BHNS MRDs for the model producing the largest MRD in Fig. 3 (lar1), considering different prescription for the Pop. III star formation rate density. Thick blue line: Hartwig et al. (2022, H22; fiducial model adopted in the main body); violet dotted line: Liu & Bromm (2020a, LB20); magenta dashed line: Skinner & Wise (2020, SW20); orange dash-dotted line: Jaacks et al. (2019, J19); yellow dash-dot-dotted line: rescaled de Souza et al. (2011, dS11). As a comparison we also plot the BHNS MRD for early Pop. II (gray line) and Pop. II-I BHNSs (black line).