Herbicide Dosage Optimization Model for Weed Control Using the Resistance Dynamics

A dynamic optimization model for weed infestation control using selective herbicide application which includes the resistance dynamics is presented. The seed bank density of the weed population and frequencies of resistant and susceptible alleles are taken as the state variables of the growing cycle. The control variable is taken as the application doses. The goal is to reduce herbicide use, maximize profit in a pre-determined period of time and minimize the environmental impacts caused by excessive use of herbicides. The optimization problem of finding the application doses is solved with a dynamic programming approach which takes into account the decreased herbicide efficacy over time due to weed resistance evolution caused by a selective pressure which varies with the applied doses. Numerical simulations for a case study with the Bidens subalternans frequent in a corn crop is presented. We used data from a green house experiment to obtain the weed response to the most widely used Atrazine herbicide. Also, the sensitivity of the optimum solution in terms of the key parameters in the seed bank dynamics that are highly influenced by environmental factors is analysed. This suggests that the optimizing solution features some robustness under a quite realistic assumption that there are imported seeds in the system.