If you are talking about this study, no semitic J1 linage were sampled at all. All J1 linages are counted as "moorish" although they most likely predated Moors, Greeks,... by thousands of years.
http://www.nature.com/ejhg/journal/v17/n6/full/ejhg2008258a.html
You can take a look at the tables in the Supplementary Data section of Boattini et al, which divides the J1 in Italy into "J1e" and non J1e. One table also provides the strs. That one is by area.
http://www.plosone.org/article/info:doi/10.1371/journal.pone.0065441#pone.0065441.s012
I agree that the presence of J1 in Italy has been misinterpreted. The vast majority of it is, from more recent data, Neolithic era. The erroneous conclusions were partly based, imo, on very glib interpretations of Italian history, as well as the fact that J1 was treated as a monolithic clade. It wasn't until it was more resolved that it became clear that there is extremely little "Semitic" ydna J1 in Italy.
That, of course, means that interpretations of the extent of Moorish genetic influence in Italy must be re-examined, as it would imply that it has either been vastly over estimated, or there were very few Arabs involved and it was mostly a Berber phenomenon.
Given that the levels of E-M81 (the so called "Berber" clade) in southern Italy are in the low single digits, my personal take away is that the Moorish influence has been over-estimated,
and that what influence there was stemmed mainly from Berber settlement drawn from the coastal areas, although there was, according to historical analysis, an elite "Arabic" layer, which from the almost non-existent traces remaining, must have been very small, and/or went into exile. If you're interested in the history of Sicily, or southern Italy in general in terms of the Moorish conquests, I highly recommend the book, A History of Muslim Sicily, by Leonard C. Chiarelli, 2011. It's very long, but it is groundbreaking in its analysis.
Btw, I don't make any claims about how many of them actually settled in Sicily, in particular, because the historical evidence is extremely sketchy. It may be that they came in rather substantial numbers but that most of them were indeed expelled.
As to your comment to Aberdeen about J2, I would point out that J2b is not the only J2 y lineage. Grugni et al 2012 Figure 2 shows, in the first column, the distribution of a J1 clade as well as various J2 clades. (The second column shows variance)
http://www.plosone.org/article/info:doi/10.1371/journal.pone.0041252#pone-0041252-g002
As to the topic of J2 in Italy generally, I think, as I
speculated above (which is all any of us are doing) that some of it may indeed have a late Neolithic source from the Balkans, including Greece, and from Crete, or at least that wouldn't surprise me, but I would find it extraordinary if all of the Metal Ages movements from Crete, the other islands, and Greece proper into the mainland and Sicily did not impact those levels significantly, and that doesn't even take into account any
possible, and I emphasize possible movement involved in the formation of the Etruscan culture in the Bronze Age by migrants from Anatolia or the eastern Aegean directly into Tuscany, should that ever be proven. (Although interestingly enough, Tuscany itself, based on the Boattini2 data as well as the composite data put together by Maciamo, is rather low in J2 compared to other areas.) Then there are inputs from Greek maritime trading on the coasts of Liguria and Venezia, and possible Byzantine era influences to be considered, although their input may have been extremely minor. There are also the population movements engineered by the Romans through the creation of veterans colonies in the north, which may have spread the J2 into those areas.
,
Therefore, as I said above, I think J2 frequency in Italy today is probably the result of numerous different layers of migration from the direction of the southeast, some perhaps from the late Neolithic, and some, perhaps more, which took place during the Metal Ages, a flow which also spread from the northern Mediterranean coastline into France and Iberia. Those Grugni graphics are pretty informative in that regard.
It's a mistake in my view to look at even J2a as a monolithic clade. Different sub-groups were, in my opinion, doubtlessly brought or spread at different times.
Only ancient dna will bring us closer to the answers. Modern distributions provide only hints, and are very difficult to interpret in any precise way.