We use our model for the formation and evolution of galaxies within a two-phase galaxy formation scenario, showing that the high-redshift domain typically supports the growth of spheroidal systems, whereas at low redshifts the predominant baryonic growth mechanism is quiescent and may therefore support the growth of a disc structure. Under this framework, we investigate the evolving galaxy population by comparing key observations at both low and high redshifts, finding generally good agreement. By analysing the evolutionary properties of this model, we are able to recreate several features of the evolving galaxy population with redshift, naturally reproducing number counts of massive star-forming galaxies at high redshifts, along with the galaxy scaling relations, star formation rate density and evolution of the stellar mass function. Building upon these encouraging agreements, we make model predictions that can be tested by future observations. In particular, we present the expected evolution to z= 2 of the supermassive black hole mass function, and we show that the gas fraction in galaxies should decrease with increasing redshift in a mass, with more and more evolution going to higher and higher masses. Also, the characteristic transition mass from a disc to bulge-dominated system should decrease with increasing redshift.