I've seen similar studies in regards as to how Islam will supplant Christianity because they tend on average to have larger families. The only demographic group in America other than Muslims with larger families, are Hispanics (This is according to the studies I've read). "White" Americans tend to have 1.4 children on average. The studies traced the decline of civilizations with less than the 2.1 that you spoke of. They showed that no civilization was able to exist without the 2.1 child per couple average. (I did my part...I had 7)