BOSTON — From V-shaped squadrons of Canada geese to wheeling clouds of starlings, how flocks hold themselves together can spark robust debates among bird experts.
Now, a pair of physicists has joined the fray, offering what the two call a universal theory of flocking. Borrowing from the physics of fluids, they have crafted an explanation of how birds in a flock move in the same direction without a clear leader, even when individual birds make mistakes, and when each bird can only see its nearest half-dozen neighbors.
With further refinement, they say, the theory could be applied to the collective motions of bacteria in a petri dish, wildebeests thundering along the Serengeti, and problems of traffic flow.
In essence, the flocking problem is one of discovering how "short-range interactions lead to long-range order," says John Toner, a physicist at the University of Oregon in Eugene and one of the theory's authors. Birds form flocks to find unevenly distributed food or to detect and defend against predators, researchers say. But how birds stay together in flight is still an open question.
University of Rhode Island ornithologist Frank Heppner says he suspects that mathematical rules may govern aspects of starling flocks. The birds return over their roost each night with barely enough energy to survive until dawn, he explains. Yet just before they land, they wheel and turn for as much as 45 minutes. That makes no sense from a survival point of view, he says. Instead, "it may be a byproduct of the mathematics of flying flocks."
The first physicist to tackle flocking, Dr. Toner explains, did so in 1993. At the time, Hungarian physicist Tamas Vicsek was watching films of bacteria colonies. As the colonies grew, parts of them began to move in circles - some to the right, some to the left, but definitely as a "flock."
What Vicsek saw reminded him of atoms in an iron bar as it becomes magnetized. Each iron atom has a tiny magnetic field with a north and south pole. When the bar is magnetized, all the billions of north poles line up in the same direction. As they align, each individual atom responds only to its closest neighbors. But if one atom's field becomes slightly out of whack with those of its neighbors, the error spreads like falling dominoes until the iron loses its magnetism. Moreover, a deeply held physics theorem holds that the alignment process works only in three-dimensional objects, Toner says, adding that birds often flock in 2-D formations.
In a computer simulation based on magnetism principles, Vicsek designed "virtual birds." Then he designated the flock size, space between birds, how often birds check their positions, and how far off the flock's course any one bird might stray before correcting itself. Then he gave his birds a prod. They quickly organized and on average moved in the same direction. "At first glance that doesn't seem strange," Toner says, "except that it happened in two dimensions," thus violating the rigorously proved theorem dealing with magnetism.
The difference seemed to hinge on motion. Atoms in a magnet are essentially stationary; birds are not. So Toner and fellow physicist Yuhai Tu, of the IBM Watson Research Center in Yorktown Heights, N.Y., based their approach on the motion of fluids. When they ran their simulation, it not only verified that motion invalidated the theorem involving magnetism. It also yielded realistic predictions of how densely the birds would be packed and how that density changes over time.
In essence, he says, the theory deals well with cloud-like flocks, but not with birds such as geese that maintain a clear shape. Dr. Heppner holds that Toner's and Dr. Tu's approach, published in this month's issue of the journal Physical Review E, appears similar to simulations he and colleagues published in 1990.
Computers may be about the only tools for studying flocking behavior. He recalls spending months training pigeons and preparing equipment for one field experiment, only to have the flock blast apart and vanish after being released. A hawk had seen the birds and "came out of the woods like a locomotive," he says. "The birds took off and never came back."