Do you know about the mouse utopia experiment of John B. Calhoun? What happens to mice in a closed space with all the food they could want? As population grows, birthrate starts falling to almost 0. Same thing can be applied to humans, with Earth as our closed off space.
Evolutionary traits are kicking in to stop overpopulation. All natural. Might drive us to extinction, might not.
Just took a trip through North Dakota and Montana: There is so much open space in the US that overcrowding will not be a problem. I sem to recall the drop in birth rate is natural when one's kids stop dying in childhood.