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Consider this answer to an interesting question. It's not possible to prove completely that someone is the descendant of someone else, there's always a nonzero probability that the results are a coincidence.

How confident can you get that genome T is the descendant of four unrelated grandparents? How would you tell?

Restrictions: You're not allowed to sequence all other humans and rule out other possible parents. Time traveller is has the normal number of chromosomes. You can test people's parents if that would help.

The maternal grandmother would share mitochondrial DNA, and the paternal grandfather would share the Y-chromosome, or the paternal grandparents would have one X chromosome between them. I'm not an expert on SNP accumulation but would there be enough information to conclude this person was from the future? Would there be too much mutation in two generations to pick out the relationships under it?

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This should be pretty easy to demonstrate. Over the two generations, there would be 200-300 mutations in the entire genome of 3.3*109 base pairs, i.e. about 1*10-7 of the base pairs should be altered. If Time Traveler is male, for example, imply sequencing the Y chromosome and mitochrondrial DNA and comparing to the paternal grandfather and maternal grandmother should be adequate to decisively validate the claim.

If this isn't sufficiently satisflying could then move on to the autosomes and note that only about 200-300 base pairs max should be different from the union of the four grandparental genomes. The chances of this occurring given random set of four unrelated genomes will be vanishingly small.

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