et al (1988) quantify the QSO population as having a luminosity function $\phi_{qso}(L/L_*)\propto \phi_o(L/L_*)^{-3.7}$ with $L_*=L_o(1+z)^{3.2}$. Integrating to obtain the number of objects per comoving volume brighter than $L_1$ gives $$\begin{aligned}
N(>L_1) &=& \int^\infty_{L_1/L_*}\phi_{qso}\left(\frac{L}{L_*}\right)
              d\left(\frac{L}{L_*}\right)
\\
&=& \frac{\phi_o}{2.7}\left(\frac{L_1}{L_*}\right)^{-2.7}
\nonumber\\
&=& \frac{\phi_o}{2.7}\left(\frac{L_1}{L_o}\right)^{-2.7}(1+z)^{5.9},
\nonumber\end{aligned}$$ which has a proportionality that is consistent with the evolution for $z<2$ shown in Fig. \[qsoevol.fig\] and in Schmidt et al (1995).

The intention behind Fig. \[qsoevol.fig\] is to show that at least one population of luminous object does evolve very steeply with redshift. An association between AGN activity and galaxy merging or interaction remains to be definitively established, although there is evidence that “warm,” ultraluminous infrared galaxies may be an evolutionary step in the evolution of optically selected QSOs (cf. Surace et al 1998). Interestingly, the $z\approx 0$ number density of ultraluminous FIR galaxies is comparable to the $z\approx 0$ density of luminous QSOs, as illustrated in the figure. Furthermore, Saunders et al (1990) deduced a density evolution ${\propto}(1+z)^{6.7}$ for their 60$\mu$m sample, although subsequent study by Ashby et al (1996) did not find the tail to high redshift expected if this were indeed the case. The evolution rate ${\propto}(1+z)^{4.5}$ explored in the lower panel of Fig. 