When to be discrete: the importance of time formulation in understanding animal movement

Latent trajectory models for spatio-temporal dynamics in Alaskan ecosystems

The Alaskan landscape has undergone substantial changes in recent decades, most notably the expansion of shrubs and trees across the Arctic. We developed a Bayesian hierarchical model to quantify the impact of climate change on the structural transformation of ecosystems using remotely sensed imagery. We used latent trajectory processes to model dynamic state probabilities that evolve annually, from which we derived transition probabilities between ecotypes. Our latent trajectory model accommodates temporal irregularity in survey intervals and uses spatio-temporally heterogeneous climate drivers to infer rates of land cover transitions. We characterized multi-scale spatial correlation induced by plot and subplot arrangements in our study system. We also developed a Pólya-Gamma sampling strategy to improve computation. Our model facilitates inference on the response of ecosystems to shifts in the climate and can be used to predict future land cover transitions under various climate scenarios.

Crabs ride the tide: incoming tides promote foraging of Giant Mud Crab (Scylla serrata)

BACKGROUND

Effective fisheries management of mobile species relies on robust knowledge of animal behaviour and habitat-use. Indices of behaviour can be useful for interpreting catch-per-unit-effort data which acts as a proxy for relative abundance. Information about habitat-use can inform stocking release strategies or the design of marine protected areas. The Giant Mud Crab (Scylla serrata; Family: Portunidae) is a swimming estuarine crab that supports significant fisheries harvest throughout the Indo-West Pacific, but little is known about the fine-scale movement and behaviour of this species.

METHODS

We tagged 18 adult Giant Mud Crab with accelerometer-equipped acoustic tags to track their fine-scale movement using a hyperbolic positioning system, alongside high temporal resolution environmental data (e.g., water temperature), in a temperate south-east Australian estuary. A hidden Markov model was used to classify movement (i.e., step length, turning angle) and acceleration data into discrete behaviours, while also considering the possibility of individual variation in behavioural dynamics. We then investigated the influence of environmental covariates on these behaviours based on previously published observations.

RESULTS

We fitted a model with two well-distinguished behavioural states describing periods of inactivity and foraging, and found no evidence of individual variation in behavioural dynamics. Inactive periods were most common (79% of time), and foraging was most likely during low, incoming tides; while inactivity was more likely as the high tide receded. Model selection removed time (hour) of day and water temperature (°C) as covariates, suggesting that they do not influence Giant Mud Crab behavioural dynamics at the temporal scale investigated.

CONCLUSIONS

Our study is the first to quantitatively link fine-scale movement and behaviour of Giant Mud Crab to environmental variation. Our results suggest Giant Mud Crab are a predominantly sessile species, and support their status as an opportunistic scavenger. We demonstrate a relationship between the tidal cycle and foraging that is likely to minimize predation risk while maximizing energetic efficiency. These results may explain why tidal covariates influence catch rates in swimming crabs, and provide a foundation for standardisation and interpretation of catch-per-unit-effort data-a commonly used metric in fisheries science.

Categorizing the geometry of animal diel movement patterns with examples from high-resolution barn owl tracking

BACKGROUND

Movement is central to understanding the ecology of animals. The most robustly definable segments of an individual's lifetime track are its diel activity routines (DARs). This robustness is due to fixed start and end points set by a 24-h clock that depends on the individual's quotidian schedule. An analysis of day-to-day variation in the DARs of individuals, their comparisons among individuals, and the questions that can be asked, particularly in the context of lunar and annual cycles, depends on the relocation frequency and spatial accuracy of movement data. Here we present methods for categorizing the geometry of DARs for high frequency (seconds to minutes) movement data.

METHODS

Our method involves an initial categorization of DARs using data pooled across all individuals. We approached this categorization using a Ward clustering algorithm that employs four scalar "whole-path metrics" of trajectory geometry: 1. net displacement (distance between start and end points), 2. maximum displacement from start point, 3. maximum diameter, and 4. maximum width. We illustrate the general approach using reverse-GPS data obtained from 44 barn owls, Tyto alba, in north-eastern Israel. We conducted a principle components analysis (PCA) to obtain a factor, PC1, that essentially captures the scale of movement. We then used a generalized linear mixed model with PC1 as the dependent variable to assess the effects of age and sex on movement.

