Models of desert locust phase changes

Desert locust population dynamics were modelled using the logistic equation with switches in r and K to mimic phase changes. An earlier model with stepwise switches of reproductive rates was modified to include switches of carrying capacity, dependent on population density and random environmental variation. This model reproduced the bi-stable pattern of plagues and recessions found in observed records. The mean duration and variance of plague lengths was dependent on parameter values, with lower values of both when the rates of reproduction were high enough to induce chaotic dynamics. A second family of models was explored in which the phase changes are treated as a catastrophic process governed by a cusp catastrophe function. Although it was necessary to constrain the models to prevent negative population values, these models also successfully reproduced the general pattern observed in nature, provided the parameters were held within limits and there was adequate environmental variation.