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# Polygamy

## Question

Say there is a new society of ten unrelated people.  Each time a person is born into their society, that person immediately becomes an adult while another random same-gender adult dies at the other's birth.  These individuals live for four days, providing them four opportunities to mate before expiring at the end of the fourth day.  Each male randomly mates with another female.  In order to conceive one must mate with another who is less than 10% related to themselves.  What is the probability this population will sustain itself for a week?

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Just a request for clarification or correction to the following assumptions and implications.
An assumption is that the ten unrelated people at the beginning of the problem are five males and five females.
An assumption is that the resultant birthling, if any, enters society immediately the day following the mating, with equal chances of being involved in mating as those already existing in the society.
And, and an assumption is made that conception occurs automatically where the two parents are at least 10% related.
An implication is that each adult only performs the ritual of mating no more than once per day, and due to there being a possibility a gender surplus or shortage respective of the other gender, not every adult will mate on a given day.
An implication is that incestous matings can occur, though the result of that mating is no offspring.

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This is an intriguing problem that i find myself mulling over in my mind,

I have the same questions that DejMar raises, plus some others.

1. Does every male mate mate exactly once every day with a random female?
2. Do the original ten citizens live for exactly 4 days?
3. How is percentage relationship reckoned?
For example: siblings=100%; cousins=50%; 2nd cousins=25%; father-daughter=50%? Just guessing here.
4. Does "sustain" require only that after 7 days at least one citizen is living?

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2 hours ago, bonanova said:

This is an intriguing problem that i find myself mulling over in my mind,

I have the same questions that DejMar raises, plus some others.

1. Does every male mate mate exactly once every day with a random female?
2. Do the original ten citizens live for exactly 4 days?
3. How is percentage relationship reckoned?
For example: siblings=100%; cousins=50%; 2nd cousins=25%; father-daughter=50%? Just guessing here.
4. Does "sustain" require only that after 7 days at least one citizen is living?

I have the same questions that DejMar raises, plus some others.

1. Does every male mate mate exactly once every day with a random female?  - yes, everyone mates at most once a day.
2. Do the original ten citizens live for exactly 4 days? yes. they were all miraculously born on the same day and none of them related.
3. How is percentage relationship reckoned? Common parents account for 25%, common grandparents account for 12.5%, common great grandparents 6.25% and so on.
4. Does "sustain" require only that after 7 days at least one citizen is living? Yes. Will this society at least survive a week.
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I have the same questions that DejMar raises, plus some others.

1. Does every male mate mate exactly once every day with a random female?  - yes, everyone mates at most once a day.
2. Do the original ten citizens live for exactly 4 days? yes. they were all miraculously born on the same day and none of them related.
3. How is percentage relationship reckoned? Common parents account for 25%, common grandparents account for 12.5%, common great grandparents 6.25% and so on.
4. Does "sustain" require only that after 7 days at least one citizen is living? Yes. Will this society at least survive a week.

If mating is random, a male (female) could mate with their mother (father). How is that % calculated? Or (a) it doesn't matter because it's >10%, or (b) must citizens mate only with those of their own generation, thus prohibiting aunts, uncles, cousins of differing generations, etc. Actually the more I think of it, probably ANY relation closer than 2nd cousins (common great grandparents) will not bear offspring. Can we just make that simplifying assumption?

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2 hours ago, bonanova said:

If mating is random, a male (female) could mate with their mother (father). How is that % calculated? Or (a) it doesn't matter because it's >10%, or (b) must citizens mate only with those of their own generation, thus prohibiting aunts, uncles, cousins of differing generations, etc. Actually the more I think of it, probably ANY relation closer than 2nd cousins (common great grandparents) will not bear offspring. Can we just make that simplifying assumption?

Yes.  Mating is random so anyone may end up with anyone but if they are related by more than 10% no offspring we be produced.  Also, we are assuming that any mating that occurs with someone not too related will always result in pregnancy.

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