They are basically seeing whether there are many private haplotypes in the Uyghur population compared to East Asian and European populations. They don't find this to be the case, thus suggesting that Uyghurs are the result of a recent admixture process.
Haplotype-Sharing Analysis Showing Uyghurs Are Unlikely Genetic Donors
Shuhua Xu, Wenfei Jin and Li Jin
Molecular Biology and Evolution 2009 26(10):2197-2206
Abstract: The Uyghur (UIG) are a group of people primarily residing in Xinjiang of China, which is geographically located in Central Asia, from where modern humans were presumably spread in all directions reaching Europe, east, and northeast Asia about 40 kya. A recent study suggested that the UIG are ancestry donors of the East Asian (EAS) gene pool. However, an alternative hypothesis, that is, the UIG is an admixture population with both EAS and EUR ancestries is also supported by our previous studies. To test the two competing hypotheses, here we conducted a haplotype-sharing analysis (HSA) based on empirical and simulated data of high-density single nucleotide polymorphisms. Our results showed that more than 95% of UIG haplotypes could be found in either EAS or EUR populations, which contradicts the expectation of the null models assuming that UIG are donors. Simulation studies further indicated that the proportion of UIG private haplotypes observed in empirical data is only expected in alternative models assuming that UIG is an admixture population. Interestingly, the estimated ancestry contribution of 44%:56% (EAS:EUR) based on HSA is consistent with our previous estimation with STRUCTURE analysis. Although the history of UIGs could be complex, our method is explicit and conservative in rejecting the null hypothesis. We concluded that the gene pool of modern UIGs is more likely a sole recipient with contribution from both EAS and EUR.