It is important to distinguish cluster galaxies from field galaxies. Whilst field galaxies may be thought of as the low mass end of the mass function as described by Press-Schechter theory, the formation of cluster galaxies may be affected by their location in a region of high over-density.
Clues to differences in the evolution of field galaxies and cluster galaxies are plentiful in observations of galaxies. Perhaps most compelling is the difference in morphological-mix between field and cluster galaxies. Galaxies in clusters are often dominated by a massive cD galaxy and the general population (in the cores of clusters) has a majority of early-type E and S0 galaxies with relatively few spirals. The exact mix has been shown to change as a function of projected density, and hence distance from the cluster centre (Dressler 1980, Whitmore & Gilmore 1991, Whitmore et al. 1993). In contrast galaxies in the field are mainly late-type spirals with fewer early-type galaxies and no cD galaxies (Oegerle & Hill 2001). There is evidence in the form of the Butcher-Oemler effect that the fraction of blue, late-type galaxies increases at higher redshift, while the fraction of S0 galaxies decreases, suggestive of morphological evolution (Butcher & Oemler 1984).
The two most commonly held views on early-type galaxy formation are those of monolithic collapse (e.g. Eggen et al. 1962) and hierarchical merging (e.g. Cole et al. 1994). Hierarchical merging is perhaps more consistent with the framework of structure formation presented in section 1.3. In a hierarchical merging picture galaxies form by a series of mergers over their lifetime (e.g. Kauffmann et al. 1993). Mergers between galaxies may be accompanied by bursts of star formation, unless merging is almost dissipationless. If galaxy merging is almost dissipationless then significant star formation will not occur (since if most gas is already in the form of stars there will be little radiative loss of energy, Bender et al. 1992). This is more likely to be the case in massive galaxies. Note also that in hierarchical merging as opposed to random merging higher mass galaxies have a higher chance of merging due to dynamical friction (Kauffmann & Charlot 1998a) and their location in the denser, central parts of the cluster.
Note that merging between galaxies in clusters will not necessarily occur over the whole lifetime of a cluster. Because galaxies in clusters have higher velocities than galaxies in the field the chances of mergers occurring are reduced. Diaferio et al. (2001) present simulations of galaxy evolution in the field and in clusters based on a hierarchical merging model in which it is shown that there is very little change in the numbers of massive galaxies in any given cluster since 
, although there is a significant change in the number of clusters.
In the alternative model of monolithic collapse galaxies (and the stars within) are all formed in a single burst at the epoch of the collapse of the cluster. After the initial burst of star formation, the galaxies evolve only in luminosity as their stars age and fade. This picture presents an extremely homogeneous population of galaxies with only a little variation in age resulting from the variation in initial mass function of the galaxies.
A more detailed discussion of the formation and evolution of galaxies in clusters is presented in chapter 4. Chapters 5 and 6 present observational results on the evolution of cluster galaxies.