To close the gap between the local luminosity function of the optically selected active galactic nuclei and the population properties of distant (z< or approx. =2) quasars, we propose a model of differential luminosity evolution which is astrophysically based and contains a minimal number of free parameters. We discuss the advantages of the model and its predictions, and indicate how to extend it for z > 2 to cover the beginning of the quasar era.