>> In fact, most of Ashkenazi Jewry can have their DNA traced to about 350 people in Germany in the 1300-1400s. Which is why there is a relatively high number of Recessive diseases among Ashkenazi Jews. Be that as it may, we still do not differ much from the Non-Jews of the Mediterranean area. (arabs, etc.)
the fact that Ashkenazim come from a small group of _men_ (the way I heard it, more variety and European admixture on female side) makes us different from even Sephardim. Mathematically, think about this way – you have a large multi-dimensional population. Take a 100 random samples – distribution of that small sample will be different from the whole population. That is, you can find some out of 1,000s variables that will separate these 100 from the whole. With time, those differences are reinforced. So, it is not by chance that medieval Europe starts depicting Jews with specific features, like long noses. I don’t think Romans or Persians ascribed specific features to Jews.
And also diet and public health make impact. It is in halakha, I forgot the source, that modern Jews are weaker – because weak children are saved by medicine. In older times, people who have a hard time fasting for a day would not be asking shailos about it, as they would have died in childhood on a day there was not enough food.