I promised a post on Jewish Genealogy a couple of weeks ago, but things keep going wrong in getting it written. Most humorously, voice-to-joke while I was driving in an area where there was poor reception gave me results like "Moroccan who are working for narrow call to flag it, are closer to Connecticut than Ashkenazy," and "they have a band and Mediterranean cruise throughout," which even an hour later when I tried to use it for outline I could not fathom what I had said to produce this. The power of the word that one sees can easily overwhelm what it must have sounded like. One more bit of evidence that writing is not language. Speech is language, and writing is only an approximate representation. Yet readers tend to regard the written word, with its stability, as "real" language, and speech as sloppy. In its extreme, we get foolishness like regarding a particular era of Latin and Greek as better versions of language that English (or French or German) should emulate in order to be proper - creating horrible artificial rules of grammar.
Much of the recent "Cambrian explosion" in knowledge of Jewish (and all) genetics comes from two sources. The development of techniques of Identity By Descent, and the commercial ancestry groups providing millions of samples to be studied. The wiki link has a nice colored graphic of IBD that you might favor over my explanation, but I am going to give it a try.
Until very recently, when I thought of inheriting genes from your two parents, I though of it as a coin flip proposition at each point. At marker 347 you got Mom's gene, at 348 you got Dad's, then you got two in a row of Mom's at 349 and 350, then one more at Dad's, etc. It's not like that. In recombination, you get whole long strings of Mom's or Dad's genes. They come in big batches. Overall, it works out to fifty-fifty. Actually, it's between 40-60% of each parent, which follows naturally from the genes coming in big chunks like that. If it were a coin flip at each point, the number would hover very close to 50-50 at the end. But with long unbroken sequences, one gets more variation.
It helps identify how closely you are related to someone. There are only a few breaks in the chromosome sequence - where you switch from Mom's genes to Dad's - every generation. So if you you have lots of long sequences that you share identically with someone, it means it has only been a few generations since you shared an ancestor. In a small breeding population of a few hundred two people might share a lot of ancestry. But looking at the strings you can discern if they are first cousins. You are more closely related to some siblings than others (though still 40-60%).
This gets very interesting when two populations mix. Take, for example, my son from Romania and his wife from the Philippines. They do not share an ancestor for thousands of years. In their daughters' DNA you will see long strings of Transylvania followed by long strings of Luzon, and if you compared the daughters, there would be enough long sequences of identical material that you would know they are siblings. But when those girls marry and their DNA recombines with some man of other ancestry, the switches will almost certainly not occur at the same places. Their DNA chain will switch at places that also have long strings, but one string might be 30% Filipino followed by 70% Romaneste, while the next is 80-20 in the other direction. When recombining, their DNA doesn't know where the switches were last time.
You can use this to see how long ago two populations mixed. The y-DNA tells you where the men came from and the mtDNA where the women were from, and the length of the sequences tells you how many times the DNA has recombined. As this occurs at a regular rate, you can set a range. Thus, in American Blacks, where there is European ancestry it occurs in fairly long sequences, as it came in 15 generations ago, max. There is R1a and R1b yDNA in the Ashkenazi, and with IBD, we can see
that it came in early, likely in the Western Mediterranean Jews while
Rome was still an empire, not from Germans a thousand years later.
When genetic histories identify that the Ashkenazi formed between 750-1000AD, but that there were male lineages that became part of it that coalesced earlier, say 3rd C, while the female lineages firmed up later, say 600AD, and some slight Slavic admixture came in around 1600 in NE Europe, this is how they can tell.