Nicholas Wade of the NYT lucidly describes some of the results from the two new Jewish genetics study (one of which you can read here):
The shared genetic elements suggest that members of any Jewish community are related to one another as closely as are fourth or fifth cousins in a large population, which is about 10 times higher than the relationship between two people chosen at random off the streets of New York City, Dr. Atzmon said.
Race is all about who your relatives are, and, not coincidentally, answers to the question of who you are related to turn out to be unavoidably relativistic.
Unfortunately, human beings don't deal well cognitively with things that are inherently relative. People are good at noticing that A is more likely than B, but they aren't good at formally reasoning about this relativistic comparison. Some will say that A is always true, while others will smugly attempt to disprove that "A is more likely than B" by pointing out exceptions in which B is true, as if the exception disproves the tendency.
Ashkenazic and Sephardic Jews have roughly 30 percent European ancestry, with most of the rest from the Middle East, the two surveys find. The two communities seem very similar to each other genetically, which is unexpected because they have been separated for so long.
One explanation is that they come from the same Jewish source population in Europe. The Atzmon-Ostrer team found that the genomic signature of Ashkenazim and Sephardim was very similar to that of Italian Jews, suggesting that an ancient population in northern Italy of Jews intermarried with Italians could have been the common origin. The Ashkenazim first appear in Northern Europe around A.D. 800, but historians suspect that they arrived there from Italy.