Tuning Spatial Profiles of Selection Pressure to Modulate the Evolution of Drug Resistance*

Spatial heterogeneity plays an important role in the evolution of drug resistance, but relatively little is known about resistance in complex spatial profiles of selection pressure. Here we use a toy model of stochastic microbial dynamics to investigate how different spatial profiles of selection pressure impact the time to fixation of a resistant allele. Using mean first passage time calculations, we show that spatial heterogeneity accelerates resistance evolution when the rate of spatial migration is sufficiently large relative to mutation but slows fixation for small migration rates. We also demonstrate that optimal tuning of the spatial profile can dramatically slow the spread and fixation of resistant subpopulations, even in the absence of a fitness cost for resistance. Finally, we incorporate a fitness cost associated with the resistant allele and observe that the intermediate regime in which spatial heterogeneity can speed or slow resistance is much larger and the effect of heterogeneity can be greatly amplified. Our results may lay the groundwork for optimized, spatially resolved drug dosing strategies for mitigating the effects of drug resistance.