  Using a model for self-regulated growth of black holes (BHs) in mergers
involving gas-rich galaxies, we study the relationship between quasars and the
population of merging galaxies and predict the merger-induced star formation
rate density of the Universe. Mergers drive nuclear gas inflows, fueling
starbursts and 'buried quasars' until accretion feedback expels the gas,
rendering a briefly visible optical quasar. Star formation is shut down and
accretion declines, leaving a passively evolving remnant with properties
typical of red, elliptical galaxies. Based on evolution of these events in our
simulations, we demonstrate that the observed statistics of merger rates,
luminosity functions (LFs) and mass functions, SFR distributions, specific
SFRs, quasar and quasar host galaxy LFs, and elliptical/red galaxy LFs are
self-consistent and follow from one another as predicted by the merger
hypothesis. We use our simulations to de-convolve both quasar and merging
galaxy LFs to determine the birthrate of black holes of a given final mass and
merger rates as a function of stellar mass. We use this to predict the merging
galaxy LF in several observed wavebands, color-magnitude relations, mass
functions, absolute and specific SFR distributions and SFR density, and quasar
host galaxy LFs, as a function of redshift from z=0-6. We invert this and
predict e.g. quasar LFs from observed merger LFs or SFR distributions. Our
results agree well with observations, but idealized models of quasar
lightcurves are ruled out by comparison of merger and quasar observations at
>99.9% confidence. Using only observations of quasars, we estimate the
contribution of mergers to the SFR density of the Universe even to high
redshifts z~4.
