Not sure I totally buy the Mexico one. The correspondence just isn't as strong as in some of the other ones, and in some places is confounded by modern state borders.
I don’t know that these are all cause and effect, but just interesting overlays. The Mexico one is clear to Americans - people who immigrate from Mexico choose to stay nearer to Mexico. Similar cultures, weather, etc. The areas previously being a part of Mexico is just coincidence.
There were a substantial number of people of Spanish-Imperial descent (of a variety of conditions) who didn't just move south when the border moved. Even now you see old families who identify as Mexican with the submotto "we didn't cross the border, the border crossed us". Keep in mind that much of that area was under Spanish and/or Mexican control for almost twice as long as it has been in the US (~1550-1846 vs 1846-present).
I don't (I'd imagine it's of a similar quality to people in the US northeast whose ancestors came over on the Mayflower). However, I wouldn't be surprised at the finding that their presence has had a network effect (and a cultural effect) that encouraged people coming from Mexico more recently to settle in that area rather than (for example) spread into the Louisiana Purchase territory, for the same reasons that immigration from other countries also tends to settle and self-perpetuate in enclaves.
Sure, I just mean that the line is a lot fuzzier than most of the other examples. Like if you showed me just the modern Polish map in the first one, I could clearly draw a pretty accurate approximation of the historical German border. But I don't think you could get nearly as accurate of a historical Mexican border from the modern population map. And in few areas where you can, it's also a modern border (Texas-Louisiana for example).
It's just a less compelling example than the others.
