Cumulative fraction of non-AGN LAEs as a function of Lyα luminosity. Black dots are from the Nilsson et al. (2009) sample. Coloured points are from publications at redshifts z = 0.3 (Atek et al. 2009; Cowie et al. 2010; Finkelstein et al. 2009; Scarlata et al. 2009), z = 2.1 (Guaita et al. 2010), z = 3 (Gronwall et al. 2007; Ouchi et al. 2008) and at z ~ 4−5 (Wang et al. 2004; Ouchi et al. 2008). Lines indicate best-fit models (see text for details).