Relation between metallicity and SFR at epochs of 30 Myr (left panel) and 100 Myr (right panel). The colored symbols are obtained for different initial gas masses, M_ini, SFRs, and IMFs. The size of the symbols is scaled by M_ini. Calculations are made for M_ini = 1.3 × 10¹² M_⊙ (largest symbol), M_ini = 5 × 10¹¹ M_⊙, M_ini = 3 × 10¹¹ M_⊙, M_ini = 1 × 10¹¹ M_⊙, and M_ini = 5 × 10¹⁰ M_⊙ (smallest symbol). The crosses correspond to calculations for a initial SFR ψ_ini = 10³ M_⊙ yr^-1, the filled circles to ψ_ini = 3 × 10³ M_⊙ yr^-1 and the stars to ψ_ini = 10⁴ M_⊙ yr^-1. The black, green, cyan, magenta, and blue colors denote the Salpeter, mass-heavy, top-heavy, Larson 1, and Larson 2 IMF, respectively. The dark grey shaded region indicates the range of the metallicity and SFR based on observations of QSOs at z > 6. The vertical dashed lines represent the lower and upper limits of the observationally derived SFRs. The light grey shaded area accounts for the uncertainty of the upper limit of the metallicity. The horizontal dashed lines mark the lower and possibly upper limit of the metallicity.