The Southwest Asian component appears in light turquoise on the graph. Not plotted are the Saudis, who have a 76% Southwest Asian component in K=10 Dodecad run.
We've established that it is plausible that Modern Assyrians are representative of inhabitants of the Fertile Cresent from the Middle Assyrian Period. I'll be specific and say that they are representative of middle northern Fertile Crescent inhabitants from approximately 1500BC. Using Assyrians as a "snapshot", we've inferred diffusion rates for populations from Saudi Arabia, Cyprus, Egypt and Babylonia. We've examined the small contribution that far flung traders have made to the modern population of the middle northern Fertile Crescent (Modern Syria). Finally, we've applied the First Order diffusion model, and have worked backward to a First Arrival Date in the Fertile Crescent for people from Southwest Asia.
The First Order Model diffusion rates yield a Southwest Asian (SWA) First Arrival Date of approximately 4000BC. The First Order Model implies that diffusion of SWA populations has been underway among Fertile Crescent inhabitants for approximately 2500 years before the Middle Assyrian Period.
It is important to keep in mind that these diffusion rates were estimated from a mid point diffusion in time and distance from coalescence. In the graph, a best fit of the slope of the First Order Model, Normal Distribution Model, and the Unbounded Exponential Diffusion Model are obtained at the diffusion mid point. From this fitting, we can estimate that the SWA First Arrival Date for the Normal Distribution is
1500BC + (2500BC)1.4 = 5000BC
where the factor of 1.4 has been estimated from the point where the SWA population density is less than 2%.
For the Unbounded Diffusion Model, the SWA First arrival date is estimated to be:
1500BC + (2500BC)2 = 6500BC
Summarizing Fertile Crescent SWA First Arrival Dates:
First Order Model: 4000BC
Normal Distribution Model: 5000BC
Unbounded Diffusion Model: 6500BC