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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 14853-5908; Phytopathology 80:410-416. Accepted for publication 15 October 1989. Copyright 1990 The American Phytopathological Society. DOI: 10.1094/Phyto-80-410.

A stochastic model was developed to relate pathogen population size, the probability of fungicide-resistant 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 N₀ 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 N₀, 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 N₀ is small, high values of 1 ? ? result in lower probabilities of R occurring. As N₀ 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.