Human Evolution: Issues

"One's ethnicity/race is, at best, a probabilistic guess at one's true genetic makeup."~ Unfinished Race

If this is true, then does it imply that race cannot be accurately determined by DNA? Then, if race cannot be determined completely by DNA then which other avenues should we explore in defining ethnicity/race?

I wrestled with these two questions after class and during fall break and I must say I only arrived at the notion that perhaps race is a social construction consisting of observed phenotypes in a historically/anthropologically isolated population. As a Filipina society, as evidenced by demographic surveys, has categorized me as Asian. However, it is possible that I may have more genetic similarities to a Hispanic say, Eva Longoria than to a fellow Asian say, Lucy Liu. That said, I don't think it is completely reliable to approach race from a genetic standpoint. 

But another question also arose during my ruminations on race: in today's society what importance/use does race have in categorizing human populations? I'm thinking specifically about multiracial individuals. In the U.S., a country with an extensive history of immigration, I believe race has always been a problematic subject. Especially, now with the growing numbers of interracial reproductive unions and subsequent multiracial children, I'm curious as which race these children identify with and if there is some discrepancy between their self-racial identity and the identity society places upon them. President Obama made it a point that race was not going to be major discussion topic during the election race and yet many consider him America's first Black president despite him having a Caucasian mother.