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.