Evening, Peter! Sorry for the belated reply. Got an unexpected offer to tour the reconstructed Apollo-era Mission Operations Control Room today before it opens to the public Monday. Awfully darned cool, with detail right down to, at the console stations, ashtrays with pipes sitting in them and 1969 steel RC Cola cans. Amazing we were even able to hit the moon; the Apollo Guidance Computer for Apollo 11, a big upgrade from the previous missions, had a massive 2k of memory and 32k of read-only data storage. Not a typo.
Thanks for including the graph you were referencing. Made things clearer. I do admit, though, that I went to bed last night wondering how we got off on this seeming tangent. Then an "ah hah!" moment after reading Frank's post. It was my failure to connect the dots; it wasn't a tangent at all.
Pointing to the Coop blog post initially threw me. I didn't immediately snap because, well, nobody's 6g-grandparents have ever taken a DNA test.
I believe what you've done, though, is make a strong case for rewriting the text that appears in the "DNA Connections" panel. But I'll close with that.
As we all know, it isn't dates and generations that drive what we see with autosomal DNA diversity and dilution. It's the meiosis that occurs at gametogenesis. For the very reason that WikiTree only shows "DNA Connections" out horizontally on the tree to our 3rd cousins--if we're sitting on their or our profile--whether or not an individual shares an identifiable DNA segment with a distant ancestor is moot, from the standpoint of using DNA for genealogy, unless a current or recent descendant in that biological line has taken a DNA test with whom results can be compared.
A same-distance descendant to your 6th great-grandparents would be your 7th cousin. At that point you aren't looking at Coop's numbers for an eight-generation separation. You're looking at a 16-generation separation because there have been 16 separate instances of conception. Technically, there have been 32 distinct instances of gametogenesis and genetic recombination, arriving at 16 different recombined, diploid genomes.
Coop's graph that you showed tracks only to 15 recombined genomes, and at that point he shows that any likelihood of having a shared "block" of DNA converges on zero.
Experimental, peer-reviewed results, as I linked to in the Henn study, are in general agreement. At that level, after 16 recombined genomes, the study predicts a 98.9% chance that 7th cousins will share no detectable atDNA whatsoever. The expected amount of DNA sharing is shown as a sex-averaged 0.22cM, which is equivalent to 0.0031% of the genome.
I won't dive into other factors, for example that Coop uses 33 as the sex-averaged number of times crossover occurs per conception event, which is about the lowest average of means I've seen (Harvard geneticist David Reich has used a mean of 45 crossovers for the oocyte and 26 for the spermatozoa for an average of 35.5; using the MLH1 DNA mismatch repair protein as a marker, Gruhn, et. al., arrived at a mean of 69.25 for females and 49.09 for males). Because, yeah, though just some quick and dirty math, I think Coop's numbers are quite reasonable.
Bringing me back to the "DNA Connections" panel. The first description under the "DNA Connections" panel reads: "It may be possible to confirm family relationships by comparing test results with [name] or other carriers of his ancestors' Y-chromosome or mitochondrial DNA." (Remove reference to the Y chromosome and change "him" to "her" for profiles of women.) Then in almost the same breath: "It is likely that these autosomal DNA test-takers will share DNA with [name]." Which is in reference to whatever profile we're viewing, even if someone born in the mid-18th century.
Aren't we implicitly conflating two very different things? We talk about uniparental DNA, yDNA and mtDNA, as a tool by which "it may be possible to confirm family relationships by comparing test results." Which is point-on relevant because genealogists are interested in compiling evidence. But then we shift gears and abandon the "it may be possible...by comparing" to make the relatively pointless statement that someone's 6th great-grandmother might have passed down some tiny segment of atDNA to a list of people who may also be descended from the same person...who was likely born between 1740 and 1800.
Why do we word it that way? I wonder if we could get a show of hands to determine how many WikiTreers believe those lists of autosomal test-takers are intended to provide clues as to whom they might want to research for a DNA match? (Or, a corollary, how many feel those lists actually denote a DNA match?)
I have no idea how the WikiTree algorithm is constructed or how/if it might be modified. We're careful to make 3rd cousins a working atDNA threshold for a couple of different things, "DNA Connections" and autosomal triangulation included, but then we show names under the "DNA Connections" panel that for autosomal DNA--by Coop's numbers, the Henn study, and others--would be as far removed as 7th cousins and 16 recombined genomes, and have a 99% chance of sharing zero detectable DNA. Is that more likely to be useful or misleading to the average WikiTreer? Shouldn't we at least change the explanatory text to make it unambiguously clear that distant relationships have a high probability of yielding no autosomal DNA evidence?
To quote Frank: "But still, there's a bit of absurdity in being told what modern day people 'probably share DNA with' my ancestor who died in 1901." Or in many cases, who died much earlier. A 40-year-old test taker's 6g-grandparents, assuming a conservative 25 years per generation, would have been born in 1804.
But I'm back on track now, thanks. I've matched up the exact text under the "DNA Connections" panel to reality.