Mathematics of Hunting

When sharks and other ocean predators can’t find food, their movement patterns shift in surprising ways that are associated with particle physics rather than animal behavior. They abandon Brownian motion, the random motion seen in swirling gas molecules, for what’s known as Lévy flight — a mix of long trajectories and short, random movements found in turbulent fluids.

Computer models suggest Lévy flight is the optimal search pattern for predators in low-prey areas, and maximizes the chance of a random encounter. But real-world studies have been inconclusive, with reports of Lévy flight countered by doubts about data gathering and interpretation. As the animals went from areas of high ecological abundance to low, the equations describing their movement switched from Brownian motion to Lévy flight.

The findings raise the question of where Lévy flight comes from — whether it’s an instinctive or learned behavior, a property of individuals or a function of spatial distributions governed by as-yet-unknown laws — and how it first evolved. “Animals’ behavior is much more plastic than previously thought,” said Pade. “They have a huge repertoire of movement strategies and patterns.”

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