A behavior seen among colonies of some ants has mystified scientists for more than 30 years. It’s their ability to suddenly burst into action, despite no leader telling the others when to start. What triggers this community call to action has remained a mystery — until now.

Colonies of acorn ants often spend long stretches resting quietly. It’s like everyone’s asleep. Then, points out a trio of researchers, “like a cascade of dominoes, a massive spike of activity sweeps through the nest.” It’s one example of what’s known as collective behavior. That trio — a biologist and two engineers — teamed up to explore what might serve as the alarm that tells everyone to wake up and get to work.

Since they couldn’t tap into the ants’ thinking, the researchers decided to model what they were observing. And to do this, they turned to math.

Their new computer model confirms that a single ant is all it takes to get things moving. Its motion kick-starts activity in the ants it meets, who in turn do the same to every ant they meet. But — and this is important — the model finds that the initial ant can spark activity throughout the rest of its colony only when three conditions line up.

Michael Napoli and Maurizio Porfiri are engineers at New York University in New York City. Biologist Simon Garnier works at the New Jersey Institute of Technology in Newark. They shared their new findings August 5 in PRX Life.

How one ant wakes a colony

Their model starts with a colony of quiet ants. Then, it lets any member start moving. Who it is can be quite random. As a moving ant bumps a neighbor, it sets that second ant into action. But once an ant stops moving, the model found, it would need to rest for a while before it can become active again.

Three conditions seem to limit whether an individual can spark everyone else into action. The first is how quickly activity can travel through the colony. Think of a game of tag. You tag more people if you run fast — or if the playground is packed and someone’s always within reach. Ants work the same way. Activity spreads when ants move fast enough to keep bumping into nestmates or when the nest is crowded. In a really packed nest, the first ant (and all the rest) barely need to move before others are being jostled.

Condition two is how easily ants respond to being bumped. When a moving ant reaches a still one, that neighbor has to be likely to start moving, too. If ants are hard to stir, the spark fizzles. One ant wanders the nest but wakes nobody; everyone else stays asleep.

The last condition is the trickiest. The whole colony has to switch off — go into rest mode — before the next spark. This, it turns out, is a balancing act. If ants settle down too slowly, the colony never fully settles down. But if they settle too quickly, the early motions die out before they can spread to many others.

In the model, colonies that met all three conditions burst. Those that fell short of any one of those conditions didn’t. Scientists call this kind of flip — from a colony that never bursts to one that does — a phase transition. Physicists use this term for “drastic shifts, like liquid water freezing into solid ice,” the team explains.

How well does the model match real ants?

The team built its model using measurements that others had made on real acorn ants. These included how fast they walk and how long they walk before stopping. A few features, such as the resting period, had to be estimated from the behavior of whole colonies.

Kirsten Prior expected a more biological explanation, such as a chemical signal or some form of decision-making. “Instead, this study suggests bursts come down to simply speed and contact rate,” she says. “That’s a bit humbling to me as an ant biologist.”

Prior, who works at Binghamton University in New York, studies how ants shape forests by carrying seeds around. She had no role in the new work.

“Since this paper relies on computer [models], experiments with real colonies will be necessary to test the predictions of the model,” says Grant Navid Doering. A biologist at Bilkent University in Ankara, Turkey, he studies how ant colonies coordinate their behaviors. Napoli, Garnier and Porfiri used measurements from Doering’s earlier work to set some of the numbers in their new model.

Elva Robinson wants to know what purpose the bursts serve. The model, she says, has opened a “black box” on one behavior — how bursts happen. But it does not explore what a colony gains from them. And that is of particular interest to Robinson, who tracks individual ants inside colonies. An ecologist, she works at the University of York in England.

Ants may not be the only creatures that work this way, the new study’s authors point out. They suspect the same conditions could apply anywhere individuals set each other off. Take a 2015 study of grazing sheep, for instance. There, one animal moving close to its neighbor started a chain reaction that caused the whole herd to pack tightly together. As with the ants, no one gave an order. But once action starts, it spreads to the whole group.