Schematic overview of the different metal-dependent SFR models adopted here. Upper panel: overview of the detailed Universe model, based on observational scaling relations. Lower panel: overview of the model based on the average SFR and metallicity evolution across cosmic time. The plots on the right illustrate the metallicity distributions as a function of redshift for our different prescriptions. For the average metallicity evolution model, we show the distributions assuming both ${\stackrel{\sim }{\sigma }}_{\mathrm{Z}}=0.1$ and 0.6.