Joint modelling of multi‐scale animal movement data using hierarchical hidden Markov models

Abstract

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.

Hidden Markov models identify major movement modes in accelerometer and magnetometer data from four albatross species

“…There are multiple approaches for increasing the resolution of behaviors using an HMM framework: a more complicated 4-, 5-, or even 6-state model could fit increasingly nuanced behaviors, for example distinguishing resting from sit-and-wait foraging, which is used frequently by black-footed and grey-headed albatrosses [ 12 , 52 ] and accounts for 35% of prey consumed by grey-headed albatrosses [ 52 ]. Alternatively, one could apply a hierarchical HMMs to classify behavioral states occurring at different time scales [ 32 , 33 ].…”

“…While they found that all methods performed similarly, they concluded that HMMs provide advantages over other methods given their ability to test the effect of predictor variables on state transition probabilities and because HMMs explicitly model serial autocorrelation [ 26 , 30 , 31 ]. Further, HMMs can incorporate multiple types of data [ 32 , 33 ], a feature that is highly relevant to biologging studies since IMU devices typically record simultaneous data streams from multiple sensors (e.g. accelerometers, magnetometers, gyroscopes).…”

Uncovering ecological state dynamics with hidden Markov models

“…One of the earliest and most flexible HMM packages, depmixS4 (Visser and Speenkenbrink, 2010), can accommodate multivariate HMMs, multiple observation sequences, parameter covariates, parameter constraints and missing observations. Similar to depmixS4 in terms of features and flexibility, momentuHMM (McClintock and Michelot, 2018) can also be used to implement mixed HMMs (DeRuiter et al ., 2017), hierarchical HMMs (Leos‐Barajas et al ., 2017a; Adam et al ., 2019a), zero‐inflated probability distributions (Martin et al ., 2005) and partially observed state sequences. In addition to the R packages presented in Table 2, there are numerous R and stand‐alone software packages that are less general and specialise on particular HMM applications in ecology, as well as general statistical programs with which these types of models can be relatively easily implemented (see Appendix B in Supplementary Material).…”

“…alternative stable states), or it could simply be used to account for unobservable state dynamics at lower levels of the hierarchy as a component of a larger (non‐Markovian) ecosystem‐level process model. Recent HMM methodological developments such as hierarchical formulations that allow data collection and/or state transitions to occur at multiple temporal resolutions (Fine et al ., 1998; Leos‐Barajas et al ., 2017a; Adam et al ., 2019a), nonparametric approaches avoiding restrictive distributional assumptions (Yau et al ., 2011; Langrock et al ., 2018) and coupled HMMs for interacting state processes associated with different sequences (Sherlock et al ., 2013; Touloupou et al ., 2020) extend our capability to incorporate complex data structures and hierarchical relationships scaled from the individual to ecosystem level.…”

Toward Efficient Bayesian Approaches to Inference in Hierarchical Hidden Markov Models for Inferring Animal Behavior

“…Data were assumed to stem from two behavioral processes, operating on distinct temporal scales: a crude-scale process that identifies the general behavioral mode (e.g., migration), and a fine-scale process that captures the behavioral mode nested within the large-scale mode (e.g., resting, foraging, traveling). Intuitively, the former may persist for numerous consecutive dives, whereas the latter agrees to the more nuanced state transitions at the dive-by-dive level, given the general behavioral mode (Leos Barajas et al, 2017;Adam et al, 2019). Hence, a behavior occurring at the crude time scale can be connected to one of the finite internal states, such that each internal state generates a distinct HMM, the internal states of which in turn are linked to the actual observation at a specific point in time.…”