Named after French mathematician Paul Lévy, a Lévy walk is characterized by many small moves combined with a few longer trajectories. It is one type of random walk, in which each successive move is chosen randomly and uninfluenced by any previous move. Think of a drunk stumbling along, where a step to the right is just as likely as a step left, with no memory of the route he has taken.
In a Lévy walk, most of the steps are within a small area, but longer routes are taken on occasion.
“The Lévy-like pattern has been found in insects, marine predators like sharks and tuna, terrestrial mammals — really a wide swath of organisms,” said study author and University of Arizona anthropologist David Raichlen. Evidence of Lévy walks has even been found in the way people wander through university campuses, urban environments, and Disney World.
The study, published online Monday in the Proceedings of the National Academy of Sciences, used GPS-tracking devices strapped to the belts or arms of 44 members of the Hadza, a group of hunter-gatherers in northern Tanzania. They wore them from dawn to dusk, during which each individual walked several miles a day to find food. The majority of the foraging treks were best described as a Lévy walk, as opposed to alternative statistical models of motion.
In the past decade or so, scientists started to find this Lévy-like behavior in how all sorts of creatures — from bacteria to penguins — poked around for a meal.
“All these organisms from across the natural world, with varying degrees of complexity, and yet this same pattern seems to emerge,” he said.
Raichlen, who specializes in the evolution of human locomotion, wanted to investigate hunter-gatherers to perhaps give clues on how ancient man moved. He thought human foragers might use a different search methodology, given their high cognitive ability to use memory and environmental cues.
The Hadza subjects hunted and gathered nearly 95 percent of their food from the wild and traded for the remaining 5 percent. They don’t use cars or guns and lack access to electricity. They travel by foot.
“The Hadza move around a great deal; it’s astounding,” said study author and Yale University anthropologist Brian Wood. For instance, the men walked more than seven miles per day on average. “In a year, that’s like walking from Philadelphia to Reno.”
The men go after mobile game like wart hog and porcupine, taking them down with bow and poison-tipped arrows, or fresh honey. Women forage for potato-like tubers — best enjoyed roasted over a fire — or leafy greens. Wood predicted that there could be differences in the way men and women forage, or perhaps strategies would change from wet to dry season. But the Lévy walk persisted through close to half of the 342 total forays.
“It makes intuitive sense,” said Wood, who has worked with the Hadza tribe for 10 years. “You make long trips to some general location, then you do a more close inspection of an area and look around in more fine detail.”
Humans may just use the same technique as other species for one important reason — it works.
One large study of marine predators such as sharks and tuna found Lévy walks alternated with another type of movement called Brownian motion, which tends to keep you within a tighter region size without the longer trajectories. How food is distributed is a likely factor. When prey is abundant, Brownian seemed to be the right choice — sort of picking through a close area at random, collecting the bounty.
However, when food is sparse, Lévy patterns emerge.
“It ends up helping you search for widely and randomly distributed food without revisiting the same patches, compared to something like a Brownian walk,” Raichlen said.
For the Hadza, food is spread out in patches, and the subjects had a set plan for the day, Wood said, adding that the women tend to forage in groups with spirited debates beforehand about where to go.
Both Wood and Raichlen say they are interested in pursuing more detailed data collection, including talking to the subjects to find out their intentions, following them on treks and taking note of what they bring back.
Kim is a freelance science journalist based in Philadelphia.