The population interaction termed biological exploitation includes what has formerly been called predation, as well as other interactions in which 1 population takes advantage of another (e.g., grazing, parasitism, Batesian mimicry). An instantaneous, deterministic theory using graphs of the properties of difficult and even unknown autonomous nonlinear differential equation systems was developed to simplify greatly the task of understanding the dynamics of such systems and of predicting qualitative properties of their solutions. This review shows how the theory may be used to account for some of the observed dynamics of well-known laboratory systems including their oscillatory periods and neighborhood stability. It also extends the theory to cover situations where the predator prefers to attack weak or otherwise vulnerable victims. In this case, an upper limit is shown to be added to victim oscillations which can serve to promote the survival probabilty of the system despite the fact that it may diminish the system''s ability to return to a steady state following perturbation. Finally, the theory is applied to the problem of management of a pest by biocides. An important result of earlier predation theory, which has tended to be discarded because of the oversimplifications in that work, is shown to hold in many of the more realistic situations described by graphical exploitation theory: addition of a biocide can actually increase the average population densities of the species one intended to attack. The principle at work here may account for some modern instances of crop-pest population explosions, and could have helped to predict which pests were likely candidates for control by chemical means and which were not.