Source-linked AI summary
Analysis of animal accelerometer data using hidden Markov models
Vianey Leos-Barajas, Theoni Photopoulou, Roland Langrock, Toby A. Patterson, Yuuki Watanabe, Megan Murgatroyd, Yannis P. Papastamatiou
TL;DR
Sequential acceleration data contain dependence between observations, while accelerometers provide quantitative activity measurements where direct observation is unavailable. The paper describes inference of animal activity states and reports tidal, temporal, depth, and temperature-related shark activity patterns, while cautioning that inferred states may not map directly to specific behaviours.
Problem
Sequential acceleration observations are naturally dependent, although this dependence has often been ignored in analyses of animal activity.
Method
The paper uses likelihood-based inference to estimate activity states, including direct numerical maximization of the likelihood for unsupervised learning.
Results
Shark activity increased during crepuscular or nocturnal periods with a tidal component, peaking near high tide and at the surface in 28–29 C waters, but becoming inactive above 29 C.
Takeaways & Limitations
Accelerometer measurements support quantitative analysis of animal activity when direct observation is unavailable.
Takeaways & Limitations
Estimated states do not necessarily map directly to specific animal behaviours, so behavioural interpretation is required after state estimation.
Abstract
from arXiv · showhide
Use of accelerometers is now widespread within animal biotelemetry 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 movement or 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, either a supervised or an unsupervised learning approach can be applied. Under a supervised context, an HMM is trained to classify unlabelled acceleration data into a finite set of pre-specified categories, whereas we will demonstrate how an unsupervised learning approach can be used to infer new aspects of animal behaviour. We will provide the details necessary to implement and assess an HMM in both the supervised and unsupervised context, and discuss the data requirements of each case. We outline two applications to marine and aerial systems (sharks and eagles) taking the unsupervised 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. The ability to combine direct observations of animals activity and combine it with statistical models which account for the features of accelerometer data offer a new way to quantify animal behaviour, energetic expenditure and deepen our insights into individual behaviour as a constituent of populations and ecosystems.
1 Introduction
Animal accelerometers provide quantitative activity measurements, but sequential observations are dependent and this dependence is often ignored. The paper presents HMMs, especially unsupervised models, as a framework for modelling temporal structure and inferring behavioural drivers.
- Sequential acceleration observations are naturally dependent because animal behaviours often persist longer than the sampling frequency.
- Most classification approaches ignore serial dependence, whereas HMMs explicitly model it through persistent latent states.
- Supervised HMMs require pre-defined states and corresponding data from direct observations, which may be difficult to obtain for free-ranging animals.
- Classification identifies behavioural states, but relating those states to environmental covariates is needed to identify behavioural drivers.
- In unsupervised HMMs, states are allocated from the data and can represent interpretable activity levels or proxies for behavioural modes.
- The paper reviews HMM analysis of animal accelerometer data and demonstrates applications using marine and aerial systems.
2 Accelerometer data
Accelerometer data capture movement across body axes, but meaningful analysis typically requires windowed summary features. These features can describe movement, posture, activity, energy expenditure, and behaviour-related signals.
- Accelerometers record movement relative to the animal’s body, commonly across three axes, and three-dimensional measurement is important for flying or swimming animals.
- Acceleration signals can indicate regular movement, bursts associated with prey pursuit or conflict, posture, and other behavioural patterns.
- HMMs and other classifiers generally require features computed over observation windows rather than raw acceleration alone.
- Common features include means, variances, dynamic body acceleration, pitch, and correlations among acceleration axes.
- Feature selection should reflect the movement classes of interest, and no single optimal feature set exists.
- ODBA, VeDBA, MSA, posture, speed, and stroke frequency can summarize exertion, energy expenditure, activity, or foraging-related processes.
3 Analysis of accelerometer data
The paper describes HMMs as models with latent state processes and state-dependent observations, suitable for serially dependent accelerometer data. It covers supervised classification and data-driven unsupervised inference, including model assessment and covariate-dependent transitions.
- 3.3 Inference using unsupervised learning: Unsupervised HMMs estimate states from the data rather than assigning them known behavioural labels, making them useful when labels are unavailable.
- 3.1 Hidden Markov models: An HMM combines an observable state-dependent process with an unobservable finite-state process whose transitions follow the Markov property.
- 3.1 Hidden Markov models: HMMs model serial correlation by allowing behavioural states to persist and support inference on state-switching dynamics and environmental drivers.
- 3.2 Classification based on supervised learning: Supervised model assessment can use training, validation, and testing data, with temporal dependence and repeated series from animals considered during splitting.
- 3.2 Classification based on supervised learning: Supervised HMM classification uses labelled sequences to train models that assign unlabelled observations to pre-defined classes.
4 Real data examples
The examples use unsupervised HMMs to model animal activity from accelerometer-derived measures and assess environmental correlates in an eagle and a shark. In the eagle, increasing wind speed was associated with more time in the active state, while shark activity varied by time of day, tide, depth, and temperature.
- 4.1 Modelling activity in a soaring raptor: Because direct behavioural observations were unavailable, MSA was used as an activity proxy in a two-state HMM.The states represented lower-activity movement and more active movement, rather than specific named behaviours.
- 4.1 Modelling activity in a soaring raptor: The selected eagle model included wind speed alone, based on both AIC and BIC.Wind speed, temperature, and their interaction were initially considered as covariates affecting transition probabilities.
- 4.1 Modelling activity in a soaring raptor: As wind speed increased, the eagle generally remained longer in the active state and spent more time there overall.The estimated chance of switching from low to high activity increased only slightly, while active-state dwell duration increased more clearly.
- 4 Real data examples: The HMM framework identifies changes in behavioural states while accommodating serially dependent acceleration data.The examples demonstrate its use for relating latent activity states to temporal, atmospheric, and tidal variables.
5 Discussion
The discussion contrasts supervised and unsupervised HMM analyses, emphasizing that HMMs model serial dependence while supporting joint inference about environmental effects on animal activity. It also highlights interpretive limits, data requirements, and extensions for more complex behaviour dynamics.
- Supervised HMMs classify observations into pre-defined behavioural categories, whereas unsupervised HMMs can reveal new aspects of animal behaviour.
- Post-hoc interpretation of latent states requires species-specific biological knowledge because behaviours may not map exclusively to one state.Repeatedly identifiable behavioural bouts may nevertheless indicate important elements of an animal’s behavioural repertoire.
- Ignoring serial dependence can produce biologically unrealistic classifications and potentially spurious results from subsequent statistical tests.This issue is especially important when observations are processed over short intervals or when behavioural classes lack clear boundaries.
- HMMs account for serial dependence directly, avoiding post-hoc filtering of classifications when behaviours such as prey handling occur in consecutive observations.
- Joint modelling is preferred to multi-stage analyses because it propagates uncertainty in state estimates and addresses serial correlation in decoded states.
- Unsupervised HMM applications linked raptor activity to atmospheric variables and shark activity to temporal and tidal inputs.The shark analysis also incorporated swimming depth and temperature to characterize activity patterns.
- HSMMs extend HMMs by modelling state dwell times with more flexible distributions than the geometric dwell times available in standard HMMs.