Ancestor's Tale
I've been reading Richard Dawkins's book The Ancestor's Tale and one particular message (so far) stands out. Because inheritance occurs in discrete genes and because genes get shuffled, the ancestral path for different bits of DNA is different. At a particular allele, (non-identical) siblings might each be more closely related to separate chimpanzee individuals and the common ancestors of both humans and chimpanzees than they are to each other. Blood types seem to be an example. I find this to profoundly non-intuitive, but quite undeniable.
Overall, of course, the siblings share many more genes with each other than with chimps, but that is in some sense an average effect. Because chimps and humans separated at least 6 million years ago, the separate blood types (and their genes) must have persisted simultaneously through all the 400,000 or so generations in between - there hasn't likely been gene flow in the interim.
Of the 2^400,000 ancestral slots from six-million years ago (all filled by at most a few million individuals), different genes are almost equally likely to come from any of them. Most of these ancestors probably don't contribute any DNA to the individual alive today, and most of the rest will contribute only one gene or a few. Of course those few million individuals were all genetically very much alike, so you still have nearly as much in common with those that provided you no DNA as those whod did provide your DNA.
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