We fit a parametric model comprising a mixture of multi-dimensional Gaussian functions to the 3.6 to 8µm colour and optical photometric redshift distribution of galaxy populations in the ELAIS-N1 and Lockman Fields of the Spitzer Wide-area Infrared Extragalactic Legacy survey (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 semianalytic 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 is entirely 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. Population C a is found to consist of dusty star-forming systems such as ULIRG's, over a broad redshift range. Low redshift late-type spirals are found in population C b , where PAH emission dominates at 8µm, making these sources very red in longer wavelength IRAC colours. Population C c consists of dusty starburst systems with high levels of star-formation activity at intermediate redshifts. Low redshift early-type spirals and ellipticals are found to dominate Population C d . We thus find a greater variety of galaxy types than one can with optical photometry alone.-2 -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 midinfrared 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 ⊙ .