tokens: to be the main reason for our different conclusions. 7.4. [α/Fe]–[Fe/H] relations As shown in Fig 7 , the intrinsic scatter of the [ α /Fe]–[Fe/H] data is large as a result of the complex galactic gas and metal distribution, and stars may form outside the main progenitor halo ( Jeon et al. 2017 ). Our mean galactic metal evolution track assumes that all the gas is always well mixed and thus cannot explain the metal abundance of individual single stars. The best-fit model that applies the IGIMF theory is comparable with the solutions given by Lacchin et al. (2020) , which are shown as the dashed and dash-dotted lines in Fig 7 , especially for metal-rich stars. The highest [ α /Fe] value at the metal-poor end of the plots from Lacchin et al. (2020) is lower than our results and fits the data not as well as our model, however. The highest [ α /Fe] value should be the IMF-weighted [ α /Fe] value of all the massive stars with Z = 0 and a lifetime shorter than the first time step, δ t = 10 Myr, that is, the IMF-weighted thin solid line within the red shaded region of Fig. 8 . Because the IMF-weighted value should be higher than the lowest value in the red region, it is clear that the initial [Mg/Fe] should be higher than 0.5, which agrees with our result and disagrees with Lacchin et al. (2020) . Fig. 8. Stellar metal yield ratios of stars with different mass and metallicity given by Kobayashi et al. (2006) . The yields from Kobayashi et al. (2006) for massive stars are connected to the yields for low- and intermediate-mass stars as given by Marigo (2001) . The yields for M * > 40 M ⊙ are the same as the yields for M * = 40 M ⊙ stars. The red shaded region with log 10 ( M *, initial [ M ⊙ ]) > 1.3073 indicates zero-metallicity stars with lifetimes shorter than 10 Myr, according to Yan et al. (2019) . The [ α /Fe] plateau can be enhanced by a more complicated gas-flow model, a larger stellar-mass bin, or a larger model time step. A non-simultaneous star formation combined with local stellar wind pollution can also complicate the model prediction, which requires more elaborate hydrochemical simulations. We note that the metal-poor part of the [ α /Fe]–[Fe/H] relations is affected by the small number of stars that are formed at the earliest time steps. This shows that the metal-poor part is not reliable because of the small number of massive stars that affect it, the uncertainty of the stellar winds of these massive stars, and whether or not they explode as supernovae. Stars that are more massive than 40 M ⊙ share the same adopted stellar yield table, which is certainly not the ideal setup to discuss the chemical abundance of the extremely metal-poor era of a galaxy. 7.5. Star formation history The tested SFT in Lacchin et al. (2020) is generally longer than our best-fit models. Because the gas flow and star formation criteria in the chemical evolution model are uncertain, the best-fit SFH is not conclusive. Here we compare it with the independently
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O B-Model I-Model I-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O