A simple model for the dynamics of a host-parasite-hyperparasite interaction

Hyperparasites can play a crucial role in the control of a host-parasite interaction if they are successfully established in the community. We investigated the specific traits of the hyperparasite and those of the release event which allow a successful regulation of primary parasite populations. This study has been motivated by the case study of chestnut-Cryphonectria parasitica-Cryphonectria Hypovirus interaction. We use a model of SIR/SIS type which assumes a limited diffusion of the parasite. Our model emphasizes the thresholds for invasion linked to the ecological specificities of both the pathogen and the hyperparasite (transmission rates and virulence) and to the initial conditions of the system (population sizes of the different categories). The predictions are consistent with data on the observed spread of the virus. "Mild" strains of the hyperparasite, characterized by a high vertical transmission rate and low virulence, are more prone to establish than "severe" strains. It also demonstrates that the horizontal transmission of the virus, which is controlled by a vegetative incompatibility system in the fungus, is not the unique constraint for the virus establishment. This study may contribute to theoretical and practical aspects of the biological control of plant diseases with a hyperparasite and to the ecology of biological invasions.