You know, this is an interesting thing.

We all accept that once societies industrialize population drops.

What you rarely see discussed is why this may be.

Here's a possible thought.

If you are poor (unable to meet your and your family's needs for livelyhood), you are an undesirable mate, and as your children are likely to be equally less desiarable you are less likely to see your genes propegate. How do you solve this problem? Have more kids. By putting more of your genes out there you increase the likelyhood that at least one of these undesirable children of yours will find an equally undesirable mate and thusly pass on your genes.

By contrast, if you are rich (able to meet your and your family's needs for livelyhood), you are a desirable mate, and your children are likely to be equally desirable. Since you are desirable, and your children are desirable, you have little reason to doubt that your children will find equally desirable mates, and thusly you have less incentive to have more children since this can only lower the desirablity of your offspring by limiting familial resources available.

By this notion, humans are antitribbles, to limit their population you simply have to feed them. The more their needs are met, the less need they have for abundnat children. You will always have naturally fecund persons in a group, but by ensuring that all are cared for you ensure that the number to be cared for never rises above a sustainable level.

Longevity can throw this estimate off, but longevity may have a peak for humans in their 80's (since we are not pushing the outward age limit as fast as we did when we first industrialized and sanitized societies). Once longevity stabelizes and all humans are fed, human population should remain relativly constant going forward, we may even start to have population bust problems, as couples of two wind up with only one child (the ammount needed to pass on genes), and more and more choose to remain childless (as cultural contributions may begin to outweigh genetic contributions).