Narwhals are enigmatic marine mammals, who fascinate us with their unique appearance and secret lifestyle under the Arctic sea ice.
But while we still have a lot to learn about narwhals – including how to save some endangered populations from ourselves – scientists have also made some key discoveries in recent years.
Known for their extremely deep dives to nearly 2 kilometers (1.2 miles) below the surface and their reliance on sea ice for their life cycle, the narwhal’s movements in the oceans are a complex affair to watch.
Now, with a little help from chaos theory, researchers have now managed to shed light on what appeared to be erratic daily behavior in the movements of narwhals off the coast of East Greenland.
“While animal-borne ocean sensors continue to advance and collect more data, there is a lack of adequate methods to analyze records of erratic behavior,” says Evgeny A. Podolskiy, a geoscientist at Hokkaido University in Japan and first author of the new study.
Hoping to fix this, Podolskiy teamed up with Mads Peter Heide-Jørgensen, a marine biologist at the Greenland Institute of Natural Resources, to develop a new way of finding patterns in the seemingly random habits of narwhals.
Chaos theory is the study of activity that appears unpredictable but is governed by strict sets of laws.
Like the proverbial butterfly that starts a hurricane with one wing, it’s a case of reliable physics piling up in ways no system can track.
Likewise, like many animals, the narwhal’s meanderings do not make their daily activities clear to our human brains.
The new insight into narwhal behavior came from an adult male narwhal whose movements were recorded over 83 days by a satellite depth-time recorder attached to the animal’s back.

Combining their respective specialties in signal processing and biology, Podolskiy and Heide-Jørgensen developed a method that uses mathematical tactics borrowed from chaos theory to understand chaotic behavior in dynamic environments.
These techniques can reveal hidden states, known as “attractors,” toward which chaotic systems tend to evolve, the researchers explain.
They can help scientists find hard-to-detect patterns in some complex processes, including the cryptic behavior of narwhals.
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The tools of chaos theory helped reveal a hidden daily pattern for this narwhal, including new details about how these habits can be affected by variables such as seasonal change.
Here’s what they found: the tagged narwhal tended to rest closer to the surface around noon, but when it dived at this time, it went too deep.
Dusk and night dives took place in shallower water but were also more intense, the researchers report, perhaps because the narwhal was hunting squid.
The narwhal also adapted its patterns in response to the prevalence of sea ice, according to the study.
Not only did it reduce its surface activity during times when sea ice was more abundant, the researchers report, but it also exhibited more intense diving behavior.
Narwhals are not listed as endangered species by the International Union for Conservation of Nature, but are still considered vulnerable to human activities, from ship traffic and water pollution to climate change. Some populations may be at risk of extinction.
The lives of narwhals are intertwined with sea ice, which is rapidly shrinking due to global climate change, and knowledge about their behavior could be valuable for their conservation.
Chaos theory could also be useful for the broader analysis of animal behavior, the researchers write.
It may help us understand the challenges other Arctic wildlife face due to rising temperatures and fading sea ice, for example, although this approach is still in its infancy.
More research (and more narwhals) will be needed, as the new study is based on just one person’s behavior.
However, it covers “an unusually long period” of almost three months, the researchers add, noting that comparable records often cover only a few days.
“Our approach is relatively simple to implement,” the authors explain, “and can map and annotate long-term data, identifying differences between the behavior of individual animals and across species, and also detecting disruptions in behavior caused by changing influences.” .
The study was published in PLOS Computational Biology.