Why swarming insects have perplexing spatial statistics

Unlike flocks of birds and schools of fish that show net motion and synchronized motion, insect mating swarms are stationary and lack velocity ordering. Their collective nature when unperturbed is instead evident in their spatial statistics. In stark contrast with bird flocks, wherein the number density can fluctuate enormously from flock to flock, the number density of individuals in laboratory swarms of the midge Chironomus riparius is approximately constant. Nonetheless, as swarms grow more populous, individuals cluster more and more. Here with the aid of stochastic trajectory models I show that these two seemingly contradictory behaviours can be attributed to the presence of multiplicative noise. The modelling also predicts that swarms are most stable when they are asymptotically large.