Locust Dynamics: Behavioral Phase Change and Swarming

Abstract

Locusts exhibit two interconvertible behavioral phases, solitarious and gregarious. While solitarious individuals are repelled from other locusts, gregarious insects are attracted to conspecifics and can form large aggregations such as marching hopper bands. Numerous biological experiments at the individual level have shown how crowding biases conversion towards the gregarious form. To understand the formation of marching locust hopper bands, we study phase change at the collective level, and in a quantitative framework. Specifically, we construct a partial integrodifferential equation model incorporating the interplay between phase change and spatial movement at the individual level in order to predict the dynamics of hopper band formation at the population level. Stability analysis of our model reveals conditions for an outbreak, characterized by a large scale transition to the gregarious phase. A model reduction enables quantification of the temporal dynamics of each phase, of the proportion of the population that will eventually gregarize, and of the time scale for this to occur. Numerical simulations provide descriptions of the aggregation's structure and reveal transiently traveling clumps of gregarious insects. Our predictions of aggregation and mass gregarization suggest several possible future biological experiments.

Biological Aggregation Driven by Social and Environmental Factors: A Nonlocal Model and Its Degenerate Cahn--Hilliard Approximation

“…We investigate this problem within the framework of (29). The locust model in [66] includes additional effects-crucially, the phase change from solitarious to gregarious locusts-but an understanding of the interaction between locusts and food sources even in the absence of phase change is an appropriate starting point for investigation. …”

“…The aggregation equation has recently been the subject of a rich and rapidly growing literature, including [10,12,13,15,16,17,18,22,23,39,40,46,47,48,63,68] and has also been adapted to describe specific biological organisms, such as locusts [66]. Crucially, (3) minimizes an energy, (4) E(u) = 1 2 u(x)Q(|x − y|)u(y) dy dx,…”

Codimension-Two Bifurcations in Animal Aggregation Models with Symmetry

“…This shows that for a given species with fixed social behaviour parameters, aggregation patterns can emerge in a fixed domain if the total population density increases beyond a threshold at which equal left-and right-moving homogeneous distributions are no longer sustainable. Density dependent patterning is seen, for instance, in locust aggregation outbreaks [6,46].…”

Fronts under arrest: Nonlocal boundary dynamics in biology

“…A variety of natural mechanisms lead to nonlocal effects: An animal's ability to see and hear its surroundings leads to convolutional averages in swarming, aggregation, and alignment models of collective behavior [1][2][3][4][5][6][7]; The propensity of a species to broadly forage according to super diffusive processes, such as Lévy flights, motivates the use of fractional Laplacians in partial differential equation (PDE) models of albatrosses, sharks, and criminals [8][9][10][11]; The physical coupling between neurons also leads to nonlocal operators in continuum models for nerve signal propagation and hallucinations [12][13][14][15]. Even local PDEs used for understanding phase transitions and optics, such as the Allen-Cahn equation and singularly perturbed reaction-diffusion systems, exhibit an effective nonlocal coupling at the interface between different domain boundaries [16][17][18].…”