Empirical backward galaxy evolution models for infrared bright galaxies are constrained using multi-band infrared surveys. We developed a new Monte-Carlo algorithm for this task, implementing luminosity dependent distribution functions for the galaxi
es infrared spectral energy distributions (SEDs) and for the AGN contribution, allowing for evolution of these quantities. The adopted SEDs take into account the contributions of both starbursts and AGN to the infrared emission, for the first time in a coherent treatment rather than invoking separate AGN and star-forming populations. In the first part of the paper we consider the quantification of the AGN contribution for local universe galaxies, as a function of total infrared luminosity. It is made using a large sample of LIRGs and ULIRGs for which mid-infrared spectra are available in the Spitzer archive. In the second part we present the model. Our best-fit model adopts very strong luminosity evolution, $L=L_0(1+z)^{3.4}$, up to $z=2.3$, and density evolution, $rho=rho_0(1+z)^2$, up to $z=1$, for the population of infrared galaxies. At higher $z$, the evolution rates drop as $(1+z)^{-1}$ and $(1+z)^{-1.5}$ respectively. To reproduce mid-infrared to submillimeter number counts and redshift distributions, it is necessary to introduce both an evolution in the AGN contribution and an evolution in the luminosity-temperature relation. Our models are in plausible agreement with current photometry-based estimates of the typical AGN contribution as a function of mid-infrared flux, and well placed to be compared to upcoming Spitzer spectroscopic results. As an example of future applications, we use our best-fitting model to make predictions for surveys with Herschel.
