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Background Inertial measurement units (IMUs) with high-resolution sensors such as accelerometers are now used extensively to study fine-scale behavior in a wide range of marine and terrestrial animals. Robust and practical methods are required for the computationally-demanding analysis of the resulting large datasets, particularly for automating classification routines that construct behavioral time series and time-activity budgets. Magnetometers are used increasingly to study behavior, but it is not clear how these sensors contribute to the accuracy of behavioral classification methods. Development of effective classification methodology is key to understanding energetic and life-history implications of foraging and other behaviors. Methods We deployed accelerometers and magnetometers on four species of free-ranging albatrosses and evaluated the ability of unsupervised hidden Markov models (HMMs) to identify three major modalities in their behavior: ‘flapping flight’, ‘soaring flight’, and ‘on-water’. The relative contribution of each sensor to classification accuracy was measured by comparing HMM-inferred states with expert classifications identified from stereotypic patterns observed in sensor data. Results HMMs provided a flexible and easily interpretable means of classifying behavior from sensor data. Model accuracy was high overall (92%), but varied across behavioral states (87.6, 93.1 and 91.7% for ‘flapping flight’, ‘soaring flight’ and ‘on-water’, respectively). Models built on accelerometer data alone were as accurate as those that also included magnetometer data; however, the latter were useful for investigating slow and periodic behaviors such as dynamic soaring at a fine scale. Conclusions The use of IMUs in behavioral studies produces large data sets, necessitating the development of computationally-efficient methods to automate behavioral classification in order to synthesize and interpret underlying patterns. HMMs provide an accessible and robust framework for analyzing complex IMU datasets and comparing behavioral variation among taxa across habitats, time and space., Movement Ecology, 9 (1), ISSN:2051-3933

We acknowledge funding from Mitacs Canada, the Canadian Association of Zoos and Aquariums, Canadian Wildlife Federation, Environment and Climate Change Canada, Hauser Bears, Natural Sciences and Engineering Research Council of Canada, Polar Bears International, Polar Continental Shelf Project, Quark Expeditions, United States Department of the Interior (Bureau of Ocean Energy Management), and World Wildlife Fund Canada. 1. The energetic gains from foraging and costs of movement are expected to be key drivers of animal decision-making, as their balance is a large determinant of body condition and survival. This fundamental perspective is often missing from habitat selection studies, which mainly describe correlations between space use and environmental features, rather than the mechanisms behind these correlations. 2. To address this gap, we present a novel parameterisation of step selection functions (SSFs), that we term the energy selection function (ESF). In this model, the likelihood of an animal selecting a movement step depends directly on the corresponding energetic gains and costs, and we can therefore assess how moving animals choose habitat based on energetic considerations. 3. The ESF retains the mathematical convenience and practicality of other SSFs and can be quickly fitted using standard software. In this article, we outline a workflow, from data gathering to statistical analysis, and use a case study of polar bears Ursus maritimus to demonstrate application of the model. 4. We explain how defining gains and costs at the scale of the movement step allows us to include information about resource distribution, landscape resistance and movement patterns. We further demonstrate this process with a case study of polar bears and show how the parameters can be interpreted in terms of selection for energetic gains and against energetic costs. 5. The ESF is a flexible framework that combines the energetic consequences of both movement and resource selection, thus incorporating a key mechanism into habitat selection analysis. Further, because it is based on familiar habitat selection models, the ESF is widely applicable to any study system where energetic gains and costs can be derived, and has immense potential for methodological extensions. Postprint

Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomenon of interest, and their parameters often have a clear interpretation. These advantages come at the cost of requiring a relatively simple model specification. We propose a flexible model for SDEs with time-varying dynamics where the parameters of the process are nonparametric functions of covariates, similar to generalized additive models. Combining the SDE and nonparametric approaches allows for the SDE to capture more detailed, non-stationary, features of the data-generating process. We present a computationally efficient method of approximate inference, where the SDE parameters can vary according to fixed covariate effects, random effects, or basis-penalty smoothing splines. We demonstrate the versatility and utility of this approach with three applications in ecology, where there is often a modelling trade-off between interpretability and flexibility.Supplementary materials accompanying this paper appear online.

