Isn't all this equally true of population growth as well as shrinkage?
The only major time i can think of where there were major depopulation events are in the times of the Fertile Crescent civilizations and perhaps in Asia in Angkor Wat. In both of the scenarios this massive depopulation led to the extinction of those civilizations.
Nah, at least not of this magnitude. The world's population only hit a billion at about 1800, two billion around WWII. We're now at nearly eight. The idea that we understand all the consequences of that is silly; we're only just recently starting to understand the climate change aspect of it.
However the childhood mortality rates have gone down so raw # of children per household could be lower and still have a higher growth rate.