Septemeber, 2014 / by Jennifer Viegas 
[dropcap]S[/dropcap]harks behave as though they are brilliant mathematicians, finds new research, although they may be more sensible than clever.
The mathematician-like behavior attributed to sharks and certain other marine predators, animals and organisms is known as Lévy flight. It is a seemingly complex form of random walk comprising clusters of short step lengths with longer movements between them.
“Lévy flights, named after the French mathematician Paul Lévy, arose in a purely mathematical context in the first half of the last century,” Andy Reynolds of Rothamsted Research told Discovery News. “Sharks and other marine predators use Lévy flight to locate their prey. “
NOAA image by Walter Heim.
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He explained that the technique’s movements “can be advantageous when searching for randomly distributed resources because they reduce ‘over sampling’ without the need for cognitive maps and sophisticated navigational abilities.”
For the study, published in the latest issue of Proceedings of the Royal Society A, Reynolds began by asking a simple question, namely how do sharks perform Lévy flights? As he said, “They are not mathematicians. “
He examined the possibility that sharks use cues from their environment, such as the turbulent waters that surround them.
“This seemed reasonable,” he said, “because turbulent flows are very complex — the whirls within whirls within whirls like the ones Leonardo da Vinci drew — and within which could be lurking the necessary clues.”
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Using the mathematics of what is known as “turbulent theory,” he showed that the programming for Lévy flight movements arises naturally if the predators change their direction of travel only after encountering patches of relatively strong turbulence.
Reynolds next ran computer simulations of shark movements in turbulent flows. The theoretical predictions and simulation data fitted together perfectly.
“There is no need for sharks to have evolved sophisticated neurological and physiological processes for the execution of the Lévy flights, which are the lead to optimal foraging, ” he said. “Lévy flights will come for free if they just turn away from patches of strong turbulence.”
