Albatross forage with fractal-like flight

New data support mathematical pattern in birds’ hunting behavior

Flight plans reminiscent of fractals could help hungry birds find food. Albatross sometimes hunt by following a mathematical pattern that repeats itself at smaller and smaller scales, researchers report online April 23 in the Proceedings of the National Academy of Sciences.

When food is scarce, the wandering albatross’s movements match a mathematical pattern called Lévy flight that has fractal qualities. N. Gasco

Called Lévy flight, this type of movement includes clusters of small movements every which way, punctuated by the occasional long trip in one direction. It’s thought to be a particularly efficient way to locate scarce prey.

“Think about searching for your car keys,” says David Sims, a behavioral ecologist at the Marine Biological Association of the United Kingdom in Plymouth. “You intensively search in one area, but if you don’t find them there, you jump to someplace else and search there.”

Sims isn’t the first person to claim to have seen this pattern in albatross flights. Reporting in 1996 in Nature, physicists at Boston University found Lévy flights in data collected by the British Antarctic Survey that showed when the birds were dry (flying) and wet (landing on the ocean).

But as the ancient mariner learned, albatross can bring both good and bad fortune. A reanalysis of the data reported in 2007 in Nature showed that some dry periods thought to correspond to long flights were actually just times when the birds sat on their nests. Once those still periods were accounted for, the Lévy flight patterns disappeared.

The latest study gives new wings to the idea with better data, thanks to GPS devices on 88 albatrosses that relayed the birds’ positions either every one or 10 seconds. Sometimes the animals moved in small random steps, a Brownian pattern suitable for feeding when food is abundant. But when flying over the deep ocean and hunting sparse, unpredictable patches of squid, individual birds often used a truncated version of Lévy flight — a modified pattern that, unlike its pure mathematical counterpart, breaks down at very small and very large scales.

Finding this pattern “overturns the 2007 study,” says Gandhi Viswanathan, a coauthor on the 1996 paper who is now a theoretical physicist at the Federal University of Rio Grande do Norte in Natal, Brazil.

For the new study, sensors measuring the belly temperatures of wandering albatross allowed researchers to estimate how much food was caught and eaten. A typical bird in Lévy flight swallowed more than four times its daily energy needs, about 1.5 kilograms of squid and fish every day.

Though evidence for Lévy flight patterns has now been reported in everything from flies to sharks, Simon Benhamou remains unconvinced. An ecologist at the National Center for Scientific Research in Montpellier, France, he applauds the statistical rigor of the new study but questions its biological relevance. Composite patterns that mix together different types of random motion can provide a more realistic and efficient description of foraging that better fits animal movement data, he says. 

“Truncated Lévy flights would be optimal only if the alternatives were only classical Brownian [motion] and straight line,” says Benhamou.

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