  The evolution of antimicrobial resistance generally occurs in an environment
where antimicrobial concentration is variable, which has dramatic consequences
on the microorganisms' fitness landscape, and thus on the evolution of
resistance. We investigate the effect of these time-varying patterns of
selection within a stochastic model. We consider a homogeneous microbial
population of fixed size subjected to periodic alternations of phases of
absence and presence of an antimicrobial that stops growth. Combining
analytical approaches and stochastic simulations, we quantify how the time
necessary for fit resistant bacteria to take over the microbial population
depends on the alternation period. We demonstrate that fast alternations
strongly accelerate the evolution of resistance, reaching a plateau for
sufficiently small periods. Furthermore, this acceleration is stronger in
larger populations. For asymmetric alternations, featuring a different duration
of the phases with and without antimicrobial, we shed light on the existence of
a minimum for the time taken by the population to fully evolve resistance. The
corresponding dramatic acceleration of the evolution of antimicrobial
resistance likely occurs in realistic situations, and may have an important
impact both in clinical and experimental situations.
