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.Comment: Accepted by MNRA
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