Well, yeah. But that wouldn’t get the population down from some hundreds of thousands, probably, to 350.
I’m with ancesthntr. This just doesn’t make any sense.
I’m not qualified to comment on the genetic evidence, but I have studied history for several decades.
Let’s assume, without much evidence, that there were 1000,000 Jews in Europe in 1100, and somewhere around 500,000 in 1600.
Does it make any sense at all that the number dropped to 350 in the period between and then rebounded? I don’t believe it. I doubt it’s even mathematically possible, given the infant mortality rates of the time.
I think you are overestimating, especially because they are speaking of Ashkenazi only, which excludes a large number of Jews who would have been living around the Mediterranean. Here’s something from Wikipedia that gives some estimates concerning that time (for both Askenazi and Sephards):
“As regards the number of Jews in the Middle Ages, Benjamin of Tudela, about 1170, enumerates altogether 1,049,565; but of these 100,000 are attributed to Persia and India, 100,000 to Arabia, and 300,000 to an undecipherable “Thanaim”, obviously mere guesses with regard to the Eastern Jews, with whom he did not come in contact. There were at that time probably not many more than 500,000 in the countries he visited, and probably not more than 750,000 altogether. The only real data for the Middle Ages are with regard to special Jewish communities.
The Middle Ages were mainly a period of expulsions. In 1290, 16,000 Jews were expelled from England; in 1306, 100,000 from France; and in 1492, about 200,000 from Spain. Smaller but more frequent expulsions occurred in Germany, so that at the commencement of the 16th century only four great Jewish communities remained: Frankfurt, 2,000; Worms, 1,400; Prague, 10,000; and Vienna, 3,000 (Heinrich Grätz, Geschichte der Juden x. 29). It has been estimated that during the five centuries from 1000 to 1500, 380,000 Jews were killed during the persecutions, reducing the total number in the world to about 1,000,000. In the 16th and 17th centuries the main centers of Jewish population were in Poland and the Mediterranean countries, Spain excepted.”
If those estimates are correct, and there were only around 15,000 Askenazi in German lands in 1500, that does suggest quite a serious bottleneck around that time. As I said in another post, the genetic evidence does not suggest that at any time there were only 350 Ashkenazi, it only suggests that all living Ashkenazi are descended from 350 individuals. There might have been thousands more alive at the worst bottleneck, but many of their descendants did not survive subsequent events (such as the Holocaust).