These analogies seem pretty loose to me.
The immigration analogy is really talking about folks who are migrating but not becoming citizens where they move (as with Rome).
I would agree if folks immigrate and do not become citzens or assimilate that would be a better analogy, but that mostly is not happening. (Perhaps some in Europe recently)
Humans are better able to manage climate today (thought we might cause worse disruptions) still it seems hard to see it moving national boundaries.
wholesale nation border movement was a very accepted action before WWII, and has become the notable exception since then. (with Russia being the big one, and Taiwan the special case)
Still the economic fortunes of each could really swing