Summary Use of accelerometers is now widespread within animal biologging as they provide a means of measuring an animal's activity in a meaningful and quantitative way where direct observation is not possible. In sequential acceleration data, there is a natural dependence between observations of behaviour, a fact that has been largely ignored in most analyses. Analyses of acceleration data where serial dependence has been explicitly modelled have largely relied on hidden Markov models (HMMs). Depending on the aim of an analysis, an HMM can be used for state prediction or to make inferences about drivers of behaviour. For state prediction, a supervised learning approach can be applied. That is, an HMM is trained to classify unlabelled acceleration data into a finite set of pre‐specified categories. An unsupervised learning approach can be used to infer new aspects of animal behaviour when biologically meaningful response variables are used, with the caveat that the states may not map to specific behaviours. We provide the details necessary to implement and assess an HMM in both the supervised and unsupervised learning context and discuss the data requirements of each case. We outline two applications to marine and aerial systems (shark and eagle) taking the unsupervised learning approach, which is more readily applicable to animal activity measured in the field. HMMs were used to infer the effects of temporal, atmospheric and tidal inputs on animal behaviour. Animal accelerometer data allow ecologists to identify important correlates and drivers of animal activity (and hence behaviour). The HMM framework is well suited to deal with the main features commonly observed in accelerometer data and can easily be extended to suit a wide range of types of animal activity data. The ability to combine direct observations of animal activity with statistical models, which account for the features of accelerometer data, offers a new way to quantify animal behaviour and energetic expenditure and to deepen our insights into individual behaviour as a constituent of populations and ecosystems.

Summary Fine‐scale predator movements may be driven by many factors including sex, habitat and distribution of resources. There may also be individual preferences for certain movement strategies within a population which can be hard to quantify. Within top predators, movements are also going to be directly related to the mode of hunting, for example sit‐and‐wait or actively searching for prey. Although there is mounting evidence that different hunting modes can cause opposing trophic cascades, there has been little focus on the modes used by top predators, especially those in the marine environment. Adult white sharks (Carcharhodon carcharias) are well known to forage on marine mammal prey, particularly pinnipeds. Sharks primarily ambush pinnipeds on the surface, but there has been less focus on the strategies they use to encounter prey. We applied mixed hidden Markov models to acoustic tracking data of white sharks in a coastal aggregation area in order to quantify changing movement states (area‐restricted searching (ARS) vs. patrolling) and the factors that influenced them. Individuals were re‐tracked over multiple days throughout a month to see whether state‐switching dynamics varied or if individuals preferred certain movement strategies. Sharks were more likely to use ARS movements in the morning and during periods of chumming by ecotourism operators. Furthermore, the proportion of time individuals spent in the two different states and the state‐switching frequency, differed between the sexes and between individuals. Predation attempts/success on pinnipeds were observed for sharks in both ARS and patrolling movement states and within all random effects groupings. Therefore, white sharks can use both a ‘sit‐and‐wait’ (ARS) and ‘active searching’ (patrolling) movements to ambush pinniped prey on the surface. White sharks demonstrate individual preferences for fine‐scale movement patterns, which may be related to their use of different hunting modes. Marine top predators are generally assumed to use only one type of hunting mode, but we show that there may be a mix within populations. As such, individual variability should be considered when modelling behavioural effects of predators on prey species.

BackgroundCentral 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.ResultsSharks 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.ConclusionsWe 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.Electronic supplementary materialThe online version of this article (10.1186/s40462-018-0127-3) contains supplementary material, which is available to authorized users.

Hidden Markov models (HMMs) are commonly used to model animal movement data and infer aspects of animal behavior. An HMM assumes that each data point from a time series of observations stems from one of N possible states. The states are loosely connected to behavioral modes that manifest themselves at the temporal resolution at which observations are made. However, due to advances in tag technology, data can be collected at increasingly fine temporal resolutions. Yet, inferences at time scales cruder than those at which data are collected, and which correspond to largerscale behavioral processes, are not yet answered via HMMs. We include additional 1 arXiv:1702.03597v1 [stat.ME] 13 Feb 2017 hierarchical structures to the basic HMM framework in order to incorporate multiple Markov chains at various time scales. The hierarchically structured HMMs allow for behavioral inferences at multiple time scales and can also serve as a means to avoid coarsening data. Our proposed framework is one of the first that models animal behavior simultaneously at multiple time scales, opening new possibilities in the area of animal movement modeling. We illustrate the application of hierarchically structured HMMs in two real-data examples: (i) vertical movements of harbor porpoises observed in the field, and (ii) garter snake movement data collected as part of an experimental design.

