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Have there ever been two human siblings who were 75% or more genetically related?

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Yes.

A case of semi-identical twins was reported in 2006. These twins share 100% of their maternal alleles and 50% for their paternal alleles. It's hypothesized this arose from a double fertilization of the egg, followed by the formation of two 46XX/46XY twins.

Another hypothesized mechanism of twinning involves the fertilization of a polar body (essentially when the egg divides prior to fertilization; polar bodies are a normal part of meiosis, but aren't usually able to b fertilized). This would give the twins the same maternal chromosomes, but different paternal chromosomes. However, this type of twinning has not yet been observed.

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Though your question doesn't make sense to me, I believe the answer is Yes. See the following paper about "sesquizygotic" twins:

Gabbett, M.T., Laporte, J., Sekar, R., et al. 2019. Molecular support for heterogonesis resulting in sesquizygotic twinning. New England Journal of Medicine, 380(9):842-849.

Sesquizygotic multiple pregnancy is an exceptional intermediate between monozygotic and dizygotic twinning. We report a monochorionic twin pregnancy with fetal sex discordance. Genotyping of amniotic fluid from each sac showed that the twins were maternally identical but chimerically shared 78% of their paternal genome, which makes them genetically in between monozygotic and dizygotic; they are sesquizygotic. We observed no evidence of sesquizygosis in 968 dizygotic twin pairs whom we screened by means of pangenome single-nucleotide polymorphism genotyping. Data from published repositories also show that sesquizygosis is a rare event. Detailed genotyping implicates chimerism arising at the juncture of zygotic division, termed heterogonesis. opens in new tab, as the likely initial step in the causation of sesquizygosis.

It's possible this could have resulted from two sperms fertilizing one egg!

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Probably, yes.

According to this paper, siblings have a mean of 0.50146 relatedness with a standard deviation of 0.03761. This means that this is an event which is 0.25/0.03761 = 6.6471683063 standard deviations above the mean, a near-7-sigma event. This occurs once in 66,937,665,852 (67 billion) events. However, there have been around 100 billion human births. This means that yes, there have probably been humans siblings who are closer to twins than normal siblings.

(This assumes there is no kurtosis causing platykurtic behavior.)

There is a 78% chance that this has happened at least once for every 100 billion human siblings pairs, or about about 1.5 times in human history assuming there have been about 100 billion unique sibling pairings.

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    $\begingroup$ Your source belongs in the question, as evidence of an attempt to answer your question is required on this site. $\endgroup$ Feb 10 at 22:22
  • $\begingroup$ @anongoodnurse Where is that rule written for this site? (Genuine question, I can't find it.) $\endgroup$
    – BigMistake
    Feb 10 at 23:57
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    $\begingroup$ biology.stackexchange.com/help/how-to-ask $\endgroup$
    – Bryan Krause
    Feb 11 at 0:21
  • $\begingroup$ There's also this: https://biology.stackexchange.com/help/self-answer $\endgroup$ Feb 12 at 18:42
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    $\begingroup$ I think the logic needs to be expanded here. The one-in-67-billion event is between two siblings, not between all humans. You'd need to account for the distribution of sibling counts (e.g. an only child doesn't count, two siblings only count as one pair, but four siblings create six pairs). $\endgroup$ Feb 12 at 18:52

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