Strange attractor of a narwhal (Monodon monoceros)

Detecting structures within the continuous diving behavior of marine animals is challenging, and no universal framework is available. We captured such diverse structures using chaos theory. By applying time-delay embedding to exceptionally long dive records (83 d) from the narwhal, we reconstructed the state-space portrait. Using measures of chaos, we detected a diurnal pattern and its seasonal modulation, classified data, and found how sea-ice appearance shifts time budgets. There is more near-surface rest but deeper dives at solar noon, and more intense diving during twilight and at night but to shallower depths (likely following squid); sea-ice appearance reduces rest. The introduced geometrical approach is simple to implement and potentially helpful for mapping and labeling long-term behavioral data, identifying differences between individual animals and species, and detecting perturbations.Author summary: While animal-borne ocean sensors continue to advance and collect more data, there is a lack of an adequate framework to analyze records of irregular behavior. For example, in the Arctic—there sea-ice is declining but is fundamental for the life cycle of many endemic animals—near-surface dive records are usually ignored, and continuous data are reduced to a maximum depth or similar. Here, we propose to transform our way of thinking about animal motion underwater by turning to a chaos approach and using a flowing geometrical shape to understand the full diversity of behaviors on an example of a satellite-tagged narwhal. Our method may help to assess the susceptibility of narwhal and other animals to sea-ice loss and climate warming.