Tuning Spatial Distributions of Selection Pressure to Suppress Emergence of Resistance

Control measures such as insecticides or antimicrobials are used to contain biological agents such as pathogenic bacteria and vectors of human and plant diseases, respectively. Following control measure application, a resistant subpopulation may eventually rise to such frequency that the control measure will be rendered ineffective: The timescale over which this occurs is the ‘effective lifetime’ of the control measure. Prolonging this timescale relaxes urgency at which novel control measure needs to be developed. Spatial heterogeneity in control measure application can influence the rate at which resistance to the control measure evolves; in the agricultural context, this fact is exploited by distributing insecticides in mosaics across cropping regions in order to slow the rate of resistance evolution.

Contemporary and historical modeling practices, which aim to inform agricultural practices, often employ assumptions which squeeze out the impact of the spatio-temporal heterogeneity endemic to nature. In this paper, we present a minimal model of continuous dispersal and spatio-temporal heterogeneity in selection pressure distribution which exhibits a novel dynamic: The spatial distribution of selection pressure may be tuned in order to minimize the initial rate at which resistance evolves, thus increasing the effective lifetime of a pesticide.

Author summary

There are many contexts in which humans apply control measures to biological agents: pesticides are applied in fields to kill the pests that damage crops, mosquito nests are distributed to prevent the spread of malaria, and cancer drugs are applied to kill off tumors in humans. These control measures are examples of ‘selection pressures’, which select against strains which are susceptible to them. If a mutation occurs which confers resistance, the control agent will select for the resistant strain, thus reducing the efficacy of the control agent as the frequency of resistance increases in the population. This necessitates more of the control agent to be applied, or for a novel control agent to be developed. The former may have unintended consequences on the local environment, and the latter is expensive and time-intensive. It is preferable to carefully tune how the control agent is applied - perhaps instead of one massive compact region of control measure application, it is better to apply the control measure over multiple smaller regions? Here, we use a toy model of motile organisms to demonstrate that an optimal distribution exists for a variety of scenarios.