Lost of discussion about Basques below. Some interesting examples which are less speculative.
Hungary = Language changes, genes do not
The intrusion of ethnic Magyars, and later the settlement of Kipchak Turks fleeing the Mongols, within Hungary is historically attested. Additionally, down to the Reformation there were isolated settlements of Turks among the Magyars which maintained their own linguistic tradition. But digging through the literature it is very difficult to find much genetic impact. Anatolian Turks are a milder case; eastern genetic contributions can be found, but it is the minor component, and this may reflect the greater genetic distance of Turks from Europeans/Anatolians than the Ugric groups of the lower Volga.
Bulgaria = Neither language or genes change
Bulgaria is interesting because it resembled Hungary in many ways. An alien ethnic elite on top of a local substrate. In this case though the alien Bulgar elite was Slavicized, leaving only their ethnonym. Again, no genetic impact.
Japan = Language and genes change
This is a case where the preponderance of evidence seems to be that the Yayoi rice-culture bearers arrived from the continent and predominantly replaced the indigenous post-Jomon culture. The Ainu may be a residue of the Jomon natives, and a non-trivial, though minority, component of the Japanese ancestry can be traced back to the Jomon (a Uyghur treatment would clear up the case of Japan, because if admixture did occur in the manner posited above it would should up in the form of decayed linkage disequilibrium. Though the parent populations in this case are much closer than in that of the Uyghurs).
Basques & Brahui = Language does not change, genes do
Unlike the previous cases I'm a little sketchy about these instances. I can't think of a whole political nation where this occurred, but linguistic isolates are possible cases. The Basques were suggested below, but the Brahui of Afghanistan and Pakistan may be a case where the Dravidian language persisted despite long term gene replacement by their Indo-Iranian neighbors. This dynamic is most likely to occur in the case of small culturally distinctive populations surrounded by larger groups whose distinctive gene content "bleeds" into them. Some of the Romani speaking groups in Europe ("Gypsies") clearly fall into this group, especially western ones such as the Siniti. Most of these populations retain Indo-Aryan speech, but many have admixed enough with the local populations on their migrations that more of their genetic heritage is European or Middle Eastern than South Asian (though the genetics & phenotype also indicates a strong South Asian stamp in many of these groups, especially in south & east Europe, though I didn't guess that the run-down Balkan village in Borat was populated by Romanian gypsies by physical type alone).
Thinking about these extreme cases allows us to get a better intuitive sense of how different inheritance constraints of genes and culture shape our variation. We obtain 50% of our genes from each parent, but we don't need to obtain 50% of our language from each parent. We may not even share the same first language with our parents. And yet historically linguistic and genetic patterns have been related.
Note: Ashkenazi Jews may be another case where culture, if not language, persists where the ancestral genetic distinctiveness is eroded. But like the Romani speaking populations this may be a special case where relatively strong endogamy has also generated a unique genetic profile which is distinctive from their neighbors and their ancestors.
In language you have gradual partial change (borrowed vocabulary, bits of borrowed grammar, pronunciation changes influenced by neighbors) but these NEVER end up with change to a different, already existing language. The outcome language may be utterly unrecognizable in terms of the initial language, but it will not have gradually turned into one of the languages that exists alongside it. (There may be an excpetion in the case of languages already very near, like two closely-related dialects of Low German. But a Germanic language will never become a Romance language.)
This is because a language is, in a sense, a unity, which must remain functional and keep some particular kind of definite functioning structure no matter how much it changes. You can't replace Germanic parts one at a time with romance parts until finally the whole language is romance.
So in these case you can either have replacement of one language by another, or modification of the original language by "areal effects", but the given A never turns into a version of B. It will always become A', regardless of how different.
Gene pools really have no structure. If you have a small, population surrounded by a larger one and the two populations start off distinct, genes can be replaced one at a time, like mixing hot and cold water, until the larger population is slightly cooler and the smaller population a lot hotter. Even 5% intermarriage a generation (small) with three generations a century (slow)can put the original gene pool below 50% in 4 or 5 centuries.
"Hungary = Language changes, genes do not" ... "digging through the literature it is very difficult to find much genetic impact"
Perhaps you already have seen this, but if not, what about this study?...
"Probable ancestors of Hungarian ethnic groups: an admixture analysis"
Although perhaps even this isn't "much" of a genetic impact. But I do find it interesting that it depends on which Hungarians you look at, for where their (genetic) origin seems to have come from.
Another awesome post! Thank you!
I know from my ethnic group that the language issue tends to color the way others, non natives, view the history and genetics of my ethnic group.
I am Maltese. Maltese people speak a form of Semitic language but more than half its vocabulary is from Romance languages, and Maltese has incorporated grammatical forms and not found in other Semitic languages. Few of the typical Semitic language sounds exist in Maltese.
Genetically Maltese people are unlike any Middle Eastern or North African ethnic groups. The nearest to Maltese people for non European are Jews, who are either a hybrid group or due to their own genetic drift because of their culture and religion. Maltese people are similar to Southern Italians or Greek people.
Saying the above, you will find people who just want to see the Middle East or North Africa in Maltese people whether it is genetic or culture or architecture simply because of the language Maltese people speak. I guess it is hard for many folks to get their brain around the fact that language and genetics only have loose correlations.
"Gene pools really have no structure." !!!
I don't think you mean this John! Otherwise, we've got some bad news for the HapMap project. Alleles are not beans in bags, despite the math...I see your point that genes are in principle exchangeable because we all have (roughly) similarly organized chromosomes and the same system using our genes. But in practice genes don't move independently.
Don't see how Basque is a case of gene change. It is likely the descendant of the language of the original neolithic farmers of the region. The surrounding genetically similar populations could have converted to Indo-European languages without much outside genetic input, which explains why the Basques aren't too different.
Is the US another example? The ancestors of most residents were immigrants from non-English speaking countries.
I learned all of one German word from my grandfather, and a little more in high school.