Movement of Life: The Lévy Walk a Mathematical Pattern Found Throughout Nature

When looking for their next meal, sharks, honeybees and human hunter-gatherers share a mathematical pattern of movement known as a Lévy walk, according to a new study published in the Proceedings of the National Academy of Sciences.

A Lévy walk, also referred to as a Lévy flight, is a mix of long trajectories and short random movements. The pattern is something of a golden ratio - it is observed throughout the animal kingdom. But this latest research is the first to show the pattern in human movement as well.

"Scientists have been interested in characterizing how animals search for a long time," said David Raichlen, an associate professor in the Univserity of Arizona School of Anthropology, "so we decided to look at whether human hunter-gatherers use similar patterns."

The researchers traveled to Tanzania to work with the Hadza people, one of the last groups on Earth to still forage on foot with traditional methods.

"If you want to understand human hunter-gatherer movement, you have to work with a group like the Hadza," Raichlen said.

Raichlen, study co-author Herman Pontzer and their colleagues, asked members of the Hadza tribe to wear wristwatches with GPS tracking devices installed in them.

The GPS data revealed that while the Hadza were foraging on foot, the dominant pattern of their movement was a Lévy walk - the same pattern of movement common in foraging animals throughout nature.

"Detecting this pattern among the Hadza, as has been found in several other species, tells us that such patterns are likely the result of general foraging strategies that many species adopt, across a wide variety of contexts," said study co-author Brian Wood, an anthropologist at Yale University who has worked with the Hadza people since 2004.

The Lévy walk is characterized by numerous short movements within a small area, and a long stride to a distant area, where numerous shorter strides are taken again. Moving around at an amusement park for a day, or walking around an airport departures lobby before getting flight are examples of how the patten can take shape in day-to-day life.

"Think about your life," Raichlen said. "What do you do on a normal day? Go to work and come back, walk short distances around your house? Then every once in a while you take these long steps, on foot, bike, in a car or on a plane. We tend to take short steps in one area and then take longer strides to get to another area."

"We're very interested in studying why the Hadza use this pattern, what's driving their hunting strategies and when they use this pattern versus another pattern," said Pontzer, a member of the research team and an anthropologist at Hunter College in New York.