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tokens: = 5 in the top panel of Fig. 5 . The result using the Tiamat halo merger trees is shown for comparison and to indicate the convergence of the quasar luminosity function at z ∼ 5. The model is in agreement with observations at the bright end (Shen Kelly 2012 ; McGreer et al. 2013 ). We indicate the quasar luminosities of the three analogues in the top panel of Fig. 5 and find that the progenitors of ZF-1, ZF-2 and ZF-3 are bright quasars in the range that optical surveys such as SDSS are able to detect. This suggests that ZF-COSMOS-20115 is likely the descendent of a high-redshift quasar and illustrates the possible connection between MQGs and high-redshift quasars (Maiolino et al. 2012 ). Figure 5. Top panel: quasar UV 1450 Å luminosity function at z ∼ 5. The results using the Tiamat-125-HR and Tiamat halo merger trees are shown with solid and dashed lines, respectively. The shaded regions represent the 95 per cent confidence intervals around the mean using 100 000 bootstrap re-samples for the Tiamat-125-HR result. The observational data is shown with different symbols: Shen Kelly ( 2012 ) using SDSS DR7 data at z ∼ 4.75 () and McGreer et al. ( 2013 ) using SDSS, UKIDSS and MMT at z ∼ 4.7–5.1 (▵). From left to right, the vertical lines indicate the quasar UV magnitudes of ZF-1, ZF-2 and ZF-3, respectively. Bottom panel: correlation between high-redshift black hole mass ( z = 5) and low-redshift SFR ( z = 3.7). The size of the empty circle represents different stellar masses and ZF-3 is indicated with the filled circle. In order to better demonstrate this, for each massive galaxy selected at z = 5.3, we present the correlation between black hole mass and subsequent SFR at z = 3.7 in the bottom panel of Fig. 5 . ZF-3 is indicated with a filled circle. We see that galaxies with less massive black holes ( M BH 10 7.5 M ⊙ ) can have a range of subsequent star formation levels. This is due to self-regulated stellar feedback being the dominant mechanism in these galaxies. However, due to persistent AGN feedback, galaxies with more massive black holes do not have intense subsequent star formation. This indicates that a high-redshift bright quasar will likely become a MQG at later times, when its accretion disc has been completely consumed. 5.3 The reionization history The three ZF-COSMOS-20115 analogues are hosted by massive haloes, which provide deep gravitational potentials that efficiently accrete baryons. The high baryon accretion efficiency induces intense star formation at high redshift, providing a significant number of ionizing photons that reionize surrounding hydrogen at a very early time. In this section, we discuss the reionization history of ZF-COSMOS-20115 . In Fig. 6 , we show the evolution of the average neutral hydrogen fraction within boxes with different sizes around the three analogues. The neutral hydrogen fraction is calculated using 21 cmFAST (Mesinger, Furlanetto Cen 2011 ) with the galaxy catalogue provided by Meraxes (see