For a Jewish genetics researcher, being told in print that 'Hitler would certainly have been very pleased' by your work can’t be pleasant. But that’s what happened in 2010 to Harry Ostrer, a geneticist at the Albert Einstein College of Medicine, when he and his colleagues published a study showing that Jews in three different geographical areas had certain collections of genes that made them more biologically similar to one another than they were to non-Jews in the same regions. The work also showed that Jews around the world could trace their ancestry to a group of people who lived in the Middle East 2,000 years ago; that meant, however, that certain genetic signatures could be used to identify Jews, indicating that Jews share a common biological identity beyond their religious affiliation—which is what inspired the Hitler crack.
I don't plan on reading Legacy because I already read the paper which it is based on, Abraham's Children in the Genome Era: Major Jewish Diaspora Populations Comprise Distinct Genetic Clusters with Shared Middle Eastern Ancestry. It is now open access, so you can read it too. As implied in the article in The Tablet the biggest finding in this paper is that most of the world's Jewry seem to share tracts of the genome which are 'identical by descent' (IBD). You don't have to be a geneticist to intuit that being IBD implies relatively recent and elevated shared descent from a common set of ancestors. In particular the authors were looking for segments of the genome where individuals shared the same sequence of genetic markers. Very long sequences indicate a relatively recent common ancestor, while many short ones suggest more distant but numerous common ancestors. From looking at these patterns of relatedness the authors infer that despite the genetic variation in the modern Jewry, most of the world's Jews, from Iran to Morocco to Lithuania, share common ancestry from a source population which flourished ~2,500 years ago. All that being said, genetics is only part of the puzzle here. In the discussion the authors suggest that "Yet, the sharing of Iranian and Iraqi Jews of a branch on the phylogenetic tree with the Adygei suggests that a certain degree of admixture may have occurred with local populations not included in this study." I argue in my post The Assyrians and Jews: 3,000 years of common history, a clear and distinct category of "Jew" as opposed to generic North Levantine in the year 500 BC probably does not make biological sense, though it might make culturally sense (and "generic North Levantine" is obviously not accurate, as most of these individuals had strong tribal or ethnic identities at the time). Finally, I don't think I highlighted in my earlier commentary that these data imply that the rise of Christianity and Islam fundamentally stabilized the genetics of the Jewish people, insofar as much of the admixture upon the core base in the peripheral populations seems to predate the rise of these religious civilizaitons. Once Christianity and Islam marginalized the Jews, the gene flow from non-Jews to Jews diminished greatly. This is curiously analogous to the cultural involution which Jews also underwent during this period.