RESULTS

We clustered 6230 individual DARs into 7 categories representing different shapes and scale of the owls nightly routines. Five categories based on size and elongation were classified as closed (i.e. returning to the same roost), one as partially open (returning to a nearby roost) and one as fully open (leaving for another region). Our PCA revealed that the DAR scale factor, PC1, accounted for 86.5% of the existing variation. It also showed that PC2 captures the openness of the DAR and accounted for another 8.4% of the variation. We also constructed spatio-temporal distributions of DAR types for individuals and groups of individuals aggregated by age, sex, and seasonal quadrimester, as well as identify some idiosyncratic behavior of individuals within family groups in relation to location. Finally, we showed in two ways that DARs were significantly larger in young than adults and in males than females.

CONCLUSION

Our study offers a new method for using high-frequency movement data to classify animal diel movement routines. Insights into the types and distributions of the geometric shape and size of DARs in populations may well prove to be more invaluable for predicting the space-use response of individuals and populations to climate and land-use changes than other currently used movement track methods of analysis.

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.

Altered Larval Yellow Perch Swimming Behavior Due to Methylmercury and PCB126 Detected Using Hidden Markov Chain Models

Fish swimming behavior is a commonly measured response in aquatic ecotoxicology because behavior is considered a whole organism-level effect that integrates many sensory systems. Recent advancements in animal behavior models, such as hidden Markov chain models (HMM), suggest an improved analytical approach for toxicology. Using both new and traditional approaches, we examined the sublethal effects of PCB126 and methylmercury on yellow perch (YP) larvae (Perca flavescens) using three doses. Both approaches indicate larvae increase activity after exposure to either chemical. The middle methylmercury-dosed larvae showed multiple altered behavior patterns. First, larvae had a general increase in activity, typically performing more behavior states, more time swimming, and more swimming bouts per second. Second, when larvae were in a slow or medium swimming state, these larvae tended to switch between these states more often. Third, larvae swam slower during the swimming bouts. The upper PCB126-dosed larvae exhibited a higher proportion and a fast swimming state, but the total time spent swimming fast decreased. The middle PCB126-dosed larvae transitioned from fast to slow swimming states less often than the control larvae. These results indicate that developmental exposure to very low doses of these neurotoxicants alters YP larvae overall swimming behaviors, suggesting neurodevelopment alteration.

Circular‐Linear Copulae for Animal Movement Data

Animal movement is often modelled in discrete time, formulated in terms of steps taken between successive locations at regular time intervals. Steps are characterized by the distance between successive locations (step lengths) and changes in direction (turn angles). Animals commonly exhibit a mix of directed movements with large step lengths and turn angles near 0 when travelling between habitat patches and more wandering movements with small step lengths and uniform turn angles when foraging. Thus, step lengths and turn angles will typically be cross‐correlated.

Most models of animal movement assume that step lengths and turn angles are independent, likely due to a lack of available alternatives. Here, we show how the method of copulae can be used to fit multivariate distributions that allow for correlated step lengths and turn angles.

We describe several newly developed copulae appropriate for modelling animal movement data and fit these distributions to data collected on fishers (Pekania pennanti). The copulae are able to capture the inherent correlation in the data and provide a better fit than a model that assumes independence. Further, we demonstrate via simulation that this correlation can impact movement patterns (e.g. rates of dispersion overtime).

We see many opportunities to extend this framework (e.g. to consider autocorrelation in step attributes) and to integrate it into existing frameworks for modelling animal movement and habitat selection. For example, copulae could be used to more accurately sample available locations when conducting habitat‐selection analyses.