1. Energetics are a key driver of animal decision-making, as survival depends on the balance between foraging benefits and movement costs. This fundamental perspective is often missing from habitat selection studies, which mainly describe correlations between space use and environmental features, rather than the mechanisms behind these correlations. To address this gap, we present a new modelling framework, the energy selection function (ESF), to assess how moving animals choose habitat based on energetic considerations. 2. The ESF considers that the likelihood of an animal selecting a movement step depends directly on the corresponding energetic gains and costs. The parameters of the ESF measure selection for energetic gains and against energetic costs; when estimated jointly, these provide inferences about foraging and movement strategies. The ESF can be implemented easily with standard conditional logistic regression software, allowing for fast inference. We outline a workflow, from data-gathering to statistical analysis, and use a case study of polar bears (Ursus maritimus) as an illustrative example. 3. We show how defining gains and costs at the scale of the movement step allows us to include detailed information about resource distribution, landscape resistance, and movement patterns. We demonstrate this in the polar bear case study, in which the results show how cost-minimization may arise in species that inhabit environments with an unpredictable distribution of energetic gains. 4. The ESF combines the energetic consequences of both movement and resource selection, thus incorporating a key aspect of evolutionary behaviour into habitat selection analysis. Because of its close links to existing habitat selection models, the ESF is widely applicable to any study system where energetic gains and costs can be derived, and has immense potential for methodological extensions.

Energetics are a key driver of animal decision-making, as survival depends on the balance between foraging benefits and movement costs. This fundamental perspective is often missing from habitat selection studies, which mainly describe simple correlations between space use and environmental features. To address this gap, we present a new model, the energy selection function (ESF), to assess how moving animals choose habitat based on energetic considerations, thus incorporating a key aspect of evolutionary behaviour into habitat selection analysis. We outline a workflow, from data-gathering to statistical analysis, and demonstrate the model’s utility with a case study of polar bears. Our findings show how cost-minimization may arise in species that inhabit environments with an unpredictable distribution of energetic gains. Because of its close links to existing habitat selection models, the ESF is widely applicable to any study system where energetics can be derived, and has immense potential for methodological extensions.

Funding for this work was provided by the NOAA Saltonstall-Kennedy Program (#NA17NMF4270204). Fate assignment is crucial to the results of survival studies, particularly those that utilize acoustic tagging. Most current methodologies are at least partially subjective; thus, having a means of objectively assigning fates would improve the precision, accuracy, and utility of such studies. We released 57 acoustically tagged fish belonging to six deepwater grouper species off North Carolina, USA, via surface release and recompressed release with descender devices. We applied a three‐state hidden Markov model (HMM) in a novel way: to distinguish movement patterns between fish that were alive and fish that were dead (and might have been eaten by predators). We assigned fates using two approaches that differed in their reliance on HMMs. When HMMs were the predominant source of fate assignment, we estimated survival of 40 deepwater groupers released with descender devices at the continental shelf break (66–120‐m depth) to be 0.46 (95% CI = 0.33–0.65). When a combination of HMMs and prior information was utilized, we estimated survival of the same 40 groupers to be 0.61 (95% CI = 0.47–0.80). Both estimates represented a substantial improvement over the survival of surface‐released groupers (n = 9; survival ~0.0). Furthermore, HMMs estimated zero survival for an additional five descended groupers at a wreck site in 240‐m depth, although one analysis using prior information suggested that survival was possible in that depth. These estimates were aided by the objectivity of HMMs, and we recommend that future survival studies involving acoustic tagging employ similar methodologies. The improved survival of groupers after descending is an important finding for management, as this taxon contains several species of impaired stock status or fishery status. Postprint

Background Tackling behavioural questions often requires identifying points in space and time where animals make decisions and linking these to environmental variables. State-space modeling is useful for analysing movement trajectories, particularly with hidden Markov models (HMM). Yet importantly, the ontogeny of underlying (unobservable) behavioural states revealed by the HMMs has rarely been verified in the field. Methods Using hidden Markov models of individual movement from animal location, biotelemetry, and environmental data, we explored multistate behaviour and the effect of associated intrinsic and extrinsic drivers across life stages. We also decomposed the activity budgets of different movement states at two general and caching phases. The latter - defined as the period following a kill which likely involves the caching of uneaten prey - was subsequently confirmed by field inspections. We applied this method to GPS relocation data of a caching predator, Persian leopard Panthera pardus saxicolor in northeastern Iran. Results Multistate modeling provided strong evidence for an effect of life stage on the behavioural states and their associated time budget. Although environmental covariates (ambient temperature and diel period) and ecological outcomes (predation) affected behavioural states in non-resident leopards, the response in resident leopards was not clear, except that temporal patterns were consistent with a crepuscular and nocturnal movement pattern. Resident leopards adopt an energetically more costly mobile behaviour for most of their time while non-residents shift their behavioural states from high energetic expenditure states to energetically less costly encamped behaviour for most of their time, which is likely to be a risk avoidance strategy against conspecifics or humans. Conclusions This study demonstrates that plasticity in predator behaviour depending on life stage may tackle a trade-off between successful predation and avoiding the risks associated with conspecifics, human presence and maintaining home range. Range residency in territorial predators is energetically demanding and can outweigh the predator’s response to intrinsic and extrinsic variables such as thermoregulation or foraging needs. Our approach provides an insight into spatial behavior and decision making of leopards, and other large felids in rugged landscapes through the application of the HMMs in movement ecology.

