Locusts and other migrating insects form cohesive swarms that travel over huge distances and can have a devastating effect on crops, leading to famine and starvation. Understanding the factors that enable the long-term cohesion of such swarms is therefore of paramount importance. When placed in an annular arena, a population of locusts march together in a common direction, which may be reversed at later times. These directional switches are more frequent at lower population numbers. We propose a novel, minimal, spatially-homogenous model of locust interactions to investigate the individual-based mechanisms of the observed density-dependent macroscopic-level effect. This model successfully replicates the density-dependent properties of the experimental data as a consequence of the demographic noise inherent at low population numbers. The ability of our non-spatial model to replicate the experimental data indicates that the switching behaviour is a fundamental property of the way locusts interact rather than an effect of the environmental geometry. However, to match the data it is necessary to include higher-order interactions in the model, indicating that locusts can incorporate information from at least two neighbouring individuals travelling in the opposite direction. We derive a stochastic differential equation from our individual-based model, and demonstrate agreement between its drift and diffusion coefficients and those calculated numerically directly from the experimental data. Using the experimental data to parameterise our model, we demonstrate that the model replicates both the qualitative form of the time-dependent data and quantitative statistics such as the mean switching time and stationary probability distribution.
A minimal model captures the collective behaviour of locusts
Christian A. Yates, Louise Dyson, Jerome Buhl, Alan J. McKane
Via Complexity Digest