the relative increase of the rates with $z$ as compared to models with the same DTD without a metallicity enhancement. This is similar in spirit, but less dramatic, than the relative evolution likely due to stellar metallicity seen in the cosmic GRB rate (e.g., @Kistler). Both models are also broken down by delay time in Fig. \[Iahist\] (thin dotted, dashed lines), which illustrates the underlying effect of altering the DTD.

As discussed for the specific SN Ia rate, there is again a degeneracy between altering the DTD and including the effect of metallicity, although not quite as strong. That the metallicity effect works in the same direction as decreasing the index in the DTD in both cases, as seen in Fig. \[Iarate\] and Fig. \[Iahist\], is something of a coincidence, owing to the fact that galaxy ages and metallicities both decrease with decreasing mass and the cosmic SFR rises with increasing $z$. This didn’t have to be the case, though. We thus reiterate that an estimate of one component must account for the other until this degeneracy is broken. It is possible to perform a more elaborate study by varying all the parameters involved (see, e.g., @Horiuchi and @Graur for 