This work was supported by the Marine Fisheries Initiative program of the U.S. National Marine Fisheries Service. Movement is a central feature of the ecology of fish, yet the study of fish movement has been inhibited due to its multidimensional nature and technological and analytical limitations. We used a relatively new fine-scale acoustic tracking system to quantify movements of an economically valuable, demersal marine fish species (gray triggerfish Balistes capriscus) on a natural hardbottom reef on the continental shelf of North Carolina, USA. Overall, 30 fish were tagged and released, and 104,170 highly precise (-1–3 m) spatial positions were estimated during the 43-d study. To quantify gray triggerfish movements, we used a combination of exploratory data analyses and hidden Markov models (HMM), the latter of which can identify and elucidate normally hidden behavioral states. Both methods suggested gray triggerfish movements varied by diel period and among individuals, and that some of the variation among individuals could be explained by fish size. Depending on model specification, HMMs identified two or three behavioral states, one of which was likely resting that occurred mostly at night and another was likely foraging or transit that occurred mostly during the day. Moreover, resting at night occurred in small, discrete patches within the study area, whereas foraging or transit behaviors occurred broadly throughout the study area. We encourage a wider use of acoustic telemetry and HMMs to shed light on the normally hidden behaviors of demersal fishes. Postprint

The detection and characterization of chemical adducts on proteins is of increasing interest. Here, we described a step-by-step procedure to identify unknown chemical adduct modifications on proteins resulting from the interaction with a given reactive compound. The protocol can be divided into two equally important parts: (1) the wet laboratory work, to produce high quality mass spectrometry (MS) data of in vitro modified proteins and (2) the dry laboratory work, to analyze the generated MS data and provide highly confident qualitative and quantitative results on the chemical composition and amino acid localization of adducts. This protocol is applicable to the study of any pharmaceutical or chemical compound forming covalent protein adducts, detectable in LC-MS/MS experiments.

TM was supported by the Centre for Advanced Biological Modelling at the University of Sheffield, funded by the Leverhulme Trust, award number DS-2014-081. 1. The utilisation distribution of an animal describes the relative probability of space use. It is natural to think of it as the long-term consequence of the animal's short-term movement decisions: it is the accumulation of small displacements which, over time, gives rise to global patterns of space use. However, many estimation methods for the utilisation distribution either assume the independence of observed locations and ignore the underlying movement (e.g. kernel density estimation), or are based on simple Brownian motion movement rules (e.g. Brownian bridges). 2. We introduce a new continuous-time model of animal movement, based on the Langevin diffusion. This stochastic process has an explicit stationary distribution, conceptually analogous to the idea of the utilisation distribution, and thus provides an intuitive framework to integrate movement and space use. We model the stationary (utilisation) distribution with a resource selection function to link the movement to spatial covariates, and allow inference about habitat preferences of animals. 3. Standard approximation techniques can be used to derive the pseudo-likelihood of the Langevin diffusion movement model, and to estimate habitat preference and movement parameters from tracking data. We investigate the performance of the method on simulated data, and discuss its sensitivity to the time scale of the sampling. We present an example of its application to tracking data of Steller sea lions (Eumetopias jubatus). 4. Due to its continuous-time formulation, this method can be applied to irregular telemetry data. The movement model is specified using a habitat-dependent utilisation distribution, and it provides a rigorous framework to estimate long-term habitat selection from correlated movement data. The Langevin movement model can be approximated by linear model, which allows for very fast inference. Standard tools such as residuals can be used for model checking. Postprint

