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Disease Detection and Losses

Weibull Distribution of Lesion Size in the Stagonospora Leaf Spot of Orchardgrass. R. T. Sherwood, Plant pathologist, U.S. Department of Agriculture, Agricultural Research Service, U.S. Regional Pasture Research Laboratory, University Park, PA 16802; Phytopathology 77:715-717. Accepted for publication 10 October 1986. This article is in the public domain and not copyrightable. It may be freely reprinted with customary crediting of the source. The American Phytopathological Society, 1987. DOI: 10.1094/Phyto-77-715.

Five resistant and five susceptible genotypes of Dactylis glomerata were inoculated with Stagonospora arenaria in two replicated greenhouse tests. Distributions of lesion length and area were determined for populations of lesions on single leaves, using samples of 50 lesions per leaf. The two trials gave closely similar results. The null hypothesis that size was normally distributed could be rejected for resistant genotypes but not for suceptible, using the Shapiro-Wilk w statistic at P = 0.01. The sample of all genotypes showed positive skewness (tail to the right). The lognormal distribution could be rejected in favor of the Weibull distribution in all samples at α = 0.01. All samples showed a good fit to the Weibull distribution with location (a) set at minimum spot size. Weibull maximum likelihood estimates for shape (?) were significantly lower than c expected for a normal distribution; this further demonstrated positive skewness. Values for a, c, and slope (*) were significantly lower for resistant genotypes than for susceptible genotypes. Two additional tests with other genotypes gave the same trends.