  We present a simple model of how quasars occupy dark matter halos from z=0 to
z=5 using the observed mBH-sigma relation and quasar luminosity functions. This
provides a way for observers to statistically infer host halo masses for quasar
observations using luminosity and redshift alone. Our model is deliberately
simple and sidesteps any need to explicitly describe the physics. In spite of
its simplicity, the model reproduces many key observations and has predictive
power: 1) model quasars have the correct luminosity function (by construction)
and spatial clustering (by consequence); 2) we predict high redshift quasars of
a given luminosity live in less massive dark matter halos than the same
luminosity quasars at low redshifts; 3) we predict a factor of ~5 more
10^8.5Msun black holes at z~2 than is currently observed; 4) we predict a
factor of ~20 evolution in the amplitude of the mBH-Mhalo relation between z=5
and the present day; 5) we expect luminosity dependent quasar lifetimes of
between tQ~10^(7-8)yr, but which may become as short as 10^(5-6)yr for quasars
brighter than L*; 6) while little luminosity dependent clustering evolution is
expected at z<1, increasingly strong evolution is predicted for L>L* quasars at
higher redshifts. These last two results arise from the narrowing distribution
of halo masses that quasars occupy as the Universe ages. We also deconstruct
both "downsizing" and "upsizing" trends predicted by the model at different
redshifts and space densities. Importantly, this work illustrates how current
observations cannot distinguish between more complicated physically motivated
quasar models and our simple phenomenological approach. It highlights the
opportunities such methodologies provide.
