A Model Relating the Probability of Foliar Disease Incidence to the Population Frequencies of Bacterial Plant Pathogens

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Abstract
A model was developed that relates pathogen population size on individual leaves at time t0 to disease incidence at some later time t1. The lognormal distribution is used to describe population size of pathogenic bacteria on individual leaves, and the probit function is used to describe the probability of disease, given a bacterial population size. When integrated with respect to bacterial population frequency, the product of the probability of disease, given a bacterial population size, for individual leaves and the frequency of pathogenic bacteria on individual leaves results in a cumulative normal frequency distribution. This distribution function describes the probability of disease incidence (as frequency of diseased leaflets) in a field. To illustrate its use, the model was applied to bacterial brown spot of beans caused by Pseudomonas syringae pv. syringae. A maximum-likelihood technique was used to estimate the mean and variance of bacterial population size from censored samples.