A differential equation model of the interaction between the migration of the Senegalese grasshopper, Oedaleus senegalensis, its predators, and a seasonal habitat

The Senegalese grasshopper, Oedaleus senegalensis, is periodically an important pest of graminaceous crops in Africa and India. A conceptual model, based on movements of the Inter-Tropical Convergence Zone (ITCZ) in the Sahelian region of West Africa, suggested that O. senegalensis migration is a major contributing factor towards the generation of outbreaks in this region. We now present data which provides evidence of high levels of egg-pod predation and develop a model of the interaction between O. senegalensis and its predators using a form of the Lotka-Volterra equations modified to incorporate seasonal fluctuation in the carrying capacity of the O. senegalensis habitat. The model simplifies the Sahelian habitat into northern and southern zones, both potentially capable of supporting O. senegalensis and predator populations. By linking the two zones, the dynamics of the O. senegalensis populations were investigated in relation to the extent of migration, the seasonality of the habitat and the level of predation. Conditions which result in high levels of oviposition in the drier northern zone have been postulated to generate O. senegalensis outbreaks. Modelling supports this hypothesis provided that no account is taken of natural regulatory mechanisms. Both migration between zones and greater dry season abundance (as eggs) can lead to greater stability in predator populations and to lower O. senegalensis population size during the cropping season. It is possible that mechanisms which are often regarded as adaptations to a seasonal habitat (migration and egg diapause) may reduce rather than exacerbate the risk of outbreaks.