Smoothing splines of apex predator movement: Functional modeling strategies for exploring animal behavior and social interactions

The collection of animal position data via GPS tracking devices has increased in quality and usage in recent years. Animal position and movement, although measured discretely, follows the same principles of kinematic motion, and as such, the process is inherently continuous and differentiable. I demonstrate the functionality and visual elegance of smoothing spline models. I discuss the challenges and benefits of implementing such an approach, and I provide an analysis of movement and social interaction of seven jaguars inhabiting the Taiamã Ecological Station, Pantanal, Brazil, a region with the highest known density of jaguars. In the analysis, I derive measures for pairwise distance, cooccurrence, and spatiotemporal association between jaguars, borrowing ideas from density estimation and information theory. These measures are feasible as a result of spline model estimation, and they provide a critical tool for a deeper investigation of cooccurrence duration, frequency, and localized spatio-temporal relationships between animals. In this work, I characterize a variety of interactive relationships between pairs of jaguars, and I particularly emphasize the relationships in movement of two male-female and two male-male jaguar pairs exhibiting highly associative relationships.

A random walk model that accounts for space occupation and movements of a large herbivore

Animal movement has been identified as a key feature in understanding animal behavior, distribution and habitat use and foraging strategies among others. Large datasets of invididual locations often remain unused or used only in part due to the lack of practical models that can directly infer the desired features from raw GPS locations and the complexity of existing approaches. Some of them being disputed for their lack of biological justifications in their design. We propose a simple model of individual movement with explicit parameters, based on a two-dimensional biased and correlated random walk with three forces related to advection (correlation), attraction (bias) and immobility of the animal. These forces can be directly estimated using individual data. We demonstrate the approach by using GPS data of 5 red deer with a high frequency sampling. The results show that a simple random walk template can account for the spatial complexity of wild animals. The practical design of the model is also verified for detecting spatial feature abnormalities and for providing estimates of density and abundance of wild animals. Integrating even more additional features of animal movement, such as individuals’ interactions or environmental repellents, could help to better understand the spatial behavior of wild animals.

Combining Regional Habitat Selection Models for Large-Scale Prediction: Circumpolar Habitat Selection of Southern Ocean Humpback Whales

Machine learning algorithms are often used to model and predict animal habitat selection—the relationships between animal occurrences and habitat characteristics. For broadly distributed species, habitat selection often varies among populations and regions; thus, it would seem preferable to fit region- or population-specific models of habitat selection for more accurate inference and prediction, rather than fitting large-scale models using pooled data. However, where the aim is to make range-wide predictions, including areas for which there are no existing data or models of habitat selection, how can regional models best be combined? We propose that ensemble approaches commonly used to combine different algorithms for a single region can be reframed, treating regional habitat selection models as the candidate models. By doing so, we can incorporate regional variation when fitting predictive models of animal habitat selection across large ranges. We test this approach using satellite telemetry data from 168 humpback whales across five geographic regions in the Southern Ocean. Using random forests, we fitted a large-scale model relating humpback whale locations, versus background locations, to 10 environmental covariates, and made a circumpolar prediction of humpback whale habitat selection. We also fitted five regional models, the predictions of which we used as input features for four ensemble approaches: an unweighted ensemble, an ensemble weighted by environmental similarity in each cell, stacked generalization, and a hybrid approach wherein the environmental covariates and regional predictions were used as input features in a new model. We tested the predictive performance of these approaches on an independent validation dataset of humpback whale sightings and whaling catches. These multiregional ensemble approaches resulted in models with higher predictive performance than the circumpolar naive model. These approaches can be used to incorporate regional variation in animal habitat selection when fitting range-wide predictive models using machine learning algorithms. This can yield more accurate predictions across regions or populations of animals that may show variation in habitat selection.

Analysis of local habitat selection and large-scale attraction/avoidance based on animal tracking data: is there a single best method?

BACKGROUND

New wildlife telemetry and tracking technologies have become available in the last decade, leading to a large increase in the volume and resolution of animal tracking data. These technical developments have been accompanied by various statistical tools aimed at analysing the data obtained by these methods.

METHODS

We used simulated habitat and tracking data to compare some of the different statistical methods frequently used to infer local resource selection and large-scale attraction/avoidance from tracking data. Notably, we compared spatial logistic regression models (SLRMs), spatio-temporal point process models (ST-PPMs), step selection models (SSMs), and integrated step selection models (iSSMs) and their interplay with habitat and animal movement properties in terms of statistical hypothesis testing.

