World heath physician Hans Rosling is staying population won’t peak over 11 billion.
He oversimplifies the factors involved in determining population growth but his 11 billion number is in general agreement with the Limits to Growth model predictions.
The big question though is what happens then? How far and how fast will it decline and by what means?. One thing is certain: It will not simply stay at 11 billion (or whatever the number turns out to be).
The best we can hope for is that with the exhaustion of easy to extract fossil fuels and other resources, the ensuing economic decline will lead to a slow but steady population decline as has
been happening in Russia since the dissolution of the USSR .
There are signs that similar factors are already starting to appear here in the US where
Life expectancy has fallen in each of the last 2 years.This is what happens when complex societies begin to collapse. Historically this has always happened eventually - with exhaustion of important resources usually a major causative factor.
A good book on the subject is
Joseph Tainter's The Collapse of Complex SocietiesThe difference now is that human society is now global. Regional collapses may predate the global wide collapse (and has already begun in some regions) but eventually, because of our interconnectedness, all societies will join in. My sense from the small contacts I have with some of the global elites, is that most of them recognize this but are doing everything possible to keep the house of cards up at all costs and keep the general populace from recognizing what's coming.
People tend to get all emotional and suffer from severe cognitive dissonance when faced with this issue. They accuse those who point out resources limits and the inevitable decline in human population of wanting it to happen. No, it's just that some people are able to face and discuss the issue rationally while others prefer to do the equivalent of holding their hands over their ears and singing "La La La La".