The Langevin diffusion as a continuous‐time model of animal movement and habitat selection

Time-varying habitat selection analysis: A model and applications for studying diel, seasonal, and post-release changes

Resource selection functions are commonly used to evaluate animals' habitat selection, for example, the disproportionate use of habitats relative to their availability. While environmental conditions or animal motivations may vary over time, sometimes in an unknown manner, studying changes in habitat selection usually requires an a priori segmentation of time in distinct periods. This limits our ability to precisely answer the question "When is an animal's habitat selection changing?" Here, we present a straightforward and flexible alternative approach based on fitting dynamic logistic models to used/available data. First, using simulated datasets, we demonstrate that dynamic logistic models perform well in recovering temporal variations in habitat selection. We then show real-world applications for studying diel, seasonal, and post-release changes in the habitat selection of the blue wildebeest (Connochaetes taurinus). Dynamic logistic models allow the study of temporal changes in habitat selection in a framework consistent with resource selection functions but without the need to segment time in distinct periods, which can be a difficult task when little is known about the process studied or may obscure interindividual variability in timing of change. These models should undoubtedly find their place in the movement ecology toolbox. We provide R scripts to facilitate their adoption. We also encourage future research to focus on how to account for temporal autocorrelation in location data, as this would allow statistical inference from location data collected at a high frequency, an increasingly common situation.

A multistate Langevin diffusion for inferring behavior-specific habitat selection and utilization distributions

The identification of important habitat and the behavior(s) associated with it is critical to conservation and place-based management decisions. Behavior also links life-history requirements and habitat use, which are key to understanding why animals use certain habitats. Animal population studies often use tracking data to quantify space use and habitat selection, but they typically either ignore movement behavior (e.g., foraging, migrating, nesting) or adopt a two-stage approach that can induce bias and fail to propagate uncertainty. We develop a habitat-driven Langevin diffusion for animals that exhibit distinct movement behavior states, thereby providing a novel single-stage statistical method for inferring behavior-specific habitat selection and utilization distributions in continuous time. Practitioners can customize, fit, assess, and simulate our integrated model using the provided R package. Simulation experiments demonstrated that the model worked well under a range of sampling scenarios as long as observations were of sufficient temporal resolution. Our simulations also demonstrated the importance of accounting for different behaviors and the misleading inferences that can result when these are ignored. We provide case studies using plains zebra (Equus quagga) and Steller sea lion (Eumetopias jubatus) telemetry data. In the zebra example, our model identified distinct "encamped" and "exploratory" states, where the encamped state was characterized by strong selection for grassland and avoidance of other vegetation types, which may represent selection for foraging resources. In the sea lion example, our model identified distinct movement behavior modes typically associated with this marine central-place forager and, unlike previous analyses, found foraging-type movements to be associated with steeper offshore slopes characteristic of the continental shelf, submarine canyons, and seamounts that are believed to enhance prey concentrations. This is the first single-stage approach for inferring behavior-specific habitat selection and utilization distributions from tracking data that can be readily implemented with user-friendly software. As certain behaviors are often more relevant to specific conservation or management objectives, practitioners can use our model to help inform the identification and prioritization of important habitats. Moreover, by linking individual-level movement behaviors to population-level spatial processes, the multistate Langevin diffusion can advance inferences at the intersection of population, movement, and landscape ecology.

Integrated animal movement and spatial capture-recapture models: Simulation, implementation, and inference

Over the last decade, spatial capture-recapture (SCR) models have become widespread for estimating demographic parameters in ecological studies. However, the underlying assumptions about animal movement and space use are often not realistic. This is a missed opportunity because interesting ecological questions related to animal space use, habitat selection, and behavior cannot be addressed with most SCR models, despite the fact that the data collected in SCR studies - individual animals observed at specific locations and times - can provide a rich source of information about these processes and how they relate to demographic rates. We developed SCR models that integrated more complex movement processes that are typically inferred from telemetry data, including a simple random walk, correlated random walk (i.e., short-term directional persistence), and habitat-driven Langevin diffusion. We demonstrated how to formulate, simulate from, and fit these models with standard SCR data using data-augmented Bayesian analysis methods. We evaluated their performance through a simulation study, in which we varied the detection, movement, and resource selection parameters. We also examined different numbers of sampling occasions and assessed performance gains when including auxiliary location data collected from telemetered individuals. Across all scenarios, the integrated SCR movement models performed well in terms of abundance, detection, and movement parameter estimation. We found little difference in bias for the simple random walk model when reducing the number of sampling occasions from T = 25 to T = 15. We found some bias in movement parameter estimates under several of the correlated random walk scenarios, but incorporating auxiliary location data improved parameter estimates and significantly improved mixing during model fitting. The Langevin movement model was able to recover resource selection parameters from standard SCR data, which is particularly appealing because it explicitly links the individual-level movement process with habitat selection and population density. We focused on closed population models, but the movement models developed here can be extended to open SCR models. The movement process models could also be easily extended to accommodate additional "building blocks" of random walks, such as central tendency (e.g., territoriality) or multiple movement behavior states, thereby providing a flexible and coherent framework for linking animal movement behavior to population dynamics, density, and distribution.