RESULTS

We demonstrated that only iSSMs and ST-PPMs showed nominal type I error rates in all studied cases, whereas SSMs may slightly and SLRMs may frequently and strongly exceed these levels. iSSMs appeared to have on average a more robust and higher statistical power than ST-PPMs.

CONCLUSIONS

Based on our results, we recommend the use of iSSMs to infer habitat selection or large-scale attraction/avoidance from animal tracking data. Further advantages over other approaches include short computation times, predictive capacity, and the possibility of deriving mechanistic movement models.

Analysing detection gaps in acoustic telemetry data to infer differential movement patterns in fish

A wide array of technologies are available for gaining insight into the movement of wild aquatic animals. Although acoustic telemetry can lack the fine-scale spatial resolution of some satellite tracking technologies, the substantially longer battery life can yield important long-term data on individual behavior and movement for low per-unit cost. Typically, however, receiver arrays are designed to maximize spatial coverage at the cost of positional accuracy leading to potentially longer detection gaps as individuals move out of range between monitored locations. This is particularly true when these technologies are deployed to monitor species in hard-to-access locations.Here, we develop a novel approach to analyzing acoustic telemetry data, using the timing and duration of gaps between animal detections to infer different behaviors. Using the durations between detections at the same and different receiver locations (i.e., detection gaps), we classify behaviors into "restricted" or potential wider "out-of-range" movements synonymous with longer distance dispersal. We apply this method to investigate spatial and temporal segregation of inferred movement patterns in two sympatric species of reef shark within a large, remote, marine protected area (MPA). Response variables were generated using network analysis, and drivers of these movements were identified using generalized linear mixed models and multimodel inference.Species, diel period, and season were significant predictors of "out-of-range" movements. Silvertip sharks were overall more likely to undertake "out-of-range" movements, compared with gray reef sharks, indicating spatial segregation, and corroborating previous stable isotope work between these two species. High individual variability in "out-of-range" movements in both species was also identified.We present a novel gap analysis of telemetry data to help infer differential movement and space use patterns where acoustic coverage is imperfect and other tracking methods are impractical at scale. In remote locations, inference may be the best available tool and this approach shows that acoustic telemetry gap analysis can be used for comparative studies in fish ecology, or combined with other research techniques to better understand functional mechanisms driving behavior.

A hierarchical machine learning framework for the analysis of large scale animal movement data

BACKGROUND

In recent years the field of movement ecology has been revolutionized by our ability to collect high-accuracy, fine scale telemetry data from individual animals and groups. This growth in our data collection capacity has led to the development of statistical techniques that integrate telemetry data with random walk models to infer key parameters of the movement dynamics. While much progress has been made in the use of these models, several challenges remain. Notably robust and scalable methods are required for quantifying parameter uncertainty, coping with intermittent location fixes, and analysing the very large volumes of data being generated.

METHODS

In this work we implement a novel approach to movement modelling through the use of multilevel Gaussian processes. The hierarchical structure of the method enables the inference of continuous latent behavioural states underlying movement processes. For efficient inference on large data sets, we approximate the full likelihood using trajectory segmentation and sample from posterior distributions using gradient-based Markov chain Monte Carlo methods.

RESULTS

While formally equivalent to many continuous-time movement models, our Gaussian process approach provides flexible, powerful models that can detect multiscale patterns and trends in movement trajectory data. We illustrate a further advantage to our approach in that inference can be performed using highly efficient, GPU-accelerated machine learning libraries.

CONCLUSIONS

Multilevel Gaussian process models offer efficient inference for large-volume movement data sets, along with the fitting of complex flexible models. Applications of this approach include inferring the mean location of a migration route and quantifying significant changes, detecting diurnal activity patterns, or identifying the onset of directed persistent movements.

