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A similar scenario played out in the 1990s, when a Tennessee naturalist named Lynn Faust read the confident published assertion of a scientist named Jon Copeland that there were no synchronous fireflies in North America. Faust knew then that what she had been watching for decades in the nearby woods was something remarkable.

Faust invited Copeland and Moiseff, his collaborator, to see a species in the Great Smoky Mountains called Photinus carolinus. Clouds of the male fireflies fill forests and clearings, floating at about human height. Instead of blinking in tight coordination, these fireflies emit a burst of quick flashes within a few seconds, then go quiet for several times that long before loosing another burst. (Imagine a crowd of paparazzi waiting for celebrities to appear at regular intervals, snapping a salvo of photos at each appearance, and then twiddling their thumbs in the downtime.)

Copeland and Moiseff’s experiments showed that isolated P. carolinus fireflies really did try to flash on beat with a neighboring firefly — or a blinking LED — in a nearby jar. The team also set up high-sensitivity video cameras at the edges of fields and forest clearings to record flashes. Copeland went through the footage frame by frame, counting how many fireflies were illuminated at each moment. Statistical analysis of this painstakingly gathered data proved that all the fireflies within the cameras’ view at a scene really did emit flash bursts at regular, correlated intervals.

Two decades later, when Peleg and her postdoc, the physicist Raphaël Sarfati, set out to collect firefly data, better technology was available. They designed a system of two GoPro cameras placed a few feet apart. Because the cameras took 360-degree video, they could capture the dynamics of a firefly swarm from within, not just from the side. Instead of counting flashes by hand, Sarfati devised processing algorithms that could triangulate on firefly flashes caught by both cameras and then record not just when each blink happened but where it occurred in three-dimensional space.

Sarfati first brought this system into the field in Tennessee in June 2019 for the P. carolinus fireflies that Faust had made famous. It was his first time seeing the spectacle with his own eyes. He had imagined something like the tight scenes of firefly synchrony from Asia, but the Tennessee bursts were messier, with bursts of up to eight quick flashes over about four seconds repeated roughly every 12 seconds. Yet that messiness was exciting: As a physicist, he felt that a system with wild fluctuations could prove far more informative than one that behaved perfectly. “It was complex, it was confusing in a sense, but also beautiful,” he said.

Random but Sympathetic Flashers

In her undergraduate brush with synchronizing fireflies, Peleg first learned to understand them through a model proposed by the Japanese physicist Yoshiki Kuramoto. This is the ur-model of synchrony, the granddaddy of mathematical schemes that explain how synchrony can arise, often inexorably, in anything from groups of pacemaker cells in human hearts to alternating currents.

At their most basic, models of synchronous systems need to describe two processes. One is the inner dynamics of an isolated individual — in this case a lone firefly in a jar, governed by a physiological or behavioral rule that determines when it flashes. The second is what mathematicians call coupling, the way the flash of one firefly influences its neighbors. With fortuitous combinations of these two parts, a cacophony of different agents can quickly pull itself into a neat chorus.

In a Kuramoto-esque description, each individual firefly is treated as an oscillator with an intrinsic preferred rhythm. Picture fireflies as having a hidden pendulum swinging steadily inside them; imagine a bug flashes every time its pendulum sweeps through the bottom of its arc. Suppose also that seeing a neighboring flash yanks a firefly’s pace-setting pendulum a little bit forward or back. Even if the fireflies start off out of sync with each other, or their preferred internal rhythms vary individually, a collective governed by these rules will often converge on a coordinated flash pattern.

Several variations on this general scheme have emerged over the years, each tweaking the rules of internal dynamics and coupling. In 1990, Strogatz and his colleague Rennie Mirollo of Boston College proved that a very simple set of firefly-like oscillators would almost always synchronize if you interconnected them, no matter how many individuals you included. The next year, Ermentrout described how groups of Pteroptyx malaccae fireflies in Southeast Asia could synchronize by speeding up or slowing down their internal frequencies. As recently as 2018, a group led by Gonzalo Marcelo Ramírez-Ávila of the Higher University of San Andrés in Bolivia devised a more complicated scheme in which fireflies switched back and forth between a “charging” state and a “discharging” state during which they flashed.

But when Peleg and Sarfati’s cameras began capturing three-dimensional data from the burst-then-wait Photinus carolinus fireflies in the Great Smokies in 2019, their analyses revealed new patterns.

One was the confirmation of something that Faust and other firefly naturalists had long reported: A burst of flashes would often start in one place and then cascade through the forest at about half a meter per second. The contagious ripples suggested that the coupling of fireflies was neither global (with the entire swarm connected) nor purely local (with each firefly caring only about close neighbors). Instead, the fireflies seemed to pay attention to other fireflies at a mix of distance scales. This could be because the fireflies can only see flashes that occur within an unbroken sightline, Sarfati said; in the forests, vegetation often gets in the way.

Real fireflies also seem to flout the core premise of Kuramoto-flavored models, which treat each individual as periodic. When Peleg and Sarfati released a single P. carolinus firefly in a tent, it emitted bursts of flashes randomly instead of following any strict rhythm. Sometimes it waited just a few seconds, other times a few minutes. “That already takes you out of the universe of all existing models,” Strogatz said.

But once the team dumped in 15 or more fireflies, the entire tent lighted up with collective flash bursts spaced about a dozen seconds apart. The synchrony and the group periodicity were purely emergent products of the fireflies hanging out together. In a draft paper uploaded to the biorxiv.org preprint server last spring, the Peleg group, working with the physicist Srividya Iyer-Biswas of Purdue University and the Santa Fe Institute, suggested a brand-new model for how this could happen.

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