We follow the evolution of the galaxy population in a ΛCDM cosmology by means of high-resolution N-body simulations in which the formation of galaxies and their observable properties are calculated using a semi-analytic model. We display images of the spatial distribution of galaxies in the simulations that illustrate its evolution and provide a qualitative understanding of the processes responsible for the various biases that develop. We consider three specific statistical measures of clustering at Graphic and Graphic: the correlation length (in both real and redshift space) of galaxies of different luminosity, the morphology–density relation and the genus curve of the topology of galaxy isodensity surfaces. For galaxies with luminosity below L∗, the Graphic correlation length depends very little on the luminosity of the sample, but for brighter galaxies it increases very rapidly, reaching values in excess of 10-h−1Mpc. The ‘accelerated’ dynamical evolution experienced by galaxies in rich clusters, which is partly responsible for this effect, also results in a strong morphology–density relation. Remarkably, this relation is already well-established at Graphic. The genus curves of the galaxies are significantly different from the genus curves of the dark matter, however this is not a result of genuine topological differences but rather of the sparse sampling of the density field provided by galaxies. The predictions of our model at Graphic will be tested by forthcoming data from the 2dF and Sloan galaxy surveys, and those at Graphic by the DEEP and VIRMOS surveys.