  In swarms of flying insects, the motions of individuals are largely
uncoordinated with those of their neighbors, unlike the highly ordered motion
of bird flocks. However, it has been observed that insects may transiently form
pairs with synchronized relative motion while moving through the swarm. The
origin of this phenomenon remains an open question. In particular, it is not
known if pairing is a new behavioral process or whether it is a natural
byproduct of typical swarming behavior. Here, using an "adaptive-gravity" model
that proposes that insects interact via long-range gravity-like acoustic
attractions that are modulated by the total background sound (via "adaptivity"
or fold-change detection) and that reproduces measured features of real swarms,
we show that pair formation can indeed occur without the introduction of
additional behavioral rules. In the model, pairs form robustly whenever two
insects happen to move together from the center of the swarm (where the
background sound is high) toward the swarm periphery (where the background
sound is low). Due to adaptivity, the attraction between the pair increases as
the background sound decreases, thereby forming a bound state since their
relative kinetic energy is smaller than their pair-potential energy. When the
pair moves into regions of high background sound, however, the process is
reversed and the pair may break up. Our results suggest that pairing should
appear generally in biological systems with long-range attraction and adaptive
sensing, such as during chemotaxis-driven cellular swarming.
