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A Stochastic Model of Horizontal Resistance Based on Frequency Distributions. D. I. Rouse, Graduate research assistant, Department of Plant Pathology, The Pennsylvania State University, University Park 16802, Current address of senior author: Department of Plant Pathology, University of Wisconsin, Madison 53706; R. R. Nelson(2), and D. R. MacKenzie(3). (2)(3)Evan Pugh Professor, and associate professor, respectively, Department of Plant Pathology, The Pennsylvania State University, University Park 16802. Phytopathology 70:951-954. Accepted for publication 7 February 1980. Copyright 1980 The American Phytopathological Society. DOI: 10.1094/Phyto-70-951.

Data were collected on the frequency distributions associated with sampling number of powdery mildew colonies and leaf area on individual leaves, and number of colonies formed from groups of 10 conidia on leaves in growth chamber experiments with seedlings of the wheat cultivar Chancellor. The frequency of colonies on leaves was found to approximate the negative binomial distribution in field and growth chamber studies. Additional studies indicated that leaf area could be described by the gamma distribution and number of conidia forming elongating secondary hyphae in groups of 10 conidia was binomial distributed. These results were used as the basis for development of a theoretical statistical model for colonies on leaves with parameters representing sporulation potential and infection efficiency. Possible application of this model for the detection of relative levels of these components of horizontal resistance is discussed.

Additional keywords: Erysiphe graminis f. sp. tritici.