I don't think it's set in stone. Some countries which previously had very low fertility rates have seen a recent upswing, notably France and a few Scandinavian countries.
It's interesting to plot the position of each country in Europe in this cycle, from Scandanavia through Italy/Spain to Greece/Portugal.
For the 3rd world or 'human resource rich countries' - it's different. You have to look at the population in the industrial revolution 200years ago. People living on farms in the countryside had lots of children to run the farm, to provide for them in their old age and because many wouldn't survive. They move to the cities and have the same number of children - but more of these survive (however bad conditions in the 18C towns were - they were better than the countryside!)
Then as people become more prosperous they have less children and the population stabilizes - but at the new higher level