Drift by its very nature cannot be positively demonstrated. To do this it would be necessary to show that selection has definitely NOT operated, which is impossible. Much indirect evidence has been obtained, however, which purports to favour the drift position. The book by Harrison et al. is quite interesting because it goes on for several pages discussing the controversy. The relative importance of drift and selection depends, in part, on estimated population sizes.
Drift is much more important in small populations.
It is these demes that evolve. Studies of evolution at the molecular level have provided strong support for drift as a major mechanism of evolution. Observed mutations at the level of gene are mostly neutral and not subject to selection. One of the major controversies in evolutionary biology is the neutralist-selectionist debate over the importance of neutral mutations. Since the only way for neutral mutations to become fixed in a population is through genetic drift this controversy is actually over the relative importance of drift and natural selection.