Hidden Markov models are prevalent in animal movement modelling, where they are widely used to infer behavioural modes and their drivers from various types of telemetry data. To allow for meaningful inference, observations need to be equally spaced in time, or otherwise regularly sampled, where the corresponding temporal resolution strongly affects what kind of behaviours can be inferred from the data. Recent advances in biologging technology have led to a variety of novel telemetry sensors which often collect data from the same individual simultaneously at different time‐scales, for example step lengths obtained from GPS tags every hour, dive depths obtained from time‐depth recorders once per dive, or accelerations obtained from accelerometers several times per second. However, to date, statistical machinery to address the corresponding complex multi‐stream and multi‐scale data is lacking. We propose hierarchical hidden Markov models as a versatile statistical framework that naturally accounts for differing temporal resolutions across multiple variables. In these models, the observations are regarded as stemming from multiple connected behavioural processes, each of which operates at the time‐scale at which the corresponding variables were observed. By jointly modelling multiple data streams, collected at different temporal resolutions, corresponding models can be used to infer behavioural modes at multiple time‐scales and in particular, help to draw a much more comprehensive picture of an animal's movement patterns, for example with regard to long‐term versus short‐term movement strategies. The suggested approach is illustrated in two real‐data applications, where we jointly model (a) coarse‐scale horizontal and fine‐scale vertical Atlantic cod Gadus morhua movements throughout the English Channel, and (b) coarse‐scale horizontal movements and corresponding fine‐scale accelerations of a horn shark Heterodontus francisci tagged off the Californian coast.

Animal behavior should optimize the difference between the energy they gain from prey and the energy they spend searching for prey. This is all the more critical for predators occupying the pelagic environment, as prey is sparse and patchily distributed. We theoretically derive two canonical swimming strategies for pelagic predators, that maximize their energy surplus while foraging. They predict that while searching, a pelagic predator should maintain small dive angles, swim at speeds near those that minimize the cost of transport, and maintain constant speed throughout the dive. Using biologging sensors, we show that oceanic whitetip shark (Carcharhinus longimanus) behavior matches these predictions. We estimate that daily energy requirements of an adult shark can be met by consuming approximately 1–1.5 kg of prey (1.5% body mass) per day; shark-borne video footage shows a shark encountering potential prey numbers exceeding that amount. Oceanic whitetip sharks showed incredible plasticity in their behavioral strategies, ranging from short low-energy bursts on descents, to high-speed vertical surface breaches from considerable depth. Oceanic whitetips live a life of energy speculation with minimization, very different to those of tunas and billfish.

Hidden Markov models (HMMs) and their extensions are attractive methods for analysing ecological data where noisy, multivariate measurements are made of a hidden, ecological process, and where this hidden process is represented by a sequence of discrete states. Yet, as these models become more complex and challenging to understand, it is important to consider what pitfalls these methods have and what opportunities there are for future research to address these pitfalls. In this paper, we review five lesser known pitfalls one can encounter when using HMMs or their extensions to solve ecological problems: (a) violation of the snapshot property in continuous‐time HMMs; (b) biased inference from hierarchical HMMs when applied to temporally misaligned processes; (c) sensitive inference from using random effects to partially pool across heterogeneous individuals; (d) computational burden when using HMMs to approximate models with continuous state spaces; and (e) difficulty linking the hidden process to space or environment. This review is for ecologists and ecological statisticians familiar with HMMs, but who may be less aware of the problems that arise in more specialised applications. We demonstrate how each pitfall arises, by simulation or example, and discuss why this pitfall is important to consider. Along with identifying the problems, we highlight potential research opportunities and offer ideas that may help alleviate these pitfalls. Each of the methods we review are solutions to current ecological research problems. We intend for this paper to heighten awareness of the pitfalls ecologists may encounter when applying these more advanced methods, but we also hope that by highlighting future research opportunities, we can inspire ecological statisticians to weaken these pitfalls and provide improved methods.

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