According to family lore, my maternal grandfather's maternal grandmother was Cherokee, descended from one of the "Five Civilized Tribes" that in the 1830s had been coercively removed from their aboriginal homelands to Indian Territory. Planters had developed a lust for cotton land following Eli Whitney's 1793 invention of a low-cost way to separate the seeds from the fiber. Whitney's gin promised cotton so inexpensive that it might replace wool in the garb of the common folk, but that increased the demand for many interior acres that had previously been of modest agricultural value. Well-watered and fertile, about the best potential cotton land in the nation was occupied by the five tribes. Through a succession of treaties, the United States nibbled away at that territory.
The treaties the U. S. negotiated with the Cherokee entitled the tribe to punish U. S. citizens who violated the reservation boundary.  But organized bands of well-armed squatters often prevented the tribe from exercising that power along the reservation borders. As more and more squatters invaded, it would ultimately become hazardous for the Cherokee even to enter the margins of their own reservation. The border region having become of little practical use to the tribe, the U. S. would then negotiate still another treaty through which that territory would be ceded by the Cherokee.
There was nothing especially remarkable that the Cherokee gave up land. Eastern Hemisphere lands were still substantially more labor- and capital-intensive than those in the Western Hemisphere, so land was more valuable to the settlers than to the land-rich aboriginal tribes. What was reprehensible was that so much coercion was used by the militarily-superior settlers, and so little purely voluntary exchange. 
By the 1820s Cherokee territory, which had once lain in five states, was constricted to a part of north Georgia. There the Cherokee were finally overwhelmed after the 1827 Dahlonega gold strike.
The resulting gold rush, the nation's largest until '49, augmented the already festering political sentiment to move the indigenous peoples aside. Georgia seized the moment to legislate the Cherokee Nation out of existence in the view of state law, acting unilaterally to accomplish an unfulfilled promise that the national government would extinguish all sovereign Indian claims within the state's borders. 
The tribe approached the U. S. Supreme Court as a foreign nation, demanding that the judiciary enforce Cherokee treaty rights (Cherokee Nation v. Georgia, 1831). While reviewing the breadth of its authority the Court found that
"[t]he third article of the constitution describes the extent of the judicial power. The second section closes an enumeration of the cases to which it is extended, with 'controversies' 'between a state or the citizens thereof, and foreign states, citizens, or subjects.' ... [Y]et it may well be doubted whether those tribes which reside within the boundaries of the United States can, with strict accuracy, be denominated foreign nations. They may, more correctly, perhaps, be denominated domestic dependent nations. ... If it be true that the Cherokee nation have rights, this is not the tribunal in which those rights are to be asserted."
The Cherokee petition presented a political question, requiring direct action by Congress. Unfortunately for the Cherokee, favorable Congressional action proved to be politically inexpedient.
Instead, Congress passed the Removal Act, signed by President Jackson in 1830, and the five tribes were strong-armed into an exchange of their shrunken territories for plots well beyond the Mississippi River, a region that they hardly knew. Notably, none of the tribes retired westward with enthusiasm, and terrible suffering and attrition accompanied them along the way. Well before century's end, large parts of the tribes' treaties had been abrogated by the U. S. government, and much of what had once been promised had in its turn been taken back.
My "trail-of-tears" heritage may surprise some associates, who reasonably will have concluded that by habit and appearance I more closely resemble a cowboy. And truth be told, I am far more cowboy than Indian. My father was a rancher on the western margin of Oklahoma, for one thing, nearly three hundred miles from the reservation that the Cherokee had been allotted. The Indians that I knew as a child were Kiowa or Comanche or Cheyenne (nomads native to that area), Apache (who had been forcibly removed there from Arizona), or were from Mexico. Each of those groups had been very different linguistically and culturally from "my people." The Apache seem even to have entered America during a much later wave of migration. By my childhood years, however, we all spoke English most if not all of the time, and went to the same schools and churches as the county's other residents.
Moreover, my father's heritage was, as far as we know, totally Appalachian. Appalachians are predominately of British stock, though I have never traced his lineage further east than Tennessee. Certainly English, Welsh, Irish, and Scottish names are the only ones ever mentioned in surviving family records. Judging from his name, my maternal grandfather's other line -- up his father's side -- also was British at least in part, and possibly Appalachian as well. And my maternal grandmother was beyond question of German heritage -- her parents had arrived in Nebraska three years before her birth, and she was fluent only in German as she entered the first grade.
By a casual estimate, then, my genetic heritage seems to be about ten times as British and four times as German as it is Indian. And culturally I am just an Oklahoman, and proud enough of it. Yet if I documented my heritage I could likely enroll as an Indian in the eyes of the law. Nationally, the minimum many tribes impose on members is 1/16th Indian ancestry, sometimes even less, and for most purposes a tribe's determination is dispositive for federal questions.
But I am no Indian in any meaningful sense. Indeed, as I will demonstrate below, a statistically significant number of those of us who have 1/16th Indian ancestry nonetheless have absolutely no Indian genes. By merely looking in the mirror I cannot dismiss the conjecture that I have missed out. I regret the way that my Indian ancestors were treated, quite possibly by my Appalachian ancestors. But they are gone, all of them, and there is little to be done now but to remember the injustices that they suffered so that similar ones might be avoided in the future.
To be sure, many people live in Oklahoma and the rest of the nation whose genetic relationship with tribal ancestors is well above whatever tribal minimum applies in their case, and who follow at least a few ancient tribal customs, cultural practices of which I am profoundly ignorant. I begrudge them none of the meager unabrogated privileges that remain from those extracted by their Indian ancestors. If a state wants to end their special status, as states often do, it should stay out of Washington and negotiate with the tribes themselves.
But the idea that I might share (and dilute) that special place while my cousins on my father's side cannot is absurd. There is no rational way for my cousins to claim to be Indians, but there is no reasonable way that I can make such a claim either. Any cultural connection is nonexistent, the genetic one trivial if not broken entirely. In time a similar fate likely awaits all Amerindian lines.
Property is often retained within a family line and conveyed parent to child over many generations. Even when that property originated through a government grant, few would suggest that it should be confiscated merely because the present holder has little genetic or cultural connection with the ancestor who originally obtained it. Though their holdings are modest per capita, Indian tribes have a substantial amount of property in aggregate, much of it recognized through treaty. It is not suggested here that such property be treated in any extraordinary way.
But tribes were granted something else, sovereignty, that governments virtually never grant to ordinary citizens. That sovereignty was granted because both the tribes and the United States wanted Indians to be set apart to run their own affairs. But that raises the twin issues of which individuals should be entitled to claim that sovereignty today, and what becomes of it when there are no real Indians left? If there are no relevant living individuals left in a tribe, it is desirable that the sovereignty be terminated.