Congenial Times has a blog post and a long comment on Amish demographics. There are now somewhere approaching a quarter of a million Amish in the U.S., up from less than 10,000 a century ago. At the current growth rate of doubling every twenty years, there would be approaching eight million Amish by 2110. (Warning: Projections 100 years into the future not likely to turn out right.)

My impression is that the Amish are not a major drain on the taxpayers the way the polygamous Fundamentalist Mormons are, who put their junior wives on welfare and run a lot of scams to get federal and state funds for the their town on the Utah-Arizona border. Of course, an all-Amish country wouldn't work due to the pacifism of the Amish.

Somebody might wish to create a model of the optimal sect for increase in share of the population. The components would consist of:

1. Fertility rates 2. Retention rates 3. Conversion rates 4. Death rates (which usually are pretty much the same these days, as long as the sect doesn't oppose vaccination, or whatever).

The Amish, for example, have quite high fertility rates, high but not 100% retention rates, and very low conversion rates. There are probably trade-offs between the different components.

It seems plausible that the human race in 3000 A.D. will largely be descended from cultures that achieved optimal combinations of these trade-offs for population growth.