How the Hui became Han(ish)

I was doing some digging around on the genetics of Central Asia and stumbled upon the data that 7% of the mtDNA lineages of the Hui, Muslims who speak Chinese, are West Eurasian. This is opposed 0% for the Han, and 40-50% for the Uyghur. No surprises. But then I thought, what sort of exogamy rates would result in the Hui becoming, operationally, 90% Han during their stay in China? I think 10% is a conservative proportion for how much total genome content they have that is West Eurasian because the historical records suggest a male bias in the migration (so mtDNA would underestimate the proportion of West Eurasian), but, many of the individuals were probably of mixed or Turkic origin to begin with and so would be "back-migrating" those lineages to East Eurasia.

The standard model assumes that the Hui derive from the Yuan dynasty, when the Mongols brought Central Asians to administer China for them in the 13th and 14th centuries, while others argue that the existence of large Muslim populations is attested as far back as the 8th century. So let's split the difference and say 1,000 years, and 25 years per generation, so 40 generations.

Assuming a constant rate of exogamy, what would that rate have to be per generation for the Central Asian Muslims to absorb enough distinctive Han ancestry so that they were 90% East Eurasian? Click below for the answer, but guess first.

About 5.5% exogamy per generation. In other words, 1 out of 18 marriages are between a Hui and a Han. The calculation is made easy by the very small population of Muslims vs. the large population of Han; one can ignore the fact that the exogamy is also probably changing the Han (insofar as there is plenty of historical evidence of Muslims becoming Han, especially in southern China) because of the difference in population size. Though to be honest I think a more plausible model is a lot of initial intermarriage and then stabilization of the new ethno-religious group over time. A closer inspection of the genetic variation of th Hui would get us toward an answer (e.g., is there a bottleneck in the mtDNA or not?).