A bird's-eye view on turbulence: seabird foraging associations with evolving surface flow features.

Understanding physical mechanisms underlying seabird foraging is fundamental to predict responses to coastal change. For instance, turbulence in the water arising from natural or anthropogenic structures can affect foraging opportunities in tidal seas. Yet, identifying ecologically important localized turbulence features (e.g. upwellings approximately 10-100 m) is limited by observational scale, and this knowledge gap is magnified in volatile predators. Here, using a drone-based approach, we present the tracking of surface-foraging terns (143 trajectories belonging to three tern species) and dynamic turbulent surface flow features in synchrony. We thereby provide the earliest evidence that localized turbulence features can present physical foraging cues. Incorporating evolving vorticity and upwelling features within a hidden Markov model, we show that terns were more likely to actively forage as the strength of the underlying vorticity feature increased, while conspicuous upwellings ahead of the flight path presented a strong physical cue to stay in transit behaviour. This clearly encapsulates the importance of prevalent turbulence features as localized foraging cues. Our quantitative approach therefore offers the opportunity to unlock knowledge gaps in seabird sensory and foraging ecology on hitherto unobtainable scales. Finally, it lays the foundation to predict responses to coastal change to inform sustainable ocean development.

Individuality counts: A new comprehensive approach to foraging strategies of a tropical marine predator.

Foraging strategies are of great ecological interest, as they have a strong impact on the fitness of an individual and can affect its ability to cope with a changing environment. Recent studies on foraging strategies show a higher complexity than previously thought due to intraspecific variability. To reliably identify foraging strategies and describe the different foraging niches they allow individual animals to realize, high-resolution multivariate approaches which consider individual variation are required. Here we dive into the foraging strategies of Galápagos sea lions (Zalophus wollebaeki), a tropical predator confronted with substantial annual variation in sea surface temperature. This affects prey abundance, and El Niño events, expected to become more frequent and severe with climate change, are known to have dramatic effects on sea lions. This study used high-resolution measures of depth, GPS position and acceleration collected from 39 lactating sea lion females to analyze their foraging strategies at an unprecedented level of detail using a novel combination of automated broken stick algorithm, hierarchical cluster analysis and individually fitted multivariate hidden Markov models. We found three distinct foraging strategies (pelagic, benthic, and night divers), which differed in their horizontal, vertical and temporal distribution, most likely corresponding to different prey species, and allowed us to formulate hypotheses with regard to adaptive values under different environmental scenarios. We demonstrate the advantages of our multivariate approach and inclusion of individual variation to reliably gain a deeper understanding of the adaptive value and ecological relevance of foraging strategies of marine predators in dynamic environments.

Uncovering ecological state dynamics with hidden Markov models.

Ecological systems can often be characterised by changes among a finite set of underlying states pertaining to individuals, populations, communities or entire ecosystems through time. Owing to the inherent difficulty of empirical field studies, ecological state dynamics operating at any level of this hierarchy can often be unobservable or 'hidden'. Ecologists must therefore often contend with incomplete or indirect observations that are somehow related to these underlying processes. By formally disentangling state and observation processes based on simple yet powerful mathematical properties that can be used to describe many ecological phenomena, hidden Markov models (HMMs) can facilitate inferences about complex system state dynamics that might otherwise be intractable. However, HMMs have only recently begun to gain traction within the broader ecological community. We provide a gentle introduction to HMMs, establish some common terminology, review the immense scope of HMMs for applied ecological research and provide a tutorial on implementation and interpretation. By illustrating how practitioners can use a simple conceptual template to customise HMMs for their specific systems of interest, revealing methodological links between existing applications, and highlighting some practical considerations and limitations of these approaches, our goal is to help establish HMMs as a fundamental inferential tool for ecologists.

Estimation and simulation of foraging trips in land-based marine predators.

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.

An analysis of pilot whale vocalization activity using hidden Markov models.

Vocalizations of cetaceans form a key component of their social interactions. Such vocalization activity is driven by the behavioral states of the whales, which are not directly observable, so that latent-state models are natural candidates for modeling empirical data on vocalizations. In this paper, hidden Markov models are used to analyze calling activity of long-finned pilot whales (Globicephala melas) recorded over three years in the Vestfjord basin off Lofoten, Norway. Baseline models are used to motivate the use of three states, while more complex models are fit to study the influence of covariates on the state-switching dynamics. The analysis demonstrates the potential usefulness of hidden Markov models to concisely yet accurately describe the stochastic patterns found in animal communication data, thereby providing a framework for drawing meaningful biological inference.

