MODELS OF DESERT LOCUST PHASE-CHANGES

Desert locust population dynamics were modelled using the logistic equ ation with switches in r and K to mimic phase changes. An earlier mode l with stepwise switches of reproductive rates was modified to include switches of carrying capacity, dependent on population density and ra ndom environmental variation. This model reproduced the bi-stable patt ern of plagues and recessions found in observed records. The mean dura tion and variance of plague lengths was dependent on parameter values, with lower values of both when the rates of reproduction were high en ough to induce chaotic dynamics, A second family of models was explore d in which the phase changes are treated as a catastrophic process gov erned by a cusp catastrophe function. Although it was necessary to con strain the models to prevent negative population values, these models also successfully reproduced the general pattern observed in nature, p rovided the parameters were held within limits and there was adequate environmental variation.