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We exploit the deep and extended far infrared data sets (at 70, 100 and 160um) of the Herschel GTO PACS Evolutionary Probe (PEP) Survey, in combinationwith the HERschel Multi tiered Extragalactic Survey (HerMES) data at 250, 350and 500 um, to derive the evolution of the restframe 35 um, 60 um, 90 um, andtotal infrared (IR) luminosity functions (LFs) up to z~4. We detect very strongluminosity evolution for the total IR LF combined with a density evolution. Inagreement with previous findings, the IR luminosity density increases steeplyto z~1, then flattens between z~1 and z~3 to decrease at z greater than 3.Galaxies with different SEDs, masses and sSFRs evolve in very different waysand this large and deep statistical sample is the first one allowing us toseparately study the different evolutionary behaviours of the individual IRpopulations contributing to the IR luminosity density. Galaxies occupying thewell established SFR/stellar mass main sequence (MS) are found to dominate boththe total IR LF and luminosity density at all redshifts, with the contributionfrom off MS sources (0.6 dex above MS) being nearly constant (~20% of the totalIR luminosity density) and showing no significant signs of increase withincreasing z over the whole 0.8<z<2.2 range. Sources with mass in the 10<log(M/Msun) <11 range are found to dominate the total IR LF, with more massivegalaxies prevailing at the bright end of the high-z LF. A two-fold evolutionaryscheme for IR galaxies is envisaged: on the one hand, a starburst-dominatedphase in which the SMBH grows and is obscured by dust, is followed by an AGNdominated phase, then evolving toward a local elliptical. On the other hand,moderately starforming galaxies containing a low-luminosity AGN have variousproperties suggesting they are good candidates for systems in a transitionphase preceding the formation of steady spiral galaxies.

The Herschel PEP/HerMES Luminosity Function. I: Probing the Evolution of PACS selected Galaxies to z~4