An effective hydrodynamic description of marching locusts and their local structure

The formation of locust swarms, one of the worlds’ most devastating insect plagues, begins when flightless juvenile locusts form “marching bands”. Marching through semi-arid habitats in search for nutrients and future breeding grounds, locusts show a remarkable example of coordinated motion, whose understanding can be of key importance for forecasting plagues’ progression. To better predict the movement patterns of the desert locust Schistocerca gregaria, we investigated how well movement of locust bands can be described by physical models and how they respond to external terrain restrictions (funnelling and splitting). To do so, locusts were recorded in the field negotiating obstacles and moving through funnels set up by the experimenters. Using automated video tracking, we then reconstructed individual trajectories of the locusts.

We found that locusts show highly coordinated movement and, in analogy to a two dimensional fluid, exhibited stationary flow for long periods. The highly polarized flow of locusts showed consistency with the one dimensional version of the Toner-Tu equations, a generalization of the Navier-Stokes equations to describe a flow of active particles. The effective equation relates the gradient of the pressure to the acceleration and through this we found that the ‘pressure’ is roughly linear with the density at the segments with the highest polarization.

We further analyzed the topology of the group and found that the density of nearest neighbors around a focal individual is nearly isotropic once locusts’ body shapes are accounted for, indicating random arrangement of individuals. However, despite this apparent randomness we observe that there is some degree of local ordering in the radial distribution of densities. The radial distribution function in high density regions shows visible second neighbor peaks similar to that of an ordered fluid, supporting our fluid dynamics based approach.