Models of the intensity of selection for resistance resulting from the application of heterogeneous doses of pesticide are developed. Dose heterogeneity is assumed to arise from two factors. First, a proportion of the population completely escapes treatment. Second, the rest of the population receives a distribution of doses that can be described by a probability distribution that is approximately logistic on a logarithmic scale. Various assumptions about the biology of the target population are explored, including both sexual and asexual reproduction of haploid and diploid organisms with either polygenic or monogenic inheritance of resistance. There are two major conclusions. (i) The presence of escape produces a maximum in the graph of selection intensity against dose or control; below the dose corresponding to the maximum, selection is reduced if dose is reduced, but above the maximum, selection is reduced if dose is increased. Informal arguments suggest it is unlikely that field doses would often be above the maximum dose, so selection would usually be decreased by decreasing dose. (ii) For the same control, selection for resistance is reduced by greater heterogeneity of pesticide dose, even though larger average doses may be needed.
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