But polar bears and black bears are separate species. "Races" are not. Races are more like breeds of cats, although significantly less distinct. So maybe more like gray squirrels.
Gray squirrels live all over North America, but don't look the same. Gray squirrels where I live are small and in fact, gray. Gray squirrels where my parents live are reddish brown and sort of chubby, and gray squirrels in Canada are huge and very dark, almost black. All the same species. They just look different. So maybe Canadian squirrels have fat storing genes that are, on average, 1% more efficient than the eastern American squirrels to deal with the cold. So now imagine that gray squirrels have developed air travel and boats and cars and the internet, and started meeting squirrels who looked different than they did. Now you can easily imagine some large, black squirrels who developed a fetish for tiny, gray, New England squirrels. They have babies and move here to RI, and now the eastern US has a lot of black squirrels, because black fur is a strong gene compared to light gray. But they do not share much more genetic heritage with big, black, Canadian squirrels than with midwestern squirrels.
Are the black squirrels in my back yard still the same race as the black squirrels in Canada? It depends a lot on what the word race means. If you define is "do they have black fur?" then, yes. If you define it as "do they have the same percentages of the telltale gene clusters as the black squirrels in Canada?" then, no. Maybe some of these squirrels have that more efficient fat storing gene, but only a few, since not does it not hinder their survival if they lack it, it's been watered down with the normal fat genes of the New England squirrels.
I think the issue really is that the way we define our race as individuals has very little bearing on anything other than appearance, which is a poor indicator of all but a small handful of genes, none of which relate to anything OTHER than things like hair , eye color or shape, skin color... yes, you are more likely to have a gene for sickle cell anemia if you have dark skin, but the frequency of the gene does not replicate the frequency found in most native African populations.There probably was a time in human history where there were populations which could more easily be genetically defined, but it would have to have been a time before there was any considerable interaction between cultures from different geographical areas. Which was clearly long before we knew we were made of cells, or that there was such a thing as DNA.
I plan on listening very closely when a study comes out of trying to link something like IQ to race in populations that have not had a lot of external genetic influence, but good luck designing that study. It would not be possible in the US, and good luck designing a reliable IQ testing method that will work on , say, aboriginals, isolated pockets of native Africans, and a small community deep in the Appalachian mountains. And good luck finding enough subjects to make statistical significance.