Locust Collective Motion and Its Modeling

Abstract

Over the past decade, technological advances in experimental and animal tracking techniques have motivated a renewed theoretical interest in animal collective motion and, in particular, locust swarming. This review offers a comprehensive biological background followed by comparative analysis of recent models of locust collective motion, in particular locust marching, their settings, and underlying assumptions. We describe a wide range of recent modeling and simulation approaches, from discrete agent-based models of self-propelled particles to continuous models of integro-differential equations, aimed at describing and analyzing the fascinating phenomenon of locust collective motion. These modeling efforts have a dual role: The first views locusts as a quintessential example of animal collective motion. As such, they aim at abstraction and coarse-graining, often utilizing the tools of statistical physics. The second, which originates from a more biological perspective, views locust swarming as a scientific problem of its own exceptional merit. The main goal should, thus, be the analysis and prediction of natural swarm dynamics. We discuss the properties of swarm dynamics using the tools of statistical physics, as well as the implications for laboratory experiments and natural swarms. Finally, we stress the importance of a combined-interdisciplinary, biological-theoretical effort in successfully confronting the challenges that locusts pose at both the theoretical and practical levels.

Fig 1

(A) A major behavioral characteristic of locusts in the gregarious phase is their strong propensity to form mass aggregations, as demonstrated by these desert locust nymphs. (B) Both swarming and marching start very early, already a few days after hatching, as demonstrated by these first larval instar desert locusts. (C) The endless marching bands of locust nymphs exemplify extreme coordination in their movement vectors during collective motion. (D) Road kills (nymphs hit by passing cars while the swarm crosses a road) will be immediately cannibalized by others (arrows). Locusts stopped in the midst of the swarm to feed on the cadavers will be totally ignored by others. Continuous and careful monitoring of individuals within a crowd in controlled lab experiments (E and F) have enhanced the development of quantitative analysis and theoretical modeling of individual dynamics and interactions, leading to various models of coordinated collective behavior.

Fig 2

(A) Sample trajectories for the Czirók model. Blue curve: ρ = 0.1. Red curve: ρ = 3.2. (B) Sample trajectories with individual-choice (I-C) interactions. Blue curve: ρ = 0.2. Red curve: ρ = 3.2. Note that the time scale between two models differs by a factor of ten. (C) Mean transition rates as a function of ρ. (D) The average order parameter as a function of ρ.

Fig 3. Coarse grained dynamics.

Left: the effective drift F(ϕ). Right: The effective diffusion D(ϕ). Top: for Czirók model. Middle: Buhl model. Bottom: Pause-and-go model. In both the Czirók and Buhl models, depending on concentration, either ϕ = 0 or ϕ = ~±1 are stable, but not both. However, in the pause-and-go model, all three states are stable at sufficiently high concentrations.