Human populations, along with those of many other species, are thought to have contracted into a number of refuge areas at the height of the last Ice Age. European populations are believed to be, to a large extent, the descendants of the inhabitants of these refugia, and some extant mtDNA lineages can be traced to refugia in Franco-Cantabria (haplogroups H1, H3, V, and U5b1), the Italian Peninsula (U5b3), and the East European Plain (U4 and U5a). Parts of the Near East, such as the Levant, were also continuously inhabited throughout the Last Glacial Maximum, but unlike western and eastern Europe, no archaeological or genetic evidence for Late Glacial expansions into Europe from the Near East has hitherto been discovered.The claim that "European populations are believed to be, to a large extent, the descendants of the inhabitants of these refugia" is not, in fact, a consensus belief of population geneticists. Indeed, the genetic evidence accumulated in the last decade or so has fairly decisively shifted the weight of the evidence against that belief and in favor of the value that European population genetics probably owe more to migration after the late glacial recolonization of Europe than they do to the populations in the several European refugia at that time. At the very least, there is not a consensus on the issue, with estimates of the pre-Neolithic contribution to modern European mtDNA ranging from 20% to 80%, without a whole lot of middle ground.
Here we report, on the basis of an enlarged whole-genome mitochondrial database, that a substantial, perhaps predominant, signal from mitochondrial haplogroups J and T, previously thought to have spread primarily from the Near East into Europe with the Neolithic population, may in fact reflect dispersals during the Late Glacial period, ∼19–12 thousand years (ka) ago.
The ancient DNA makes a very solid case that U4 and U5 were present in Europe prior to the Neolithic revolution, and a recent ancient DNA find from Southwest Europe has also cemented the case that there were at least some people with mtDNA haplogroup H in Iberia prior to the Neolithic revolution.
The populations where mtDNA haplogroup V is found (Berber, Basque, and Saami), and its near absence in many other European populations, likewise supports a hypothesis that this distribution may be the product of a martime migration of a population that did not engage in farming (although not necessarily before any population in Europe had adopted farming). It also isn't at all obvious to me that the currently extant lineages of mtDNA haplogroup V originated in Iberia and then migrated to North Africa, rather than originating in North Africa (probably in the Epipaleolithic) and migrating to Europe via the Strait of Gibralter (quite possibly quite a bit later).
For what it's worth, I think that the case that mtDNA haplogroups J and T probably do originate in the Near East (and perhaps Anatolia, Western Iran and the Caucasus Mountains, if they aren't included in your definition of the Near East) is quite strong, based upon their distributions and diversity.
But, I'm not at all convinced that the evidence is strong enough one way or the other to distinguish between Epipaleolithic and early Neolithic migrations.
Mutation rate dating is not precise enough to distinguish the two reliably. Dienekes notes that recent papers on the ages of different mtDNA haplogroups do not produce consistent sets of ages. And, mutation rate dates simply can't tell you where the mutation arose, only where descendants of people with that mutation started to expand.
The ancient mtDNA evidence isn't there to make the case very convincingly either. The distributions of the two haplogroups are also not sufficiently similar that I can even be comfortable that they are part of the same migration era from the same general region. Finally, I am particularly skeptical, in general, of any attempt to advance a hypothesis that has no archaeological support whatsoever, in addition to having no prior support from genetic evidence.
There doesn't seem to be any strong positive evidence that definitively rules out an Epipaleolithic entry of J and T into Europe. But, the case for this hypothesis is very thin, and there are alternatives that appear to be at least as likely, if not more likely, as a means of explaining the distribution of these mtDNA haplogroups. For example, the case that a fairly significant share of mtDNA J and T in Europe has a source in early Indo-European expansion in Europe, in migrations during the reign of the Roman Empire, and in the wanderings of the Jewish diaspora, and that much of the rest made it into Europe during the early Neolithic Linear Pottery (LBK) expansion and Cardial Pottery expansion, appears at least as plausible as the late glacial migration proposal made in this paper.
In my humble opinion, the field would be better off acknowledging what it doesn't know, recognizing the inherent limitations of inferences drawn from modern mtDNA distributions, and re-examining the archaeological evidence with the points that have been firmly established in mind.