Example of IGIMF evolution with time, plotting only the IGIMF3 model. Top panel: prescribed evolution of the SFR with time (red solid curve, left y-axis), that is the SFH, stellar mass build-up with time (blue solid curve, right y-axis) , and the metallicity evolution (upper x-axis). This example serves to show a typical evolution and therefore the curves were synthetically created. This example of how a 10¹² M_⊙ elliptical galaxy assembles over about 1 Gyr is consistent with downsizing (Recchi et al. 2009), but due to stellar evolution the stellar mass of this galaxy is 2 × 10¹¹ M_⊙ after 12 Gyr. Using the IGIMF grid, the same principle can be applied self-consistently in a chemo-dynamical code. In addition the four vertical lines represent the chosen time snapshots shown in the bottom panels. Bottom panels: four IGIMF plots at the chosen times (see top panel), showing how the IGIMF can potentially evolve throughout elliptical galaxy assembly. Shown is the top-heavy phase, but also the bottom-heavy phase during the metal-rich part of the evolution.