In this talk, I will present a selection-mutation model which was introduced in a paper by Barles and Perthame (Indiana Univ. Math. J., 2008) and further studied in many other works. The model is a non-local parabolic PDE describing the adaptive dynamics of a population structured with a phenotypical trait. The mutations and the competition for resources lead the population to concentrate around the fittest traits over time. I will discuss how this behaviour is proved analytically, based on the previous literature, and introduce an asymptotic preserving (AP) numerical scheme which complements the analytical results. This is a joint work with Vincent Calvez and Hélène Hivert.