The UN forecasts are ridiculous at any long term timescale. They assume that desire for children is not heritable so everywhere will undergo the demographic transition and just somehow magically the world will reach replacement fertility and stay there. In reality the share of births to women who already have 4, 5, 6, 7, 8+ children has been increasing in the US for over a decade and the ultra orthodox have gone from politically marginal in Israel to over 1/4 of the population. They’ll probably be a majority in my lifetime. In the US Mormons, Amish, Hutterites and Hasidim all have high to very high fertility. Absent a deliberate state driven destruction of their culture, Soviet style, that’s likely to continue and the same dynamic of cultural and biological evolution for greater fertility will just keep on working somewhere.

There will be no stabilisation of population.

All population data for the last century disagrees, and no magic is needed to explain why: the cost of raising children in modern society is so high and the child mortality rate so low that there is strong societal pressure to have less children. Sure, some fringe groups can resist this in the same way that the Amish resist electricity, but this will not be mainstream. Even the Haredim are having less children than they used to:

https://www.ynetnews.com/articles/0,7340,L-5439005,00.html

That assumes both the cost will remain the same (or a factor), and that children mortality rate will continue to be low, neither or which are a given.

Add a couple climate catastrophes and wars for resources, and we can see the landscape in 2100 or 2200...

But the US has been at or under replacement rate for births overall for a long time now.

I'm an exmormon, birth rates are higher for Mormons, certainly, but even they've been obviously dropping. I had three batchmates out of 9 in the missionary training center with 10+ kids in their family. That used to be relatively common, now it's almost unheard of for newer families.

The US has been under replacement fertility for less than 100 years, under four generations. On an evolutionary timescale this is nothing. It’s like dropping 100 thoroughbreds on a small island. Come back in 20 years and if there are still horses they’ll be maybe a hand shorter. Give it a hundred years and they’ll be ponies.

If Mormons have higher fertility than non-Mormons then they’ll grow as a share of the population, even if the modal difference is less than one child. If the average Mormon family has three children when others have two they’ll increase their population share by 50% a generation, neglecting immigration and apostasy.

> The US has been under replacement fertility for less than 100 years, under four generations. On an evolutionary timescale this is nothing.

So? Human society and culture can change absurdly fast. If the evolutionary impulse to reproduce was that strong, you wouldn't be seeing places like Singapore with comically low birth rates.

What evolution compels us to do is have sex. We've just disconnected that from reproduction.

Re:mormons, yes they have a higher fertility rate, but it's also been rapidly dropping. And without taking into account conversions/apostasy the numbers are kind of useless, and taking them into account is difficult because it's just inherently hard to predict. As an ex-mormon I'm aware that the internet has caused some major problems with retaining members for the church, because information has become so much more accessible (much of it contradicting church teachings, obviously).

The disconnect is a temporary issue. Evolution will quickly replace the desire for sex with a desire for children, or will give us traits that make successful use of birth control unlikely. There is no stronger selection pressure.

> What evolution compels us to do is have sex. We've just disconnected that from reproduction.

It compels is to do everything we do in life. There isn't a single trait ever measured in which the heritability was zero.