A unified model for wild resistance dynamics and weed control using herbicide

A major issue in the modelling of weed resistance to herbicide lies in effectively handling the wild dynamics, that is, the allele frequency prior to the herbicide application, and in particular when starting to use the herbicide. The wild allele frequency is a key variable as the resistance evolution is highly sensitive to it, moreover it is extremely difficult to measure in the agricultural field. In this paper we propose a model for weed control that handles the allele frequency in a direct manner, grounded on the very dynamics of the weed life cycle, with no need of a priori distributions nor the use of the Hardy-Weinberg equilibrium. The proposed model is individual based, stochastic, and considers some phenomena like the relative fitnesses and mutation that are prominent in the resistance dynamics without herbicide. A case study is presented for the herbicide nicosulfuron in a field with the weed Bidens pilosa. Another two models having a standard deterministic dynamics are compared with ours in terms of the initial allele frequency, its time evolution, and the resistance visualization in the field, indicating that the proposed model is effective to provide more realistic simulations for the weed resistance.