The early days of Ashkenazi Jews – that is, Jews with more recent ancestry in central and Eastern Europe – are a hot debate topic. It is believed that their ancestors migrated into Europe from Judea in the first century A.D., after the destruction of the Second Temple by the Romans, and that led to some intermarriage with Europeans later on.  

Others have argued that they have a mainly European ancestry, and arose by conversion to Judaism of indigenous Europeans, especially in Italy. While still others have even argued that they were largely assimilated in the North Caucasus during the time of the Khazar Empire, the Turkic people in the Western steppe whose rulers turned to Judaism around of the tenth century AD.

Archaeo-genetics, mapping genome analysis to migration, may help to resolve this dispute. Y-chromosome studies have shown that the male line of descent does indeed seem to trace back to the Middle East. But the female line, which can be illuminated by studies of mitochondrial DNA (mtDNA) has proved more difficult to interpret. 

The possibilities are intriguing because Judaism has been 'inherited' maternally for thousands of years.

Possible overall Near Eastern contribution and fraction of unassigned lineages. Credit and link: 

A new study looked at large numbers of whole mitochondrial genomes – sequencing the full 16,568 bases of the molecule – in many people from across Europe, the Caucasus and the Middle East. It have found that, in the vast majority of cases, Ashkenazi lineages are most closely related to southern and western European lineages – and that these lineages have been present in Europe for many thousands of years.

"This means that, even though Jewish men may indeed have migrated into Europe from Israel around 2,000 years ago, they brought few or no wives with them. They seem to have married with European women, firstly along the Mediterranean, especially in Italy, and later (but probably to a lesser extent) in western and central Europe. This suggests that, in the early years of the Diaspora, Judaism took in many converts from amongst the European population, but they were mainly recruited from amongst women. Thus, on the female line of descent, the Ashkenazim primarily trace their ancestry neither to Palestine nor to Khazaria, but to southern and western Europe," says senior author Professor Martin Richards of the Archaeogenetics Research Group at the University of Huddersfield.

Citation: Marta D. Costa, Joana B. Pereira, Maria Pala, Verónica Fernandes, Anna Olivieri, Alessandro Achilli, Ugo A. Perego, Sergei Rychkov, Oksana Naumova, Jiři Hatina, Scott R. Woodward, Ken Khong Eng, Vincent Macaulay, Martin Carr, Pedro Soares, Luísa Pereira, Martin B. Richards, 'A substantial prehistoric European ancestry amongst Ashkenazi maternal lineages', Nature Communications 4, Article number: 2543 doi:10.1038/ncomms3543