That is a very interesting question. The most obvious answer is that most of south-central China is just more suited to rice production than cattle/sheep/goats.
I still find it interesting, since many of the more successful Chinese ruling dynasties have central/north asian roots (Tang, Yuan, Qing). Considering that Genghis Khan is probably an ancestor to most of the eastern half of eurasia, once might expect those lactose-tolerant genes to be more prevalent.
Just to make sure the HN record is balanced, I point out for future readers that Wikipedia currently records that some research suggests he is a critical ancestor to approximately 0.5% of the world's population. (http://en.wikipedia.org/wiki/Descent_from_Genghis_Khan#DNA_e...)
I do this not to participate in the argument but to point uninvolved readers to objective sources.
I still find it interesting, since many of the more successful Chinese ruling dynasties have central/north asian roots (Tang, Yuan, Qing). Considering that Genghis Khan is probably an ancestor to most of the eastern half of eurasia, once might expect those lactose-tolerant genes to be more prevalent.