Using pulsewidth data for 872 isolated radio pulsars, we test the hypothesis that pulsars evolve through a progressive narrowing of the emission cone combined with progressive alignment of the spin and magnetic axes. The new data provide strong evidence for the alignment over a time-scale of about 1Myr with a log standard deviation of around 0.8 across the observed population. This time-scale is shorter than the time-scale of about 10Myr found by previous authors, but the log standard deviation is larger. The results are inconsistent with models based on magnetic field decay alone or monotonic counter-alignment to orthogonal rotation. The best fits are obtained for a braking index parameter, nγ ~ 2.3, consistent with the mean of the six measured values, but based on a much larger sample of young pulsars. The least-squares fitted models are used to predict the mean inclination angle between the spin and magnetic axes as a function of log characteristic age. Comparing these predictions to existing estimates, it is found that the model in which pulsars are born with a random angle of inclination gives the best fit to the data. Plots of the mean beaming fraction as a function of characteristic age are presented using the best-fitting model parameters.