Swarm formation as backward diffusion.

Considerable progress has been made in understanding insect swarms-forms of collective animal behaviour that unlike bird flocks, fish schools and animal herds do not possess global order. Nonetheless, little is known about swarm formation. Here we posit a mechanism for the formation of insect swarms that is consistent with recent empirical observations reported by (Patel and Ouellette 2022). It correctly predicts new features of swarm formation that have not been reported on previously. Our simple analytically tractable model shows how harmonic potential wells, a characteristic feature of swarming, and so swarm cohesion, arise from diffusion and local fission-fusion dynamics and how, in accord with observations, these wells deepen over time. The overall form of these potential wells is predicted to depend on the number and spatial distribution of all individuals, making them manifestly a collective phenomenon. Finally, swarms are predicted to 'cool' (that is, condense) as they form.