The only concern I have about their approach (from what is in the article, I presume their book has much more detail) is that what people say they will do and w

The only concern I have about their approach (from what is in the article, I presume their book has much more detail) is that what people say they will do and what they actually do are often very different things. That said, it isn't a crazy prediction given that we already see large declines in the fecundity of developed nations. So if the assumptions the UN have made about the rate of development of Africa etc. are wrong then it seems reasonable that the population projections will be inaccurate.