Relation between dust mass and stellar mass at an epoch of 30 Myr, for various initial gas masses and IMFs. Calculations are performed for a “maximum” SN efficiency and dust destruction in the ISM with M_cl = 100   M_⊙ (left panel) and M_cl = 0 (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 region indicates the mass range of stellar masses and dust masses derived from observations of QSOs at z > 6. The vertical dashed lines represent the lower and upper limits of the observed stellar masses. The light grey area illustrates the whole mass ranges derived from observations of QSOs > 5 and accounts for uncertainties in the derived quantities. The horizontal dashed lines mark the lower and upper mass limit of the derived dust masses.