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

Manh Cuong Ngô,Mads Peter Heide-Jørgensen,Susanne Ditlevsen,Bard G Ermentrout

doi:10.1371/journal.pcbi.1006425

Manh Cuong Ngô, Mads Peter Heide-Jørgensen + Show 2 more

Open Access

https://doi.org/10.1371/journal.pcbi.1006425

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Abstract

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.

Highlights

The narwhal (Monodon monoceros) primarily inhabit cold waters of the Atlantic sector of the Arctic, with the largest abundances found in East and West Greenland and in the Canadian High Arctic [1]
A dive was scored every time the depth record went deeper than 20m to exclude brief shallow submersions between respirations, otherwise it is considered time spent at the surface, summarized in the variable post-dive surface time (PD)
We extend the existing Hidden Markov models (HMMs) for diving behaviour of marine mammals to allow for dependence between state distributions, and show that the dependence has some impact on the conclusions drawn about the diving behaviour

Summary

Introduction

The narwhal (Monodon monoceros) primarily inhabit cold waters of the Atlantic sector of the Arctic, with the largest abundances found in East and West Greenland and in the Canadian High Arctic [1]. Narwhals dive to forage, and their diet consists of few prey species including Greenland halibut (Reinhardtius hippoglossoides), polar cod (Boreogadus saida), capelin (Ammodytes villosus) and squids (Gonatus sp.) [5, 6]. Narwhals depend on acoustics for sensing their environment, navigating and capturing prey at depth [7]. It is important to understand and quantitatively describe the diving activities of narwhals, by robust statistical methods, to ensure the long-term conservation of one of the most specialized species in the North Atlantic

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