Spatial structure facilitates evolutionary rescue by cost-free drug resistance

Bacterial populations often have complex spatial structures, which can impact their evolution. Here, we study how spatial structure affects the evolution of antibiotic resistance in a bacterial population. We consider a minimal model of spatially structured populations where all demes (i.e., subpopulations) are identical and connected to each other by identical migration rates. We show that spatial structure can facilitate the survival of a bacterial population to antibiotic treatment, starting from a sensitive inoculum. Indeed, the bacterial population can be rescued if antibiotic resistant mutants appear and are present when drug is added, and spatial structure can impact the fate of these mutants and the probability that they are present. Specifically, if the mutation that provides resistance is neutral or effectively neutral, its probability of fixation is increased in smaller populations. This promotes local fixation of resistant mutants in the structured population, which facilitates evolutionary rescue by cost-free drug resistance. Once the population is rescued by resistance, migrations allow resistant mutants to spread in all demes. Our main results extend to the case where there are resistant mutants in the inoculum, and to more complex spatial structures. They also extend to resistant mutants that carry a fitness cost, although the timescales involved are longer.