This is really odd, because there were a lot more Jews than that running around Europe in earlier years. For instance, the 1st Crusaders slaughtered thousands of Jews in the Rhineland on their way to Jerusalem.
I’m trying to think of a disaster between 110 and 1400 that could have reduced the population so drastically.
It wasn't the Black Death - though horrific in its consequences, it "only" killed 1/3 to 1/2 of Europe's population (not enough to reduce a reasonably large group like Ashkenazi Jews down to a breeding population of only 350). Oh, and Jews suffered from it at a somewhat reduced level due to their habit of ritually-washing their hands before any meal that includes bread, as well as the idea of making one's self more presentable on the Sabbath (like, for instance, taking a bath and changing dirty, possibly disease-laden, clothing). Of course, suffering from a hideous disease at lower rates in a time of great ignorance tends to give rise to conspiracy theories, esp. aimed at traditional scape goats, so a lot of Jews were killed for the "crime" of not getting the Black Death. But not enough to get down to 350 breeders.
The figure of 350 seems absurdly low to me. Even after the Cossack massacres of the mid-1600s, the generally-accepted belief regarding a population bottleneck is that there were roughly 100,000 Jews left in central and eastern Europe at that point. Again, 350 is an absurdly low number IMHO.
Well, just because modern Ashkenazi may all be descended from 350 individuals, does not necessarily mean that the population ever got as low as 350 at any time. There could have been many more alive at the time of the greatest bottleneck, but all their descendants were wiped out subsequently, in one or more different events.
“e figure of 350 seems absurdly low to me. Even after the Cossack massacres of the mid-1600s, the generally-accepted belief regarding a population bottleneck is that there were roughly 100,000 Jews left in central and eastern Europe at that point. Again, 350 is an absurdly low number IMHO.”
It doesn’t mean “at one time there were only 350 Jewish people in Europe.” There were many others at any given time, but their lines crossed the 350 for whatever reason.