My default position is to doubt all molecular dates until I understand how they were derived. Nonetheless, these results seem broadly consistent with the idea that Eurasian modern humans got lighter as their ancestors moved into more northern latitudes of the Old World and replaced Neandertals and others earlier Eurasian occupants, and then they got really lighter post-LGM, and then some got really really lighter with mutations in genes such as SLC24A4 (not studied here).
I suppose we will really find out who got what mutation when only through ancient DNA.
Mol Biol Evol (2012) doi: 10.1093/molbev/mss207
The timing of pigmentation lightening in Europeans
Sandra Belezal et al.
The inverse correlation between skin pigmentation and latitude observed in human populations is thought to have been shaped by selective pressures favoring lighter skin in order to facilitate vitamin D synthesis in regions far from the equator. Several candidate genes for skin pigmentation have been shown to exhibit patterns of polymorphism that overlap the geospatial variation in skin color. However, little work has focused on estimating the timeframe over which skin pigmentation has changed and on the intensity of selection acting on different pigmentation genes. To provide a temporal framework for the evolution of lighter pigmentation, we used forward Monte Carlo simulations coupled with a rejection sampling algorithm to estimate the time of onset of selective sweeps and selection coefficients at four genes associated with this trait in Europeans: KITLG, TYRP1, SLC24A5, and SLC45A2. Using compound haplotype systems consisting of rapidly evolving microsatellites linked to one SNP in each gene, we estimate that the onset of the sweep shared by Europeans and East Asians at KITLG occurred about 30,000 years ago, after the out-of-Africa migration, while the selective sweeps for the European-specific alleles at TYRP1, SLC24A5, and SLC45A2 started much later, within the last 11,000-19,000 years, well after the first migrations of modern humans into Europe. We suggest that these patterns were influenced by recent increases in size of human populations, which favored the accumulation of advantageous variants at different loci.