Some Natives have proposed using such cultural benchmarks -- knowledge of the tribe's language, residence on the reservation, participation in ceremonial activities -- as criteria for membership. But even this method has pitfalls. "Who within the tribe gets to decide what's culturally appropriate and what's not?" wonders Kim Tallbear, a Native American scholar at UC Berkeley. "Instead of the blood quantum police, then you'll have an office that polices culture?"

Garfield has no desire for such measures. "I would never force anyone to live the cultural way," she says. But she's convinced the lineal descent approach is the answer to preserving her culture, including the generosity she sees as one of its hallmarks. "We can't teach our culture to kids who don't have a heritage," she says. "And we get away from our Native American culture when we start weeding people out."

Garfield notes that people with European heritage tend to view their ancestry through the lens of lineal descent. "I don't think that when Germans intermarry they lose their German descent," she says. "That's what we need to remember, too."

But some traditionalists say the lineal descent approach leads to a loss of tribal identity, benefiting those who have no connection to Native American culture and who carry none of the burden of its history. The Cherokee Nation is a common target of ridicule in Indian Country because the tribe uses lineal descent. About 250,000 people are enrolled, and some have such a small fraction of Cherokee blood that the denominators are in the quadruple digits. "So your grandmother was a Cherokee princess?" goes the joke. (The tribe has no system of royalty.) The lineal descent method has also led to other problems for the Cherokees. Lawsuits and reams of bad press have come of the Nation's decision to oust the Freedmen, descendants of the tribe's African slaves. The Freedmen say their ancestors are on the early rolls, so by the rule of lineal descent they are Cherokees. But the tribe has repeatedly voted them out, citing their lack of Indian blood.

The lineal descent system sometimes rests on a shaky foundation. The "base rolls" that list the original members of a tribe are often flawed. In the 19th century, federal agents sometimes determined how Indian a given person was simply by examining their skin and hair. Some Natives likely exaggerated their white ancestry because it brought privileges, and others resisted registering with the federal government altogether.

Yet from a purely mathematical perspective, those tribes that require their members to have a certain proportion of tribal "blood" will either have to change their ways soon, or else calculate themselves out of existence. At this point, the alternatives are limited. The tribes can lower the percentage of blood required, create subcategories of membership or choose to include the blood of other Indian nations in their calculations. But none are permanent solutions.

"They're kicking the can down the sidewalk," MSU professor Wayne Stein says. "That's all they're doing."

The lineal descent method is perhaps the only way to preserve the tribes far into the future, as Indian blood proportions dwindle over generations. And if it comes down to closing the doors or letting in too many people, Garfield argues that the most generous option is the latter. 

"We have to claim our grandkids," she says. "I have to give the same amount of love to all my family. I can't say I'll only give you an eighth."