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Dose-Response Models in Biological Control of Plant Pathogens: An Empirical Verification. Emilio Montesinos, Food and Agricultural Technology Unit-CeRTA and Crop Sciences Section, Department of EQATA, University of Girona, Avgda., Lluís Santaló, s/n, 17071 Girona, Spain; Anna Bonaterra, Food and Agricultural Technology Unit-CeRTA and Crop Sciences Section, Department of EQATA, University of Girona, Avgda., Lluís Santaló, s/n, 17071 Girona, Spain. Phytopathology 86:464-472. Accepted for publication 12 December 1995. Copyright 1996 The American Phytopathological Society. DOI: 10.1094/Phyto-86-464.

Two models, based on the hyperbolic saturation relationship and probit function, that relate the densities of the biocontrol agent and pathogen with disease response were developed. The hyperbolic saturation (HS) and probit (PB) models and a modification of the negative exponential (MNE) model recently proposed by Johnson were evaluated. In the NE model, parameters c and k supply information on the efficiency of the pathogen and biocontrol agent, respectively, and provide endpoint values such as the maximum proportion of pathogen inoculum inactivated by the biocontrol agent (B). The HS model gives information on the 50% effective dose (ED50) for both the pathogen (Kx) and the biocontrol agent (Kz), asymptotic disease levels without biological control (Ymax), and the maximum proportion of pathogen the biocontrol agent can inactivate (Imax). The PB model provides information on the relative virulence of the pathogen (ι) and relative efficiency of the biocontrol agent (σ) and on the ED50 for the pathogen (λ) and biocontrol agent (μ). Two patho-systems (an aerial and a root disease) and two types of biocontrol agent (antagonistic bacteria and nonpathogenic isolates of the pathogen) were compared. The data from Mandeel and Baker on biological control of Fusarium oxysporum f. sp. cucumerinum on cucumber with nonpathogenic isolates as well as our data on biological control of Stemphylium vesicarium on pear with selected isolates of Pseudomonas and Erwinia spp. were used. Data sets of the effect of several densities of the bio-control agent and pathogen on disease levels were fitted to the models by nonlinear regression. Estimated parameters permitted quantitative comparisons among biocontrol-pathogen-host systems. The most valuable parameters obtained from the data sets that fitted adequately to the models were the proportion of pathogen potentially inactivated by the biocontrol agent, the relative efficiency and ED50 of the biocontrol agent, and the ED50 biocontrol/pathogen ratio. The values of B ranged from 0.79 to 0.98, and the values of Imax ranged from 0.96 to 1.04, indicating that a high proportion of the pathogen inoculum was susceptible to inactivation by the biocontrol agents. The values of ? ranged from 0.7 to 1.4 and were consistent with the independent action of the biocontrol agents on the pathogen. The mean ED50 for the biocontrol agent (HS and PB models) for the fungus-fungus pathogen-biocontrol system was 2 × 103 CFU/g of soil, and for the bacteria-fungus pathogen-biocontrol system, it was 6 × 106 CFU/ml. The ED50 biocontrol/pathogen ratio ranged from 1 to 10 for the fungus-fungus biocontrol-pathogen system and from 77 to 435 for the antagonistic bacteria-fungus system, indicating the existence of a lower number of targets for fungus-fungus competition for common sites than with bacteria-fungus antagonism.