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Evaluation of Epidemiological Thresholds and Asymptotes with Variable Plant Densities. David W. Onstad, University of Illinois and Illinois Natural History Survey, 607 E. Peabody Dr., Champaign, IL 61820; Phytopathology 82:1028-1032. Accepted for publication 15 June 1992. Copyright 1992 The American Phytopathological Society. DOI: 10.1094/Phyto-82-1028.

Simulations of a simple model of the temporal and spatial dynamics of a hypothetical pathogen demonstrated some limitations of Van der Plankís threshold formula, iR > 1. The threshold value of iR (total potential reproduction per pathogen) that determines whether the density of infected (latent and infectious) leaflets will increase over a pathogenís generation increased as the initial density of susceptible hosts decreased. In model simulations, levels of disease (sum of latent, infectious, and removed lesions) increased under all scenarios with various values of host density and iR. Thus, disease levels cannot be used in hypotheses to predict the population dynamics of the pathogen. Probabilistic formulas were developed as proposed thresholds for predicting the change in the number of infected hosts over a pathogen generation. These formulas are based on the proportion of a region occupied by hosts, the initial proportion of hosts that are infected, and the number of sites within the propagule dispersal neighborhood. The formulas of Van der Plank and Jeger that describe the asymptotic proportion of diseased tissue generally failed to match the simulated results because of the simplicity of the formulasí underlying model and assumptions.