We explore the epoch dependence of number density and star formation rate for submillimetre galaxies (SMGs) found at 850 mu m. The study uses a sample of 38 SMG in the Great Observatories Origins Deep Survey (GOODS)-N field, for which cross-waveband identifications have been obtained for 35/38 members together with redshift measurements or estimates. A maximum-likelihood analysis is employed, along with the 'single-source-survey' technique. We find a diminution in both space-density and star formation rate at z > 3, closely mimicking the redshift cut-offs found for quasi-stellar objects (QSOs) selected in different wavebands. The diminution in redshift is particularly marked at a significance level too small to measure. The data further suggest, at a significance level of about 0.001, that two separately evolving populations may be present, with distinct luminosity functions. These results parallel the different evolutionary behaviours of Luminous Infrared Galaxies and Ultra-Luminous Infrared Galaxies, and represent another manifestation of 'cosmic down-sizing', suggesting that differential evolution extends to the most extreme star-forming galaxies.