  We compile a number of observations to estimate the time-averaged rate of
formation or buildup of red sequence galaxies, as a function of mass and
redshift. Comparing this with the mass functions of mergers and quasar hosts,
and independently comparing their clustering properties as a function of
redshift, we find that these populations trace the same mass distribution, with
similar evolution, at redshifts 0<z<~1.5. Knowing one of the quasar, merger, or
elliptical mass/luminosity functions, it is possible to predict the others.
Allowing for greater model dependence, we compare the rate of early-type
buildup with the implied merger and quasar triggering rates as a function of
mass and redshift and find agreement. Over this redshift range, observed merger
fractions can account for the entire bright quasar luminosity function and
buildup of the red sequence at all but the highest masses at low redshift
(>~10^11 M_solar at z<~0.3) where 'dry' mergers appear to dominate. This
supports a necessary prediction of theories where mergers between gas-rich
galaxies produce ellipticals with an associated phase of quasar activity, after
which the remnant becomes red. These populations trace a similar characteristic
transition mass, possibly reflecting the mass above which the elliptical
population is mostly (>~50%) assembled at a given redshift, which increases
with redshift over the observed range in a manner consistent with suggestions
that cosmic downsizing may apply to red galaxy assembly as well as star
formation. These mass distributions as a function of redshift do not uniformly
trace the all/red/blue galaxy population, ruling out models in which quasar
activity is generically associated with star formation or is long lived in
'old' systems.
