In the past few years two different approaches have been widely used to interpret faint galaxy data . In the simplest version of what I will call the `traditional' scheme, a one-to-one mapping between galaxies at the present epoch and their distant counterparts is assumed: one starts from the local measurements of the distribution of galaxies as a function of luminosity and Hubble type and models their photometric evolution assuming some redshift of formation and a set of parameterized star formation histories . These, together with an initial mass function (IMF) and a cosmological model, are then adjusted to match the observed number counts, colors, and redshift distributions. Beyond the intrinsic simplicity of assuming a well defined collapse epoch and pure-luminosity evolution thereafter, the main advantage of this kind of approach is that it can easily be made consistent with the classical view that ellipticals and spiral galaxy bulges (both redder than spiral disks and containing less gas) formed early in a single burst of duration 1 Gyr or less . Spiral galaxies, by contrast, are characterized by a slower metabolism, i.e. star formation histories that extend to the present epoch. In these models, typically, much of the action happens at high-redshifts.
A more physically motivated way to interpret the observations is to construct semianalytic hierarchical models of galaxy formation and evolution . Here, one starts ab initio from a power spectrum of primordial density fluctuations, and follows the formation and hierarchical merging of the dark matter halos that provide the early seeds for later galaxy formation. Baryonic gas gets accreted onto the halos and is shock-heated. Various prescriptions for gas cooling, star formation, feedback, and dynamical friction are adopted, and tuned to match the statistical properties of both nearby and distant galaxies. In this scenario, there is no period when bulges and ellipticals form rapidly as single units and are very bright: rather, small objects form first and merge continually to make larger ones. Galaxy do not evolve as isolated objects, and the rate of interaction was higher in the past.
The bulk of the galaxy population is predicted to have been assembled quite recently, and most galaxies never experience star formation rates in excess of a few solar masses per year.