I read the book by David Reich, Who we are and how we got here. He is a Harvard scientist who helped run some of the first studies confirming the "intermixing" of Homo sapiens and Homo neanderthalensis.
It's a "popular science" book -- not a textbook on evolutionary biology, not to mention a collection of journal articles. But still, it is more than most people read.
Reich's collaborator Nick Patterson is an applied mathematician who developed a simple statistic to prove with high probability when genetically distinguishable populations admix -- for instance, to prove that the homo sapiens who left the Near East and spread throughout Europe and Asia admixed with Neanderthals.
But this test only proves that admixture occurred -- it doesn't tell you which DNA portions you have that came from Neanderthals.
I had been wondering how it was determined which DNA portions in modern humans were confirmed as coming from Neanderthal ancestors. This article:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4031459/
seems to me to state that the answer is quite boring. The bottleneck, it seems, was getting really high quality sequences of Neanderthal genomes. Once this was done, you could compare with a lot of modern human genomes, which are much easier to sequence. At some loci, 100% of the homo sapiens specimens had the same nucleotide (i.e., A, T, C, or G) while the sampled Neanderthal genome differed. My thinking was that even if you checked this, there was no guarantee that the Neanderthal didn't just have a "private variant" produced in, say, the previous 30 generations of Neanderthals -- not representative of all Neanderthals. But this seems to be how these DNA positions are identified. So perhaps there are some that are specific to the Neanderthal sequence, and not characteristic of all Neanderthals. But this is a small percentage, and the more Neanderthal genomes are sequenced, the smaller this percentage can be made.
To answer your question: my 23andme results report on Neanderthal variants. Each company customizes the chip it uses a little. No major test measures your enitre genome, so they customize to determine which positions they measure. 23andme might be the only company to customize to include these Neanderthal positions.
