  The details of the stellar mass assembly of brightest cluster galaxies (BCGs)
remain an unresolved problem in galaxy formation. We have developed a novel
approach that allows us to construct a sample of clusters that form an
evolutionary sequence, and have applied it to the Spitzer IRAC Shallow Cluster
Survey (ISCS) to examine the evolution of BCGs in progenitors of present-day
clusters with mass of (2.5-4.5)x10^{14}Msun. We follow the cluster mass growth
history extracted from a high resolution cosmological simulation, and then use
an empirical method that infers the cluster mass based on the ranking of
cluster luminosity to select high-z clusters of appropriate mass from ISCS to
be progenitors of the given set of z=0 clusters. We find that, between z=1.5
and 0.5, the BCGs have grown in stellar mass by a factor of 2.3, which is
well-matched by the predictions from a state-of-the-art semi-analytic model.
Below z=0.5 we see hints of differences in behavior between the model and
observation.
