You need more assumptions, in particular what are the ancestors doing? And what's the death pattern? I mean if you say that you have just one kid, that kid always has just one kid, and no-one dies before they reproduce, then lineage is forever. 1/
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You're assuming (at least one) SOMETHING that cuts the lineage short, but it's not clear from your tweet what that hidden assumption is. Is the point girls vs boys and surname? Is it a DISTRIBUTION of kids with mean of N, but not exactly N? Is it an assumption of early death? //
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Where do they live. Probably the environment has a big impact.
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I was thinking of mitochondrial eve, so for some people like that or Genghis Khan it would be a big outlier. And consider infant mortality rates in pre-history.
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I think the keyword you want is Galton-Watson process: https://en.wikipedia.org/wiki/Galton%E2%80%93Watson_process …
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This caused me to look up my surname which has apparently been going strong for 2700 years if you believe Chinese genealogies
https://en.wikipedia.org/wiki/Yuan_(surname) …
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Not the answer to your question, but given enough generations - you will eventually be the ancestor of all living humans, or none. (assuming there are no completely isolated populations)
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