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To follow and model evolution of a microbial population in the chemostat, parameters are needed that give an indication of the absolute extent of evolution at a high resolution of time. In this study the evolution of the maximum specific growth rate (μmax) and the residual glucose concentration was followed for populations of Escherichia coli K-12 under glucose-limited conditions at dilution rates of 0·1 h−1, 0·3 h−1 and 0·53 h−1 during 500–700 h in continuous culture. Whereas μmax improved only during the initial 150 h, the residual glucose concentration decreased constantly during 500 h of cultivation and therefore served as a convenient parameter to monitor the evolution of a population at a high time resolution with respect to its affinity for the growth-limiting substrate. The evolution of residual glucose concentrations was reproducible in independent chemostats with a population size of 1011 cells, whereas no reproducibility was found in chemostats containing 107 cells. A model based on Monod kinetics assuming successive take-overs of mutants with improved kinetic parameters (primarily K
s) was able to simulate the experimentally observed evolution of residual glucose concentrations. Similar values for the increase in glucose affinity of mutant phenotypes (K
s(mutant)
0·6×K
s(parent)) and similar mutation rates per cell per generation leading to these mutant phenotypes (1–5×10−7) were estimated in silico for all dilution rates. The model predicts a maximum rate of evolution at a dilution rate slightly below μmax/2. With increasing and decreasing dilution rates the evolution slows down, which also explains why in special cases a selection-driven evolution can exhibit apparent clock-like behaviour. The glucose affinity for WT cells was dependent on the dilution rate with highest values at dilution rates around μmax/2. Below 0·3 h−1 poorer affinity was mainly due to the effects of rpoS.