  We fit a parametric model comprising a mixture of multi-dimensional Gaussian
functions to the 3.6 to 8um colour and optical photo-z distribution of galaxy
populations in the ELAIS-N1 and Lockman Fields of SWIRE. For 16,698 sources in
ELAIS-N1 we find our data are best modelled (in the sense of the Bayesian
Information Criterion) by the sum of four Gaussian distributions or modes (C_a,
C_b, C_c and C_d). We compare the fit of our empirical model with predictions
from existing semi-analytic and phenomological models. We infer that our
empirical model provides a better description of the mid-infrared colour
distribution of the SWIRE survey than these existing models. This colour
distribution test is thus a powerful model discriminator and complementary to
comparisons of number counts. We use our model to provide a galaxy
classification scheme and explore the nature of the galaxies in the different
modes of the model. C_a consists of dusty star-forming systems such as ULIRG's.
Low redshift late-type spirals are found in C_b, where PAH emission dominates
at 8um. C_c consists of dusty starburst systems at intermediate redshifts. Low
redshift early-type spirals and ellipticals dominate C_d. We thus find a
greater variety of galaxy types than one can with optical photometry alone.
Finally we develop a new technique to identify unusual objects, and find a
selection of outliers with very red IRAC colours. These objects are not
detected in the optical, but have very strong detections in the mid-infrared.
These sources are modelled as dust-enshrouded, strongly obscured AGN, where the
high mid-infrared emission may either be attributed to dust heated by the AGN
or substantial star-formation. These sources have z_ph ~ 2-4, making them
incredibly infrared luminous, with a L_IR ~ 10^(12.6-14.1) L_sun.
