Significant for whom, for what? It may be significant for the person, and nobody else. (For someone to know, or even to believe, that there is a certain ancestry may be like this.) It may be significant for a given group, and nobody else. (Who is to say whether someone who identifies as African-American and is recognized by the black community as such shouldn’t call him or herself such, no matter the fraction?)

Then there is the question of “official” race statistics and laws and regulations that are based on race membership. I think they have a problem no matter what, and the question isn’t how much is enough— for me, the question is how to make this work at all.