where did you read the word "significant"?
on average it was never significant but it was not present in copper age and appears first during iron age here in these samples. it is still present in late antiquity and medival times
so if we assume that it was introduced through migrants who went to rome during roman times this would speak against the theory that the ancestry of imperial rome just disappeared because of depopulation.
why should we compare it to morocco HG in Portugal and Spain?
Do you see it in the Mesolithic, or Neolithic, or Copper Age?
So, can we ASSUME it came in the Republican Era, Imperial Age, and perhaps in Late Antiquity?
If it's this insignificant, and it is, why are you so interested in it? In the midst of all these important questions, this is your main focus? Unless you're t-rolling, of course, which you so often do.
Did I ever say or even imply that these people left NO trace of their sojurn in Rome? That would be stupid, and no one has ever accused me of being stupid. Just so that there is no question, I have no doubt that there was probably some intermarriage and traces of their dna remain. Do some "white" New Yorkers marry Puerto Ricans? Yes, they do. Do some marry East Asians? Yes, they do. Do a few marry African-Americans? Some, but even less. What would happen if there was no more migration of Puerto Ricans, East Asians and African Americans, and a lot of the population of New York City died or scattered?
Christ, it took 1000 years for the Anatolian farmers in Europe to really start intermarrying with the hunter-gatherers.
In Greece, you couldn't legally marry non-citizens, and a child produced with a non-citizen, even one resident in the city-state, had no citizenship rights. If people go around digging up Classical Greeks, are all the samples they'll find going to be the ancestors of modern day Greeks in large proportions?
Ashkenazi Jews lived alongside Slavs for 6-700 years and never intermarried.
Barely 70 something years ago, northern Italians like my paternal grandfather wouldn't allow their children to marry Southern Italians.
I could go on and on.
Human behavior doesn't change all that much. Only our toys do.
However, it's absolutely clear from the data that the "trail" to the Near East, all those kinds of people who plotted south and southeast of Southern Italians are gone relatively quickly. That kind of thing happens when you have a wave that stops, i.e. no replenishment, and the population is killed or is scattered.
There has to be a reason, and some Goth and Vandal tribesman are not the answer. There's just not enough of their y dna around. Hell, 70% R1b where I come from, and we still plot as North Central Italians.
If you're sincerely interested in this and not just t-rolling, go back and read the Supplement. The authors state over and over again that the populations were HETEROGENEOUS, and remained so over time, and were not HOMOGENEOUS.