All the elements concur in favour of a large scale migration of horse-riding Indo-European speakers to Western Europe between 2500 to 2100 BCE, contributing to the replacement of the Neolithic or Chalcolithic lifestyle by a inherently new Bronze Age culture, with simpler pottery, less farming, more herding, new rituals (single graves) and new values (patrilinear society, warrior heroes) that did not evolve from local predecessors.
This transition would have been on top of a transition between European hunter-gathers and early Neolithic European farmers (starting ca. 6000 BCE) that would have been probably more dramatic genetically in some places and would have had some significant genetic impact in most places in Europe, although these pages put less emphasis on this transition, while most population genetic researchers would have more confidence in the Paleolithic-Neolithic transition (particularly outside the Western Europe and Europe's Southern coast), and less about genetic element of the Indo-European transition.
The site suggests that Y-DNA haplogroup I was indigenous, but there seems to be at least some emerging evidence that there was at least one layer of significant genetic shift even within the Neolitic in some parts of Europe at least, and that I is itself mostly a Neolithic or later arrival in Europe. Recovering ancient Y-DNA and autosomal DNA is much harder than recovering ancient mtDNA, or at least it was until recently, and so there are far more ancient mtDNA data points out there than there are Y-DNA datapoints, making speculations about the Y-DNA make up of prehistoric Europe quite speculative.
I recognize that their position is not universally held, although almost everyone does agree that there were probably some population genetic traces of both the Neolithic transition and the shift to Indo-European languages. The "purely cultural" transition theory is pretty much ruled out in the vast majority of Europe.
Almost everyone also expects that matrilines in Europe have been more stable than patrilines. But, it is clear that at least some new matrilines arrived in Europe at both the time of the Neolithic transition, and at the time of the Indo-European migration.
One big challenge in the field is to build consensus of not just the absolute extent of population replacement at these transitions, but also the relatively amount of change in Y-DNA v. mtDNA v. autosomal population genetics in these transitions. What share of existing patrilines and matrilines in European populations can be traced to migration into Europe in these various eras. Similar isuses are central to the field outside Europe. Naiively, one would expect that Y-DNA mix to be the most biased toward recent time periods, the mtDNA mix to be the most biased towards ancient time periods, and the autosomal mix to split the difference, although there is more to the analysis.
Ancient DNA studies and new techniques for analyzing population genetic data, along with increased multidisciplinary linkages between genetic and non-genetic anthropological data sets over the last decade have made the case for significant and multiple instances of significant population genetic shifts through the Holocene much stronger than it was previously. But, it has also undermined that absolutist total replacement scenario.
We now know that even Neanderthals (in almost all non-Africans) and Asian archaic hominins called Denisovians (in Melanesians, Australian Aborigines, Philippino Negritos, people admixed with these populations, and at a much, much more diluted level the most autochronous Southeast Asians) left a measurable genetic trace in the autosomal genomes of modern populations attributable to admixture with them, and there are weaker genetic signals of similar admixtures with archaic hominins in the genomes of Bushmen and Pygmies in Africa. Realistically, very few replacements of one modern human population by another have been as complete as the replacement of archaic hominins by modern humans.
An important to do list, then, is to look more carefully at what can be done to quantify the differences in replacement rates between patrilines and matrilines in Europe (and ultimately elsewhere as well) in specific prehistorical events that took place in specific regions of Europe that influenced modern gene pools significantly. Some of the very first estimates put an overall Europeanwide estimate of Paleolithic ancestry at 20% for both genders, but the state of knowledge has advanced so dramatically since those early estimates were made that they can't be given much credence and the notion of a European-wide average having much meaning itself has declined as well.
It also makes evident the need to create "residual" maps of population genetic distributions that look at the mix of non-recent contributions to local populations, to the extent possible, to make sense of those patterns. A map of raw percentages of genetic haplotypes in modern populations artificially remove from the landscape a sense of the continuities that may have existed between relict populations prior to replacement events and may also show different kinds of regional trends, since multiple waves of migrants may all tend to follow the same paths for reasons of geography.