Competitive Displacement and Biological Control in Parasitoids: A Model

California red scale, an insect that is a worldwide pest of citrus, is controlled in many areas by parasitoids of the genus Aphytis. In southern California, Aphytis lingnanensis provided inadequate control of red scale in inland valleys. Aphytis melinus was introduced, competitively displaced A. lingnanensis within a few red scale generations, and caused satisfactory biological control. Aphytis melinus can obtain female offspring from smaller-sized scale than A. lingnanensis, and we present a stage-structured parasitoid-host model in which the two parasitoid species are the same except for A. melinus's size-dependent advantage in sex allocation. This model can account for the competitive displacement of A. lingnanensis in such a short time and the improvement in biological control. Aphytis melinus can also obtain an additional female egg from larger red scale, and this increases its advantage in competition, the speed of displacement, and the degree of host suppression. We examine the effects of other model parameters and discuss the implications of our findings for a predictive theory of biological control.