  The age matching model has recently been shown to predict correctly the
luminosity L and g-r color of galaxies residing within dark matter halos. The
central tenet of the model is intuitive: older halos tend to host galaxies with
older stellar populations. In this paper, we demonstrate that age matching also
correctly predicts the g-r color trends exhibited in a wide variety of
statistics of the galaxy distribution for stellar mass M* threshold samples. In
particular, we present new measurements of the galaxy two-point correlation
function and the galaxy-galaxy lensing signal as a function of M* and g-r color
from the Sloan Digital Sky Survey, and show that age matching exhibits
remarkable agreement with these and other statistics of low-redshift galaxies.
In so doing, we also demonstrate good agreement between the galaxy-galaxy
lensing observed by SDSS and the signal predicted by abundance matching, a new
success of this model. We describe how age matching is a specific example of a
larger class of Conditional Abundance Matching models (CAM), a theoretical
framework we introduce here for the first time. CAM provides a general
formalism to study correlations at fixed mass between any galaxy property and
any halo property. The striking success of our simple implementation of CAM
provides compelling evidence that this technique has the potential to describe
the same set of data as alternative models, but with a dramatic reduction in
the required number of parameters. CAM achieves this reduction by exploiting
the capability of contemporary N-body simulations to determine dark matter halo
properties other than mass alone, which distinguishes our model from
conventional approaches to the galaxy-halo connection.
