  This article is a presentation of specific recent results describing scaling
limits of individual-based models. Thanks to them, we wish to relate the
time-scales typical of demographic dynamics and natural selection to the
parameters of the individual-based models. Although these results are by no
means exhaustive, both on the mathematical and the biological level, they
complement each other. Indeed, they provide a viewpoint for many classical
time-scales. Namely, they encompass the timescale typical of the
life-expectancy of a single individual, the longer one wherein a population can
be characterized through its demographic dynamics, and at least four
interconnected ones wherein selection occurs. The limiting behavior is
generally deterministic. Yet, since there are selective effects on randomness
in the history of lineages, probability theory is shown to be a key factor in
understanding the results. Besides, randomness can be maintained in the
limiting dynamics, for instance to model rare mutations fixing in the
population.