Inferring an animal's environment through biologging: quantifying the environmental influence on animal movement

BACKGROUND

Animals respond to environmental variation by changing their movement in a multifaceted way. Recent advancements in biologging increasingly allow for detailed measurements of the multifaceted nature of movement, from descriptors of animal movement trajectories (e.g., using GPS) to descriptors of body part movements (e.g., using tri-axial accelerometers). Because this multivariate richness of movement data complicates inference on the environmental influence on animal movement, studies generally use simplified movement descriptors in statistical analyses. However, doing so limits the inference on the environmental influence on movement, as this requires that the multivariate richness of movement data can be fully considered in an analysis.

METHODS

We propose a data-driven analytic framework, based on existing methods, to quantify the environmental influence on animal movement that can accommodate the multifaceted nature of animal movement. Instead of fitting a simplified movement descriptor to a suite of environmental variables, our proposed framework centres on predicting an environmental variable from the full set of multivariate movement data. The measure of fit of this prediction is taken to be the metric that quantifies how much of the environmental variation relates to the multivariate variation in animal movement. We demonstrate the usefulness of this framework through a case study about the influence of grass availability and time since milking on cow movements using machine learning algorithms.

RESULTS

We show that on a one-hour timescale 37% of the variation in grass availability and 33% of time since milking influenced cow movements. Grass availability mostly influenced the cows' neck movement during grazing, while time since milking mostly influenced the movement through the landscape and the shared variation of accelerometer and GPS data (e.g., activity patterns). Furthermore, this framework proved to be insensitive to spurious correlations between environmental variables in quantifying the influence on animal movement.

CONCLUSIONS

Not only is our proposed framework well-suited to study the environmental influence on animal movement; we argue that it can also be applied in any field that uses multivariate biologging data, e.g., animal physiology, to study the relationships between animals and their environment.

SUPPLEMENTARY INFORMATION

Supplementary information accompanies this paper at 10.1186/s40462-020-00228-4.

ACCOUNTING FOR DEPENDENT ERRORS IN PREDICTORS AND TIME-TO-EVENT OUTCOMES USING ELECTRONIC HEALTH RECORDS, VALIDATION SAMPLES, AND MULTIPLE IMPUTATION

Data from electronic health records (EHR) are prone to errors, which are often correlated across multiple variables. The error structure is further complicated when analysis variables are derived as functions of two or more error-prone variables. Such errors can substantially impact estimates, yet we are unaware of methods that simultaneously account for errors in covariates and time-to-event outcomes. Using EHR data from 4217 patients, the hazard ratio for an AIDS-defining event associated with a 100 cell/mm3 increase in CD4 count at ART initiation was 0.74 (95%CI: 0.68-0.80) using unvalidated data and 0.60 (95%CI: 0.53-0.68) using fully validated data. Our goal is to obtain unbiased and efficient estimates after validating a random subset of records. We propose fitting discrete failure time models to the validated subsample and then multiply imputing values for unvalidated records. We demonstrate how this approach simultaneously addresses dependent errors in predictors, time-to-event outcomes, and inclusion criteria. Using the fully validated dataset as a gold standard, we compare the mean squared error of our estimates with those from the unvalidated dataset and the corresponding subsample-only dataset for various subsample sizes. By incorporating reasonably sized validated subsamples and appropriate imputation models, our approach had improved estimation over both the naive analysis and the analysis using only the validation subsample.

Using approximate Bayesian inference for a "steps and turns" continuous-time random walk observed at regular time intervals

The study of animal movement is challenging because movement is a process modulated by many factors acting at different spatial and temporal scales. In order to describe and analyse animal movement, several models have been proposed which differ primarily in the temporal conceptualization, namely continuous and discrete time formulations. Naturally, animal movement occurs in continuous time but we tend to observe it at fixed time intervals. To account for the temporal mismatch between observations and movement decisions, we used a state-space model where movement decisions (steps and turns) are made in continuous time. That is, at any time there is a non-zero probability of making a change in movement direction. The movement process is then observed at regular time intervals. As the likelihood function of this state-space model turned out to be intractable yet simulating data is straightforward, we conduct inference using different variations of Approximate Bayesian Computation (ABC). We explore the applicability of this approach as a function of the discrepancy between the temporal scale of the observations and that of the movement process in a simulation study. Simulation results suggest that the model parameters can be recovered if the observation time scale is moderately close to the average time between changes in movement direction. Good estimates were obtained when the scale of observation was up to five times that of the scale of changes in direction. We demonstrate the application of this model to a trajectory of a sheep that was reconstructed in high resolution using information from magnetometer and GPS devices. The state-space model used here allowed us to connect the scales of the observations and movement decisions in an intuitive and easy to interpret way. Our findings underscore the idea that the time scale at which animal movement decisions are made needs to be considered when designing data collection protocols. In principle, ABC methods allow to make inferences about movement processes defined in continuous time but in terms of easily interpreted steps and turns.

