Tuning spatial distributions of selection pressure to suppress emergence of resistance

Combatting pathogenic bacteria with antibiotics, pests with pesticides, and tumours with cancer drugs all prompt an evolutionary response: the emergence of resistance to the control agent, i.e., the selection pressure, meant to control the population. What measures can be taken to suppress the emergence of resistance while not foregoing the benefits of population control? More specifically, we here ask whether the selection pressure can be applied in a way that minimises the rise of an existing resistant subpopulation.

Motivated by the control of pests in agriculture, we employ a one-dimensional model with agents diffusing and selection applied temporarily on a sub-region only. We find that an optimal size of this sub-region exists which minimises resistance emergence per area protected. We observe that this result carries over to higher dimensions and determine analytical bounds for the location of the optimum.

We extend the results to environments consisting of equally spaced subregions that are protected temporarily. This allow us to answer how a large given region can be subdivided to optimally suppress resistance emergence. These findings are a step towards optimised protocols for pesticide application that protect crop and suppress emergence of resistance at the same time.