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SWARM BREWINGThe desert locust, Schistocerca gregaria, can rapidly switch from a solitary insect to part of a swarming mass. Physicists are studying how that change occurs in hopes of better controlling locust plagues.Gabriel Miller

Mathematicians have now figured out the dynamics that drive locusts across the landscape, devastating everything underfoot — and the math says people will never be able to predict where the little buggers will go.

The new analysis, reported in an upcoming issue of Physical Review E, suggests that random factors accumulate and influence how swarming locusts collectively decide to change course.

“These swarms are driven by intrinsic dynamics,” says team member Iain Couzin, a biologist at Princeton University. “In all practical terms, predicting when a swarm is going to change direction is going to be impossible.”

Still, others say the information may one day allow researchers to better inform locust-control efforts — for instance, by suggesting the best times and places to apply insecticide ahead of an approaching swarm.

Desert locusts, Schistocerca gregaria, normally live in arid parts of Africa and Asia but can explode over millions of square kilometers during plagues, as happened during the late 1980s. Researchers understand much of the basic biology behind locust swarms — even how the insects change color as they mass together — but the physics describing their collective behavior has been something of a mystery.

That began to change a few years ago, when an interdisciplinary group of mathematicians, biologists and others were inspired to look at the basic physics of locust swarming. By putting more and more locusts into a ring-shaped arena 80 centimeters in diameter, the team watched as, at a critical density, the locusts switched from wandering around on their own to behaving as a group.

In new work, Carlos Escudero of the Consejo Superior de Investigaciones Científicas in Madrid looked further at the mathematics underlying this change in behavior. From watching locusts in the arena he and his colleagues came up with an equation, called a Fokker-Planck equation, that describes how the density of particles (or in this case, insects) changes over time.

Further analysis showed that a number of random factors influence when the insects decide to change direction. Mathematically, the change in the locusts’ direction is similar to switches in magnetic properties that occur among clumps of magnetic particles at high temperatures, Escudero says. In both cases, random influences accumulate until suddenly the whole system changes its behavior.

“It’s impossible to know when the next switch will happen,” Escudero says. “Still, we have a little bit more understanding on how these perturbations are produced, and we hope that in the long run we can apply this practically.”

Jerome Buhl, a biologist at the University of Sydney in Australia, notes that swarming locusts typically start their morning in a dense clump and spread out over the course of the day. The best time to target spraying, he says, might therefore be right after the insects start marching, because over time their behavior will become less predictable.

“What we need to do now is to work out the maths behind this,” Buhl says, “and we’ll be able to determine which way to lay the barriers ahead of a band to more likely be optimal, potentially saving on the amount of insecticide used and minimizing the impact of control.”

Buhl and other researchers are gearing up for an imminent expected plague of a different locust species in Australia. The team plans to glue tiny reflectors to locusts, then fly unmanned aerial vehicles over the swarms to track the behavior of individuals within the group.

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