Swarming is a form of collective animal behavior in which a self-organized non-equilibrium system remains cohesive although it exhibits no clear order parameter. Such behavior is observed in a variety of species, such as fish, bats and flying insects. We proposed a model for the behavior of flying insects (midges) whose main ingredients are effective pull by acoustic long range (power-law) interactions and a non-linear modification of the response in the form of adaptivity, as most sensory systems in biology have.

The model described many of the mean-field features of the observed swarms. In addition to steady-state features, recent observations have found intriguing formation of synchronized pairs of midges, which typically oscillate with respect to each other at higher frequency and with a small distance between them, while they move together through the swarm. Here we report that pairing is a byproduct of the non-linear nature of the same model of adaptive long-range interactions (ALRI), without any modifications. Therefore pairing can be viewed as an emergent phenomenon, which is a natural outcome of the same interactions that lead to swarm formation.