We explore a simple near neighbor linear diffusion model for Syria to estimate the source populations for this country. From the solution of the diffusion equation, we know after their initial establishment, populations will spread out spatially in x as a function of a decaying exponential exp(-x). Using a Taylor series expansion, we can approximate this function to first order as
Using this idea, we can begin to guess at the diffusion processes that have led to the subcomponent combinations that form the modern population of Syria. Furthermore, because the diffusion equation is linear, we can use linear superposition to sum the contributions of the various "x" direction contributing populations to Syria.
We use the modern populations of adjacent countries for the estimates, even though it is understood that demic diffusion has been at work on these populations for millenia. The subcomponent groupings, West Asian, Northwest African, etc. for these three countries are derived from an ADMIXTURE analysis of 40 living Eurasian populations.
To justify this simple approach, we also assume that the diffusion constant D, described in equation (41) of the linked paper, is small. That is equivalent to saying that although the populations have been spreading out in space, the composition of the source populations hasn't changed very much during the time in question.
We subtract by a fixed increments of "population" from "Syria", as shown in the graph below.
Because it is known that Egypt occupied Syria from the 14th century BC, as a first choice, we subtract "Egyptians" from Syrians.
Next, since the model doesn't present a population for Syria's eastern neighbor Iraq, we substract a proxy, Pakistani Burushos. That's a big assumption, but we know that Syria traded with Mesopotamia. We can see that there is a quite visible South Asian component in Syria and it's most likely source is via Mesopotamia.
Using this "1-x" approximation, where "x" are the modern populations of Egypt and a population from Pakistan, Burushos, we've now approximated a source of the East African and South Asian subcomponents in Syrians.
Next, we subtract Cypriots, an obvious and nearest neighbor trading partner throughout history. The likely source for the Southern European in Syrians is through millenia old trade throughout the Mediterranean.
Finally, we subtract equally from Saudis and Georgians, near neighbors who are likely to be the sources for the Southwest Asian and West Asian components. It is true that the path of these populations into Syria is by way of Turkey and Jordan, but for the sake of simplicity, we choose Saudi Arabia and Georgia.
The results, in the 7 "x directions", where x = x1, x2, x3, x4, x5, x6, and x7 yields:
Cyprus(x1) = 36%
Saudis or Arabian Peninsula(x2) = 24%
Georgians(x3) = 22%
Egyptians(x4) = 12%
Pakistani Burushos, via Iraq or Mesopotamia(x5) = 6%
East Africa(x6) = less than 0.5%
West Africa(x7) = less than 0.5%
All this "1-x" subtraction suggests that Cypriots, followed by people from the Arabian peninsula, followed by people from the Western Caucasus, are the dominant players in the composition of modern Syrians.
The model suggests that there is a contribution to Syria from Egyptians at about 12% and from India or Pakistan, by way of Mesopotamia, at about 6%.
The remaining Syrian components are a West African component at less than 0.5% and an East Africa component at less than 0.5%.
Using linear superposition, we can sum the contributions from these seven populations. That's the modern population of Syrians.
From what we know about ancient Mediterranean trading routes, we can guess that the contributing population from Cyprus was the largest contribution. The contribution from Egypt may be due to the occupation of Syria 3500 years ago, but may also be due to a continuous diffusion process from Egypt, through Jordan and into Syria. The contribution from India or Pakistan is interesting. It's probably old, a over time scale similar to that from Cyprus, but from a smaller and more distant source population.
Finally, the contribution from Georgia and the Arabian peninsula may be very old. Both of these are candidate populations for Syria prior to the develop of farming and trade in the Fertile Crescent and Mesopotamia.