What determines the fraction of elliptical galaxies in clusters?
  We study the correlation between the morphological mix of cluster galaxies
and the assembly history of the parent cluster by taking advantage of two
independently developed semi-analytic models for galaxy formation and
evolution. In our models, both the number of cluster members and that of
elliptical members increase as a function of cluster mass, in such a way that
the resulting elliptical fractions are approximately independent of cluster
mass. The population of cluster ellipticals exhibit a marked bimodal
distribution as a function of galaxy stellar mass, with a dip at masses $\sim
10^{10}\,{\rm M}_{\odot}$. In the framework of our models, this bimodality
originates from the combination of a strongly decreasing number of galaxies
with increasing stellar mass, and a correspondingly increasing probability of
experiencing major mergers. We show that the correlation between the measured
elliptical fraction and the assembly history of the parent cluster is weak, and
that it becomes stronger in models that adopt longer galaxy merger times. We
argue that this results from the combined effect of a decreasing bulge
production due to a reduced number of mergers, and an increasing survival
probability of pre-existing ellipticals, with the latter process being more
important than the former.
