It'd be interesting to know what is going on. If you argue from a sort of Malthusian ideological-lowering-of-subsistence-wages, that doesn't explain it since the subsistence wage is still way below the regular wage and ought to allow indefinite over-reproduction of the subpopulation. And these subpopulations often isolate themselves from the world and denigrate it as much as possible, so the world's standards shouldn't matter too much to them.
My own suspicion is that there's some sort of diseconomy of scale to these subpopulations: they grow like gangbusters but the growth tapers off until total retention rate matches overall population growth rate.
But I don't know this for sure. I don't know that members start leaving the large subpopulation for the main population at sufficient rates to offset the fertility, or why the leaving rates would change as the group grows. Certainly the Amish seem to be continuing to grow without a problem. It may be that there's a certain formula (decentralization?) which only a few have hit upon recently.
I was browsing my RSS feed, as one does, and came across a New York Times article, "A Village With the Numbers, Not the Image, of the Poorest Place", about the Satmar Hasidic Jews of Kiryas Joel (NY).
Their interest lies in their extraordinarily high birthrate & population growth, and their poverty - which are connected. From the article:
From Wikipedia:
Robin Hanson has argued that uploaded/emulated minds will establish a new Malthusian/Darwinian equilibrium in "IF UPLOADS COME FIRST: The crack of a future dawn" - an equilibrium in comparison to which our own economy will look like a delusive dreamtime of impossibly unfit and libertine behavior. The demographic transition will not last forever. But despite our own distaste for countless lives living at near-subsistence rather than our own extreme per-capita wealth (see the Repugnant Conclusion), those many lives will be happy ones (even amidst disaster).
So. Are the inhabitants of Kiryas Joel unhappy?