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Influence of Host Diversity on Development of Epidemics: An Evaluation and Elaboration of Mixture Theory

First and second authors: Wageningen University, Department of Plant Sciences, Biological Farming Systems Group, P.O. Box 9101, 6709 PG Wageningen, The Netherlands; third author: Plant Research International, P.O. Box 16, 6700 AA Wageningen, The Netherlands; fourth author: Department of Mathematics and Statistics, Utah State University, Logan 84322; and fifth author: Wageningen University, Department of Plant Sciences, Crop and Weed Ecology Group, P.O. Box 430, 6709 RZ Wageningen, The Netherlands

A spatiotemporal/integro-difference equation model was developed and utilized to study the progress of epidemics in spatially heterogeneous mixtures of susceptible and resistant host plants. The effects of different scales and patterns of host genotypes on the development of focal and general epidemics were investigated using potato late blight as a case study. Two different radial Laplace kernels and a two-dimensional Gaussian kernel were used for modeling the dispersal of spores. An analytical expression for the apparent infection rate, r, in general epidemics was tested by comparison with dynamic simulations. A genotype connectivity parameter, q, was introduced into the formula for r. This parameter quantifies the probability of pathogen inoculum produced on a certain host genotype unit reaching the same or another unit of the same genotype. The analytical expression for the apparent infection rate provided accurate predictions of realized r in the simulations of general epidemics. The relationship between r and the radial velocity of focus expansion, c, in focal epidemics, was linear in accordance with theory for homogeneous genotype mixtures. The findings suggest that genotype mixtures that are effective in reducing general epidemics of Phytophthora infestans will likewise curtail focal epidemics and vice versa.

Additional keywords: crop arrangement , dispersal kernels , genotype mixtures , Solanum tuberosum .