Dan asked in Science & MathematicsMathematics · 1 month ago

# What number cousin is the cut off between related and not related?

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• 1 month ago

There is no special cutoff. You could be 1000th cousin to somebody; you are still related. But as a general rule, I would consider 5th cousins to be not related, in the sense that they share the same genes (on average) as any other person of the same general genetic group.

• 1 month ago

Humans have 3,000,000,000 base pairs in their DNA and 99.5% of that is common to everyone, meaning that 0.5% is what makes you the individual human being that you are.

3 * 10^9 * 0.5/100 =>

1.5 * 10^7 =>

150,000,000

Full-blooded siblings (excluding identical siblings) share about half of that 150,000,000.  1st cousins are at 12.5%, 2nd cousins are at 3.125%, 3rd cousins are at 0.78125%, and the numbers keep dropping by a factor of 4.  In general, nth cousins are related by a 2 * 2^(-2 * (n + 1)) factor.

So, it could be said that when 2 people share only the basic DNA that is common to all humans, then they are as unrelated as possible, even if it can be demonstrated that they have a relatively recent common ancestry.

There should be some notes here before we continue

1) Males who share a common patrilineal line will have DNA in the Y-chromosome which is pretty much identical.  So my sons and the sons of my male cousin who is the son of my father's brother will have y-chromosomal DNA which is virtually identical.  This can go on for a very long time and evidence of relatedness will persist, even when all other DNA is completely different.

2) The same thing happens with people who share a common matrilineal line.  The children of my mother's sisters will have mtDNA that is almost identical to mine.  Any children that the daughters of my mother's sisters have will also have almost identical mtDNA.  Similar to point #1, relatedness will be demonstrable even when everything else is different.

3) This model assumes no inbreeding.  Once you start inbreeding, even at the distance of 3rd or 4th cousins, the coefficient of relationship increases.  So the number we get can be seen as a lower limit for your question.

2 * 2^(-2 * (n + 1)) * 150,000,000 < 1

When nth cousins share less than 1 base pair of uncommon DNA, then they are as unrelated as can be.

300,000,000 * 2^(-2 * (n + 1)) < 1

300,000,000 < 2^(2 * (n + 1))

ln(300,000,000) < 2 * (n + 1) * ln(2)

ln(300,000,000) / ln(4) < n + 1

n > ln(300,000,000) / ln(4)  -  1

n > 13.080193629910027482208147189931...

Round up to 14, since n = 13 will give you at least 1 base pair showing common relatedness.

So, at the rank of 14th cousins, you're just as related to a person as you are to someone with a completely different ancestry.

• 1 month ago

There is no cutoff. If You have a bloodline then you are still related.

Marriage laws vary by state.

• 1 month ago

Maybe third or fourth I would say