on the one hand, yes ecology and math bio is cool. On the other, the demographic transition does not fall out of these models whatsoever. Humans decided to do something very weird for whatever reason.

The actual population size during demographic transition looks very logistic-y. You'd be forgiven for thinking Verhulst applies. (though K is very much an empirical constant in that case, since you can't easily predict it from anything I don't think.)

I think the demographic transition overshoot (https://en.wikipedia.org/wiki/Demographic_transition#Stage_f...) we see is unexpected though.

Yeah the demographic transition is something nobody predicted (afaik). On the other hand, LTG (https://en.wikipedia.org/wiki/The_Limits_to_Growth) is a neo-Malthusian prediction that seems to match early data, and a surprising number of people revisit it and find its conclusions seem to hold. We'll be finding out around 2040, give or take. ¯\_(ツ)_/¯