Mean acceleration as a function of position.
(a,b) Mean acceleration conditioned on position in (a) the vertical direction and (b) one horizontal direction. The conditional acceleration varies linearly with a negative slope as a function of position. (c,d) Effective “spring constants” extracted from linear fits to the data in (a) and (b). The effective elastic potentials are stiffer in both directions for smaller swarms. (e) Mean-squared displacement as a function of time averaged over all midges. The dashed line indicates a t2 power law and the data (solid) follow that trend, implying ballistic flight. This power law breaks down only at the swarm edges.