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Ecology and Epidemiology
Using the BetaBinomial Distribution to Describe Aggregated Patterns of Disease Incidence. G. Hughes, Institute of Ecology and Resource Management, University of Edinburgh, West Mains Road, Edinburgh EH9 3JG, Scotland, UK; L. V. Madden, Department of Plant Pathology, Ohio Agricultural Research and Development Center, Ohio State University, 1680 Madison Avenue, Wooster 446914096. Phytopathology 83:759763. Accepted for publication 22 February 1993. Copyright 1993 The American Phytopathological Society. DOI: 10.1094/Phyto83759.
We discuss the use of the betabinomial distribution for the description of plant disease incidence data, collected on the basis of scoring plants as either “diseased” or “healthy”. The betabinomial is a discrete probability distribution derived by regarding the probability of a plant being diseased (a constant in the binomial distribution) as a betadistributed variable. An important characteristic of the betabinomial is that its variance is larger than that of the binomial distribution with the same mean. The betabinomial distribution, therefore, may serve to describe aggregated disease incidence data. Using maximum likelihood, we estimated betabinomial parameters p (mean disease incidence) and ϑ (an index of aggregation) for four previously published sets of disease incidence data in which there were some indications of aggregation. Goodnessoffit tests showed that, in all these cases, the betabinomial provided a good description of the observed data and resulted in a better fit than did the binomial distribution. The relationship between the parameters of the betabinomial distribution and those of variancemean relationships for aggregated diseaseincidence data is shown.
