An Effective Hydrodynamic Description of Marching Locusts

Abstract: A fundamental question in complex systems is how to relate interactions between individual components ("microscopic description") to the global properties of the system ("macroscopic description"). Another fundamental question is whether such a macroscopic description exists at all and how well it describes the large-scale properties. Here, we address these questions using as a canonical example of a self-organizing complex system - the collective motion of desert locusts. One of the world's most devastating insect plagues begins when flightless juvenile locusts form "marching bands". Moving through semiarid habitats in the search for food, these bands display remarkable coordinated motion. We investigated how well physical models can describe the flow of locusts within a band. For this, we filmed locusts within marching bands during an outbreak in Kenya and automatically tracked all individuals passing through the camera frame. We first analysed the spatial topology of nearest neighbors and found individuals to be isotropically distributed. Despite this apparent randomness, a local order was observed in regions of high density with a clear second neighbor peak in the radial distribution function, akin to an ordered fluid. Furthermore, reconstructing individual locust trajectories revealed a highly-aligned movement, consistent with the one-dimensional version of the Toner-Tu equations, which are a generalization of the Navier-Stokes equations for fluids, used to describe the equivalent macroscopic fluid properties of active particles. Using this effective Toner-Tu equation, which relates the gradient of the pressure to the acceleration, we show that the effective "pressure" of locusts increases as a linear function of density in segments with highest polarization. Our study thus demonstrates an effective hydrodynamic description of flow dynamics in plague locust swarms.