Emergent periodicity in the collective synchronous flashing of fireflies

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.

Marmosets mutually compensate for differences in rhythms when coordinating vigilance

“…The Kuramoto model can indeed tolerate some level of variability in natural frequencies, but when the distributions are not narrow, as in the case of Photinus carolinus fireflies’ inter-flash intervals [82] or vigilance and feeding durations of marmosets, modifications to previous models are required. Akin to Sarfati et al’s extension to the integrate-and-fire model [67], our extension to the Kuramoto model allows users to implement it even when individual oscillators are not perfectly periodic and makes the model applicable to a much wider spectrum of biological phenomena. While the non-periodic model fit provides a more realistic estimate of the coupling strength, estimating other parameters, such as the critical coupling constant or time required to attain synchrony, is not straightforward.…”

“…Our predictions are threefold: 1) Most biological oscillators are not perfectly periodic, yet there are abundant examples of synchronisation in the animal world. We do not expect marmoset head oscillations to be periodic in the absence of any input from conspecifics, but we predict that they will still show anti-phase synchrony with a partner, given that the probability of an individual being vigilant when its partner is feeding has been shown to be higher than chance [63,[66][67][68]. 2) If marmosets are following simple, fixed interaction rules to coordinate vigilance, we would expect the coupling strengths to be more-or-less uniform across feeding bouts.…”

“…The Kuramoto model assumes that all oscillators are inherently periodic. However, Sarfati et al [67] recently showed that fireflies that do not inherently periodically flash can synchronise their flashing. Inspired by this phenomenon and the fact that we do not expect individual marmosets to demonstrate perfect periodicity in head oscillations, we came up with a modified form of the Kuramoto model, which does not assume that the oscillators are inherently periodic.…”

“…The Kuramoto model is one way to model the development of synchrony and its temporal variations, but it assumes that the individual oscillators are inherently periodic. We thus additionally developed a non-periodic version of the Kuramoto model, as many biological systems are not expected to be inherently periodic [66,67]. Further, we used a control model based on the behaviour (vigilance and feeding) of each of the individuals in the pair when they were situated alone on the feeding basket to model the amount of coupling behaviour that can be expected by chance.…”

Fantastic beasts and how to study them: rethinking experimental animal behavior

“…In contrast, some animals would rather avoid or even eat same-sex conspecifics, as they represent competitors for food and mates ( Vijendravarma, 2023 ). Sophisticated behaviors can also emerge from individuals operating on relatively simple nearest-neighbor algorithms without an inherent social structure ( Bialek et al, 2012 ; Ding et al, 2019 ): at high density, locust swarms start migrating due to each individual avoiding being eaten by a conspecific ( Guttal et al, 2012 ), and some fireflies synchronize their pulses with the flashes from another ( Sarfati et al, 2023 ).…”