  Previous work on the quasar mass-luminosity plane indicates the possibility
that quasars of the same central black hole mass might follow a common
evolutionary track, independent of the properties of the host galaxy. We
consider two simple models for the evolution of individual quasars. Requiring
these tracks to lie within the observed quasar locus at all redshifts strongly
constrains the model parameters, but does allow some solutions. These solutions
include a family of tracks with similar shape but different initial masses that
might match the observed quasar distributions at all redshifts z < 2.0. This
family of solutions is characterized by short (1-2 Gyr) lifetimes, a duty cycle
in which the quasar is on at least 25% of the time, and a rapid decline in
Eddington ratio, perhaps with L/L_Edd ~ t^-6 or steeper.
