Predicting variability in biological control of a plant-pathogen system using stochastic models

A stochastic model for the dynamics of a plant-pathogen interaction is deve loped and fitted to observations of the fungal pathogen Rhizoctonia solani (Kuhn) in radish (Raphanus sativus L.), in both the presence and absence of the antagonistic fungus Trichoderma viride (Pers ex Gray). The model incor porates parameters for primary and secondary infection mechanisms and for c haracterizing the time-varying susceptibility of the host population. A par ameter likelihood is developed and used to fit the model to data from micro cosm experiments. It is shown that the stochastic model accounts well for o bserved variability both within and between treatments. Moreover, it enable s us to describe the time evolution of the probability distribution for the variability among replicate epidemics in terms of the underlying epidemiol ogical parameters for primary and secondary infection and decay in suscepti bility. Consideration of profile likelihoods for each parameter provides st rong evidence that T. viride mainly affects primary infection. By using the stochastic model to study the dependence of the probability distribution o f disease levels on the primary infection rate we are therefore able to pre dict the effectiveness of a widely used biological control agent.