The Mathematics of Genetic Ghosts

A flow chart showing how the chromosomes of any man, even the son of God, become systematically divided so that by generation 7, there is virtually no randomized expectation that a person has a Chromosome from Adam, might help dramatize the distinction.

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To be clear, it is at about 20 generations before most our ancestors become genetic ghosts, not seven.

And yes, we have diagrams =).

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@swamidass

I use Seven only because if you divide 64 in half, and then divide the result in half, and so on … you no longer have a whole chromosome after 7 divisions.

If you have diagrams… it is practically malpractice not to use them. Maybe there is a folder where we can put images of diagrams, flow charts and schematics?

Frequently I’ve spent an hour looking for just the right chart … with no consideration of any narrative that might or could go with it!

I love that you are working out the math. That is really phenomenal.

You are almost right, but missed a key process: recombination.

Recombination cuts Chromosomes into pieces, creating 30 new ones each generation. So if you go back seven generations, you have 22 + 30 * 7 pieces, or 232, which means you have about 232 / 64 = 3.6 pieces from each parent.

How many at 20 generations?

There are about 50*20 = 1000 pieces, (dropping the 22 for brevity), and 2^{20} = 1048576 ancestors. So that gives you 1000 / 1048576 = 0.09\% chance of inheriting any “pieces” of DNA from a particular ancestor. Of course, this assumes zero interbreeding, which is a bit pessimistic. The true amount will be somewhat higher.

Still, it is that type of math that leads us to say, however, that most our genealogical ancestors leave us no DNA. They are genetic ghosts. The literature reported number is 15 to 20 generations, which is just several centuries.

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One of the best ones is this one from Dr. Coop. Where did your genetic ancestors come from? | gcbias. The Coop blog post is a must read. He has a beautiful simulation which illustrates how genetic ancestry is not genealogical in a GIF animation:

Have fun with that one.

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If you are curious how interbreeding affects things, it reduces the base of the exponent to about 1.8 (if I remember right). So…

How many at 20 generations? There are about 50 g / 1.8^g = 0.78\% chance of inheriting any “pieces” of DNA from a particular ancestor a particular ancestor at 20 generations in the past. Not much different than 0.09\%, for no interbreeding. Cool right? I’d have to look up that 1.8 to verify, but as long as we are above 1.3 or so, this is going to be the result.

Oh wow! It’s ANIMATED! Fantastic !!! Stupendous!

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To plug in the numbers for generation 7, 50*7 / 1.8^7 > 100\%, which means most our ancestors at 7 generations give us DNA.

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@swamidass

Well, I had heard about Recombination, but was not competent to explain it.
Lab works confirms that the average fertilized ovum INCLUDES up to 300 new recombinations?
Really?! Man, that’s a crap load (< scientific jargon)!!!

Are these 300 recombinant fragments measured in terms of genes?.. so 300 genes get moved around with each fertilization?

Or are some of these pieces bigger than just one gene?

Yup. Its pretty cool. Well not so much. I made an error there. It is actually about 50 per generation, give or take. [Sorry about earlier error that said 300, will fix that in back posts]

Cuts them up, and pasts them back together.

There are about 20,000 genes, so that is groups of about 1/50 th that many genes in each recombination block.

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