  We analyze the clustering of red and blue galaxies from four samples spanning
a redshift range of 0.4<z<2.0 to test the various scenarios by which galaxies
evolve onto the red sequence. The data are taken from the UKIDSS Ultra Deep
Survey, DEEP2, and COMBO-17. The use of clustering allows us to determine what
fraction of the red sequence is made up of central galaxies and satellite
galaxies. At all redshifts, including z=0, the data are consistent with ~60% of
satellite galaxies being red or quenched, implying that ~1/3 of the red
sequence is comprised of satellite galaxies. More than three-fourths of red
satellite galaxies were moved to the red sequence after they were accreted onto
a larger halo. The constant fraction of satellite galaxies that are red yields
a quenching time for satellite galaxies that depends on redshift in the same
way as halo dynamical times; t_Q ~ (1+z)^{-1.5}. In three of the four samples,
the data favor a model in which red central galaxies are a random sample of all
central galaxies; there is no preferred halo mass scale at which galaxies make
the transition from star-forming to red and dead. The large errors on the
fourth sample inhibit any conclusions. Theoretical models in which star
formation is quenched above a critical halo mass are excluded by these data. A
scenario in which mergers create red central galaxies imparts a weaker
correlation between halo mass and central galaxy color, but even the merger
scenario creates tension with red galaxy clustering at redshifts above 0.5.
These results suggest that the mechanism by which central galaxies become red
evolves from z=0.5 to z=0.
