  Population dynamics and in particular microbial population dynamics, though
they are complex but also intrinsically discrete and random, are conventionally
represented as deterministic differential equations systems. We propose to
revisit this approach by complementing these classic formalisms by stochastic
formalisms and to explain the links between these representations in terms of
mathematical analysis but also in terms of modeling and numerical simulations.
We illustrate this approach on the model of chemostat.
