  We explore the variation in stellar population ages for Coma cluster galaxies
as a function of projected cluster-centric distance, using a sample of 362
red-sequence galaxies with high signal-to-noise spectroscopy. The sample spans
a wide range in luminosity (0.02-4 L*) and extends from the cluster core to
near the virial radius. We find a clear distinction in the observed trends of
the giant and dwarf galaxies. The ages of red-sequence giants are primarily
determined by galaxy mass, with only weak modulation by environment, in the
sense that galaxies at larger cluster-centric distance are slightly younger.
For red-sequence dwarfs (with mass <10^10 Msun), the roles of mass and
environment as predictors of age are reversed: there is little dependence on
mass, but strong trends with projected cluster-centric radius are observed. The
average age of dwarfs at the 2.5 Mpc limit of our sample is approximately half
that of dwarfs near the cluster centre. The gradient in dwarf galaxy ages is a
global cluster-centric trend, and is not driven by the ongoing merger of the
NGC 4839 group to the south west of Coma. We interpret these results using
environmental histories extracted from the Millennium Simulation for members of
massive clusters. Hierarchical cluster assembly naturally leads to trends in
the accretion times of galaxies as a function of projected cluster-centric
radius. On average, simulated galaxies now located in cluster cores joined
halos above any given mass threshold earlier than those now located in the
outskirts of clusters. We test environmental quenching models, in which star
formation is halted in galaxies when they enter halos of a given mass, or
become satellite galaxies. The models broadly reproduce the gradients observed
in Coma, but for dwarf galaxies the efficiency of environmental quenching must
be very high to match the strong trends observed.
