Fig. 5.

Numerical simulations of the population dynamics model. (A) Theoretical dose-response curves estimated for each bacterial strain: a susceptible wild-type ($B_{\mathrm{wt}}$), a mildly-resistant type ($B_m$) and a strongly resistant strain ($B_s$). Resistant mutations occur at a rate $ϵ$ (see inset). A trade-off between resistance and fitness-cost is represented by resistant strains surviving at higher drug concentrations, albeit with a reduced density at lower doses with respect to $B_{\mathrm{wt}}$. (B) Rate of adaptation as a function of the strength of selection. Solid lines represent the rate of adaptation computed for Phase 1, while dotted lines denote the rate of adaptation estimated for Phase 3. The increase in rate of adaptation is maximized at intermediate strengths of selection; therefore, we argue resistance acquisition accelerates (gray arrow). (C,D) Relative frequencies of each bacterial type as a function of time computed by numerically simulating the evolutionary experiment; from an initial population composed exclusively of $B_{\mathrm{wt}}$ cells, we simulate a serial dilution experiment (boxes on top of each plot denote the environmental conditions: drug-free in light color and high drug concentrations in dark). After solving the system for two days in drug-free media, we simulate an adaptive ramp with different strengths of selection (Phase 1). (C) considering mild selection, and, (D) under strong selection. In both cases, once the level of resistance has achieved a 10-fold increase relative to the first day, the antibiotic is withdrawn from the environment for 7 days (Phase 2), before re-starting the adaptive ramp (Phase 3). Crucially, the duration of Phase 3 is shorter than Phase 1, suggesting that drug resistance adaptation accelerated at intermediate selective pressures.