To achieve their extraordinary coordination, starling flocks in flight behave mathematically like metals becoming magnetized, researchers say.

The same group previously described aspects of starling flocking with equations used to describe avalanches. The birds’ aerial formations don’t just transcend biology, but span multiple physical phenomena.

“They are an example of a system where collective phenomena emerge from short-range interactions. This is the kind of phenomenon that statistical physicists are used to dealing with,” said statistical physicist Irene Giardina of the University of Rome, co-author of a March 13 Proceedings of the National Academy of Sciences starling study.

Though flocks of common starlings — murmurations of Sturnus vulgaris vulgaris, in technical and taxonomical parlance — can be found across North America and western Europe, Rome’s flocks are renowned for their size, making them natural subjects for Giardina’s team.

Using multiple video cameras and software that tracks the trajectories of individual birds, the researchers analyze flock dynamics from second to second, in purely mathematical terms.

In a 2010 study, they showed that changes in the velocity of any one bird affected the velocity of all other birds in a flock, regardless of the distance between them.

That sort of relationship is known as a scale-free correlation, and is seen in systems poised at the edge of criticality, like snow crystals in the moments before an avalanche.

In the new study, the researchers looked not at velocity but at orientation, measuring how a change in direction by one bird affected others.

Rather than affecting every other flock member, orientation changes caused only a bird’s seven closest neighbors to alter their flight. That number stayed consistent regardless of flock density, making the equations “topological” rather than critical in nature.

“The orientations are not at a critical point,” said Giardina. Even without criticality, however, changes rippled quickly through flocks — from one starling to seven neighbors, each of which affected seven more neighbors, and so on.

The closest statistical fit for this behavior comes from the physics of magnetism, and describes how the electron spins of particles align with their neighbors as metals become magnetized.

In future research, Giardina’s team plans to study flocking in other organisms, such as local species of midges, which demonstrate other patterns of collective flight.

Giardina wonders if different purposes give rise to different collective behaviors. Starling flocks seem optimized to evade predators, for example, while the purpose of midge flights seems to be mating. She also wants to study Rome’s starlings in higher video resolution, over longer periods of time.

“People are used to the flocks here, but they always wonder how it’s possible for them to act in such complex ways,” she said. “We looked at the flocks and said, ‘We should be able to do something about this. We should be able to understand.'”

Video: 1) Starling murmurations in the skies above Rome. (Starflag Project/CNR-INFM) 2) Starlings flocking near Oxford, England. (Dylan Winter)

Citation: “Statistical mechanics for natural flocks of birds.” William Bialek, Andrea Cavagna, Irene Giardina, Thierry Mora, Edmondo Silvestri, Massimiliano Viale and Aleksandra M. Walczak. Proceedings of the National Academy of Sciences, Vol. 109 No. 11, March 13, 2012.