It's very dangerous to try and compare human behavior to any pattern seen in nature— particularly human behavior in aggregate. While humans are animals like any other, we are also very much not simple beasts beholden to environmental conditions.

To wit: the current human population is beyond the natural carrying capacity of the places we live. The only reason we can sustain 7bn people today is because we've artificially increased local carrying capacity through artificial fertilizer. If we lost that technology today, a majorty of humans alive now would starve to death.

There's really no reason to assume any environmental factors that don't physically preclude human occupation will have any effect on overall population numbers. We can artificially extend our ecosystem to support essentially unlimited people. The only real hard limit is space to physically put bodies and the amount of energy our society can use without boiling the oceans with waste heat.

If population growth levels out, it won't be for any natural reason because we are already well beyond any natural limit.

But we are beholden to environmental conditions! All of our technology, including the base materials for artificial fertilizer come the environment. The unique thing about humans is the inter-dependence. We need people specialized in tasks to keep everything running. This requires the use of 'money' in whatever form to do the bookkeeping on distributing resources. I think what we are seeing is that the 'money' aspect our human interactions seems to be key constraint on people having more babies.