Mathematicians explain how some fireflies flash synchronously

At the right time of year, at the Cook State Forest in Pennsylvania, you can see one of nature's most spectacular light shows: swarms of fireflies flickering in sync, like Christmas lights in the dark
.

A new study by mathematicians at Pitt University suggests that mathematics borrowed from neuroscience can describe how these unique insects coordinate their light displays, capturing key details
of their behavior in the wild.

Professor Jonathan Rubin, chair of the Department of Mathematics at the Kenneth P.
Dietrich College of Arts and Sciences, said: "This firefly has a quick sequence of flashes and then a big pause
before the next flash.
" "We knew a good modeling framework that captured a lot of features, and we were curious how far
we could push it.
"

The belly of male fireflies emits a glow to call for a potential mate, and a blinking pattern in the dark to pursue females of their kind
.
Photinus carolinus, a species of synchronised fireflies, goes further, blinking in coordination throughout the colony
.
It's a rare trait — there are only a few such species in North America — and the amazing light they emit draws people to places where
insects gather.

They also attract the interest of mathematicians, who want to understand how they blink in sync
.
This is just one example of how synchronization has evolved from randomness, a process that has fascinated mathematicians
for centuries.
A famous example from the 17th century shows that pendulums hanging together are synchronized by vibrations within walls, and the same branch of mathematics can be used to describe everything
from gut movements to audience applause.

"Synchronicity is important for many things, both good and bad," said co-author Bard Ermentrout, a distinguished professor
of mathematics at Dietrich College.
"Physicists, mathematicians, we are all interested in synchronization"

To crack the glow of fireflies, Pete's team used a more complex model called an elliptical burst to describe the behavior
of brain cells.
The duo and then-undergraduate Madeline McCrea (Class of A&S 22) published details
of their model in the Oct.
26 issue of the Royal Society Interface Journal.

The first step is to simulate the blink of a firefly, then expand to a pair to see how they match each other's flashing rates
.
Next, the team studied a larger simulated insect colony to see how number, distance, and flight speed affected the resulting blink effect
.

They found that changing the distance at which each firefly could "see" each other and respond to each other changed the insect's light display: by adjusting the parameters, they could produce a blinking pattern
that looked like ripples or spirals.

The findings are consistent with several recently published observations of synchronized fireflies in real life — for example, individual fireflies flash inconsistently, while swarms of fireflies flicker more regularly, and when new fireflies join the colony, they are already perfectly
timely.

"It captures a lot of the finer details that they see in biology, which is cool
," Ermentrout said.
"That's what
we didn't expect.
"

Mathematics can also make predictions that can inform firefly research—for example, light pollution and the time of day may both alter patterns of their production by changing how well fireflies blink at each other
.

McCree participated in the research as an undergraduate student under the Academy's Painter Fellowship grant, which provided her with funding
to work on the project all summer.
Rubin said: "She was excellent on this project and very persistent
.

The team is the first to use this particular brain-cell framework to simulate fireflies, and several different research teams are trying to understand this
with different types of math.
"It's more of a Wild West research topic," Ermentrout said
.
"It's just getting started, and who knows how things will play out?"

Ermentrout and Rubin also hope that this mathematical approach will spark the imagination
of those inspired by the glow of fireflies.
During the course of the project, Rubin himself decided to travel to the Cook State Forest to see if he could find his research subjects
directly.

"I convinced my wife to travel for a few days
during the tourist season," he said.
"It's not clear if we've seen synchronized activity, but we have all kinds of fireflies
around us.
It's amazing
.
”