Semi-Markov Arnason-Schwarz models.

We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled as a first-order Markov chain, though second-order models have also been proposed and fitted to data. However, low-order Markov models may not accurately represent the underlying biology. For example, specifying a (time-independent) first-order Markov process involves the assumption that the dwell time in each state (i.e., the duration of a stay in a given state) has a geometric distribution, and hence that the modal dwell time is one. Specifying time-dependent or higher-order processes provides additional flexibility, but at the expense of a potentially significant number of additional model parameters. We extend the Arnason-Schwarz model by specifying a semi-Markov model for the state process, where the dwell-time distribution is specified more generally, using, for example, a shifted Poisson or negative binomial distribution. A state expansion technique is applied in order to represent the resulting semi-Markov Arnason-Schwarz model in terms of a simpler and computationally tractable hidden Markov model. Semi-Markov Arnason-Schwarz models come with only a very modest increase in the number of parameters, yet permit a significantly more flexible state process. Model selection can be performed using standard procedures, and in particular via the use of information criteria. The semi-Markov approach allows for important biological inference to be drawn on the underlying state process, for example, on the times spent in the different states. The feasibility of the approach is demonstrated in a simulation study, before being applied to real data corresponding to house finches where the states correspond to the presence or absence of conjunctivitis.

Maximum penalized likelihood estimation in semiparametric mark-recapture-recovery models.

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.

Nonparametric inference in hidden Markov models using P-splines.

Hidden Markov models (HMMs) are flexible time series models in which the distribution of the observations depends on unobserved serially correlated states. The state-dependent distributions in HMMs are usually taken from some class of parametrically specified distributions. The choice of this class can be difficult, and an unfortunate choice can have serious consequences for example on state estimates, and more generally on the resulting model complexity and interpretation. We demonstrate these practical issues in a real data application concerned with vertical speeds of a diving beaked whale, where we demonstrate that parametric approaches can easily lead to overly complex state processes, impeding meaningful biological inference. In contrast, for the dive data, HMMs with nonparametrically estimated state-dependent distributions are much more parsimonious in terms of the number of states and easier to interpret, while fitting the data equally well. Our nonparametric estimation approach is based on the idea of representing the densities of the state-dependent distributions as linear combinations of a large number of standardized B-spline basis functions, imposing a penalty term on non-smoothness in order to maintain a good balance between goodness-of-fit and smoothness.

Combining hidden Markov models for comparing the dynamics of multiple sleep electroencephalograms.

In this manuscript, we consider methods for the analysis of populations of electroencephalogram signals during sleep for the study of sleep disorders using hidden Markov models (HMMs). Notably, we propose an easily implemented method for simultaneously modeling multiple time series that involve large amounts of data. We apply these methods to study sleep-disordered breathing (SDB) in the Sleep Heart Health Study (SHHS), a landmark study of SDB and cardiovascular consequences. We use the entire, longitudinally collected, SHHS cohort to develop HMM population parameters, which we then apply to obtain subject-specific Markovian predictions. From these predictions, we create several indices of interest, such as transition frequencies between latent states. Our HMM analysis of electroencephalogram signals uncovers interesting findings regarding differences in brain activity during sleep between those with and without SDB. These findings include stability of the percent time spent in HMM latent states across matched diseased and non-diseased groups and differences in the rate of transitioning.

Flexible and practical modeling of animal telemetry data: hidden Markov models and extensions.

We discuss hidden Markov-type models for fitting a variety of multistate random walks to wildlife movement data. Discrete-time hidden Markov models (HMMs) achieve considerable computational gains by focusing on observations that are regularly spaced in time, and for which the measurement error is negligible. These conditions are often met, in particular for data related to terrestrial animals, so that a likelihood-based HMM approach is feasible. We describe a number of extensions of HMMs for animal movement modeling, including more flexible state transition models and individual random effects (fitted in a non-Bayesian framework). In particular we consider so-called hidden semi-Markov models, which may substantially improve the goodness of fit and provide important insights into the behavioral state switching dynamics. To showcase the expediency of these methods, we consider an application of a hierarchical hidden semi-Markov model to multiple bison movement paths.

Big-data approaches lead to an increased understanding of the ecology of animal movement.