A continuous-time state-space model for rapid quality control of argos locations from animal-borne tags

BACKGROUND

State-space models are important tools for quality control and analysis of error-prone animal movement data. The near real-time (within 24 h) capability of the Argos satellite system can aid dynamic ocean management of human activities by informing when animals enter wind farms, shipping lanes, and other intensive use zones. This capability also facilitates the use of ocean observations from animal-borne sensors in operational ocean forecasting models. Such near real-time data provision requires rapid, reliable quality control to deal with error-prone Argos locations.

METHODS

We formulate a continuous-time state-space model to filter the three types of Argos location data (Least-Squares, Kalman filter, and Kalman smoother), accounting for irregular timing of observations. Our model is deliberately simple to ensure speed and reliability for automated, near real-time quality control of Argos location data. We validate the model by fitting to Argos locations collected from 61 individuals across 7 marine vertebrates and compare model-estimated locations to contemporaneous GPS locations. We then test assumptions that Argos Kalman filter/smoother error ellipses are unbiased, and that Argos Kalman smoother location accuracy cannot be improved by subsequent state-space modelling.

RESULTS

Estimation accuracy varied among species with Root Mean Squared Errors usually <5 km and these decreased with increasing data sampling rate and precision of Argos locations. Including a model parameter to inflate Argos error ellipse sizes in the north - south direction resulted in more accurate location estimates. Finally, in some cases the model appreciably improved the accuracy of the Argos Kalman smoother locations, which should not be possible if the smoother is using all available information.

CONCLUSIONS

Our model provides quality-controlled locations from Argos Least-Squares or Kalman filter data with accuracy similar to or marginally better than Argos Kalman smoother data that are only available via fee-based reprocessing. Simplicity and ease of use make the model suitable both for automated quality control of near real-time Argos data and for manual use by researchers working with historical Argos data.

Generalizing the first-difference correlated random walk for marine animal movement data

Animal telemetry data are often analysed with discrete time movement models. These models are defined with regular time steps. However, telemetry data from marine animals are observed irregularly. To account for irregular data, a time-irregularised first-difference correlated random walk model with drift is introduced. The model generalizes the commonly used first-difference correlated random walk with regular time steps by allowing irregular time steps, including a drift term, and by allowing different autocorrelation in the two coordinates. The model is applied to data from a ringed seal collected through the Argos satellite system, and is compared to related movement models through simulations. Accounting for irregular data in the movement model results in accurate parameter estimates and reconstruction of movement paths. Further, the introduced model can provide more accurate movement paths than the regular time counterpart. Extracting accurate movement paths from uncertain telemetry data is important for evaluating space use patterns for marine animals, which in turn is crucial for management. Further, handling irregular data directly in the movement model allows efficient simultaneous analyses of several animals.

Capturing foraging and resting behavior using nested multivariate Markov models in an air-breathing marine vertebrate

BACKGROUND

Matching animal movement with the behaviors that shape life history requires a rigorous connection between the observed patterns of space use and inferred behavioral states. As animal-borne dataloggers capture a greater diversity and frequency of three dimensional movements, we can increase the complexity of movement models describing animal behavior. One challenge in combining data streams is the different spatial and temporal frequency of observations. Nested movement models provide a flexible framework for gleaning data from long-duration, but temporally sparse, data sources.

