Every time I look at a map of the United States coloured by something proportional to population density, I see a stark vertical line going from northeast North Dakota, through SD, NE, KS, OK, and finally reaching southern Texas. For instance, here it is in a map of light pollution:
Here you can see it in nighttime satellite imagery:
and even in confirmed COVID-19 cases:
Finally, here it is in terms of raw population density data by counties:
My current hypothesis is it's mostly determined by climate---for instance, here is a map of the Köppen climate types of the United States:
However, the cold semi-arid (BSk) climate only starts in the western parts of the states that the line crosses in the east. I found a slightly higher correlation by looking at a map of rainfall:
So, is this line mainly determined by climate? If so, why is the line so stark, and still so cleanly visible, perhaps a hundred years after the main wave of migration? Could this be better explained by specific historical circumstances and demarcations; for instance, a boundary between land that was ceded by the Native Americans, and land that wasn't?
For instance, the map of land cessions seems to line up pretty well with the line in Texas:
Are there any historical reasons other than "geography"for this divide?
The answer is related to the map you posted about rainfall. The population of the eastern third of the continental US is denser because of settlement patterns that reflect the local availability of water resources. This quirk of human geography occurs because of the need for irrigation. As detailed by Harvey Leifert in "Dividing line: The past, present and future of the 100th Meridian":
In his 1878 “Report on the Lands of the Arid Region of the United States,” [John Wesley] Powell identified the “arid region” as the land west of the 51-centimeter-per-year rainfall line, which closely tracked the 100th meridian. This amount of rainfall per year is about the minimum that permits farming without irrigation, and it also greatly influences the types of crops that can be grown. The line Powell noted as dividing the arid and humid sections of the continent has become known as the “effective” 100th meridian.
That population is much denser on the east side of the line is apparent in historical demography nearly as soon as masses of settlers arrived there in the mid-1800s; check out this neat animated map.
With more limited water, farms had to be bigger to make money west of the line. Possibly related to farming conditions and market size, insurance was more available east of the line.