The Annals of Applied Statistics

A multivariate mixed hidden Markov model for blue whale behaviour and responses to sound exposure

Stacy L. DeRuiter, Roland Langrock, Tomas Skirbutas, Jeremy A. Goldbogen, John Calambokidis, Ari S. Friedlaender, and Brandon L. Southall

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Characterization of multivariate time series of behaviour data from animal-borne sensors is challenging. Biologists require methods to objectively quantify baseline behaviour, and 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 a more nuanced characterization of behaviour changes.

Article information

Ann. Appl. Stat., Volume 11, Number 1 (2017), 362-392.

Received: February 2016
Revised: December 2016
First available in Project Euclid: 8 April 2017

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Forward algorithm hidden Markov model multivariate time series numerical maximum likelihood random effects blue whales


DeRuiter, Stacy L.; Langrock, Roland; Skirbutas, Tomas; Goldbogen, Jeremy A.; Calambokidis, John; Friedlaender, Ari S.; Southall, Brandon L. A multivariate mixed hidden Markov model for blue whale behaviour and responses to sound exposure. Ann. Appl. Stat. 11 (2017), no. 1, 362--392. doi:10.1214/16-AOAS1008.

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Supplemental materials

  • Supplement A: Detailed experimental methods for “A multivariate mixed hidden Markov model for blue whale behaviour and responses to sound exposure”. This supplement provides additional detail on the field data collection protocols used to collect the dataset.
  • Supplement B: Supplemental figures for “A multivariate mixed hidden Markov model for blue whale behaviour and responses to sound exposure”. This supplement provides figures of the input data (and decoded states from the final model) for all 37 whales in the dataset.