Sharks Have Math Skills

A new study suggests that some sharks and other marine predators can follow strict mathematical strategies when foraging for dinner. The work, reported online June 9 in Nature, is the latest aiming to show whether animals sometimes move in a pattern called a Lévy walk.

Unlike random motion — in which animals take similar-sized steps in any direction, like a drunk stumbling around — Lévy walks are punctuated by rare, long forays in any direction. Draw a Lévy walk on a graph, and its squiggly pattern echoes a fractal, the mathematical phenomenon whose shape remains similar no matter the viewing scale.

“Living organisms, when allowed to make freely willed decisions, seem to end up obeying some kind of mathematical law,” says Gandhimohan Viswanathan, a theoretical physicist at the Federal University of Alagoas in Maceió, Brazil, who was not involved in the study.

Biologists had long thought that animal foraging was dominated by random walks. But in 1996 a team led by Viswanathan reported that wandering albatrosses, fitted with radio-tracking devices, made the occasional long flight that is the hallmark of a Lévy pattern.

Soon, biologists were reporting Lévy behavior in everything from deer to bumblebees and speculating how it might drive human migrations or the spread of genetically engineered crops. But many of those studies were flawed, says David Sims, a researcher at the Marine Biological Association of the United Kingdom in Plymouth. “Patchy data could mean you think you have a Lévy flight when you haven’t,” he says. And in 2007, researchers debunked the original 1996 albatross paper by noting that many of the reported “Lévy walks” — in which the birds’ transmitters remained dry, supposedly during extended flight — actually were birds resting on their nests.

Now, however, Sims and his colleagues say they have firm evidence for Lévy behavior in 14 species of open-ocean marine predators, including tuna, swordfish, marlin and sharks (although not great whites). The key is the sheer amount of data, on depth and location, gathered by electronic tags, says Sims. His group collected more than 12 million data points describing how the animals swam in the ocean over 5,700 days.

Many of the animals displayed Lévy behavior at least some of the time, Sims and his colleagues report — “the strongest evidence yet that these Lévy patterns are exhibited by wild animals,” he says. Lévy behavior showed up more often in waters where plankton, fish and other food was scarce. In regions with plentiful food, random motion dominated. This observation, says Viswanathan, fits with earlier suggestions that “animals may use a Lévy flight motion to improve their chances of finding prey.”

Not all experts are on board with the new study. Simon Benhamou, an ecologist at the National Center for Scientific Research, or CNRS, in Montpellier, France, hasn’t analyzed the new marine data but says that statistical errors can often suggest Lévy behavior where it doesn’t exist. Benhamou also argues that Lévy pattern studies wrongly assume that predators are “fully stupid, unable to process information and act accordingly” as their environment changes.

Others say Lévy patterns are a logical strategy for animals to take when hunting for food. “From the biological point of view, it makes sense that this way of searching should evolve,” says H. Eugene Stanley, a physicist at Boston University.

Sims and his team are now looking to identify Levy behavior in lower marine animals such as octopuses. The researchers also want to probe the evolutionary history of Lévy behavior — for instance by monitoring the movements of the “living fossil” known as the nautilus, which has not evolved much for hundreds of millions of years, as well as by analyzing fossil traces of other marine animals.