Counts of optically selected quasars as a function of magnitude and redshift show the effects of strong evolution. If quasars have relatively short life times, then the observed numbers at a given redshift are mostly determined by their birth rate and mean luminosity over their lifetime. In this case the evolution of the luminosity function can be described by density evolution, where the rate of evolution may depend on luminosity and other properties. On the other hand, if all quasars were formed at large redshift and have been decaying in luminosity since that time, then the evolution of the luminosity function is best described in terms of luminosity evolution. We discuss some of the consequences of luminosity evolution for the mass of quasars and for the X-ray background.
We explore the observational aspects of the redshift cutoff of quasars. The situation is complicated by the unavoidable bias in slitless surveys against weak-line objects. Since quasar emission lines show a wide range of equivalent widths, a spectral survey will be characterized by a distribution of limiting continuum magnitudes rather than by a single value. The decline in the space density of quasars at large redshift may depend on luminosity, and may also have structure, such as a steep drop, but not a total cutoff, in density at a redshift near 3.