Modelling the biological control of insect pests: a review of host-parasitoid models

Successful biological control results when an introduced natural enemy, very often a parasitoid, is able to suppress the abundance of an insect pest to a level at which it no longer causes economic damage. We review the host-parasitoid models that have been developed to describe the process of biological control by parasitoids or more specifically, the dynamics of interacting host and parasitoid populations. We trace the origins and basic framework for both discrete time (Nicholson-Bailey) models and continuous time (Lotka-Volterra) models, through the search for stabilizing mechanisms in local populations to the more recent focus on spatial and temporal heterogeneity in the distribution of parasitoid attack. In particular, we review the functional response that underlies all consumer-resource models, partial host refuges generated by spatial heterogeneity or temporal asynchrony of parasitoid attack or by host stage structure, the co-existence of competing parasitoid species, and size-dependent host feeding and sex allocation by parasitoids. The mechanistic explanations for biological control derived from these host-parasitoid models are then compared with the few case studies of successful biological control projects that have received sufficient study. We conclude by questioning, and suggesting improvements for, the basic assumptions of discrete-time and continuous-time models for biological pest control.