Predicted AGN fraction in groups (10^13.5<M< 10^14.3M_⊙, left panel) and clusters (M> 10^14.5M_⊙, right panel) for AGN L_X> 10⁴² erg s^-1, hosted by galaxies brighter than M_R< − 20. The predictions of our model are represented by shaded regions: black for IT and red for the fiducial case for DI. The shaded region with red-dashed lines represents the prediction for the DI scenario with decreased normalization α = 2, the two black-dashed lines in the groups plot represent the limits of the prediction for the IT scenario obtained with a slightly brighter threshold for galaxies (M_R< − 21, see text for more details). Green symbols are data from Pentericci et al. (2013), red symbol from Eastman et al. (2007), black symbols from Martini et al. (2009), and blue symbols from Arnold et al. (2009). Uncertainties and upper limits are computed by using the low-number statistics estimator (at 1σ) by Gehrals (1986).