They all arrived during the Neolithic to italy
Well, not according to Boattini et al...
I'll preface this by saying that the dating issue is unresolved in my mind. The authors themselves advise taking their dates, based on the germline rate, not the evolutionary rate, with a great deal of caution. I especially think that's warranted because they use very few STR's, although the ones they chose are the ones least subject to saturation.
Leaving that aside, and looking at their figures, they concluded that " In fact, in contrast to mtDNA age estimates, almost all Y-chromosome estimates fall between late Neolithic and the Bronze Age. "
Later, however, they say" it is worth noting the older age estimate obtained for Y-haplogroup G2-P15 (15,020 YBP) that, coupled with its high frequency (11.09%), makes it the most probable candidate for a continuity with Italian Mesolithic populations (although a Neolithic origin for G2-P15 is discussed,
[22],
[23]). The most frequent G2-P15 cluster (12,643 YBP,
Table 2), besides being evenly diffused in NWI and SEI, it encompasses almost all Sardinian G2-P15 individuals (
Figure 2,
Table 1). These facts, together with the higher degree of isolation of Sardinia to Neolithic and Post-Neolithic migration processes, support the antiquity of this haplogroup in Italy. Despite obtaining similar time estimates for G2a in Italy (12,899 YBP), Rootsi et al. (2012)
[62] explain the diffusion of its main sub-lineages in this country solely as a consequence of Neolithic and Post-Neolithic events."
So, while they acknowledge that other interpretations are possible, they posit a mesolithic origin for the pan-Italian and Sardinian cluster of G2a in Italy (It's Group 3 in their table)
There are arguments to be made on either side. The Neolithic didn't arrive in Italy until long after 13, 000 B.C. That's old even for the Neolithic in Anatolia. Even Rootsi et al's 11,000 B.C. is early. However, it's a fact that there was some demographic movement from the near East into Europe that accompanied the Neolithic transition, and G2a has been found all over the so far sampled Neolithic sites in Europe, so perhaps their dates are slightly off.
Just generally, while I think their data is very informative, I find their explanations for the NW Italy/SE Italy split rather confusing. They give a nod to the fact that, " the dates of several DAPC clusters fall within the range of the Metal Ages (
Table 2). During this long period (third and second millennia BC) Italy underwent important technological and social transformations finally leading to the ethnogenesis of the most important proto-historic Italic peoples. On the whole, our results indicate that these transformations, far from being exclusively cultural phenomena, actually involved relevant population events.'
However, at the same time they conclude that the differing sources of the Neolithic in Italy, i.e a more Mesolithic/Neolithic mix in NW Italy, with a more central European and western orientation and a more complete Neolithic picture in the SE with more affinities to the Balkans and Anatolia, explains the split.
Part of the problem, I think, lies in the fact, as they say, that "the model used does not account for migration. " And yet the structure looks like it could be traced back to that 3500 B.C. date that might very well indicate migration from central Europe.
As for how this impacts G2a, it seems to me that the pan Italian older cluster could most probably be connected to the Neolithic in Italy, while the NW cluster that they identify as being more similar to the German cluster, could be related to these later population migrations, and the specifically southern ones that seem to date to the Bronze Age would fit very well with migrations from the Aegean.