Many thanks, Lewis, for expanding your initial post; a lot of good info there...and more food for thought for me if I ever get around to writing that two-parter "The Trouble with Triangulations." And thanks for contacting me directly because--you're correct--I didn't receive a notification since it wasn't a reply to my comment. Also, I hadn't connected that you were the same person I'd seen answering questions at physics.stackexchange.com. Makes me a little hesitant to ever bring up anything with math in it.
And that comment was one of my more...um...concise G2G posts. And I hope the brevity didn't get me into trouble because I want to be clear I wasn't stating that your conclusions were fallacious. We all have to apply the Genealogical Proof Standard (and I'll bet the term "proof" is kind of itchy for a theoretical physicist) on a case-by-case basis. How we choose to weight specific pieces of evidence, including DNA, is a personal decision. My comment was only a cautionary statement that the casual genealogist is safest, for now at least, in treating the concept and methodology of autosomal DNA triangulation to very distant cousins as potentially fallacious. As I said, the method has never been tested in a scientific environment, and there are numerous factors which imply it shouldn't be valid. Too, the WikiTree policy for triangulation was constructed in a vacuum--it is not a genetic genealogy consensus--and, perforce, it has to try to straddle the very difficult (and sometimes mutually exclusive) line between simplicity and accuracy.
And...I've once again run afoul of the G2G 12,000 character limit, so Part 2 will follow.
I'll try not to ramble, but I tend to "think out loud" as I type, and there are several thoughts I want jot down before I sleep on it and lose them. One crucial observation you made was "We all know that statistically speaking we (or those of us sharing European heritage) all probably descend from Charlemange (about 36 generations back)."
Our genetic family trees and our on-paper versions will almost never look the same, even if we believe we have accounted for pedigree collapse. Our genealogical version might better be termed a "web," as you said, but the genetic version will be closer to a bowl of spaghetti.
It's tossed around frequently that all humans are over 99% genetically identical. While that doesn't tell the whole story, it does do a bit of level-setting regarding the spaghetti bowl. Homo sapiens has no sub-speciation and, biologically speaking, no races (which taxonomically would require a sub-species). Neanderthal DNA makes up roughly 1.7% and 1.8% percent of European and Asian genomes, respectively, and up until a year ago we thought that modern sub-Saharan African populations contained only about 0.02% Neanderthal DNA. But a study published in Cell (Chen et al., February 2020) showed that people with African ancestry actually have closer to 0.5% Neanderthal contribution, due not to direct contact but to return migrations of modern humans who went to Europe, interbred with Neanderthals, and then came back to Africa. So in that thumbnail summary, we are all pretty much as genetically similar to Neanderthals as we are different from each other.
But that 99% figure is derived in much the same way as is the fact that I'm 41% genetically the same as a banana. All multicellular life on earth has genetic similarities...for instance, that we all have cells and that cellular structure and function is coded in our DNA. We still don't know how much--or exactly which--of our DNA is free to mutate without odd phenotypic or dangerous health results, but the current thinking is that somewhere around 20 to 25 million autosomal SNPs can distinguish one human from another, and around 5 million from within the same continental-level population. To qualify as a SNP, it's generally accepted that the polymorphism needs to be common enough to occur in at least 1% of the population. A few of the problems with our microarray testing and interpretation in a moment, but since--with the somewhat rare exceptions of ancient remains testing, a la our friends the Neanderthals--we can evaluate our genetic connectedness for genealogy only with living (or recently living) test takers, we have to frame those 20-25 million SNPs in light of a global population of 7.8 billion.
I believe one of the difficulties inherent in genetic genealogy is that we have many years of genealogical data to consider, and all of it is packaged for our perception as distinct, e.g., "And unto Enoch was born Irad; and Irad begat Mehujael; and Mehujael begat Methusael; and Methusael begat Lamech." A representation of singular, threadlike lineages that remain discrete and insular as we march across time.
Jokes about jumping into the gene pool for a swim, though, actually have merit. Stan Lee's imagination and the X-Men comic books aside, humans don't fabricate blocks of new DNA. Among our 4.6 billion nucleic acids are not infrequent point mutations, but the mutation options are quaternary: the choices are only adenine, cytosine, guanine, thymine, and they can pair-up only as adenine/thymine and cytosine/guanine, so the flexibility is pretty limited. And to go to the next generation these can't be the result of any of the many thousands of DNA repair operations or millions of DNA duplications our body performs daily during mitosis...they have to be mutations that enter the germ cells.
A summary that population and evolutionary geneticist Graham Coop offers is that "nearly everyone in Europe is related to nearly everyone else over the past 1000 years, and likely everyone in the world is related over the past ~3000 years." When we move beyond recent relationships, our tests fairly quickly begin to show only a single shared segment of autosomal DNA...at least a segment of meaningful size and I, personally, don't consider 7cM meaningful as a single, standalone segment. More in a sec, but thanks to work by Tim Janzen and John Walden we know that SNP chip-reported 7cM segments survive traditional phasing only 42% of the time, meaning that 58% of the time they will be false because they appear in neither parent.
Multiple segments of a nominal size are indicative of genealogical relatedness, but single small segments should be taken with a few grains of salt. Amy Williams's research at Cornell shows, when considering segments equal to or greater than 7cM, that we seldom see more than one shared segment among 5th cousins, and almost never among 6th cousins or greater.
Coop writes, "A single example of a block of around this length [10cm] is not a particularly meaningful statement about genealogical relationship between two people..." From his published work with Peter Ralph, he concluded that "the typical age of a 10cM block shared by two individuals from the United Kingdom is between 32 and 52 generations (depending on the inferred distribution used)." And his simulations suggest that, by 12 generations back, there is a better than 80% chance that we inherit no measurable DNA from any specific ancestor.
