In hierarchical models of galaxy production, many protogalaxies merge at high redshifts. Each merger results in a spectacular wreck, which gradually restructures itself into a more unified system. Collisions engender vast conflagrations of stars as unstable gas clouds collapse and ignite thermonuclear fires. This process repeats and repeats until galaxies form as we know them today.

We see many galaxies still merging at present. In hierarchical models these late mergers are all that remain of earlier more active combining, or they result from encounters in recent dense groups. The long history of merging changes the observed galaxy distribution by destroying the conservation of galaxy numbers and by modifying the luminosity function. The first of these is easier to model; the second, at present, is really a guess. Galaxy luminosities depend on their unknown stellar initial mass functions, their subsequent star formation by merging or other violent activity, their nonthermal radiation, their production and distribution of dust, and their stellar evolution. Of these factors, only stellar evolution is reasonably well understood. On the other hand, number nonconservation depends on galaxy velocities, densities, and collision cross sections. These too must be modeled, but they seem more straightforward.

By describing the evolution of both the luminosity and the spatial distribution functions with one common formalism, we can use their mutual self-consistency to help constrain free parameters.