Illustration of the impact of the 24 μm-prior extraction on the redshift distribution at 250, 350, and 500 μm. A flux density cut of 20 mJy was used to select the SPIRE sources. The red line is the intrinsic redshift distribution, while the blue line is obtained after extracting the sources in our simulated Herschel/SPIRE maps using 24 μm positions as a prior. The histograms are normalized in order to have ^∫dN/ dz dz = 1. We compare these model predictions with the observational redshift distribution of Béthermin et al. (2012c, black diamonds). The data points were extracted in real Herschel data using position, 24-μm flux density, and redshift as a prior. This more complex method was chosen to avoid the potential biases associated with a source extraction using only 24-μm positions as a prior (see discussion in Sect. 4.1).