G2G: Genetics Mathematics Inbreeding

Question

In a closed community, there are 128 children, unrelated biologically - 64 boys, 64 girls - who will marry and have children. Assume each couple will have 2 boys and 2 girls. For the next few generations, no one will marry a spouse that is biologically related.

In what generation will it become necessary for that generation to marry a biologically related spouse as all are related.

Comments

Each of their 5*great-grandchildren can have 128 5*great-grandparents who are all different - the original 128 people.  The next generation will have 256 6*great-grandparent slots to fill from the original 128 people, so they can't be all different.

Interestingly, it makes no difference how many children they all have.

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Great answer RJ !

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Great answer RJ!   And you didn't even have to use factorials.

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Thank you ! Working on my novel RAPHAEL DESCENDING and these children are the only humans left on planet Earth.

Answer 1

I agree with R J's analysis, but there is another genetic diversity consideration as well

Each child only inherits half their parents' DNA. Two children will get a random mix each and by chance there will be an overlap. I think two children on average will get 75% of their parents' DNA between them. More importantly 25% on average is lost forever.

So although the later generations will get DNA from every founder, a lot of the founders' diversity will have been lost.

If possible the founders should have four or more children each and expand the population as much as possible which would get 93%+ of the DNA passed on.

Tim

Comments

Just wondering, if 100% of the DNA was passed on, would there be evolution?

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I'm pretty good with mathematics, but mostly ignorant of genetics, so please take this from where it comes ... I don't think it impacts evolution at all.  What is relevant to evolution is mutations, which I would also expect to impact genetics.

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Aren't mutations caused by differences in DNA?

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The permanent alteration in the DNA sequence that makes up a gene is a mutation.   It can happen in many ways and at different phases of a cell's life.

One gene mutation that's obvious in my family occurred with my gg grandmother..... who passed a mutated gene to her children, this mutation caused muscular dystrophy.   (This gene hadn't appeared in any male ancestors of my gg grandmother...... before the 1950s males with muscular dystrophy usually died before they were twenty.)  

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Michael, I think it's the other way around - mutations are changes to 1 or more genes that can occur to a person who started out with the set of genes that was passed from his/her ancestors.  When such a change happens to an egg or sperm cell, that is what changes DNA - permanently, as Peggy said.  It then gets passed to future generations.

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Evolution is simply changes in allele frequencies in a population over time.  (alleles = different variants of a gene)  In a small population, the odds of losing alleles due to random chance are increased, especially if the allele was at low frequency to begin with.  This phenomenon is called genetic drift and is one of the four basic mechanisms of evolutionary change.  (The other three are mutation, natural selection, and gene flow.)  So it's very likely that a population like the one described above would evolve, just not in the way most people usually think of "evolution."