Math clarifies how some fireflies twinkle in sync

Math borrowed from neuroscience can describe how swarms of fireflies coordinate their light show, researchers report.

Their new study captures key details about how fireflies behave in the wild.

“This firefly has a quick sequence of flashes, and then a big pause before the next burst,” says Jonathan Rubin, professor and chair of the department of mathematics at the University of Pittsburgh.

“We knew a good framework for modeling this that could capture a lot of the features, and we were curious how far we could push it,” Rubin says.

Male fireflies produce a glow from their abdomens to call out to potential mates, sending out blinking patterns in the dark to woo females of their own species. Synchronous fireflies of the species Photinus carolinus take it a step further, coordinating their blinking throughout entire swarms.

It’s a rare trait—there are only a handful of such species in North America—and the striking lights they produce draw crowds to locations where the insects are known to gather.

They’ve also attracted the interest of mathematicians seeking to understand how they synchronize their blinks. It’s just one example of how synchronization can evolve from randomness, a process that has intrigued mathematicians for centuries.

One famous example from the 1600s showed that pendulum clocks hung next to one another synchronize through vibrations that travel through the wall, and the same branch of math can be used to describe everything from the action of intestines to audience members clapping.

“Synchrony is important for a lot of things, good and bad,” says coauthor Bard Ermentrout, professor of mathematics. “Physicists, mathematicians, we’re all interested in synchronization.”

To crack the fireflies’ light show, the researchers used a more complex model called an “elliptic burster” that’s used to describe the behavior of brain cells. The duo, along with then-undergrad Madeline McCrea, published details of their model in the Journal of the Royal Society Interface.

The first step was to simulate the blinks of a single firefly, then expand to a pair to see how they matched their flashing rates to one another. Next, the team moved to a bigger swarm of simulated insects to see how number, distance, and flying speed affect the resulting blinks.

Varying the distances each firefly could “see” each other and respond to one another changed the insects’ light show: By tweaking the parameters, they could produce patterns of blinks that looked like either ripples or spirals.

The results line up with several recently published observations about real-life synchronous fireflies—for instance, that individual fireflies are inconsistent while groups flash more regularly, and that when new fireflies join the swarm, they’re already perfectly in time.

“It captured a lot of the finer details that they saw in the biology, which was cool,” says Ermentrout. “We didn’t expect that.”

The math also makes some predictions that could inform firefly research—for instance, light pollution and the time of day both may alter the patterns produced by fireflies by changing how well they can see one another’s blinks.

The team is the first to use this particular brain-cell framework to model fireflies, which several different research teams are trying to understand using different types of math.

“It’s more of a wild west research topic,” says Ermentrout. “It’s early days, and who knows where things are going to go from here?”

Source: Patrick Monahan for University of Pittsburgh