> They tend to overgrow their environment, outstrip resources, and then collapse.

That's not what's happening here. Birth rates are below 2.1 in many countries who are no where close to "outstripping their resources". There are other factors causing the contraction which have nothing to do with resource limitations.

In fact it seems like it's the opposite: richer nations with more resources tend to have lower birth rates. That's the scary part because it means there's no equilibrium to be reached. Birth rates could, in theory, remain low until humanity ceases to exist.