It's not the same. Amish fertility is 5-6 children per woman. Doubling is expected.
Native American fertility is actually below replacement (and lower than white, last I saw). But the definition of NA is more expansive, and the population can "expand" through outmarriage.
> and the population can "expand" through outmarriage
You see something very similar going on with the Reform Jewish population. Reform Jews have relatively few kids, but a very high intermarriage rate (about 80% of Reform Jews marry non-Jews!) so you see the Reform Jewish population increasing regardless.
Native American fertility is actually below replacement (and lower than white, last I saw). But the definition of NA is more expansive, and the population can "expand" through outmarriage.