A two-dimensional stochastic model of downy mildew of radish

A two-dimensional stochastic model that simulates the spread of disease over space and time was recently proposed by Xu and Ridout [Xu, X.M., Ridout, M.S., 1998. Effects of initial epidemic conditions, sporulation rate, and spore dispersal gradient on the spatio-temporal dynamics of plant disease epidemics. Phytopathology 88, 1000-1012]. In a theoretical study, the authors showed the ability of their model to generate a broad range of disease patterns and disease progress rates. The objective of our study was to test if this theoretical approach was able to describe disease progress and the disease pattern of a specific disease, downy mildew (Peronospora parasitica) of radish (Raphanus sativus L.). Two field experiments with artificial inoculation were carried out and disease incidence and spatial pattern were assessed twice a week until disease incidence was greater than 0.25. Four model parameters were estimated by an algorithm that uses a least square regression together with an evolutionary optimisation strategy. Moran's I indices of spatial autocorrelation calculated both for measured und simulated data were significantly correlated (α = 0.05, r = 0.61). Also observed variances in measurements and in simulations were closely and significantly correlated (α = 0.05, r = 0.95). Thus, disease pattern (as assessed in terms of variance inflation and spatial autocorrelation) was well described by the model. The model accounted for 94% of the variation in the disease incidence data. It has, therefore, the potential to be developed into a forecast model for risk analysis and for decision support in plant protection. However, in the specific case of downy mildew on radish more experimental data are required for model validation and to parameterise the effects of environment on infection, sporulation and spore dispersal.