Multiseasonal management of an agricultural pest. I: Development of the theory

A framework for analyzing the trade-off between economic yield from a crop and buildup of resistance to pesticide caused by repeated applications of pesticide is developed. The analysis begins with the case of age-independent pest dynamics, in which pests infest a field by arriving from an external pool. Initially, it is assumed that the pest genetics of interest are single locus, two allele, with resistance to pesticide dominant and susceptible pests more fit in the absence of spraying. The pesticide is applied only once during the season, with timing and intensity of the application as control variables. Interseasonal pest and crop dynamics are studied by solving appropriate ordinary differential equations. Intraseasonal pest dynamics are assumed to follow the Hardy-Weinberg formula. It is shown that the three class diploid model can be replaced by a two class haploid model with essentially no change in the results. A model based on partial differential equations is developed, for the case in which pest dynamics depend upon age, and it is shown that the partial differential equation model can be replaced by a pair of coupled ordinary differential equations. The main operational conclusion in this paper is that the timing of the application of pesticide can be used to control buildup of resistance and that the intensity of the application can be used to control the crop yield.