I’ve written about this before, over on my genealogy blog, but it’s only tangentially related to genealogy. It’s not really recreational mathematics, either, but I want to expand on it somewhere, and since it involves a logical proof, this seems like the least silly place to choose.
So: All humans descend from a common ancestor. Or so many people believe. Literalist believers in the Old Testament would say Adam and Eve are common ancestors of us all. Believers in evolution go further and believe all life on Earth descends from a common ancestor. I’m in the latter group.
When did the most recent common ancestor (MRCA) of all humans live? Simulations suggest it was more recently than you might expect: 2000 to 5000 years ago. (It’s been argued that all persons of European descent share a common ancestor only about 1000 years ago, and genetic analysis [paper, FAQ] seems to support that.) Furthermore, going only a few thousand more years back, you arrive at a time when literally every person then alive fell into one of two categories: Those who are ancestors of no one alive today, and those who are ancestors of everyone alive today. I don’t know if there’s a term for that state, so I’ll make one up: Universal common ancestry (UCA). Understand these are probabilistic claims; it would certainly be possible that 20,000 years ago there were people whose living descendants are some but not all of us. But the probability of such a thing is so small it is almost indistinguishable from zero: Something that improbable really cannot be expected to happen even once in the history of the universe. And even if it did, another few thousand years back a non-UCA state would be even more unlikely than that. The probability of UCA back then, and any time previous to that, is absolute certainty for all practical purposes.
Of course this doesn’t just apply to humans: We can talk about the MRCA of all chimpanzees alive today, or all hominins (humans and chimpanzees), or all ruby throated hummingbirds, or whatever.
Now, here’s the weird thing: Long ago, 5 million years or more, amongst members of the species Nakalipithecus or something like it, there lived an individual (call them Nico) who had (at least) two offspring, Chris and Harley. They were Nakalipithecus (or whatever) too, of course, and they mated with other Nakalipithecus and had Nakalipithecus children, who had more Nakalipithecus children, who had … well, you get it. But here’s the thing: All of Chris’s living descendants are chimpanzees. All of Harley’s are human.
That might surprise you. And think how surprised Chris and Harley would be.
But it’s true, and it’s provable (in, again, a certain-for-all-practical-purposes sense).
Nico, you see, was the MRCA of all living hominins. Nico has all living humans and all living chimps as their descendants, and being they’re the most recent common ancestor, no one in subsequent generations can make the same claim.
Now of course much more recent individuals are common ancestors of all living humans (and no chimps), or of all living chimps (and no humans). How about ancestors of all living humans and some living chimps? Or vice versa? But no. We have UCA for humans anytime before several thousand years ago, and I’m sure chimp UCA must be even more recent than that. More than a few thousand years ago, let alone a few million, anyone who was an ancestor of some living chimps was an ancestor of all living chimps. And likewise humans, so any individual with any living humans and any living chimps in their descendants would have to be a common ancestor to all hominins. And Nico was the MRCA, so anyone born after Nico would have to have no living descendants, or humans but no chimps, or chimps but no humans.
We know Nico must have had two or more offspring. If they had only one, then it would have been a common ancestor of all hominins and Nico would not be the MRCA. One of them was Chris, and the other was Harley… and they were born after Nico (duh). The argument above applies to anyone born after Nico, and that includes Chris and Harley. One had to be an ancestor of all living chimps (but no living humans) — that’s Chris — and the other the ancestor of all living humans (but no living chimps) — that’s Harley.
A scenario in which that makes sense is one like this. Seven million years ago, a group of Nakalipithecus woke up one morning, checked Facebook, went to work, or went out to play, or whatever, not realizing that fifty miles away there was a great huge lake held back by a natural dam which had been slowly eroding. That day the dam broke. There was an enormous flood, many of the Nakalipithecus died, and the ones that survived found themselves on two sides of a new, permanent body of water. And the topography was such that none of them were able to cross the water or go around it, so the survivors on one side never again encountered the survivors on the other.
All right, this is not a particularly likely scenario, but it’s a thought experiment, okay?
Nico, alas, died in the flood, but not before saving the life of Chris. Harley, meanwhile, was swept off and ended up on the other side of the water. Within a few thousand years all the Nakalipithecus on one side were descendants of Chris (but not Harley) and all on the other side were descendants of Harley (but not Chris). The two groups evolved apart and eventually gave rise to chimps on one side, humans on the other.
Granted, speciation doesn’t usually work like that. Much of the time geographical separation is a factor in speciation, but not necessarily all the time, and in any case the geographic separation usually isn’t instantaneous. Mountains rise slowly, rivers change course over centuries, and so on.
But it doesn’t matter whether the two groups are sundered in hours or eons. Or even if they are geographically sundered at all. The point is, for whatever reason, two groups evolve away from one another. At the start they are one species and they interbreed frequently, but the frequency of that decreases more and more. And it may decrease over a very long time period, but: There’s a single, momentary last time. A last time a member of one of the groups breeds with a member of the other group. And not long before that, a last time one individual breeds with a member of one group while their sibling breeds with a member of the other, and they have fertile offspring leading to descendants alive today. Their parent is our common ancestor, and the common ancestor of all chimps too. Their children, though, may be your ancestor, may have been Washoe’s, but are not both.