The main point of this paper is the migration of people from the Zagros and/or Caucasus to the Levant between 2500–1000 BCE. It's surprising that the authors fail to mention anything about the
Akkadian Empire (c. 2334 – 2154 BCE). The paper only says:
"
In much of the Late Bronze Age, the region was ruled by imperial Egypt, although in later phases of the Iron Age it was controlled by the Mesopotamian-centered empires of Assyria and Babylonia."
AFAIK, neither the Assyrians nor the Babylonians to their south controlled the Levant - let alone the Southern Levant, which is the focus of this study - during the Bronze Age. Only the
Neo-Babylonian Empire managed such a feat, but that was only very briefly in the 6th century BCE in what was already the Classical antiquity.
The period of the Akkadian Empire is IMO the best candidate for the diffusion of people from northern Mesopotamia (along the Zagros and southern Caucasus) to the Levant. It may not have been the Akkadians themselves, but maybe the people they displaced during their expansion. In any case, the Akkadians had a major influence in the northern Levant, imported cedar from Lebanon, etc.
The main issue with later periods is that the Southern Levant was under Egyptian rule during the New Kingdom (c.1550 to c. 1180 BCE), so I don't see how "invaders" could have settled in the region without written record. It must have been prior to 1550 BCE. That only leaves that Akkadian Empire or the Old Assyrian Empire (2025–1522 BCE). The Assyrians did expand briefly to the whole Levant under Shamshi-Adad I (1808–1776 BCE), but I doubt that this was long enough to have significantly changed the genetic make-up of a region that was hardly changed by over 1000 years of Greek, Roman and Byzantine rule.
That brings me back to the hypothesis that it was probably a mass migration of tribes displaced by the Akkadians and/or Assyrians.