We have analysed polarization data for a large number of isolated pulsars to investigate the evolution of pulsar radio beams. Assuming that a circular beam is directed along the axis of a dipolar magnetic field, we demonstrate that the distribution of magnetic inclination angles for the parent population of all pulsars is not flat but highly concentrated towards small inclination angles and that, consequently, the average beaming fraction is only ∼ 10 per cent. Furthermore, we find that there is a tendency for the beam axis to align with the rotational axis on a time-scale of ∼ 107 yr. This has interesting consequences for statistical studies of the pulsar population. Finally, the luminosity of pulsars is shown to be independent of the impact parameter, which indicates that pulsar beams are sharp-edged and have a relatively flat integrated intensity distribution.