An invocation of selection as an explanation requires evidence population continuity, otherwise changes in allele frequency may involve migration of a new frequency-differentiated new population; for example, the massive change in pigmentation in North America over the last 500 years is not due to selection but to migration of Europeans. The authors cannot reject population continuity on the basis of mtDNA haplogroup frequencies, although autosomal data may be more informative for that purpose.
In any case, the fact that the limited sample from western Europe and the much more extensive sample from eastern Europe both show a darker pigmentation than modern Europeans does suggest that interesting changes happened in Europe over the last few thousand years and samples from more recent time periods may better determine the pace of this change.
From the paper:
In sum, a combination of selective pressures associated with living in northern latitudes, the adoption of an agriculturalist diet, and assortative mating may sufficiently explain the observed change from a darker phenotype during the Eneolithic/Early Bronze age to a generally lighter one in modern Eastern Europeans, although other selective factors cannot be discounted. The selection coefficients inferred directly from serially sampled data at these pigmentation loci range from 2 to 10% and are among the strongest signals of recent selection in humans.UPDATE:
The classical Greeks did of course notice that the inhabitants of the north Pontic hinterland, collectively known as Scythians, were extraordinarily light-pigmented. This would imply that major pigmentation change occurred in the steppe over a time span of Bronze Age-Classical Antiquity rather than Bronze Age-present; this would imply even higher selection coefficients (if selection over a population exhibiting continuity is at play).
The Scythians were also thought to be recent arrivals from the east so it is not clear if they were descended from the Bronze Age population of eastern Europe; the crazy selection coefficients that would need to be assumed if there was indeed population continuity might imply that Herodotus got it right again, and the Scythians did in fact arrive from elsewhere. That would of course also imply that people from Central Asia and Siberia (where the Scythians may have come from) were originally lighter than Europeans which does find support from an older study on southern Siberian remains. Ironically, if that is the case, it would mean that the famous light-pigmented mummies of different parts of Inner Asia may not be long-lost European descendants -- as it has sometimes been presumed on the basis of modern-day clines of pigmentation. As usual, ancient DNA continues to surprise.
PNAS doi: 10.1073/pnas.1316513111
Direct evidence for positive selection of skin, hair, and eye pigmentation in Europeans during the last 5,000 y
Sandra Wilde et al.
Eye, hair, and skin pigmentation are highly variable in humans, particularly in western Eurasian populations. This diversity may be explained by population history, the relaxation of selection pressures, or positive selection. To investigate whether positive natural selection is responsible for depigmentation within Europe, we estimated the strength of selection acting on three genes known to have significant effects on human pigmentation. In a direct approach, these estimates were made using ancient DNA from prehistoric Europeans and computer simulations. This allowed us to determine selection coefficients for a precisely bounded period in the deep past. Our results indicate that strong selection has been operating on pigmentation-related genes within western Eurasia for the past 5,000 y.