Alaska's Native American population seems to be booming. At the last Census they comprised around 16% of the total population but according to this they account for over a quarter of all births in the state.
That's the case in all of the high-Native-population states except Oklahoma. For example, see South Dakota, 8.8% Native in 2000 but the birth percentage is exactly double that (17.6%). Montana is 7.4% Native, but the birth rate is 12.8%. New Mexico is 9.5% Native, but the birth rate is 12.6%.
Shouldn't be a big surprise, I would think. Mortality among Native Americans tends to be high, too (alcoholism), and many leave for major cities and blend into the rest of the population rather than hang around the Reservations. So the Native population isn't really growing rapidly in any of those states, except maybe Alaska.
Native Americans also have depressingly high infant morality rates. Alcoholism is the primary component of the primary, but basically they have a higher rate of...everything.