How many people were present in areas such as Kazakhstan and Mongolia in the period of the Mongol invasions? I ask because today Mongolia has a tiny population of 3 million people, while many of the places they invaded, such as Iran, has 77 million people. Has central Asia, specifically mongolia, always been this far behind in population or is it a more recent occurrence?
Mongolia has around 30% of its population relying on nomadic, subsistence agriculture. This, coupled with the relatively low level of urbanization has limited population growth substantially.
I can't find any good sources on what the population of Outer Mongolia ( modern-day Mongolia ) was roughly, but I do know Genghis Khan had around 110,000 warriors, so accounting for that being a significant population of the nomadic men - probably around 300-400k max with women and children plus non-combatants conservative estimate, at the most is my conservative estimate. By comparison, the Song Dynasty, circa 1120CE had around 118 million.
I can't find population estimates for the area of the Cuman-Kipchak Confederation, one of the predecessor states of the Mongol Empire. But it looks like in Mongolia, specifically, the population has had a long history of lag, as you put it.
Sources
2002 Mongolian Population PDF: https://web.archive.org/web/20090325081923/http://202.131.5.91/yearbook/2002/yearbook2002.pdf
China's Geography: Globalization and the Dynamics of Political, Economic, and Social Change (2007)
Numbers in Mongol Warfare: https://books.google.com/books?id=4jHEwSc2gEMC&pg=PA109&dq=devries+mongols&hl=en#v=onepage&q&f=false