Dependence on X-ray luminosity vs. absolute magnitude in the i′-band. GALs are marked with triangles and AGN with circles. Soft (HR < −0.2) sources are shown with open symbols and hard (HR ≥ −0.2) sources with filled symbols. The solid vertical lines M_i′ = −23.5 divide the AGN from the brighter QSOs. In the overdensity analysis (Sect. 5), we have only considered the sources locating between the solid and dashed vertical lines.