ABSTRACT
In isolation from their peers, Photinus carolinus fireflies flash with no intrinsic period between successive bursts. Yet, when congregating into large mating swarms, these fireflies transition into predictability, synchronizing with their neighbors with a rhythmic periodicity. Here we propose a mechanism for emergence of synchrony and periodicity, and formulate the principle in a mathematical framework. Remarkably, with no fitting parameters, analytic predictions from this simple principle and framework agree strikingly well with data. Next, we add further sophistication to the framework using a computational approach featuring groups of random oscillators via integrate-and-fire interactions controlled by a tunable parameter. This agent-based framework of P. carolinus fireflies interacting in swarms of increasing density also shows quantitatively similar phenomenology and reduces to the analytic framework in the appropriate limit of the tunable coupling strength. We discuss our findings and note that the resulting dynamics follow the style of a decentralized follow-the-leader synchronization, where any of the randomly flashing individuals may take the role of the leader of any subsequent synchronized flash burst.
ABSTRACT
Fireflies flashing in unison is a mesmerizing manifestation of animal collective behavior and an archetype of biological synchrony. To elucidate synchronization mechanisms and inform theoretical models, we recorded the collective display of thousands of Photinus carolinus fireflies in natural swarms, and provide the first spatiotemporal description of the onset of synchronization. At low firefly density, flashes appear uncorrelated. At high density, the swarm produces synchronous flashes within periodic bursts. Using three-dimensional reconstruction, we demonstrate that flash bursts nucleate and propagate across the swarm in a relay-like process. Our results suggest that fireflies interact locally through a dynamic network of visual connections defined by visual occlusion from terrain and vegetation. This model illuminates the importance of the environment in shaping self-organization and collective behavior.
ABSTRACT
During mating season, males of synchronous firefly species flash in unison within swarms of thousands of individuals. These strongly correlated collective displays have inspired numerous mathematical models to explain how global synchronous patterns emerge from local interactions. Yet, experimental data to validate these models remain sparse. To address this gap, we develop a method for three-dimensional tracking of firefly flashes, using a stereoscopic set-up of 360-degree cameras. We apply this method to record flashing displays of the North American synchronous species Photinus carolinus in its natural habitat as well as within controlled environments, and obtain the three-dimensional reconstruction of flash occurrences in the swarm. Our results show that even a small number of interacting males synchronize their flashes; however, periodic flash bursts only occur in groups larger than 15 males. Moreover, flash occurrences are correlated over several metres, indicating long-range interactions. While this suggests emergent collective behaviour and cooperation, we identify distinct individual trajectories that hint at additional competitive mechanisms. These reveal possible behavioural differentiation with early flashers being more mobile and flashing longer than late followers. Our experimental technique is inexpensive and easily implemented. It is extensible to tracking light communication in various firefly species and flight trajectories in other insect swarms.
