Population Genetics has some real gems. Today we calculated the specific probability that a member of an older generation is your ancestor. It turns out that as you go back in time, this number converges to about 80%!
Even cooler, we know the rate at which this happens. If you go back in time at a log rate (so it takes a looooong time) there exists some person in that population who is the ancestor of everybody on Earth today! Moreover, at rate 1.77log_2N (even slower) if you can pick out any member of that ancient generation who had at least one progeny -- a guy who managed to have just one kid before he died -- that guy is also your ancestor. And everybody else's, too.
Another gem (this one not so eye-opening, just funny): the Moran model states that a population evolves by, every once in a while, picking out two individuals.
What happens then? One dies, and the other splits in two.
When our lecturer was tracing back genealogies according to this model, she commented, regarding the guys that just got copied over and over and over: "oh, this guy had a boring life."
Still, you should have seen the other guy.
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