Understanding narwhal diving behaviour using Hidden Markov Models with dependent state distributions and long range dependence

Diving behaviour of narwhals is still largely unknown. We use Hidden Markov models (HMMs) to describe the diving behaviour of a narwhal and fit the models to a three-dimensional response vector of maximum dive depth, duration of dives and post-dive surface time of 8,609 dives measured in East Greenland over 83 days, an extraordinarily long and rich data set. Narwhal diving patterns have not been analysed like this before, but in studies of other whale species, response variables have been assumed independent. We extend the existing models to allow for dependence between state distributions, and show that the dependence has an impact on the conclusions drawn about the diving behaviour. We try several HMMs with 2, 3 or 4 states, and with independent and dependent log-normal and gamma distributions, respectively, and different covariates to characterize dive patterns. In particular, diurnal patterns in diving behaviour is inferred, by using periodic B-splines with boundary knots in 0 and 24 hours.Author summary: Narwhals live in pristine environments. However, the increase in average temperatures in the Arctic and the concomitant loss of summer sea ice, as well as increased human activities, such as ship traffic and mineral exploration leading to increased noise pollution, are changing the environment, and therefore probably also the behavior and well-being of the narwhal. Here, we use probabilistic models to unravel the diving and feeding behavior of a male narwhal, tagged in East Greenland in 2013, and followed for more than two months. The goal is to gain knowledge of the whales’ normal behavior, to be able to later detect possible changes in behavior due to climatic changes and human influences. We find that the narwhal uses around two thirds of its time searching for food, it typically feeds during deep dives (more than 350m), and it can have extended periods, up to 3 days, without feeding activity.