There seems to be a generational lag between infant mortality (or mortality before reproduction) and fertility rate.
Many places still have very high mortality-before-reproduction rates and correspondingly high birthrates, or at least generational recent ones.
It seems, simply, that overpopulation is a problem which solves itself. High standard of living seems to come with high costs and emphasis on investing in children far more combined with delaying children until proper resources can be had. The result? Fewer children.
The doom and gloom about overpopulation was overblown and doesn't look to be a problem. We have enough food production capability (especially with new lands to open up with global warming), hunger comes from dysfunctional economies, not lack of food.
It doesn't make much sense to think about global population as a whole when there is such variability. You can't compare Manhattan to sub-Saharan Africa at all, they are totally different worlds (or perhaps a hundred or two years apart developmentally).
https://en.wikipedia.org/wiki/List_of_sovereign_states_and_d...