Do travelling band solutions describe cohesive swarms? An investigation for migratory locusts

Abstract

. We explore several hypotheses for the swarming behaviour in locusts, with a goal of understanding how swarm cohesion can be maintained by the huge population of insects (up to 10⁹ individuals) over long distances (up to thousands of miles) and long periods of time (over a week). The mathematical models that correspond to such hypotheses are generally partial differential equations that can be analysed for travelling wave solutions. The nature of a swarm (and the fact that it contains a finite number of individuals) mandates that we seek travelling band (pulse) solutions. However, most biologically reasonable models fail to produce such ideal behaviour unless unusual and unrealistic assumptions are made. The failure of such models, general difficulties encountered with similar models of other migratory phenomena, and possible approaches to alleviate these problems are described and discussed.