Understanding animal movement is essential to elucidate how animals interact, survive, and thrive in a changing world. Recent technological advances in data collection and management have transformed our understanding of animal "movement ecology" (the integrated study of organismal movement), creating a big-data discipline that benefits from rapid, cost-effective generation of large amounts of data on movements of animals in the wild. These high-throughput wildlife tracking systems now allow more thorough investigation of variation among individuals and species across space and time, the nature of biological interactions, and behavioral responses to the environment. Movement ecology is rapidly expanding scientific frontiers through large interdisciplinary and collaborative frameworks, providing improved opportunities for conservation and insights into the movements of wild animals, and their causes and consequences.

Reducing vessel noise increases foraging in endangered killer whales.

Disturbance from underwater noise is one of the primary threats to the critically endangered southern resident killer whales (SRKWs). Previous studies have demonstrated that SRKWs spend less time feeding when vessels are present. In 2018, we measured the effects of a voluntary vessel slowdown action in SRKW critical habitat to assess whether ship speed (and related source level) affects foraging behaviour. Observations of SRKWs and ships were collected from land-based sites on San Juan Island, WA, USA, overlooking the Haro Strait slow-down area. Exploratory analyses found little support for a linear relationship between ship speed and SRKW behaviour, but strong support between received noise level from ships and the probability of SRKWs engaging in foraging activity. Reducing ship speed, and therefore ship noise amplitude will help decrease the probability of ship noise disrupting SRKW foraging activity and may help to increase the proportion of accessible salmon.

Movement patterns and activity levels are shaped by the neonatal environment in Antarctic fur seal pups.

Tracking studies of juveniles are rare compared to those of adults, and consequently little is known about the influence of intrinsic and extrinsic factors on activity during this critical life stage. We used hourly GPS data, collected from 66 Antarctic fur seal pups from birth until moulting, to investigate the explanatory power of multiple individual-based and environmental variables on activity levels. Pups were sampled from two nearby breeding colonies of contrasting density during two subsequent years, and a two-state hidden Markov model was used to identify modalities in their movement behaviour, specifically 'active' and 'inactive' states. We found that movement was typified by central place exploration, with active movement away from and subsequent return to a location of inactivity. The probability of such directed exploration was unaffected by several factors known to influence marine mammal movement including sex, body condition, and temperature. Compared to pups born at the high-density colony, pups at low-density were more active, increased their activity with age, and transitioned earlier into the tussock grass, which offers protection from predators and extreme weather. Our study illustrates the importance of extrinsic factors, such as colony of birth, to early-life activity patterns and highlights the adaptive potential of movement.

Performance under pressure in skill tasks: An analysis of professional darts.

Understanding and predicting how individuals perform in high-pressure situations is of importance in designing and managing workplaces. We investigate performance under pressure in professional darts as a near-ideal setting with no direct interaction between players and a high number of observations per subject. Analyzing almost one year of tournament data covering 32,274 dart throws, we find no evidence in favor of either choking or excelling under pressure.

An application of upscaled optimal foraging theory using hidden Markov modelling: year-round behavioural variation in a large arctic herbivore.

BACKGROUND: In highly seasonal environments, animals face critical decisions regarding time allocation, diet optimisation, and habitat use. In the Arctic, the short summers are crucial for replenishing body reserves, while low food availability and increased energetic demands characterise the long winters (9-10 months). Under such extreme seasonal variability, even small deviations from optimal time allocation can markedly impact individuals' condition, reproductive success and survival. We investigated which environmental conditions influenced daily, seasonal, and interannual variation in time allocation in high-arctic muskoxen (Ovibos moschatus) and evaluated whether results support qualitative predictions derived from upscaled optimal foraging theory. METHODS: Using hidden Markov models (HMMs), we inferred behavioural states (foraging, resting, relocating) from hourly positions of GPS-collared females tracked in northeast Greenland (28 muskox-years). To relate behavioural variation to environmental conditions, we considered a wide range of spatially and/or temporally explicit covariates in the HMMs. RESULTS: While we found little interannual variation, daily and seasonal time allocation varied markedly. Scheduling of daily activities was distinct throughout the year except for the period of continuous daylight. During summer, muskoxen spent about 69% of time foraging and 19% resting, without environmental constraints on foraging activity. During winter, time spent foraging decreased to 45%, whereas about 43% of time was spent resting, mediated by longer resting bouts than during summer. CONCLUSIONS: Our results clearly indicate that female muskoxen follow an energy intake maximisation strategy during the arctic summer. During winter, our results were not easily reconcilable with just one dominant foraging strategy. The overall reduction in activity likely reflects higher time requirements for rumination in response to the reduction of forage quality (supporting an energy intake maximisation strategy). However, deep snow and low temperatures were apparent constraints to winter foraging, hence also suggesting attempts to conserve energy (net energy maximisation strategy). Our approach provides new insights into the year-round behavioural strategies of the largest Arctic herbivore and outlines a practical example of how to approximate qualitative predictions of upscaled optimal foraging theory using multi-year GPS tracking data.

