation Biology 13 (1999)] will depend on the capacity of individual species to utilise modified habitat. We suggest that although the continuum concept of habitat use is reasonably well established for plants, faunal studies have often ignored the notion of a gradient of habitat use and have classified landscape areas simplistically and inappropriately as either habitat or non-habitat. Data on birds in southeastern Australia are used to illustrate how the binary view of habitat can be incorrect. Birds were sampled in landscapes that ranged from intact to relictual as defined from an anthropocentric perspective. Our data: (1) illustrated a wide range of bird responses to habitat modification including many that might have been overlooked using a simple binomial approach to habitat classification, and (2) highlighted the fact that the way in which humans perceive landscapes may not correspond to how some elements of the biota perceive the same landscape. Viewing landscapes as a species-specific gradient of states of remaining habitat and condition has important implications for undertaking studies of human impacts on biodiversity and also integrating conservation considerations in production environments. It also challenges the effectiveness of “quick fixes” such as species-based biodiversity surrogates schemes and the uncritical use of generic landscape indices to save “habitat” because the assumption that all species will conform to the same landscape pattern will not hold.     

GIS-models work well, but are not enough: Habitat preferences of Lanius collurio at multiple levels and conservation implications

Species conservation largely depends on knowledge of habitat needs of target species. GIS-models are increasingly used to assess habitat preferences and distribution of target species, but their accuracy is constrained by availability of digital data layers. We developed a two-steps approach aiming at showing pros and cons of landscape (GIS)- and site-level habitat models, identifying key habitat factors for conservation of a threatened bird species, the red-backed shrike Lanius collurio. A spatially explicit GIS-model was generated using landscape variables, and a second model at site level was developed using fine-scale variables measured on the ground. The GIS-based model was then extrapolated to the entire region to obtain a map of distribution of suitable habitats. Positive associations between shrike occurrence and both hedgerow length and partial shrub cover were detected at both scales. Shrikes were also positively associated with grassland cover at landscape level and with partial cover of untilled herbaceous vegetation at the finer scale, and negatively affected by lucerne cover. The GIS-model led to an affordable map of predicted habitat suitability which should help conservationists to focus on different local priorities, but was unable to identify effects of untilled and lucerne cover. Site-level model gave fine details for habitat management, but its application elsewhere requires ground-measurements of factors. Combining the multiscale models could indicate more urgent actions at large scales (e.g. maintaining suitable habitats, or improving connectivity among isolated patches) and draw a detailed figure of the most suitable habitat for the species. Shrike occurrence was associated with a higher number of shrub and tree species: the indicator value of the species should ensure general benefits for biodiversity from dedicated management.     

Can landscape and species characteristics predict primate presence in forest fragments in the Brazilian Amazon?

Habitat loss and fragmentation are global conservation concerns, but animal species do not respond to these threats in the same manner. At the Biological Dynamics of Forest Fragments Project (BDFFP), located 80 km north of Manaus, Amazonas, Brazil, the distribution and persistence of six native primate species differ among fragments that were isolated in 1980s. We identified both landscape and species characteristics predicting the presence of primates in these forest fragments. Fragment size positively and distance to nearest forested area negatively predicted primate species richness in the fragments; however, these relationships were not straightforward because these two variables were correlated. The proportion of fruit in a species’ diet was the most important factor predicting its presence in the forest fragments, with species relying primarily on frugivory faring poorly. Home range size was the second-best predictor of a species’ presence; however, some species with large home ranges were present in the 10-ha forest fragments. The extent to which the individual primate species traveled in and out of the fragments varied, suggesting that further research is necessary to determine the primary factors that lead to the animals’ use of the matrix. We conclude that in addition to conserving large tracts of habitat, reducing the isolation of the forest fragments through the creation of forest corridors and through the presence of additional forest fragments within the agricultural matrix may increase animal movement across the landscape. Such changes to the matrix may be critical for those species that do not readily traverse non-forested areas.     

Small mammals, habitat patches and PVA models: a field test of model predictive ability

The results are described of comparisons between actual values for patch occupancy for two species of Australian small mammals (Bush Rat Rattus fuscipes and Agile Antechinus Antechinus agilis) determined from field sampling and predictions of patch occupancy made using VORTEX, a generic simulation model for Population Viability Analysis (PVA). The work focussed on a fragmented forest in south-eastern Australia comprised of a network of 39 patches of native eucalypt forest surrounded by extensive stands of exotic softwood Radiata Pine (Pinus radiata) plantation. A range of modelling scenarios were completed in which four broad factors were varied: (1) inter-patch variation in habitat quality; (2) the pattern of inter-patch dispersal; (3) the rate of inter-patch dispersal; and (4) the population sink effects of the Radiata Pine matrix that surrounded the eucalypt patches. Model predictions were made for the total number of animals, the distribution of animal density among patches, the total number of occupied patches, and the probability of patch occupancy. Predictions were then compared with observed values for these same measures based on extensive field surveys of small mammals in the patch system. For most models for the Bush Rat, the predicted relative density of animals per patch correlated well with the values estimated from field surveys. Predictions of patch occupancy were not significantly different from the actual value for the number of occupied patches in half the models tested. The better models explained 10-16% of the log-likelihood of the probability of patch occupancy. While some of the models gave reasonable forecasts of the number of occupied patches, even in these cases, they had only moderate ability to predict which patches were occupied. Field surveys revealed there was no relationship between patch area and population density for the Agile Antechinus—an outcome correctly predicted by only a few models. Five of the 18 scenarios completed for the Agile Antechinus gave predicted numbers of occupied patches not significantly different from the observed number. In each of these five cases, large standard deviations around the mean predicted value meant uncertainty generated by the simulation model limited the predictive power of the PVA. Some of the models gave reasonable predictions for the number of occupied patches, but those models were unable to predict which ones were actually occupied. The results of our study suggest that key processes influencing which specific patches would be occupied were not modelled appropriately. High levels of variability and fecundity drive the population dynamics of the Bush Rat and Agile Antechinus, making the patch system unpredictable and difficult to model accurately. Despite the fact that both the Bush Rat and the Agile Antechinus are two of the most studied mammals in Australia, there are attributes of their biology that are presently poorly understood (which were not included in the VORTEX model), but which could strongly influence patch occupancy. For example, local landscape features may be important determinants of inter-patch movement and habitat utilisation in the patch system. Further empirical studies are needed to explore this aspect of small mammal biology.     

Dynamic Models of Animal Movement with Spatial Point Process Interactions

When analyzing animal movement, it is important to account for interactions between individuals. However, statistical models for incorporating interaction behavior in movement models are limited. We propose an approach that models dependent movement by augmenting a dynamic marginal movement model with a spatial point process interaction function within a weighted distribution framework. The approach is flexible, as marginal movement behavior and interaction behavior can be modeled independently. Inference for model parameters is complicated by intractable normalizing constants. We develop a double Metropolis–Hastings algorithm to perform Bayesian inference. We illustrate our approach through the analysis of movement tracks of guppies (Poecilia reticulata).