Evolution history of the SNII rate. Similar to Fig. 1, but for the SNII rate of the best-fit IGIMF-R14 model. The initial spike SNII rate is due to the discontinuous 10 Myr time step where the metallicity increases from [Z] = − 7 to [Z] = − 4 at the second time step that leads to a sudden change in gwIMF according to the IGIMF-R14 formulation (see Fig. 4). The blue dashed line is the blue dashed line in Lacchin et al. (2020, their Fig. 5), i.e., their 3BooI-IGIMF model.