A Stochastic Model of Horizontal Resistance Based on Frequency Distributions

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Abstract
Data were collected on the frequency distributions associated with sampling number of powdery mildew [Erysiphe graminis f. sp. tritici] 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 [Triticum aestivum] cultivar Chancellor. The frequency of colonies on leaves approximated the negative binomial distribution in field and growth chamber studies. Leaf area could be described by the gamma distribution and number of conidia forming elongating secondary hyphae in groups of 10 conidia was of binomial distribution. 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.

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