The two dominant approaches for the analysis of species-habitat associations in animals have been shown to reach divergent conclusions. Models fitted from the viewpoint of an individual (step selection functions), once scaled up, do not agree with models fitted from a population viewpoint (resource selection functions). We explain this fundamental incompatibility, and propose a solution by introducing to the animal movement field a novel use for the well-known family of Markov chain Monte Carlo (MCMC) algorithms. By design, the step selection rules of MCMC lead to a steady-state distribution that coincides with a given underlying function: the target distribution. We therefore propose an analogy between the movements of an animal and the movements of a MCMC sampler, to guarantee convergence of the step selection rules to the parameters underlying the population's utilisation distribution. We introduce a rejection-free MCMC algorithm, the local Gibbs sampler, that better resembles real animal movement, and discuss the wide range of biological assumptions that it can accommodate. We illustrate our method with simulations on a known utilisation distribution, and show theoretically and empirically that locations simulated from the local Gibbs sampler give rise to the correct resource selection function. Using simulated data, we demonstrate how this framework can be used to estimate resource selection and movement parameters.

Summary Due to the substantial progress in tracking technology, recent years have seen an explosion in the amount of movement data being collected. This has led to a huge demand for statistical tools that allow ecologists to draw meaningful inference from large tracking data sets. The class of hidden Markov models (HMMs) matches the intuitive understanding that animal movement is driven by underlying behavioural modes and has proven to be very useful for analysing movement data. For data that involve a regular sampling unit and negligible measurement error, these models usually are sufficiently flexible to capture the complex correlation structure found in movement data, yet are computationally inexpensive compared to alternative methods. The R package moveHMM allows ecologists to process GPS tracking data into series of step lengths and turning angles, and to fit an HMM to these data, allowing, in particular, for the incorporation of environmental covariates. The package includes assessment and visualization tools for the fitted model. We illustrate the use of moveHMM using (simulated) movement of the legendary wild haggis Haggis scoticus. Our findings illustrate the role our software, and movement modelling in general, can play in conservation and management by illuminating environmental constraints.

This work was funded by the Natural Environment Research Council and the Department for Business, Energy and Industrial Strategy. The development of foraging strategies that enable juveniles to efficiently identify and exploit predictable habitat features is critical for survival and long-term fitness. In the marine environment, meso- and sub-mesoscale features such as oceanographic fronts offer a visible cue to enhanced foraging conditions, but how individuals learn to identify these features is a mystery. In this study, we investigate age-related differences in the fine-scale foraging behaviour of adult (aged ≥ 5 years) and immature (aged 2-4 years) northern gannets Morus bassanus. Using high-resolution GPS-loggers, we reveal that adults have a much narrower foraging distribution than immature birds and much higher individual foraging site fidelity. By conditioning the transition probabilities of a hidden Markov model on satellite-derived measures of frontal activity, we then demonstrate that adults show a stronger response to frontal activity than immature birds, and are more likely to commence foraging behaviour as frontal intensity increases. Together, these results indicate that adult gannets are more proficient foragers than immatures, supporting the hypothesis that foraging specialisations are learned during individual exploratory behaviour in early life. Such memory-based individual foraging strategies may also explain the extended period of immaturity observed in gannets and many other long-lived species. Publisher PDF

1. Discrete‐time hidden Markov models (HMMs) have become an immensely popular tool for inferring latent animal behaviours from telemetry data. While movement HMMs typically rely solely on location data (e.g. step length and turning angle), auxiliary biotelemetry and environmental data are powerful and readily‐available resources for incorporating much more ecological and behavioural realism. However, complex movement or observation process models often necessitate custom and computationally demanding HMM model‐fitting techniques that are impractical for most practitioners, and there is a paucity of generalized user‐friendly software available for implementing multivariate HMMs of animal movement. 2. Here, we introduce an open‐source R package, momentuHMM, that addresses many of the deficiencies in existing HMM software. Features include: (1) data pre‐processing and visualization; (2) user‐specified probability distributions for an unlimited number of data streams and latent behaviour states; (3) biased and correlated random walk movement models, including dynamic “activity centres” associated with attractive or repulsive forces; (4) user‐specified design matrices and constraints for covariate modelling of parameters using formulas familiar to most R users; (5) multiple imputation methods that account for measurement error and temporally irregular or missing data; (6) seamless integration of spatio‐temporal covariate raster data; (7) cosinor and spline models for cyclical and other complicated patterns; (8) model checking and selection; and (9) simulation. 3. After providing an overview of the main features of the package, we demonstrate some of the capabilities of momentuHMM using real‐world examples. These include models for cyclical movement patterns of African elephants, foraging trips of northern fur seals, loggerhead turtle movements relative to ocean surface currents, and grey seal movements among three activity centres. 4. momentuHMM considerably extends the capabilities of existing HMM software while accounting for common challenges associated with telemetry data. It therefore facilitates more realistic hypothesis‐driven animal movement analyses that have hitherto been largely inaccessible to non‐statisticians. While motivated by telemetry data, the package can be used for analysing any type of data that is amenable to HMMs. Practitioners interested in additional features are encouraged to contact the authors.

