  We investigate galaxy evolution in protoclusters using a semi-analytic model
applied to the Millennium Simulation, scaled to a Planck cosmology. We show
that the model reproduces the observed behaviour of the star formation history
(SFH) both in protoclusters and the field. The rate of star formation peaks
$\sim0.7\,{\rm Gyr}$ earlier in protoclusters than in the field and declines
more rapidly afterwards. This results in protocluster galaxies forming
significantly earlier: 80% of their stellar mass is already formed by $z=1.4$,
but only 45% of the field stellar mass has formed by this time. The model
predicts that field and protocluster galaxies have similar average specific
star-formation rates (sSFR) at $z>3$, and we find evidence of an enhancement of
star formation in the dense protoclusters at early times. At $z<3$,
protoclusters have lower sSFRs, resulting in the disparity between the SFHs. We
show that the stellar mass functions of protoclusters are top-heavy compared
with the field due to the early formation of massive galaxies, and the
disruption and merging of low-mass satellite galaxies in the main haloes. The
fundamental cause of the different SFHs and mass functions is that dark matter
haloes are biased tracers of the dark matter density field: the high density of
haloes and the top-heavy halo mass function in protoclusters result in the
early formation then rapid merging and quenching of galaxies. We compare our
results with observations from the literature, and highlight which observables
provide the most informative tests of galaxy formation.
