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When stretched with light signals, rummy-nose tetra schools snap back like rubber bands thanks to purely social forces.

Andriy Kotlyarov/

How a school of fish is like a rubber band

BOSTON—Physicists have long noted striking similarities between the movements of flocks of animals and the behavior of atoms and molecules. Now, one physicist has gone further and devised a way to measure the springiness and “temperature” of a school of fish. Such methods may aid physicists in their efforts to analyze flocks of animals as objects made of living “active matter.”

To a physicist’s eye, hordes of animals often resemble inanimate physical systems in uncanny ways. For example, mackerel in a school tend to swim in the same direction, aligning their bodies to their neighbors much as iron atoms align their spins to make the metal magnetic. Similarly, a murmuration of starlings wheeling across the sky looks much like fluid droplets as they flow, stretch, and swirl in response to some unseen stirring (perhaps the wind).

Such collective behavior arises not because of some grand design, but because each individual moves in response to the animals next to it. “Flocks are held together because the individuals are tracking their neighbors,” says Nigel Goldenfeld, a physicist at the University of Illinois in Urbana who was not involved in the new work. “They’re not paying any attention to the flock as a whole.”

Describing a flock as a material system isn’t easy, however, because the individual interactions aren’t physical but social. Nevertheless, James Puckett, a physicist at Gettysburg College in Pennsylvania, and his students have found a way to measure material properties of a school of rummy-nose tetras (Hemigrammus rhodostomus), a freshwater tropical fish about 3.5 centimeters long that originated in South America. The tetras stick together but have no social hierarchy and avoid light, Aawaz Pokhrel, an undergraduate student working with Puckett told a meeting of the American Physical Society here on 4 March. That makes them ideal for group experiments.

To measure the school’s elasticity or springiness, Pokhrel placed 50 tetras in just a few centimeters of water in a large tank, so the fish could only swim horizontally. He shone a light from above, causing the fish to congregate in a square shadow about 25 centimeters wide in the center of the tank. Using computer controls, Pokhrel then split the shadow and moved the two halves apart. In response, the school of fish would stretch out until it suddenly snapped back, with fish darting to one shadow or the other. Pokhrel filmed it all using infrared light the fish cannot see. “Basically, the social forces overcome the external perturbation” of the light, Pokhrel says.

Were the school the same as a simple spring, the rate at which the fish accelerate toward the center would increase in proportion with their distance from it. By tracking individual fish, Pokhrel found that, on average, that’s exactly what happened. From the data, he extracted the rate at which acceleration increases with distance—the spring constant—and found that a school of rummy-nose tetra is extremely elastic: Stretch it a given amount and it pulls back with only about one–ten-thousandth the force of a rubber band.

Similarly, Julia Giannini, a graduate student at Syracuse University in New York—who until recently worked with Puckett—reported a way to measure an effective “temperature” of a school of tetras. In an ordinary material, temperature is a measure of the average energy of the constituent atoms or molecules.

Using the tank, she confined 50 or 100 tetras in a circular shadow about 30 centimeters in radius and then shrank the circle at different speeds, causing the fish to crowd together. Using infrared tracking, she tallied the density of fish in the shadow. Using the individual fishes’ speeds, she calculated a quantity analogous to pressure. Just as with a volume of gas, the pressure increased in proportion to the density. And the constant of proportionality, which depends on the speed at which the circle shrinks, then plays the role of temperature, Giannini told the meeting. A fast-shrinking circle, for example, leads to “hotter” fish. Thus, the school of tetras acts like a gas with a constant, well-defined temperature.

The goal of such work is to describe the dynamics of a school of fish or flock of birds using its macroscopic “material” properties, without tracking the individual animals, Puckett says. Just how far you can push the materials analogy remains unclear, he acknowledges. For example, in thermodynamics, when gases of two different temperatures mix, they equilibrate at a common intermediate temperature. It’s not clear whether that would happen with the fish—or even how you could do that experiment, Giannini says.

The work has a lot of promise, Goldenfeld says. “They’ve got a way of doing controlled experiments that you can’t do with starlings,” he says. He adds that the work is still in its infancy, but after the talks, Goldenfeld buttonholed Puckett and his team to talk about a possible collaboration.