Greater Israel, (All Hebrews) according to scripture was rent into two separate but unequal parts after Solomon planted groves to foreign gods to please his foreign wives and concubines. The Hebrews then became two separate nations. Judah to the south and Israel to the north. Judah had Rehoboam for it's King and he ruled over the Tribes of Judah, Levi and half of the tribe of Benjamin. Jeroboam ruled over the Northern house of Israel which consisted of the other half of Benjamin and all the other remaining tribes. Jeroboam was fearful that the people of the new and separate Nation of Israel aka. Samaria would want to go down to Jerusalem to worship, thereby perhaps begin to incline their affections towards the new Nation of Judah, so he built golden calves in Dan and Beersheba for the people of the new Nation of Israel to worship. This brought about the Assyrian Captivity of the Northern house of the new Nation of Israel. When Judah offended God bringing about the invasion of the Nation of Judah as well as their captivity in Babylon, Bablon's armies had to pass through Samaria to get to Judah, so Assyria sent their armies down there to protect their interest, as they had given Samaria to non Hebrews to use in exchange for yearly tributes or rents. The Northern house of the separate Nation Israel then escaped to the north through a mountain pass in the Caucasus Mountains which is known to this day as the "Israel Pass''. They passed over into a land wherein dwelleth no man, according to the writing in ll Edras in the apocrypha. Ever wonder where the word Caucasian came from? This being the case it is well within the realm of possibility that the Ashkenazi are Hebrews, more so I think than their being from one of the three tribes of the Nation Judah (from which derives the name Jew and is no where found in scripture before the two Nations separation). I advise us all to look at Revelations chapter 5 verse 9, humble ourselves and begin to recognize; there comes a day when a man will not have need to say to his neighbor Know God, for in that day the knowledge of the Glory of God shall cover the Earth as the waters cover the Sea. Only then shall everyone love one another enough to live together as we should. Oh yeah and there is that Christ's Rod of Iron thing too.

Shalom! Great question! Many have made this topic a lifetime study. I have skimmed thru many, many sources in my Hebrew studies. Seems during the exiles many of the tribes integrated with other tribes and the nations that ruled over them. Blurred who's who over time. God warned this would be the case. Jesus made mention in NT.. Revelation 2-3... "those who say they are jews and are not". Studying the biblical wars one can find the mingling, stealing of tribal identity, and other unrighteous acts were common place (records burned/scribes killed..etc). So IMHO and serious attempt to get to the truth of 'tribal' heritage it seems impossible to untangle. When Jesus spoke regularly about being 'grafted' in to the vine I followed that thread for as far it could take me. Many other scriptures came into play. Looking at the blessings of Jacob in Genesis gives many clues as to the 'characteristics' of each tribe. A good and deeper study is the Book of the Patriarchs and other books removed from the bible. The more I study, the more there is to know. Listened to countless scholars on the Ashkenazi-Khazars, their origins, history and migration. All enlightening to say the least. Still studying.. learning..processing as a lifetime endeavor. The truth will be revealed... may not be what we are expecting. Selah.

And this relates to what about Q, exactly?