Not claiming this modelling is valid.
Sorry. Perhaps next time you might explain what you mean when you just post a model.
I'm glad we're not going to hear from the American-Padanian Association or their Italian equivalent and their mythology of 500,000 Germans victoriously pouring into mainly Northern Italy to make them Ubermenschen.
Personally, I find the estimates based on the earliest records the most persuasive, and they put the number of Lombards moving into Italy at 60,000 Lombards plus 20,000 Saxons, and some sundry small additional groups, putting the total number, as proposed by some historians, at 80-100,000 people. The same sources propose that the Saxons supposedly subsequently returned north. However, even if they didn't it would make little difference. Other historians place the number at 150,000. One puts it at 200,000.
The Padania contingent found one American professor who supported the idea of a much larger group. It is a minority position from what I can find. Doctoring up the Lombard entry in Wiki, and implying Paul the Deacon was prejudiced against his own people because he was a Christian is pretty low, as well as being quite obvious to anyone who has studied the history. By the way, his "prejudice" is "proved" by the fact that he thinks one of the stories about how they got their name is "silly". I have no idea what that has to do with their original numbers. If anything, his "prejudice" is squarely with his own people, and against the people in whose country he lived. His descriptions of the differences between northerners and southerners could have come out of some Nordicist handbook.
As for their entrance into Italy, they were no horde of heroic conquerors. We know from the paper on the Langobards that they entered Italy as a group of ragged, starving, battle scarred survivors of wars with other wandering "Barbarian" groups who had defeated them. They were seeking refuge in an Italy plundered and supine from the depredations of both the Goths and the Byzantines, but with a population still numbering in the millions.
Since none of us has crystal balls or a time travel machine, other than contemporary documents, which also, it is true, might be problematical, we must turn to genetics, both uniparental and autosomal.
We have ancient Langobard dna. They have, so far, been northern Germanic R1b lines, one I1 at each site if I remember correctly, 1R1a and maybe some I2a2. On could add in some more I1 for the Goths, maybe. That still doesn't bring you anywhere near 20% for Toscana based on the yDna found in this province. Now, I see from Khan's blog that Mr. Rocca is proposing the idea that the invading Germans could have carried some clades of U-152.
It's possible, but I doubt it. I don't remember any from the paper on the Langobards. He is basing this on the fact that U-152 was probably already in Hungary, Austria, Southern Germany etc., by the time of the "Germanic invasions". I agree that this lineage was already present in the modern areas he listed before the arrival of the Germanic tribes. However, I see no evidence that the Germanic or even Balto-Slavic tribes moving from much further north carried those lineages, nor that the ones who made it to Italy absorbed lots of men carrying those lineages. The Langobards certainly did not.
Nor does autosomal analysis support such high levels of Germanic admixture into Toscana, leading me to the conclusion that there must be something wrong with the modeling in this paper.