Chapter 13 (lucky number 13!), subhead "Cousinhood of Man", pages 344+. I'm going to start my quotation on page 345 and will edit out what I view as superfluous language where possible (this guy goes on and on and on).
"In fact, no human being (of any race) can be less closely related to any other human than approximately 50th cousin, and most of us (no matter what color our neighbors) are a lot closer."
Notice how _strong_ that is. "Everyone" means "everyone."
"Indeed this low magnitude for the lineal compass of mankind is accepted by the leading geneticists I have consulted (from J.B.S. Haldane to Theodosius Dobzhansky to Sir Julian Huxley), and it means simply that the family trees of all of us, of whatever origin or trait, must meet and merge into one genetic tree of all humanity by the time they have spread into our ancestries for about fifty generations."
Notice how _clear_ that is. This isn't based on "amount of genetic material". This is a genealogical argument. "Cousin" means "cousin."
"This is not a particularly abstruse fact for simple arithmetic demonstrates that, if we double the number of our ancestors for each generation as we reckon backward..." We all know where that's going. "if we assume 25 years to a generation."
So we are in agreement on the length of a generation as well.
"But you cannot reasonably go on doubling your ancestors for more than a very few generations into the past because inevitably the same ancestor will appear on both your father's and your mother's sides of your family tree..."
He has pedigree collapse.
"These populations of course are the fertile portions of past societies..." Not crucial, but good that he understands this.
"If people all over the earth always married at random, choosing their mates by lot regardless of what country, race, class, or religion they came from, it would take something like 35 to 40 generations for all their family trees thus to merge completely in common ancestors, the time beyond 30 generations needed because of the aforementioned slowdown in backward ancestral multiplication, a rate which progressively decreases from two to one and ultimately even below one when the family trees begin to encompass all humankind, whose numbers were of course smaller in earlier centuries."
He has the shape of the tree right, and understands the basis for the mathematical argument.
"But obviously people do not mate at random,"
Long digression about endogamy and exogamy.
"Weighing the marriage customs of Earth, then, as annotated in reports from Westermarck's classic History of Human Marriage to the latest sexological research, it appears that the rules of endogamy have generally been enforced less rigorously than the rules of exogamy."
I want it to be true, and with a complex handwave, I will pretend it is. Also, I won't mention geography or technology, because then it would be obvious that I am wrong. Then a paragraph about "exotic consort" and not marrying one's sister, ending with, "In sum, it would seem a reasonable estimate that, while geographical factors in historic times must have held back the gene flow between a man and mankind by perhaps ten generations, other factors have more or less canceled out to keep human kinship confined to about the fiftieth cousinhood range."
Okay, he concedes the geographical issue, and asks to be let off with a ten generation (250 year) fine.
"It is practically impossible to set limits on where any man's family connections may reach upon the habitable earth." If I assert it, maybe that will make it true. "And the very proliferation and complexity of his relations is incomprehensible to most of us" -- if you don't agree with my argument, it's because you don't understand it. "for, even if you assume only two children to a couple, as I have done in the accompanying simplified diagram (a quota actually too low to permit humanity to survive), everyone on the average must have 4 first cousins ..." A retread of the previous numerical argument: That's A Big Number/A Job Lot of People!
"This is not to claim that there has been more than a trickle of intercontinental travel in bygone milleniums in which Celts, Phoenicians, Vikings and Polynesians are now known to have sailed to America, and Papuans, Melanesians, Malays and Negritos to have trafficked in Australia -- but, in the nature of things, a trickle is all it takes to establish close cousinhoods."
It's hard to tell just what that means, but I _think_ it means that he thinks that Celts, Phoenicians, etc. or some subset thereof left lineage in the Americas that is still around today. I doubt you could get anyone to sign on for that idea in 2011, but I'd be interested in links to current, active debate in scientific journals. I am _not_ interested in a bunch of speculation by "independent scholars". I'm capable of speculation.
"It is scarcely possible, I admit, for the most perspicacious of minds to visualize cause and effect reliably over thousands of years and tens of thousands of miles... But it is demonstrable nonetheless that a single indirect genetic contact between Africa and Asia in a thousand years can make every African closer than fiftieth cousin to every Chinese. Surprisingly, this may happen without any natives of either continent doing any particular traveling at all, but simply in consequence of the wanderings of nomads in intermediate territory. No single nomad would have to travel more than two or three hundred miles in his lifetime either, a meager enough total for a carefree tent-dwelling hersdman. Yet inevitably every generation produces at least a few would-be Marco Polos, mettlesome young bloods who keep going for thousands of miles, zestfully overcoming every hazard, swimming rivers, running borders, fighting brigands, making off with girls as they find them -- and obviously it needs only a couple of brothers of this stamp to make first cousins of their own children on opposite sides of the earth -- first cousins who, like as not, do not even know of each other's existence. If you can accept this fact"
BIG if. You not only need to accept the existence of a couple brothers -- they have to have done that over a thousand years ago. And not a _lot_ over a thousand years ago, or you get too far above about 50th cousin.
"that an African family in the Sudan, for example, can be first cousins of a Chinese family in Hangchow" in around 1000 A.D. "without any Africans leaving Africa or any Chinese leaving China, then it shouldn't be too much for you to understand that there must be thousands of relationships at least as close as fifth cousin at comparable distances and that the tremendous genetic circumfusion [sic] of fiftieth cousinhood cannot help but take in the bulk of mankind."
Interestingly, while he is deploying the common, but deplorable, rhetorical strategy of repeating himself in hopes _that_ will convince the reader, he is _simultaneously_ backing away from his initial thesis: now it is "bulk" not "everyone".