Classifying grey seal behaviour in relation to environmental variability and commercial fishing activity - a multivariate hidden Markov model.

Classifying movement behaviour of marine predators in relation to anthropogenic activity and environmental conditions is important to guide marine conservation. We studied the relationship between grey seal (Halichoerus grypus) behaviour and environmental variability in the southwestern Baltic Sea where seal-fishery conflicts are increasing. We used multiple environmental covariates and proximity to active fishing nets within a multivariate hidden Markov model (HMM) to quantify changes in movement behaviour of grey seals while at sea. Dive depth, dive duration, surface duration, horizontal displacement, and turning angle were used to identify travelling, resting and foraging states. The likelihood of seals foraging increased in deeper, colder, more saline waters, which are sites with increased primary productivity and possibly prey densities. Proximity to active fishing net also had a pronounced effect on state occupancy. The probability of seals foraging was highest <5 km from active fishing nets (51%) and decreased as distance to nets increased. However, seals used sites <5 km from active fishing nets only 3% of their time at sea highlighting an important temporal dimension in seal-fishery interactions. By coupling high-resolution oceanographic, fisheries, and grey seal movement data, our study provides a scientific basis for designing management strategies that satisfy ecological and socioeconomic demands on marine ecosystems.

Activity seascapes highlight central place foraging strategies in marine predators that never stop swimming.

BACKGROUND: Central place foragers (CPF) rest within a central place, and theory predicts that distance of patches from this central place sets the outer limits of the foraging arena. Many marine ectothermic predators behave like CPF animals, but never stop swimming, suggesting that predators will incur 'travelling' costs while resting. Currently, it is unknown how these CPF predators behave or how modulation of behavior contributes to daily energy budgets. We combine acoustic telemetry, multi-sensor loggers, and hidden Markov models (HMMs) to generate 'activity seascapes', which combine space use with patterns of activity, for reef sharks (blacktip reef and grey reef sharks) at an unfished Pacific atoll. RESULTS: Sharks of both species occupied a central place during the day within deeper, cooler water where they were less active, and became more active over a larger area at night in shallower water. However, video cameras on two grey reef sharks revealed foraging attempts/success occurring throughout the day, and that multiple sharks were refuging in common areas. A simple bioenergetics model for grey reef sharks predicted that diel changes in energy expenditure are primarily driven by changes in swim speed and not body temperature. CONCLUSIONS: We provide a new method for simultaneously visualizing diel space use and behavior in marine predators, which does not require the simultaneous measure of both from each animal. We show that blacktip and grey reef sharks behave as CPFs, with diel changes in activity, horizontal and vertical space use. However, aspects of their foraging behavior may differ from other predictions of traditional CPF models. In particular, for species that never stop swimming, patch foraging times may be unrelated to patch travel distance.

Maximum likelihood estimation for stochastic volatility in mean models with heavy-tailed distributions.

In this article, we introduce a likelihood-based estimation method for the stochastic volatility in mean (SVM) model with scale mixtures of normal (SMN) distributions (Abanto-Valle et al., 2012). Our estimation method is based on the fact that the powerful hidden Markov model (HMM) machinery can be applied in order to evaluate an arbitrarily accurate approximation of the likelihood of an SVM model with SMN distributions. The method is based on the proposal of Langrock et al. (2012) and makes explicit the useful link between HMMs and SVM models with SMN distributions. Likelihood-based estimation of the parameters of stochastic volatility models in general, and SVM models with SMN distributions in particular, is usually regarded as challenging as the likelihood is a high-dimensional multiple integral. However, the HMM approximation, which is very easy to implement, makes numerical maximum of the likelihood feasible and leads to simple formulae for forecast distributions, for computing appropriately defined residuals, and for decoding, i.e., estimating the volatility of the process.