RESULTS

Using a two-layer nested model, we combined geographic and vertical movement to infer traveling, foraging and resting behaviors of Humpback whales off the West Antarctic Peninsula. This approach refined previous work using only geographic data to delineate coarser behavioral states. Our results showed increased intensity in foraging activity in late season animals as the whales prepared to migrate north to tropical calving grounds. Our model also suggests strong diel variation in movement states, likely linked to daily changes in prey distribution.

CONCLUSIONS

Using a combination of two-dimensional and three-dimensional movement data, we highlight the connection between whale movement and krill availability, as well as the complex spatial pattern of whale foraging in productive polar waters.

Habitat selection and seasonal movements of young bearded seals (Erignathus barbatus) in the Bering Sea

The first year of life is typically the most critical to a pinniped's survival, especially for Arctic phocids which are weaned at only a few weeks of age and left to locate and capture prey on their own. Their seasonal movements and habitat selection are therefore important factors in their survival. During a cooperative effort between scientists and subsistence hunters in October 2004, 2005, and 2006, 13 female and 13 male young (i.e., age <2) bearded seals (Erignathus barbatus) were tagged with satellite-linked dive recorders (SDRs) in Kotzebue Sound, Alaska. Shortly after being released, most seals moved south with the advancing sea-ice through the Bering Strait and into the Bering Sea where they spent the winter and early spring. The SDRs of 17 (8 female and 9 male) seals provided frequent high-quality positions in the Bering Sea; their data were used in our analysis. To investigate habitat selection, we simulated 20 tracks per seal by randomly selecting from the pooled distributions of the absolute bearings and swim speeds of the tagged seals. For each point in the observed and simulated tracks, we obtained the depth, sea-ice concentration, and the distances to sea-ice, open water, the shelf break and coastline. Using logistic regression with a stepwise model selection procedure, we compared the simulated tracks to those of the tagged seals and obtained a model for describing habitat selection. The regression coefficients indicated that the bearded seals in our study selected locations near the ice edge. In contrast, aerial surveys of the bearded seal population, predominantly composed of adults, indicated higher abundances in areas farther north and in heavier pack ice. We hypothesize that this discrepancy is the result of behavioral differences related to age. Ice concentration was also shown to be a statistically significant variable in our model. All else being equal, areas of higher ice concentration are selected for up to about 80%. The effects of sex and bathymetry were not statistically significant. The close association of young bearded seals to the ice edge in the Bering Sea is important given the likely effects of climate warming on the extent of sea-ice and subsequent changes in ice edge habitat.

Integrating direct observation and GPS tracking to monitor animal behavior for resource management

Monitoring the behavior of pack animals in protected areas informs management about use patterns and the potential associated negative impacts. However, systematic assessments of behavior are uncommon due to methodological and logistical constraints. This study integrated behavior mapping with GPS tracking, and applied behavior change point analysis, as an approach to monitor the behaviors of pack animals during overnight periods. The integrated approach identified multiple grazing patterns (i.e., locally intense grazing, ambulatory grazing) not feasible through a single methodology alone. Monitoring behavior and corresponding environmental conditions aid managers in implementing strategies designed to mitigate impacts associated with pack animals in natural areas. Results also contrast the influence of temporal scale on behavior segmentation to inform decisions for further monitoring and management of domestic animal use and impacts in natural areas. This integrated approach reduced time and logistical constraints of each method individually to promote ongoing monitoring and highlight how multiple management tactics could reduce impacts to sensitive habitats.

A hidden Markov movement model for rapidly identifying behavioral states from animal tracks

