Let's review the component signature for the Fertile Crescent populations:
Repeating the same process with Modern Turk or Armenian samples to infer a "Mystery Composite" leads to an interesting result. It turns out that there is no solution with these populations. There is too much "West Asian". Even if "Mystery Composite" has no "West Asian" at all, combining these Turkish or Armenian populations with a South Europe-North Europe Mystery Composite will yield a Tuscan population that is too rich in the "West Asian" component.
What this tells us is that there is an upper bound on the West Asian component in the Tuscan Fertile Crescent contributor. Keeping the South European component the same as for Turks and trading off West Asian with Southwest Asian, the upper bound for the normalized Fertile Crescent signature is approximately 56% West Asian, 26% South European, and 18% Southwest Asian. Plotting this West Asian upper bound signature (see stacked bar 3 in the graph) with the other Fertile Crescent signatures gives us some idea as to its geographic origin:
Using this 56%-26%-18% guess for the Fertile Cresent contributor to Tuscans, we get a 42% contribution from the Fertile Crescent and a 58% contribution from "Mystery Composite". In this case, "Mystery Composite" is composed of 57% South European and 43% North European. In this bounding case, there is no West Asian component in "Mystery Composite."
This solution would indicate a Southern Anatolian origin and would concur with genetic evidence.