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Ecology and Epidemiology
A Stochastic Model for the Initial Occurrence and Development of Fungicide Resistance in Plant Pathogen Populations. Michael G. Milgroom, Department of Plant Pathology, Cornell University, Ithaca, NY 148535908; Phytopathology 80:410416. Accepted for publication 15 October 1989. Copyright 1990 The American Phytopathological Society. DOI: 10.1094/Phyto80410.
A stochastic model was developed to relate pathogen population size, the probability of fungicideresistant individuals (R) occurring, and the strength of selection for resistance (fungicide efficacy). The model is based on binomial probabilities that R individuals are present in the initial population of size N_{0} or occur during an epidemic after selective fungicide is applied. If an R mutant occurs early in the epidemic, the final frequency (q_{t}) and number of R (N_{R}) increase to higher levels than if the mutation occurs later. The probability of q_{t} reaching some given value is always higher when N_{0}, the pathogen growth rate (r), or mutation rate to resistance (p) is large. The effects of fungicide efficacy (1 ? ?) depend on the other parameters. When N_{0} is small, high values of 1 ? ? result in lower probabilities of R occurring. As N_{0} increases, this trend is reversed. These results suggest that intensive use of fungicides may be a rational means of resistance management when population sizes are initially small. However, caution must be employed in applying these results to real systems.
