[Paper Review] A multivariate mixed hidden Markov model to analyze blue whale diving behaviour during controlled sound exposures

Stacy L. DeRuiter, Roland Langrock+5 more|arXiv (Cornell University)|Feb 21, 2016

Marine animal studies overview37 references18 citations

TL;DR

This study develops a multivariate mixed hidden Markov model (HMM) to identify latent behavioral states—shallow feeding, traveling, and deep feeding—in blue whales using high-resolution biologging data. The model incorporates individual variability via discrete random effects and quantifies how controlled mid-frequency active sonar (MFAS) and pseudo-random noise (PRN) affect transition probabilities between states, revealing that whales are significantly less likely to initiate deep foraging during acoustic exposure.

ABSTRACT

Characterization of multivariate time series of behaviour data from animal-borne sensors is challenging. Biologists require methods to objectively quantify baseline behaviour, then assess behaviour changes in response to environmental stimuli. Here, we apply hidden Markov models (HMMs) to characterize blue whale movement and diving behaviour, identifying latent states corresponding to three main underlying behaviour states: shallow feeding, travelling, and deep feeding. The model formulation accounts for inter-whale differences via a computationally efficient discrete random effect, and measures potential effects of experimental acoustic disturbance on between-state transition probabilities. We identify clear differences in blue whale disturbance response depending on the behavioural context during exposure, with whales less likely to initiate deep foraging behaviour during exposure. Findings are consistent with earlier studies using smaller samples, but the HMM approach provides more nuanced characterization of behaviour changes.

Motivation & Objective

• To objectively quantify baseline blue whale diving behavior using multivariate time series from animal-borne tags.
• To model individual variability in behavior across tagged whales using computationally efficient discrete random effects.
• To assess the impact of controlled mid-frequency active sonar (MFAS) and pseudo-random noise (PRN) on behavioral state transitions.
• To provide a quantitative, hypothesis-driven framework for analyzing behavioral responses to anthropogenic noise in marine mammals.
• To support Population Consequences of Disturbance (PCoD) modeling by linking behavioral changes to potential fitness and population-level effects.

Proposed method

• A multivariate HMM is applied to high-resolution biologging data (sound, movement, depth) from 37 tagged blue whales.
• Latent states are inferred using the forward algorithm and numerical maximum likelihood estimation to fit the model parameters.
• Inter-individual differences are modeled via a discrete random effect that allows for heterogeneous behavioral patterns across whales.
• Covariates representing experimental sound exposure (MFAS and PRN) are incorporated into the transition probability matrix to assess their effect on state transitions.
• The model is fitted using a likelihood-based approach, enabling statistical inference on the influence of acoustic disturbance on behavior.
• Three primary behavioral states are identified: shallow feeding (state 1), traveling (state 2), and deep feeding (state 3), based on movement and dive characteristics.

Experimental results

Research questions

• RQ1 How can multivariate biologging data from blue whales be objectively segmented into biologically meaningful behavioral states?
• RQ2 To what extent do individual whales differ in their baseline diving behavior, and how can this be modeled efficiently?
• RQ3 How does controlled exposure to mid-frequency active sonar (MFAS) and pseudo-random noise (PRN) alter the probability of transitioning between behavioral states?
• RQ4 Is the behavioral response to acoustic disturbance context-dependent, varying with the whale’s current behavioral state?
• RQ5 What are the quantitative effects of sound exposure on the initiation of deep foraging behavior, a key energy-gaining activity?

Key findings

• Whales were significantly less likely to initiate deep foraging behavior (state 3) during exposure to mid-frequency active sonar (MFAS) and pseudo-random noise (PRN).
• The rate of transition from directed travel (state 2) to shallow feeding (state 1) increased during exposure, but only in behavioral context 1, suggesting context-specific vigilance or behavioral re-evaluation.
• The model successfully grouped dives with zero, one, or several lunges into a single shallow-diving state (state 1), indicating behavioral similarity beyond lunge count.
• The results are consistent with prior studies showing reduced foraging effort during acoustic disturbance, but provide a more nuanced, quantitative characterization using a mixed HMM framework.
• The study demonstrates that behavioral responses to noise are highly context-dependent, with the apparent intensity of response varying based on baseline behavior.
• The mixed HMM approach enables robust, individual-specific modeling of complex behavioral dynamics while incorporating environmental covariates, supporting future PCoD modeling.