Ralph and Coop do the best job of explaining it, I think. It's important to read the whole paper, but this will give you an idea.
http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.1001555
"We can only hope to learn from genetic data about those common ancestors from whom two individuals have both inherited the same genomic region. If a pair of individuals have both inherited some genomic region from a common ancestor, that ancestor is called a “genetic common ancestor,” and the genomic region is shared “identical by descent” (IBD) by the two.
Here we define an “IBD block” to be a contiguous segment of genome inherited (on at least one chromosome) from a shared common ancestor without intervening recombination (see
Figure 1A). A more usual definition of IBD restricts to those segments inherited from some prespecified set of “founder” individuals (e.g.,
[8],
[27],
[28]), but we allow ancestors to be arbitrarily far back in time. Under our definition, everyone is IBD everywhere, but mostly on very short, old segments
[29].
We measure lengths of IBD segments in units of Morgans (M) or centiMorgans (cM), where 1 Morgan is defined to be the distance over which an average of one recombination (i.e., a crossover) occurs per meiosis. Segments of IBD are broken up over time by recombination, which implies that older shared ancestry tends to result in shorter shared IBD blocks."
Could you provide a reference for an average of 20% in Turkey? I've never seen anything anywhere that high for an average in any academic paper.
Ultimately, it wouldn't matter, however. Nowhere did the authors say that there was
no IBD sharing between Turkey and other Middle East countries and Italy. They just said it was old.
From the Supplement to the paper:
" "The IBD segments shared between the Italians and the other European populations are longer than the IBD segments shared between Italians and Turkish/Middle Eastern individuals, indicating that the admixture events between Italians and other Europeans are the most recent."
There is also the broader issue of "West Asian" as an admixture component, and by that I mean the admixture component modal in Iran, Armenia, the Caucasus and modern Turkey. As I pointed out upthread, the Northern Italians have just about the same amount as the Hungarians, a little less actually. TSI Tuscans are a bit higher, about 4 points. Central Italians, which in that project are some Romans and some people from the Abruzzi, have about as much as the Romanians and Bulgarians and no doubt the Albanians and Serbians. Did the Etruscans settle in Bulgaria and Albania too? That just won't cut it as an explanation. Nor, as I said upthread, will some mythical settlement of Parthian slaves as it would have to have occurred all over the Balkans (and not in central or western Europe or Iberia or anywhere else.
There are other processes involved as well, older, in my opinion, having to do perhaps with late Neolithic and early Bronze Age gene flows, perhaps mediated partly through Crete and the Myceneans, and then additional gene flow during the period of Greek colonization.