"To see how such interrelationships work, look at the illustration (next page), in which an old nomad living in Persia has eight sons, who, one after the other, set off to seek their fortunes, each in a different direction. The son who goes to China predictably marries a Chinese girl and has half-Chinese children who are first cousins of the half-black offspring of the son who went to Africa and married a black girl on the upper Nile, all of this new generation of course being grandchildren of the old nomad of Persia. Later the African son's descendants naturally increase in number with each succeeding generations until they include practically everyone in his tribe along about the thirteenth generation (even assuming only two children per family) by when his genes must inevitably have spread (through raids, wars, migrations and resulting infractions of endogamic law) to various other tribes, whose members in turn all become descendants of the old nomad by about the twenty-fifth generation. And after that his spreading waves of progeny must irregularly continue to advance tribe by tribe all over Africa and beyond, relentlessly filling up each endogamous pocket until by the fiftieth generation it can hardly help but include everyone."
You know, if people had the same level of pile-improbability-upon-impossibility when they were doing disaster planning, I would be okay with nuclear power. We _should_ be planning on the unlikely taken to a big exponent. But we never do. Except when we _want_ it to happen.
""How do you know," I heard you ask, "that there were actually enough raids, wars and migrations in the past twelve hundred and fifty years to carry the old nomad's genes from tribe to tribe at the rate you claim?""
By putting up a straw man, he distracts us from the real question: how do we know the pregnancy was carried to term and the child made it to reproductive age? Infanticide, abortion, and killing the rape victim are not exactly uncommon in the time period he's looking at, and those are _really_ effective way to deal with violations of reproductive rules.
His answer, surprisingly, is really bad!
""How do you know," I reply, "that flowers in the garden will be cross-fertilized by the bees as the bees collect their food?"" Dude, wrong counter-question in a world worried about massive-bee dieoffs. 'Course, he couldn't have anticipated _that_ in the 1970s.
"The two questions are analogous, both having to do with probability in genetic combinations on a broad statistical scale. And they are close to the well-known mathematical laws of rolling dice and the roulette tables of Las Vegas..." Essentially, he anticipates the simulation work done in the 2004 paper in Nature by Rohde et al (and Rohde et al implemented the simulation, but produces results involving MRCA which related to the 50th cousin hypothesis via a strict inequality, thus not completely disproving the hypothesis but providing no support for it, either).
Okay, so he's waved math at people. Is that it? Are we done? Nope.
"Of course a few snobbish people will protest,"
Now we're _insulting_ people who disagree with this argument!!!
"But my family is an exception. We traced our ancestry back eleven hundred years and they all came from an isolated community on the Isle of Man where they spoke Manx and never had any marriage contact with the outside world.
"Statements of that sort cannot possibly stand up to close scrutiny. Genealogists, I admit, will often trace a prominent family name back for hundreds of years -- which involves only the relatively simple procedure of following one male line of descent."
Hey! That's doing it the wrong way!
"But the average person has approximately a million ancestors with some thousand names just in the last 500 years and it is patently impossible to trace any large portion of them. Even such a well-publicized lineage as the Mayflower descendants from Plymouth, Massachusetts, can hardly begin to track down their relatives of 350 years, and a little knowledge of early Yankee seamanship and fecundity in the tea and slave ports of Asia and Africa, plus mathematics, will show that their ranks probably now include more than a million Chinese in China, a comparable number of Hindus in India and blacks in Africa -- not to mention several million Americans and Europeans."
Again, a _whole_ lot of optimism about probable lineage continuity when starting with, say, a prostitute in a seaport. Anyone who does genealogy and includes brothers and sisters sees how _many_ lines never make it down to the present day.
"Even if at some period there really was an isolated, highly inbred clan on the Isle of Man, could anyone possibly prove it had maintained complete sexual segregation for even a hundred years?" Yes. I keep telling you who it was, too. "Any boy who escaped to the mainland or adventurer who arrived from anywhere might have established a relationship between it and the rest of the world." That lineage has to make it down to today or it does not matter.
"Is it not likely that some such incidents took place in every generation?" Not just not likely: totally impossible for such incidents to take place in many places for many generations. And you're not allowed to use fiction like the offspring of Vikings or Phoenicians or Celts in America, either. That's as bad as making up extra children of someone to bag the Mayflower.
"To be sure, the traditionally proud family archives..." okay, so again, if you're arguing with him, it's because you are creepily bigoted.
"There is probably more than enough interracial gene flow right inside your own country to make you a close cousin of practically anybody imaginable." Well, except for my much beloved next door neighbor. And one of my favorite people at preschool pickup. I could go on.
"Dr. N.C. Botha, the immunologist who worked with Dr. Christiaan Barnard's heart transplant team in South Africa, calculated that the "white" people of Dutch extraction there have an average of 7 percent "nonwhite" genes, while the two million so-called colored people have 34 percent "white" genes." Nice. Pick a contiguous, well-populated area. Fish. Barrel. More of the same in the paragraph.
With the full argument laid out, including informal sourcing (I chatted up some geneticists over cocktails and they agreed with me so I would shut up and go away, or possibly were too drunk to figure the math at the time <-- my interpretation), it is completely obvious what a piece of crap this 50th cousin thing is.
To be clear: YES we are all related. NO we are not all 50th cousins or closer. At this point in time, it is actually quite creepy to argue that Yankee traders spread their genetic material all over Asia and Africa, even if the goal of the argument is the cousinhood of "Man".