Insect swarms can be bound together by repulsive forces

. The cohesion of insect swarms has been attributed to the fact that the resultant internal interactions of the swarming insects produce, on the average, a centrally attractive force that acts on each individual. Here it is shown how insect swarms can also be bound together by centrally forces that on the average are repulsive (outwardly directed from the swarm centres). This is predicted to arise when velocity statistics are heterogeneous (position-dependent). Evidence for repulsive forces is found in laboratory swarms of Chironomus riparius midges. In homogeneous swarms, the net inward acceleration balances the tendency of diffusion (stochastic noise) to transport individuals away from the centre of the swarm. In heterogenous swarms, turbophoresis --the tendency for individuals to migrate in the direction of decreasing kinetic energy-- is operating. The new finding adds to the growing realization that insect swarms are analogous to self-gravitating systems. By acting in opposition to central attraction (gravity), the effects of heterogeneous velocities (energies) are analogous to the effects of dark energy. The emergence of resultant forces from collective behaviours would not be possible if individual flight patterns were themselves unstable. It is shown how individuals reduce the potential for the loose of flight control by minimizing the influence of jerks to which they are subjected. Graphical abstract