Locust Dynamics: Behavioral Phase Change and Swarming

TL;DR

This paper develops a mathematical model to understand how locusts switch between solitary and gregarious phases and form large swarms, providing insights into the dynamics of hopper band formation.

Contribution

It introduces a novel partial integrodifferential equation model capturing collective phase change and movement, enabling prediction of swarm formation and outbreak conditions.

Findings

Model predicts conditions for outbreak and large-scale gregarization.

Quantifies the temporal dynamics of phase change and population proportions.

Simulations show transient traveling gregarious insect clumps.

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.