We examine the role of quasars, and the black holes that power them, in cosmological evolution. By using a model of black hole growth and the associated wind and jet heating processes, we simulate a population of active galactic nuclei interacting with the intergalactic medium in a cosmologically representative volume. The use of a representative volume allows us to make predictions about the autocorrelation function of quasars. To predict the evolution of black hole growth and the associated quasar luminosity, we track mergers of dark matter halos, a process which is known to predict the luminosity function of quasars at high redshift with great accuracy. The heating processes are then modelled under the assumption that matter is consumed at the Eddington rate for a predicted dynamical time. By following the hydrodynamic evolution of the gas fuelling the growth of quasars, we are able to examine whether we reproduce the "anti-hierarchical" turn-off in the luminosity function for quasars. While we predict the correlation function with great accuracy, the outflows in our simulations, for an equivalent efficiency, have a smaller impact on the luminosity function than in a similar semi-analytic model. We attribute this difference to the inclusion of in-shock cooling and halo substructure within the simulation.