  (Abridged) We study the link between quasars and the red galaxy population
using a model for the self-regulated growth of supermassive black holes in
mergers involving gas-rich galaxies. Using a model for quasar lifetimes and
evolution motivated by hydrodynamical simulations of galaxy mergers, we
de-convolve the observed quasar luminosity function at various redshifts to
determine the rate of formation of black holes of a given final mass.
Identifying quasar activity with the formation of spheroids in the framework of
the merger hypothesis, this enables us to deduce the corresponding rate of
formation of spheroids with given properties as a function of redshift. This
allows us to predict, for the red galaxy population, the distribution of galaxy
velocity dispersions, the mass function, mass density, star formation rates,
the luminosity function in many observed wavebands (NUV, U, B, V, R, I, J, H,
K), the total red galaxy number density and luminosity density, the
distribution of colors as a function of magnitude and velocity dispersion for
several different wavebands, the distribution of mass to light ratios vs. mass,
the luminosity-size relations, and the typical ages and distribution of ages
(formation redshifts) as a function of both mass and luminosity. For each of
these quantities, we predict the evolution from redshift z=0-6. Each of our
predictions agrees well with existing observations, without the addition of
tunable parameters; the essential observational inputs come from the observed
quasar luminosity function. These predictions are skewed by several orders of
magnitude if we adopt simpler, traditional models of quasar lifetimes in which
quasars turn on/off or follow simple exponential light curves, instead of the
more complicated evolution implied by our simulations.
