NONLOCAL INTERACTIONS AND THE DYNAMICS OF DISPERSAL IN IMMATURE INSECTS

A simple mathematical model is developed to explain the appearance of oscillations in the dispersal of larvae from the food source in experi mental populations of certain species of blowflies. The life history o f the immature stage in these flies, and in a number of other insects, is a system with two populations, one of larvae dispersing on the soi l and the other of larvae that burrow in the soil to pupate. The obser ved oscillations in the horizontal distribution of buried pupae at the end of the dispersal process are hypothesized to be a consequence of larval crowding at a given point in the pupation substrate. It is assu med that dispersing larvae are capable of perceiving variations in den sity of larvae buried at a given point in the substrate of pupation, a nd that pupal density may influence pupation of dispersing larvae. The assumed interaction between dispersing larvae and the larvae that are burrowing to pupate is modeled using the concept of non-local effects . Numerical solutions of integro-partial differential equations develo ped to model density-dependent immature dispersal demonstrate that var iation in the parameter that governs the non-local interaction between dispersing and buried larvae induces oscillations in the final horizo ntal distribution of pupae. (C) 1997 Academic Press Limited.