Jason Collins and Lionel Page write,
The United Nations produces forecasts of fertility and world population every two years. As part of these forecasts, they model fertility levels in post-demographic transition countries as tending toward a long-term mean, leading to forecasts of flat or declining population in these countries. We substitute this assumption of constant long-term fertility with a dynamic model, theoretically founded in evolutionary biology, with heritable fertility. Rather than stabilizing around a long-term level for post-demographic transition countries, fertility tends to increase as children from larger families represent a larger share of the population and partly share their parents’ trait of having more offspring. Our results suggest that world population will grow larger in the future than currently anticipated.
Collins is humble about the ability of any model to project fertility, given the importance of cultural evolution. I have not seen the paper, but I would like to know whether they tested their model against actual data in any way. For example, you could “backcast” the model and see how well it “predicts” population in, say, 1980 or 1950.