The greatest demographic change in Asia during this time period was the rise of the Mongol Empire as is noted in Post #6. The Mongols established the largest empire the world had ever seen, even larger than that of Alexander. During their reign, the Silk Roads became a profitable means of trade again, as they policed the roads and prevented robbers, etc. from interfering. Because the Mongols did not trust local people, they often brought in people from other areas to assist in administration. They themselves were not fond of administration, they were fighters, not governors. An interesting element is that they insisted that the Chinese, where the Mongols held a large Empire, remain segregated from the Mongol population. The Chinese were forbidden to learn the Mongol language, were forced to dress in a separate fashion, and also required to wear their hair in the long pony-tail fashion known as the queue.
The Mongols also exercised some limited control over Russia, but not over Thailand, Vietnam, and other forested areas, as their horses did not function well when not on the steppes of Eurasia. Their Empire might have extended further (European powers could not stop them) except they abandoned their conquest of Europe when Genghis Khan died.