The question is a valid one; however, I am getting very tired of these increasingly bizarre and badly created amateur "maps" and "calculators". "Kurd" over at anthrogenica seems to know what he is doing, and his methodology is absolutely transparent. He also is clearly aware of the problems involved and how easy it is either wittingly or unwittingly to create "biased" or just incorrect results. However, even in his case, I question whether an analysis of IBS with ancient samples can really be reliable, especially given the quality of these ancient samples. IBD analysis is even more problematical. I took a look at the results by country at the analysis over at eurogenes. In many cases, out of a sample set of, say, twelve, often 10 can show no sharing whatsoever, but an "average" is computed using the remaining two. I'm not at all convinced by this kind of methodology. If anyone wants to look at the mathematics and the algorithms necessary to come to any meaningful conclusions about IBD, even using high quality modern genomes, I would suggest going to the methodology section of the Ralph and Coop paper:
http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.1001555
I highly doubt this has much to do with North African domination, as anyone who has paid any attention to y Dna and IBD analysis of Europe in general or of Italy in comparison to countries like Spain or Portugal would know.
The yDna analyses have been discussed endlessly on this site, particularly in reference to North African specific subclades of both yDna and mtDna, and people should be aware of them.
As to IBD analyses there is the much criticized, by some, Botigue et al. Still, with the usual caveats as to direction and timing of gene flow, and the small percentages involved, it still indicates the general trends, in my opinion, and the fact that it is doubtful this has any major part to play.
http://www.pnas.org/content/110/29/11791.abstract
As discussed on the Dienekes site:
http://dienekes.blogspot.com/2013/06/ibd-sharing-between-iberians-and-north.html
In terms of autosomal analyses there are also the results at 23andme to consider for both Iberians and southern Italians. I've never seen anything greater than 2-3% for any southern Italians. Neither do North African populations show up on oracle results in calculators, at least not for Italians, in any meaningful way.
Speaking of calculators, someone ran some of the ancient Anatolian farmers through Gedmatch.
"Gedmatch results of an Early Farmer from Anatolia
M897077 I0707 Anatolian EF
EUtest Oracle results:
Kit M897077
Admix Results (sorted):
# Population Percent
1 WEST_MED 46.98
2 EAST_MED 32.62
3 MIDDLE_EASTERN 10.57
4 ATLANTIC 9.59
5 NORTH-CENTRAL_EURO 0.21
6 EAST_AFRICAN 0.03
Single Population Sharing:
# Population (source) Distance
1 Sardinian 19.83
2 South_Italian_&_Sicilian 30.51
3 Tuscan 31.43
4 GR 31.65
5 North_Italian 33.52
6 Moroccan 33.96
7 AJ 34.13
8 PT 36.5
9 ES 36.7
10 Algerian 38.39
11 Samaritan 39.07
12 Mozabite_Berber 40.98
13 RO 41.39
14 FR 43.19
15 Druze 43.37
16 Serbian 44.14
17 TR 44.62
18 French_Basque 45.13
19 Armenian 45.38
20 Assyrian 45.63"
The FST values are high, of course.
Here are the much better (lower FST) values from Dodecad K=12b:
Dodecad K12b Oracle results:
"Kit M897077
Admix Results (sorted):
# Population Percent
1 Atlantic_Med 48.5
2 Caucasus 37.07
3 Southwest_Asian 12.16
4 Northwest_African 2.24
5 Southeast_Asian 0.03
Single Population Sharing:
# Population (source) Distance
1 Sicilian (Dodecad) 20.91
2 S_Italian_Sicilian (Dodecad) 21.09
3 C_Italian (Dodecad) 21.4
4 Tuscan (HGDP) 21.73
5 TSI30 (Metspalu) 22.27
6 Morocco_Jews (Behar) 22.5
7 Sephardic_Jews (Behar) 22.58
8 Ashkenazi (Dodecad) 24.51
9 North_Italian (HGDP) 25.24
10 Ashkenazy_Jews (Behar) 25.26
11 Sardinian (HGDP) 25.79
12 O_Italian (Dodecad) 26.53
13 Greek (Dodecad) 26.91
14 N_Italian (Dodecad) 27.31
15 Andalucia (1000Genomes) 29.51
16 Cypriots (Behar) 29.54
17 Baleares (1000Genomes) 30.29
18 Murcia (1000Genomes) 30.41
19 Canarias (1000Genomes) 31
20 Galicia (1000Genomes) 32.55"
Still not really low FST values, but a lot of water has passed under the bridge since then. So, how much of this is just because Italy harbors the most ancient Anatolian farmer ancestry, much more than do Middle Easterners or North Africans? I don't know, but I think it does have a role to play, as even some IBD analyses have shown which use the ancient samples from the Neolithic in both Anatolia and Europe and compare them to European populations. Either Tuscany or northern Italy show the highest percentages in those studies, although so far as I know southern Italian samples weren't used in the ones I saw. Indeed, as I've pointed out a number of times, when the first analysis of the Gok sample came out, the similarity to Sicilians was pointed out (after Sardinians, of course)
That's not to say that other, later migrations might not have a part to play as well. There are the Bronze Age migrations, some of which may have come from Anatolia (let's see if Drews was correct), early Iron Age migrations, as has been mentioned, and late first millennium BC colonizations from Greek city states from mainland Greece, the islands, and the western coast of Anatolia. The Phoenicians may have had some small role to play. Perhaps Byzantine era migrations also had a minor impact.
Certainly, there were no "Arabic" migrations into Tuscany and northern Italy; indeed, the vast majority of any settlements in the two hundred year occupation of Sicily was by Berbers, not Arabs, who only constituted the elite. Southern Italy was occupied only for a few decades.
In this regard I'd point out that while southern Italians and Sicilians at 23andme get some percentage of "Middle East", Middle East there is defined as Anatolia, Iran, Armenia, the Caucasus etc., not the Levant and certainly not Saudi Arabia. Saudi Arabia and other Arabian peninsula populations form part of the North Africa cluster, which has already been discussed.
I honestly don't know the explanation, and I don't think anyone else does either. Most particularly I don't think the "map" posted is either reliable or informative, in my opinion. The answer is only going to come from ancient dna.