Electronic telemetry is frequently used to document animal movement through time. Methods that can identify underlying behaviors driving specific movement patterns can help us understand how and why animals use available space, thereby aiding conservation and management efforts. For aquatic animal tracking data with significant measurement error, a Bayesian state-space model called the first-Difference Correlated Random Walk with Switching (DCRWS) has often been used for this purpose. However, for aquatic animals, highly accurate tracking data are now becoming more common. We developed a new hidden Markov model (HMM) for identifying behavioral states from animal tracks with negligible error, called the hidden Markov movement model (HMMM). We implemented as the basis for the HMMM the process equation of the DCRWS, but we used the method of maximum likelihood and the R package TMB for rapid model fitting. The HMMM was compared to a modified version of the DCRWS for highly accurate tracks, the DCRWSNOME, and to a common HMM for animal tracks fitted with the R package moveHMM. We show that the HMMM is both accurate and suitable for multiple species by fitting it to real tracks from a grey seal, lake trout, and blue shark, as well as to simulated data. The HMMM is a fast and reliable tool for making meaningful inference from animal movement data that is ideally suited for ecologists who want to use the popular DCRWS implementation and have highly accurate tracking data. It additionally provides a groundwork for development of more complex modeling of animal movement with TMB. To facilitate its uptake, we make it available through the R package swim.

Correlated velocity models as a fundamental unit of animal movement: synthesis and applications

BACKGROUND

Continuous time movement models resolve many of the problems with scaling, sampling, and interpretation that affect discrete movement models. They can, however, be challenging to estimate, have been presented in inconsistent ways, and are not widely used.

METHODS

We review the literature on integrated Ornstein-Uhlenbeck velocity models and propose four fundamental correlated velocity movement models (CVM's): random, advective, rotational, and rotational-advective. The models are defined in terms of biologically meaningful speeds and time scales of autocorrelation. We summarize several approaches to estimating the models, and apply these tools for the higher order task of behavioral partitioning via change point analysis.

RESULTS

An array of simulation illustrate the precision and accuracy of the estimation tools. An analysis of a swimming track of a bowhead whale (Balaena mysticetus) illustrates their robustness to irregular and sparse sampling and identifies switches between slower and faster, and directed vs. random movements. An analysis of a short flight of a lesser kestrel (Falco naumanni) identifies exact moments when switches occur between loopy, thermal soaring and directed flapping or gliding flights.

CONCLUSIONS

We provide tools to estimate parameters and perform change point analyses in continuous time movement models as an R package (smoove). These resources, together with the synthesis, should facilitate the wider application and development of correlated velocity models among movement ecologists.

Trackable life: Data, sequence, and organism in movement ecology

Over the past decade an increasing number of ecologists have begun to frame their work as a contribution to the emerging research field of movement ecology. This field's primary object of research is the movement track, which is usually operationalized as a series of discrete "steps and stops" that represent a portion of an animal's "lifetime track." Its practitioners understand their field as dependent on recent technical advances in tracking organisms and analyzing their movements. By making movement their primary object of research, rather than simply an expression of deeper biological phenomena, movement ecologists are able to generalize across the movement patterns of a wide variety of species and to draw on statistical techniques developed to model the movements of non-living things. Although it can trace its roots back to a long tradition of statistical models of movement, the field relies heavily on metaphors from genomics; in particular, movement tracks have been seen as similar to DNA sequences. Though this has helped movement ecology consolidate around a shared understanding of movement, the field may need to broaden its understanding of movement beyond the sequence if it is to realize its potential to address urgent concerns such as biodiversity loss.

Robustness of movement models: can models bridge the gap between temporal scales of data sets and behavioural processes?

Discrete-time random walks and their extensions are common tools for analyzing animal movement data. In these analyses, resolution of temporal discretization is a critical feature. Ideally, a model both mirrors the relevant temporal scale of the biological process of interest and matches the data sampling rate. Challenges arise when resolution of data is too coarse due to technological constraints, or when we wish to extrapolate results or compare results obtained from data with different resolutions. Drawing loosely on the concept of robustness in statistics, we propose a rigorous mathematical framework for studying movement models' robustness against changes in temporal resolution. In this framework, we define varying levels of robustness as formal model properties, focusing on random walk models with spatially-explicit component. With the new framework, we can investigate whether models can validly be applied to data across varying temporal resolutions and how we can account for these different resolutions in statistical inference results. We apply the new framework to movement-based resource selection models, demonstrating both analytical and numerical calculations, as well as a Monte Carlo simulation approach. While exact robustness is rare, the concept of approximate robustness provides a promising new direction for analyzing movement models.