Results of our model for a low-metallicity threshold in η_LGRB, with Z_th = 8.3 (i.e. at ~0.3Z_⊙) and κ = 20, normalised to the LGRB rate estimate of Ghirlanda & Salvaterra (2022) so that ${\eta }_0=7.83\cdot {10}^{-5}{M}_{\odot }^{-1}$. The figure is similar to the right part of Fig. 6, where the blue distributions correspond to the R_LGRB distributions and are compared to the results of Graham et al. (2023), Perley et al. (2016c), and Ghirlanda & Salvaterra (2022). The integrated metallicity (for z ≤ 2.5) and host galaxy mass (for z ≤ 0.5) distributions are compared to the C17 results of Graham et al. (2023) and the local LGRB sample listed in Appendix A, respectively. For more details see Fig. 6. We note that panel C shows the SFR and LGRB rates on two different scales (cf. panels C and F from Fig. 6).