  We have constructed an extended halo model (EHM) which relates the total
stellar mass and star-formation rate (SFR) to halo mass (M_h). An empirical
relation between the distribution functions of total stellar mass of galaxies
and host halo mass, tuned to match the spatial density of galaxies over 0<z<2
and the clustering properties at z~0, is extended to include two different
scenarios describing the variation of SFR on M_h. We also present new
measurements of the redshift evolution of the average SFR for star-forming
galaxies of different stellar mass up to z=2, using data from the Herschel
Multi-tiered Extragalactic Survey (HerMES) for infrared-bright galaxies.
  Combining the EHM with the halo accretion histories from numerical
simulations, we trace the stellar mass growth and star-formation history in
halos spanning a range of masses. We find that: (1) The intensity of the
star-forming activity in halos in the probed mass range has steadily decreased
from z~2 to 0; (2) At a given epoch, halos in the mass range between a few
times 10^{11} M_Sun and a few times 10^{12} M_Sun are the most efficient at
hosting star formation; (3) The peak of SFR density shifts to lower mass halos
over time; (4) Galaxies that are forming stars most actively at z~2 evolve into
quiescent galaxies in today's group environments, strongly supporting previous
claims that the most powerful starbursts at z~2 are progenitors of today's
elliptical galaxies.
