Hg J2 M172 middle/late neolithic Hungary. (Sopot & Lengyel Culture)

I largely agree with your summation of the issues as of now, except to say that some of the papers which show such a strong presence in central Italy of J2, and especially central, eastern Italy, are based on very small sample sizes. More extensive testing might change things a little.

Not to mention that J2 in central-eastern Italy is concentrated in the less populated regions.
 
Not to mention that J2 in central-eastern Italy is concentrated in the less populated regions.

Your point is very well taken. It also speaks to a larger problem with a lot of these studies & the reported haplo numbers on Eupedia. Often researchers will seek a diverse profile of a nation or ethnicity, so they'll go to the far-reaches of the geographic region to create a genetic profile. A good example is Greece. The vast majority of Greeks live on the mainland, not on islands. However, if you were interested in making a genetic profile of Greece, you might want to sample remote regions and islands, because doing so is highly informative. However, this will invariably skew the numbers toward the islands & away from the real proportions in the Greek population as a whole, because the islands will have very different genetic profiles & so island numbers will not be literally over-counted, but their impact will be disproportionate. If you wanted to make an accurate genetic profile of a nation or group, you'd have to take samples from particular regions in proportion to those regions' percentage of the whole population. Otherwise remote or unrepresentative regions are counted as if the numbers within them are no different from the rest of the areas sampled & end up having an outsized impact on the results. This speaks to the problem you're articulating in Italy, where less populated, rural regions might be typed, skewing the numbers toward the genetic makeup of those regions.
 

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