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Ecological and evolutionary dynamics have been historically regarded asunfolding at broadly separated timescales. However, these two types ofprocesses are nowadays well documented to much more tightly than traditionallyassumed, especially in communities of microorganisms. With this motivation inmind, here we scrutinize recent experimental results showing evidence of rapidevolution of tolerance by lag in bacterial populations that are periodicallyexposed to antibiotic stress in laboratory conditions. In particular, thedistribution of single-cell lag times evolves its average value toapproximately fit the antibiotic-exposure time. Moreover, the distributiondevelops right skewed heavy tails, revealing the presence of individuals withanomalously large lag times. Here, we develop a parsimonious individual-basedmodel mimicking the actual demographic processes of the experimental setup.Individuals are characterized by a single phenotypic trait: their intrinsic lagtime, which is transmitted with variation to the progeny. The model (in aversion in which the amplitude of phenotypic variations grows with theparent\'s lag time) is able to reproduce quite well the key empiricalobservations. Furthermore, we develop a general mathematical framework allowingus to describe with good accuracy the properties of the stochastic model bymeans of a macroscopic equation, which generalizes the Crow Kimura equation inpopulation genetics. From a broader perspective, this work represents abenchmark for the mathematical framework designed to tackle much more generaleco-evolutionary problems, thus paving the road to further research avenues.

Phenotypic-dependent variability and the emergence of tolerance in bacterial populations