Double irony in regard to this thread: for most of their existence DAR actively prohibited African Americans/Blacks from joining. I am not certain what percent was required to invalidate one's application. However for many years in the South "one drop" black blood" (any black ancestry) was considered enough to define one as black legally and socially. Of course Warren would be considered without question Native American if this type of standard was applied to her!
This also illustrates how slippery, complex, and often erroneous definitions of race are. The central problem of course is that "race" is a meaningless term in genetics. The classical definitions of race do not match up with the actual science. Some alleles tend to be more common in some groups than others and this can be used as an approximation of ancestry. But there is enormous variation within each group, people outside that group may nonetheless share some of the same alleles as those inside, and the boundaries are very vague. Most people are a complicated mix of different ancestries. To try to say that having 1/4 some "race-related" alleles qualifies you as that race, but 1/8 or 1/16 etc. doesn't is meaningless as well as arbitrary; it simply doesn't work like that. The genetic data cannot be interpreted that way.
This also illustrates how slippery, complex, and often erroneous definitions of race are. The central problem of course is that "race" is a meaningless term in genetics. The classical definitions of race do not match up with the actual science. Some alleles tend to be more common in some groups than others and this can be used as an approximation of ancestry. But there is enormous variation within each group, people outside that group may nonetheless share some of the same alleles as those inside, and the boundaries are very vague. Most people are a complicated mix of different ancestries. To try to say that having 1/4 some "race-related" alleles qualifies you as that race, but 1/8 or 1/16 etc. doesn't is meaningless as well as arbitrary; it simply doesn't work like that. The genetic data cannot be interpreted that way.