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Sharks Are Accidentally Good at Math

Sharks follow mathematically optimal hunting routes, but that’s more to do with laziness than innate math skills.

For decades, sharks have baffled scientists by foraging along mathematically optimized hunting paths, called Lévy flights. Lamentably, nobody has observed sharks running Monte Carlo simulations or charting out paraboloid graphs, so this uncanny ability has been written off as a mysterious adaptation that evolved over the shark's natural history.

But Andy Reynolds, a bioresearcher at Rothamsted Research, has another theory: sharks aren't natural mathletes, they just don't like being pushed around by ocean turbulence. Reynolds ran computer simulations of shark movement alongside turbulence flows and discovered that sharks followed Lévy flights to avoid choppy waters. In other words, the animals were taking their math cues from their environment, not from a hardwired talent for optimization theory.

"The sharks are not being clever, they are just being sensible," Reynolds told me. "Being pushed around can cause harm and is best avoided. The finding runs counter to the widely held view that Lévy flights are an innate, evolved searching strategy." The results of his study were published today in Proceedings of the Royal Society A.

Lévy flights—named after probability theorist Paul Lévy—were first conceived as an entirely mathematical concept, with no corroborating evidence in the real world. The basic pattern of a Lévy flight begins with a number of small movements in one region, followed by a long movement to a new region, followed by more small movements.

A graphic representation of 1,000 step Lévy flight. Image: PAR.

"The pattern keeps repeating across larger and larger scales," explained Reynolds. "The commonly occurring short movements are punctuated by more rarely occurring longer movements which, in turn, are occasionally punctuated by even rarer, even longer movements."

In the 1990s, physics graduate G.M. Viswanathan recognized this pattern in albatross colonies, leading to the establishment of the Lévy flight foraging hypothesis—the idea that natural selection favors animals who can figure out these optimized routes. It's a logical conclusion, given what a huge advantage Lévy flight foraging provides for animals that exhibit it.

"The strategy is effective when searching because it allows the immediate vicinity to be searched thoroughly but without oversampling—needless revisiting of locations—before jumping to a new location to begin searching again," said Reynolds. "We tend to do something similar when searching for lost keys. Lévy flights allow this to happen without the need for sophisticated navigational skills and mental maps."

Reynolds' examination of the routes through the lens of turbulence theory adds a new layer to the phenomenon, and not just regarding shark movement. "I suspect that Lévy flights have arisen 'accidentally' in other organisms," Reynolds told me.

We tend to do something similar when searching for lost keys.

"Lévy flight foraging is seen in T cells, immune cells that seek out invaders; honeybees, when lost and searching for home, or when searching for food; and human hunter gatherers," such as the Hadza tribe, he said. In addition, other marine predators, like penguins, turtles, and bonyfish, have observed following these optimal pathways.

"My theory applies to all these predators," he continued. "There is even evidence in 'trace fossils,' the preserved form of tracks made by organisms that occupied ancient sea beds. With this accumulation of evidence, the key question is now: how do organisms perform Lévy flights? How did sharks end up being such effective hunters?"

Those questions require more research, but it's safe to conclude that sharks didn't become top predators by acing math tests.