There has been some dispute caused by uninformed persons on the dissident Right (
not naming any names Amerika .org) regarding the nature of Irish ancestry. I will attempt to clarify this as much as possible.
About two years ago, some British newspaper headlines written by people who seem to know very little about population genetics implied that the Irish are Middle Eastern (here, here). They are only correct in that all extant Europeans, Irish included, have significant admixture from early Neolithic Anatolian farmers. However, in order to correctly understand European genetics, one must do more than reading newspaper headlines. If the bozos who wrote them had actually read through the study they were basing their claims on, and understood its significance in the context of current population genetics, then they would realize that the Irish are essentially Northwestern Europeans (but that doesn’t make for a good eye-catching sensationalist story, now, does it).
The Irish genetically cluster and overlap to a significant degree with other Northwestern European samples, and appear most closely related to the British. They are not Southern Europeans, genetically speaking. Here are principal component analyses from two separate studies showing this. In the second analysis, the Irish are practically indistinguishable from the British and also overlap with Norwegians and Dutch.
Even if one wishes to do a fine-scale analysis to reveal the genetic difference between the English and the Irish, there is still obvious genetic overlap, and the English themselves have some Insular Celtic (Irish related) ancestry in addition to Anglo-Saxon ancestry.
The Irish and all Insular Celts appear to owe the vast majority of Y-chromosomes (haplogroup R-L21), as well as their autosomal ancestry to Bronze Age inhabitants of the British Isles c. 2000-1500 BC (link). The figure below shows the varying affinities of prehistoric Irish and Hungarian genomes towards modern European populations. (The fact that the Neolithic Irish sample resembles modern southern Europeans does not mean that the modern Irish are Southern European, rather all genetic samples from the Neolithic in Western and Central Europe prior to the Indo-European expansion resemble those of southern Europeans, particularly Sardinians; see the analysis at the bottom of the page).
The Bronze Age Irish, from whom modern Irish are descended, were autosomally very close to contemporaneous Indo-European peoples in Scandinavia (Nordic Bronze Age), and the continent (Unetice culture) (see analysis below). This is the reason why the Irish to this day are genetically Northwestern Europeans, just as the British, Germans and Scandinavians are.