than the second one because our cut fall at the middle of the first one. The arrows indicate the mean stellar mass in each redshift bin.](Mass_distrib.eps)

In this paper, we base our analysis on mass-selected samples of star-forming galaxies (see Sect.\[masscat\]). We chose the same stellar mass cut of $3 \times 10^{10}$M$_\odot$ at all redshifts to be complete up to z$\sim$4. We could have used a lower mass cut at lower redshifts, but we chose this single cut for all redshifts to be able to interpret the observed evolution of the various physical parameters of the galaxies in our sample in an easier way. This cut is slightly higher than the 90% completeness limit at z$\sim$4 cited in @Ilbert2013 [1.8$\times$10$^{10}$M$_\odot$] and implies an high completeness of our sample, which limits potential biases induced by the input catalog on the results of our stacking analysis [e.g., @Heinis2013]. The exact choice of our stellar mass cut has negligible impact on the mean SEDs measured by stacking: we tested a mass cut of $2 \times 10^{10}$M$_\odot$ and $5 \times 10^{10}$M$_\odot$ and found that, after renormalization at the same L$_{\rm IR}$, the SEDs are similar ($\chi_{\rm red}^2$ = 0.57 and 0.79, respectively). These results 