How Fireflies Sync Up Their Dazzling Light Shows With Mathematical Precision
Mathematicians took a cue from nature by studying how fireflies synchronize their flashes.
Researchers used a complex elliptic burster model of brain cell behavior to understand the synchronization.
Synchronizing their flashes allows the fireflies to respond to one another.
What human mathematicians must learn how to model is just a way of life for fireflies in Pennsylvania’s forests.
A new study from researchers at the University of Pittsburgh shows that math borrowed from neuroscience can help describe how swarms of fireflies coordinate their light show. The work successfully simulated the complexities of the insects’ perfect synchrony. In their new paper, published late last month in the Journal of the Royal Society Interface, the team details the model they created.
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“Sometimes capturing the effects seen in nature requires a model to be pushed into a [behavioral model that changes over time] that we would have been unlikely to have identified and analyzed without the original observation,” Jonathan Rubin, professor and chair of Pitt’s Department of Mathematics and co-author of the study, tells Popular Mechanics.
Male fireflies, specifically Photinus carolinus, produce a glow from their abdomens to signal to potential mates. They can create blinking patterns that their species then synchronizes throughout entire swarms—a rare spectacle only a handful of species in North America can pull off. Along with attracting mates and curious human onlookers, this phenomenon intrigued mathematicians seeking to understand how they synchronize their blinks. The behavior allows random blinks to evolve into perfect synchrony to the point that new fireflies can join the swarm, immediately matching the pattern.
“Synchronization in general is a fascinating topic in the study of dynamics,” Rubin says. Dynamics, or dynamical systems, obey a specific, consistent set of laws over time. By studying them, researchers can understand how they behave, and then use them to build predictive models. Such models can predict planetary orbits and the path of a viral disease through a population.
“From a theory perspective, lots of interesting questions arise,” Rubin says. What factors between units (in this case, firefly blinks) stabilize or destabilize their synchrony, for instance? The phenomenon of synchrony is everywhere, in life and in technical applications, from mechanical systems to information processing among neurons in the brain. You can find this behavior at work when an audience applauds, as hundreds of individual claps synchronize temporarily to clap as one.
To help understand the fireflies’ light show, the Pitt team employed a complex “elliptic burster” model often used to describe the behavior of brain cells. They first simulated the blinks of a single firefly, then expanded to a pair to see how they matched their flashing rates. Next, the team moved to a bigger swarm of simulated insects to see how the number of fireflies, distance, and flying speed impacted the resulting blinks.
Varying the distances from which each firefly could see and respond to one another changed the insects’ light show, they found. By tweaking the parameters, they could produce patterns of blinks that appeared as either ripples or spirals—results that line up with observations about real-life fireflies.
“It captured a lot of the finer details that they saw in the biology, which was cool,” Bard Ermentrout, a professor of mathematics at Pitt and a co-author of the new study, says in a statement. “We didn’t expect that.”
Rubin says the elliptic burster model naturally produces the same pattern as Photinus carolinus, known to emit bursts of flashes separated by quiet periods. “Interestingly, the flashes in a single elliptic burster model with noise occur with irregular timing, yet coupling between multiple bursters causes their flashes to become much more regular, just like what happens in groups of the fireflies,” he says. “Also, when the influence of some flashing elliptic bursters causes another one to start flashing, it joins the group in sync with the ongoing flashes, again, just like the fireflies.”
Pairing this model with the example of nature can lead to new analytical insights, Rubin says. “Sometimes we have to invent new mathematical definitions to describe properties observed in nature,” he says, “and this leads to realizations about connections to existing mathematical structures and, in some cases, a new way to prove results about those existing structures.”
The connection between math and fireflies is encouraging further study. Ermentrout tells Popular Mechanics he’s already working on “modeling another species of fireflies that has a very different synchronization pattern.”
Rubin knows the field remains significant. “Synchronization and other pattern formation will continue as topics of study for me and many others in applied mathematics,” Rubin says. “Continuing with fireflies will in part depend on what new data comes out, what future students are interested in, and what sort of feedback we receive on our work so far.”
But if nothing else, Rubin has developed a newfound fascination with the flashing insects.
“I convinced my wife to go on a trip for a couple of days right in the peak of the season,” he says about fireflies putting on a show in the Cook State Forest. “It’s not clear we ever saw synchronized activity, but there were all sorts of fireflies around us. It was amazing.”
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