Mathematicians explain how some fireflies flash in sync
Stake out in Pennsylvania’s Cook State Forest at the right time of year and you can see one of nature’s great light shows: swarms of fireflies that synchronize their flashes like strings of Christmas lights in the dark.
A new study by Pitt mathematicians shows that math borrowed from neuroscience can describe how swarms of these unique insects coordinate their light show, capturing key details about how they behave in the wild.
“This firefly has a quick sequence of flashes, and then a big pause before the next burst,” said Jonathan Rubin, professor and chair of the Department of Mathematics in the Kenneth P. Dietrich School of Arts and Sciences. “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.”
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,” said co-author Bard Ermentrout, distinguished professor of mathematics in the Dietrich School. “Physicists, mathematicians, we’re all interested in synchronization.”
To crack the fireflies’ light show, the Pitt team 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 (A&S ’22) published details of their model Oct. 26 in the Journal of the Royal Society Interface. More

