The Mind of the Swarm: Math Explains How Group Behavior Is More Than the Sum of Its Parts

By Klarreich, Erica | Science News, November 25, 2006 | Go to article overview

The Mind of the Swarm: Math Explains How Group Behavior Is More Than the Sum of Its Parts


Klarreich, Erica, Science News


Few people can fail to marvel at a flock of birds swooping through the evening sky, homing in with certainty on its chosen resting place. The natural world abounds with other spectacular examples of animals moving in concert: a school of fish making a hairpin turn, an ant colony building giant highways, or locusts marching across the plains.

Since ancient times, scientists and philosophers have pondered how animals coordinate their movements, often in the absence of any leader. Coordinated groups can range in scale from just a few individuals to billions, and they can consist of an intelligent species or one whose members have barely enough brainpower to recognize each other.

Despite these differences, similar patterns of motion appear again and again throughout the animal kingdom. This congruence in behavior has led researchers to speculate for about 70 years that a few simple rules might underpin many sophisticated group motions. However, establishing just what these rules are is no easy matter.

"Imagine a space alien looking at rush hour traffic on the L.A. freeway," says Julia Parrish of the University of Washington in Seattle, who studies fish schooling. "It thinks the cars are organisms and wonders how they're moving in a polarized way without collisions. The reason is that there's a set of rules everyone knows.

"We're the space aliens looking at fish, and we don't have the driver's manual," she says.

In recent years, mathematicians and biologists have started to get glimpses of just what may be in that manual. They have constructed mathematical models of animal swarms and colonies that take inspiration from decades of physics research. In physicists' studies of magnetism, for instance, they have elucidated how simple local interactions give rise to complex, large-scale phenomena. Using a combination of computer simulations and experiments with real animals, researchers are explicating how a trio of physics and engineering principles--nonlinearity, positive feedback, and phase transitions--may be basic ingredients from which a wide variety of animal-swarming behaviors takes shape.

"This is a more and more exciting area in which to work," says Iain Couzin, who studies collective animal behavior at the University of Oxford in England and Princeton University. "We have the mathematical foundations to investigate phenomena quickly and effectively."

POSITIVE FOOD BACK Anyone who has left crumbs on the kitchen counter knows the brutal efficiency with which ants can capitalize on such a mistake. As soon as one ant discovers a tempting morsel, thousands more create and follow a trail between the food source and their nest.

'Ants follow only local rules.., but the resulting trail structure is built on a scale well beyond that of a single ant," said David Sumpter of the University of Oxford in England in an article on animal groups in the January Philosophical Transactions of the Royal Society B.

In 2001, using mathematical modeling and lab experiments, Sumpter and two colleagues studied how foraging pharaoh's ants build trails. The researchers turned up a striking group behavior: Just as water abruptly turns to ice at the freezing point, foraging behavior undergoes a "phase transition" at a certain criti cal colony size.

If an ant colony is small, foragers wander about randomly and, even if some of the ants discover food, no trail persists. If a colony is large, the ants' trails build into a superhighway to the food that they find. Somewhere in between--in the case of the experimental ants, at a colony size of 700 members--the colony's behavior switches suddenly.

While this sharp transition might seem unexpected, the researchers weren't altogether surprised to find it because the mathematical principles underlying their model of foraging behavior make such a transition likely.

When an ant discovers a food source, it deposits chemicals called pheromones along its trail back to the nest. …

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