Locust marching: A mathematical model

Abstract

A mathematical model is described that simulates the sequences of behaviour that make up the marching behaviour of the African migratory locust, Locusta migratoria migratorioides . The “model locust” was developed using the results from behavioural experiments in which locusts walked in continuous light and the predictive value of the model was tested against results of behavioural experiments obtained under a variety of other conditions. The model locust consists of two reciprocally inhibitory systems—one controlling walking, the other controlling all non-walking activities—that form a switch mechanism that prevents both systems from being active at the same time. Real locusts switch spontaneously between different behavioural activities, they will also switch from walking behaviour to non-walking activities in response to pulses of 3-kHz sound. In the model locust the spontaneous alternations in behaviour occur because the inhibitory input from the active system to the suppressed system “habituates” over time, whilst the switch from walking to non-walking induced by sound stimuli occurs when the excitatory input to non-walking is increased by a stimulus to a level higher than the inhibitory input it receives from the walking activity. The stopping threshold to sounds does not remain constant however, but falls exponentially through a bout of continuous walking. In the model this is simulated by an exponential fall in the rate at which the inhibition imposed on the non-walking activity by walking habituates. During marching the strength of the component behaviours changes over time. The observed build-up of walking activity of locusts placed in continuous light was simulated accurately by the model locust by the mechanism of post-inhibitory rebound, for when the non-walking system is active it not only inhibits the walking system, but as an after-effect it also increases its excitatory input as well. The behaviour of the model locust is consistent with these results.