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Disease Control and Pest Management

Selection for Tolerance in Organisms Exposed to Sprays of Biocide Mixtures: A Theoretical Model. P. F. Kable, Principal research scientist, New South Wales Department of Agriculture, Agricultural Research Centre, Yanco, N.S.W. 2703, Australia; H. Jeffery, research officer, New South Wales Department of Agriculture, Agricultural Research Centre, Yanco, N.S.W. 2703, Australia. Phytopathology 70:8-12. Accepted for publication 30 May 1979. Copyright 1980 The American Phytopathological Society.. DOI: 10.1094/Phyto-70-8.

A mathematical model has been constructed that simulates the process of selection that occurs when populations of organisms with a component tolerant to a particular biocide are repeatedly exposed to that biocide combined with a second biocide to which no tolerance exists. A more general model also was derived which evaluates the selection process when the population is composed of any number of subpopulations of differing sensitivity to a particular biocide. The variables included in the model are: the efficacies of the first biocide against the tolerant subpopulation and against the sensitive subpopulation; the efficacy of the second biocide, which in our evaluation is assumed to be equal for the two subpopulations; and a variable defining the degree of completeness of spray coverage (ie, the proportion of the total population contacted at each spray application). Independent joint action is modeled. To evaluate the model, we commenced with the tolerant subpopulation at a frequency of 1 × 10^–9. Major indications of the model were: That selection proceeds through many spray applications before the level of the tolerant strain builds up to 1%, but once that has happened only a few more sprays are needed for tolerance to dominate; that the variable with the greatest effect on the rate of selection was spray coverage; that when coverage is complete, selection proceeds at the same rate whether the “at-risk” biocide is used on its own or in a mixture; that under these circumstances it is advantageous to use the biocide alternately or in a planned sequence. With less complete spray coverage (< 99%) it is better to use mixtures to slow up the rate of increase of resistant forms; that rates of selection increase with increasing efficacy of the “at risk” biocide to the sensitive subpopulation; that the rate of increase of resistant individuals in a population is reduced with decreasing spray coverage; that when coverage is incomplete, the rate of selection for resistance will be slower with increasing strength of the second biocide; and that the rate of selection for resistance becomes greater as tolerance increases, but the increase is less with decreasing spray coverage.