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An Effective Sample Size for Predicting Plant Disease Incidence in a Spatial Hierarchy

September 1999 , Volume 89 , Number  9
Pages  770 - 781

L. V. Madden and G. Hughes

First author: Department of Plant Pathology, Ohio State University, Wooster 44691-4096; and second author: Institute of Ecology and Resource Management, University of Edinburgh, West Mains Road, Edinburgh EH9 3JG, Scotland

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Accepted for publication 24 May 1999.

For aggregated or heterogeneous disease incidence, one can predict the proportion of sampling units diseased at a higher scale (e.g., plants) based on the proportion of diseased individuals and heterogeneity of diseased individuals at a lower scale (e.g., leaves) using a function derived from the beta-binomial distribution. Here, a simple approximation for the beta-binomial-based function is derived. This approximation has a functional form based on the binomial distribution, but with the number of individuals per sampling unit (n) replaced by a parameter (v) that has similar interpretation as, but is not the same as, the effective sample size (ndeff ) often used in survey sampling. The value of v is inversely related to the degree of heterogeneity of disease and generally is intermediate between ndeff and n in magnitude. The choice of v was determined iteratively by finding a parameter value that allowed the zero term (probability that a sampling unit is disease free) of the binomial distribution to equal the zero term of the beta-binomial. The approximation function was successfully tested on observations of Eutypa dieback of grapes collected over several years and with simulated data. Unlike the beta-binomial-based function, the approximation can be rearranged to predict incidence at the lower scale from observed incidence data at the higher scale, making group sampling for heterogeneous data a more practical proposition.

Additional keywords: dispersion, models, quantitative epidemiology, spatial pattern.

© 1999 The American Phytopathological Society