The current state of direct-to-consumer $99 testing is that it takes a look at about 700,000 SNPs (single nucleotide polymorphisms), or fewer. The genealogy market is not very important revenue-wise to Illumina, the company that makes all the nifty microarray chips that can translate squishy biological suspension into digital readouts. So the chips the genealogy testing companies use are cross-purposed, primarily for academic population studies. Which works for us because the specific loci along the chromosomes they sample are ones which have been identified to change via mutation with a reasonable frequency; very few--but some--of the tested SNPs are contained within vital protein-encoding genes.
We're testing about 0.023% of the genome. A whole massive boatload of mathematical assumptions and imputation and probability and genotyping go into giving us data we can work with genealogically. When you dig into it all, you come out frankly surprised that we can be even remotely as accurate as we are. We typically measure segment size in centiMorgans, which isn't a physical measurement at all; it uses linear equations to estimate the frequency of crossover points along a chromosome--and the number of these points differ by as much as 30% between a female and a male genome map, so what we see from GEDmatch and the testing companies is what's called a "sex-averaged" value--in order to arrive at a comparative figure of relatedness, the centiMorgan. Not only that, but a segment of 7cM may have been assumed by a sequence of, say, 1,000 identical SNPs...along a stretch of chromosome that contains over 5 million base pairs. We're assuming that all those base pairs in between are identical if there are only a certain percentage of SNPs in the mix that don't match or are null no-calls, and despite the exact-looking start and stop positions you see at GEDmatch and elsewhere, we really don't know where the physical segment begins and ends: we can only measure to the matching SNPs.
To get to the point in the future that we can begin working with fully-sequenced genomes in the consumer market, we'll need a next-gen evolution in computing power. Gettin' all geeky, a medium-resolution full-genome BAM file, the way the full genomic sequence is stored, requires about 150Gb plus indexing overhead. Technology simply isn't at a point where we can deliver comparisons online, on demand, of even a few full genomes at a time, much less thousands or millions.
Okay. Net message is that our current technology with autosomal DNA for genealogy is really rather coarse and crude. That's why every genetic genealogist with a rep that I know of says to throw out the notion of very small segments. There can easily be a 4cM or 5cM difference between the sex-averaged numbers we see and what the valuations would be if applied to the female vs. male genome map. Not to mention that the versions of the genome maps change periodically and, again as an example only, GEDmatch is using hg36 while most universities have moved on to hg38. We really can't even compare true apples-to-apples at that most basic level. The different maps have different base pair numberings for the identified reference clusters (the actual nucleotides being identified).
So, no. Right now, autosomal DNA cannot be used as genealogical evidence dozens of generations into the past. Even Jim Bartlett, a proponent of atDNA triangulation, will use a 7cM segment in a triangulation group only because he's amassed well over 10,000 triangulated segments in over 580 triangulation groups; he knows to question or eliminate pile-up regions; and he knows to question and thoroughly research DNA evidence of pedigree collapse. One 7cM segment in the mix that turns out to be false will be only a rounding error and won't impact the validity of the triangulation group.
And no living person's atDNA can verify a genealogical linkage to any ancient remains. A linkage per Population DNA, yes. That's how the testing companies attempt to market their "ethnicity" reports. There are genomic differences typical of broad population groups, small DNA segments that seem to remain intact over even thousands of years. But the existing science is imprecise and dependent upon the datasets used and the mathematical algorithms employed in the genotyping. And while whole-genome sequencing has been improving rapidly since 2015 in academia, it's still going to take some time, likely years, before a test at, say, 23andMe and AncestryDNA will agree on the same person's population admixture.
Circling back as promised to how autosomal DNA can be used to validate a biological link back to ol' Sir Thomas Morgan. And it's how every female genealogist has to work with yDNA.
The uniparental DNA, yDNA and mtDNA, don't undergo crossover and aren't combined with the other parent's DNA to form the zygote. They are passed down generation to generation entirely intact; the only changes that occur do so due to mutations. The mitochondrial DNA molecule is really too small, only 16,569 base pairs, to be of much use as positive genealogical evidence. It's great to disprove a matrilineal hypothesis, but there just aren't enough available nucleotide combinations that can mutate without harming the organism to give us enough differentiation. Millions of living people have identical mtDNA.
The Y-chromosome, on the other hand, has over 58 million base pairs and only twice the number of coding genes as the minuscule mitochondrion. All that other stuff is free (we think) to mutate and provide oodles of differentiations that can be mapped back hundreds of generations.
If a few of Sir Thomas Morgan's direct paternal descendants, in an unbroken chain, have carefully compiled their paper-trail genealogy and carefully triangulated their yDNA results, then someone whose autosomal DNA is a strong match to those men can use that as DNA evidence back to Sir Thomas. Mind you, this is not a WikiTree "confirmed with DNA" policy or practice, but it is a commonly used tool in genetic genealogy and why many of the FTDNA surname DNA projects have as many women members as men: they're managing the yDNA kits of male relatives.
Now that I've kept this incredibly brief, as promised....