In studies of the connection between active galactic nuclei (AGN) and their host galaxies there is widespread disagreement on some key aspects stemming largely from a lack of understanding of the nature of the full underlying AGN population. Recent attempts to probe this connection utilize both observations and simulations to correct for a missed population, but presently are limited by intrinsic biases and complicated models. We take a simple simulation for galaxy evolution and add a new prescription for AGN activity to connect galaxy growth to dark matter halo properties and AGN activity to star formation. We explicitly model selection effects to produce an observed AGN population for comparison with observations and empirically motivated models of the local universe. This allows us to bypass the difficulties inherent in many models which attempt to infer the AGN population by inverting selection effects. We investigate the impact of selecting AGN based on thresholds in luminosity or Eddington ratio on the observed AGN population. By limiting our model AGN sample in luminosity, we are able to recreate the observed local AGN luminosity function and specific star formation-stellar mass distribution, and show that using an Eddington ratio threshold introduces less bias into the sample by selecting the full range of growing black holes, despite the challenge of selecting low mass black holes. We find that selecting AGN using these various thresholds yield samples with different AGN host galaxy properties.
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