Left panel: star formation rate versus redshift for HerMES Lockman+XMM+ES1 galaxies, with loci showing 500 μm selection limits for each template type. Small dots are unidentified sources. Right panel: star-formation rate versus redshift for extreme starbursts from both HerMES (Lockman+XMM+ES1, filled circles) and from the IRAS RIFSCz catalogue (crosses). Known lenses are indicated by L and cases known to be unlensed indicated by U. The unlensed object apparently above the 30 000 M _⊙ yr⁻¹ line (F14218+8345) is discussed in Sect. 4. Typical 60 and 500 μm selection limits are indicated by the red and cyan loci.