An integrated path for spatial capture-recapture and animal movement modeling

Ecologists and conservation biologists increasingly rely on spatial capture-recapture (SCR) and movement modeling to study animal populations. Historically, SCR has focused on population-level processes (e.g., vital rates, abundance, density, and distribution), whereas animal movement modeling has focused on the behavior of individuals (e.g., activity budgets, resource selection, migration). Even though animal movement is clearly a driver of population-level patterns and dynamics, technical and conceptual developments to date have not forged a firm link between the two fields. Instead, movement modeling has typically focused on the individual level without providing a coherent scaling from individual- to population-level processes, whereas SCR has typically focused on the population level while greatly simplifying the movement processes that give rise to the observations underlying these models. In our view, the integration of SCR and animal movement modeling has tremendous potential for allowing ecologists to scale up from individuals to populations and advancing the types of inferences that can be made at the intersection of population, movement, and landscape ecology. Properly accounting for complex animal movement processes can also potentially reduce bias in estimators of population-level parameters, thereby improving inferences that are critical for species conservation and management. This introductory article to the Special Feature reviews recent advances in SCR and animal movement modeling, establishes a common notation, highlights potential advantages of linking individual-level (Lagrangian) movements to population-level (Eulerian) processes, and outlines a general conceptual framework for the integration of movement and SCR models. We then identify important avenues for future research, including key challenges and potential pitfalls in the developments and applications that lie ahead.

Classifying behavior from short-interval biologging data: An example with GPS tracking of birds

Recent advances in digital data collection have spurred accumulation of immense quantities of data that have potential to lead to remarkable ecological insight, but that also present analytic challenges. In the case of biologging data from birds, common analytical approaches to classifying movement behaviors are largely inappropriate for these massive data sets.We apply a framework for using K-means clustering to classify bird behavior using points from short time interval GPS tracks. K-means clustering is a well-known and computationally efficient statistical tool that has been used in animal movement studies primarily for clustering segments of consecutive points. To illustrate the utility of our approach, we apply K-means clustering to six focal variables derived from GPS data collected at 1-11 s intervals from free-flying bald eagles (Haliaeetus leucocephalus) throughout the state of Iowa, USA. We illustrate how these data can be used to identify behaviors and life-stage- and age-related variation in behavior.After filtering for data quality, the K-means algorithm identified four clusters in >2 million GPS telemetry data points. These four clusters corresponded to three movement states: ascending, flapping, and gliding flight; and one non-moving state: perching. Mapping these states illustrated how they corresponded tightly to expectations derived from natural history observations; for example, long periods of ascending flight were often followed by long gliding descents, birds alternated between flapping and gliding flight.The K-means clustering approach we applied is both an efficient and effective mechanism to classify and interpret short-interval biologging data to understand movement behaviors. Furthermore, because it can apply to an abundance of very short, irregular, and high-dimensional movement data, it provides insight into small-scale variation in behavior that would not be possible with many other analytical approaches.

Maximum approximate likelihood estimation of general continuous-time state-space models

Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions concerning linearity and Gaussianity to facilitate inference on the model parameters via the Kalman filter. In this contribution, we provide a general continuous-time SSM framework, allowing both the observation and the state process to be non-linear and non-Gaussian. Statistical inference is carried out by maximum approximate likelihood estimation, where multiple numerical integration within the likelihood evaluation is performed via a fine discretization of the state process. The corresponding reframing of the SSM as a continuous-time hidden Markov model, with structured state transitions, enables us to apply the associated efficient algorithms for parameter estimation and state decoding. We illustrate the modelling approach in a case study using data from a longitudinal study on delinquent behaviour of adolescents in Germany, revealing temporal persistence in the deviation of an individual's delinquency level from the population mean.

A 'How to' guide for interpreting parameters in habitat-selection analyses

Habitat‐selection analyses allow researchers to link animals to their environment via habitat‐selection or step‐selection functions, and are commonly used to address questions related to wildlife management and conservation efforts. Habitat‐selection analyses that incorporate movement characteristics, referred to as integrated step‐selection analyses, are particularly appealing because they allow modelling of both movement and habitat‐selection processes.

Despite their popularity, many users struggle with interpreting parameters in habitat‐selection and step‐selection functions. Integrated step‐selection analyses also require several additional steps to translate model parameters into a full‐fledged movement model, and the mathematics supporting this approach can be challenging for many to understand.

Using simple examples, we demonstrate how weighted distribution theory and the inhomogeneous Poisson point process can facilitate parameter interpretation in habitat‐selection analyses. Furthermore, we provide a ‘how to’ guide illustrating the steps required to implement integrated step‐selection analyses using the amt package

By providing clear examples with open‐source code, we hope to make habitat‐selection analyses more understandable and accessible to end users.