I'd like to bring to the table the possibility of the "calories per acre" of rice vs. wheat being a factor. Now, both China and India do indeed use wheat, but rice is a huge, it not the main, staple in these countries, obviously. One would need to look at the population density at different points in time of regions where the main staple is wheat vs. where it's rice to really study this...
But anyway, the theory here I'm bringing up is that China and India have historically had large populations because they can grow rice and rice provides more calories per acre than wheat, which is the main staple in the Middle East and Europe (correct me if I'm wrong there).
This source shows rice having double the calories per acre of wheat. (It also shows potatoes and maize as having higher calories per acre than rice, but we're comparing Europe and the Middle East with India and China, not the Americas, which brings in factors like climate and land (potatoes used to only grow in cold S.American mountains and I've read that corn is pretty hard to domesticate) and political history (hard to measure the population of pre-disease-devastated Americas, although actually I'm sure decent estimates are out there)).