Panels a: redshift evolution of Q_H II for various choices of the magnitude limit in luminosity data: brown for M_lim = −10, orange for M_lim = −13 and beige forM_lim = −17. The light orange region represents the 68% confidence level for the worst case scenario, i.e. M_lim = −17. Left panel: escape fraction fixed to the values used by corresponding references. Right panel: escape fraction varying between zero and one. Panels b: UV luminosity density ρ_UV with redshift in logarithmic scale for three values of the magnitude limit: M_lim =−10 in the upper panel, M_lim = −13 in the middle panel and M_lim = −17 in the lower panel. Data points are from Ishigaki et al. (2015) or adapted from Robertson et al. (2015). Maximum likelihood parametrisations corresponding to Eq. (3) (continuous lines) are shown for fits using all observational constraints. The 68% confidence interval is represented as the light blue region. These results are compared with a model forced to reproduce results fromcorresponding references, drawn as the purple lines. Left panel: escape fraction fixed. Right panel: escape fraction allowed to vary between zero and one.