We discuss the semiparametric modeling of mark-recapture-recovery data where the temporal and/or individual variation of model parameters is explained via covariates. Typically, in such analyses a fixed (or mixed) effects parametric model is specified for the relationship between the model parameters and the covariates of interest. In this paper, we discuss the modeling of the relationship via the use of penalized splines, to allow for considerably more flexible functional forms. Corresponding models can be fitted via numerical maximum penalized likelihood estimation, employing cross-validation to choose the smoothing parameters in a data-driven way. Our contribution builds on and extends the existing literature, providing a unified inferential framework for semiparametric mark-recapture-recovery models for open populations, where the interest typically lies in the estimation of survival probabilities. The approach is applied to two real datasets, corresponding to gray herons (Ardea cinerea), where we model the survival probability as a function of environmental condition (a time-varying global covariate), and Soay sheep (Ovis aries), where we model the survival probability as a function of individual weight (a time-varying individual-specific covariate). The proposed semiparametric approach is compared to a standard parametric (logistic) regression and new interesting underlying dynamics are observed in both cases.

TM and TP received support from IMBER-CLIOTOP and Macquarie University Safety Net Grant 9201401743. SB was supported under an Australia Research Council Super Science Fellowship. IDJ was supported by a Macquarie Vice-Chancellors Innovation Fellowship. TAP was supported by a CSIRO Julius Career Award and the Villum Foundation. The behavior of colony-based marine predators is the focus of much research globally. Large telemetry and tracking data sets have been collected for this group of animals, and are accompanied by many empirical studies that seek to segment tracks in some useful way, as well as theoretical studies of optimal foraging strategies. However, relatively few studies have detailed statistical methods for inferring behaviors in central place foraging trips. In this paper we describe an approach based on hidden Markov models, which splits foraging trips into segments labeled as "outbound", "search", "forage", and "inbound". By structuring the hidden Markov model transition matrix appropriately, the model naturally handles the sequence of behaviors within a foraging trip. Additionally, by structuring the model in this way, we are able to develop realistic simulations from the fitted model. We demonstrate our approach on data from southern elephant seals (Mirounga leonina) tagged on Kerguelen Island in the Southern Ocean. We discuss the differences between our 4-state model and the widely used 2-state model, and the advantages and disadvantages of employing a more complex model. Publisher PDF

We consider Markov-switching regression models, i.e. models for time series regression analyses where the functional relationship between covariates and response is subject to regime switching controlled by an unobservable Markov chain. Building on the powerful hidden Markov model machinery and the methods for penalized B-splines routinely used in regression analyses, we develop a framework for nonparametrically estimating the functional form of the effect of the covariates in such a regression model, assuming an additive structure of the predictor. The resulting class of Markov-switching generalized additive models is immensely flexible, and contains as special cases the common parametric Markov-switching regression models and also generalized additive and generalized linear models. The feasibility of the suggested maximum penalized likelihood approach is demonstrated by simulation. We further illustrate the approach using two real data applications, modelling (i) how sales data depend on advertising spending and (ii) how energy price in Spain depends on the Euro/Dollar exchange rate. Publisher PDF

Stochastic volatility (SV) models mimic many of the stylized facts attributed to time\ud series of asset returns, while maintaining conceptual simplicity. The commonly made\ud assumption of conditionally normally distributed or Student-t-distributed returns, given\ud the volatility, has however been questioned. In this manuscript, we introduce a novel\ud maximum penalized likelihood approach for estimating the conditional distribution in\ud an SV model in a nonparametric way, thus avoiding any potentially critical assumptions\ud on the shape. The considered framework exploits the strengths both of the powerful\ud hidden Markov model machinery and of penalized B-splines, and constitutes a powerful\ud and flexible alternative to recently developed Bayesian approaches to semiparametric\ud SV modelling. We demonstrate the feasibility of the approach in a simulation study\ud before outlining its potential in applications to three series of returns on stocks and one\ud series of stock index returns.