Firefly courtship as the basis of the synchronization-response principle

Response to synchronization seems to be a widespread phenomenon specially in biological systems. We highlight this phenomenon studying the courtship of flashing fireflies in which arises a typical collective rhythm occurring only among the males and it is followed by a response of the females. Based on a model issued from electronic fireflies, we explain the synchronization of the males and the active responses of the females in the courtship of mingled (both sexes) populations of fireflies. The model also explains the courtship behavior of other species whose interactions follow the same logic even if their physical features are different. Moreover, the model can make predictions on the behavior of mingled and mixed (natural and artificial) groups of such animals. This finding could be considered as the basis of a new principle, namely the synchronization-response. Introduction . – Synchronization has been extensively studied as an ubiquitous phenomenon which occurs due to the coupling of self-sustained oscillators [1]. Many biological systems exhibit synchronous behavior that could constitute a manifestation of functional processes such as in cardiac cells [2] or pathological ones such as in the neurons triggering epileptic seizures [3]. On the other hand, numerous species use synchronization as a form of communication that allows the accomplishment of certain tasks and more important, it is an essential ingredient in their reproduction as a first step in the courtship. Animals have different strategies in order to attract conspecifics of opposite sex. One of these strategies consists in the aggregation of males performing displays which constitute a signal to communicate with the females. There are abundant examples of species using this strategy. Among the courtship displays performed by the males, synchronization is one of the most wellknown [4]. In several species the males synchronize their physical signals as a preliminary step in the courtship. (a)E-mail: gramirez@ulb.ac. be Synchronization in crickets [5, 6], katydids [7–10], cicadas [11], frogs [12,13], and crabs [14,15] among others, constitute examples in which males use their mechanical signals for this purpose. In each case, the communication occurs with different types of signals but exhibiting similar features for their courtship. On the other hand, fireflies use electromagnetic signals (light pulses) to communicate and they are able to synchronize their flashes. Synchronization in ensembles of fireflies is one of the most attractive biological phenomena and it was described mostly in Asian [16–18] and in American species [19–23]. Some mathematical models have attempted to explain the synchronous behavior in certain species, in particular in Photinus pyralis [24, 25] and Pteroptyx malaccae [26]. In all these models, the authors considered relaxation oscillators coupled by pulses or slight stimuli. Although the obtained results describe quite well the observations, all these models considered several simplifications and even some unrealistic features such as instantaneous flashes, thus describing only “a partial” story concerning the fireflies’ courtship: how the males are able to synchronize. However, it is crucial to include the females’ active role and its implications as Moi-