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 developed 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 incorporates parameters for primary and secondary infection mechanisms and for characterizing the time-varying susceptibility of the host population. A parameter likelihood is developed and used to fit the model to data from microcosm experiments. It is shown that the stochastic model accounts well for observed variability both within and between treatments. Moreover, it enables us to describe the time evolution of the probability distribution for the variability among replicate epidemics in terms of the underlying epidemiological parameters for primary and secondary infection and decay in susceptibility. Consideration of profile likelihoods for each parameter provides strong evidence that T. viride mainly affects primary infection. By using the stochastic model to study the dependence of the probability distribution of disease levels on the primary infection rate we are therefore able to predict the effectiveness of a widely used biological control agent.