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So this might be a slightly weird one, but I"ve seen answers to questions about minimum numbers for re-population and such, but what about a system where reproduction was controlled and coordinated, and the intent was zero population growth? The theory is, quite apart from sexual or romantic relationships, everyone in the group is the genetic parent of exactly two children (barring instances of twins/triplets/whatever), each with a different partner, so that everyone is genetically responsible for half of two children, and theoretically the closest relation anyone can have in their own generation is half-sibling, thus sharing on average only 25% of their DNA.

So how might a system like this impact the needed starting population size, assuming that eventual reintegration with a larger population was for practical purposes impossible? How many generations back does a common ancestor need to be to minimize the chances of undesirable effects of inbreeding? I know it would rely on a perfect, or near-perfect, 1:1 ratio of genetically female to genetically male, so I guess another question is how large a population do you need for the randomness of birth to reliably average out that way?

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    $\begingroup$ Try narrowing this down to only one question. $\endgroup$ – callosaurus Jun 6 '17 at 16:30
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    $\begingroup$ Siblings share far more than 25% of their DNA with each other. There are worms that share 70% of their DNA with humans. $\endgroup$ – sphennings Jun 6 '17 at 16:31
  • $\begingroup$ I think he more so meant Genes than DNA. $\endgroup$ – ggiaquin16 Jun 6 '17 at 16:51
  • $\begingroup$ I answered below, but I realized that didn't answer the last part, so here it is: there is no reliable way to ensure averages in random processes. You will need to add this to your caveats... $\endgroup$ – adonies Jun 6 '17 at 17:39
  • $\begingroup$ @sphennings And wasn't it chimpanzees who share the upper half of 99% of their DNA with humans? Something like that, though I wouldn't take poison on the exact number. $\endgroup$ – a CVn Jun 6 '17 at 18:11
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Let's suppose that you start with X population, X/2 women and X/2 men, all totally and genetically unrelated to one another. That's the zero generation.
On the first generation X children are born, can you ensure that they will be 50% boys and girls?
Let's assume you can.
When their parents die out (hopefully before the children's fertile age is passed!) they will start looking for partners. In this generation (supposing again X/2 of each sex) each will have X/2-1 good choices (i.e. barring own sibling).
On the second generation (same assumptions as before) each will have valid choice X/2-1-2 (i.e. own sibling and parent's silblings' children of opposite sex [50% probability on average]).
On the third generation, it will be X/2-1-2-4.
On the fourth generation, it will be X/2-1-2-4-8.
Yet, now we have reached the fourth degree of relatives (cousins of cousins of cousins) and we need go no further, as with each subsequent generation, some new people will become related, but also some other will become too distant, so I think an equilibrium will be reached.
It seems that the choice among the population need never be more restricted than 15 forbidden persons of the opposite sex. Getting as X/2 any number greater than 15, for example 16, creates a safely reproducting population of constant size for that sex; double that for the other sex = 32.
I would say that 32 people (16♂ + 16♀) is the absolute minimum of the constant population in your question.

Caveats:
My assumptions in italics.
Also I'm not a geneticist, I just made assumptions considering the commonly society-held beliefs of inter-marriage.
Lastly, you would need to account for: stillbirths, childlren mortality rate, people not interested in reproducing (sex-orientation, etc), male and female incapability to reproduce, mutations, ...

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  • $\begingroup$ Can we be confident that fourth generation relatives will be far enough apart in such a constrained world? $\endgroup$ – Cort Ammon Jun 6 '17 at 17:17
  • $\begingroup$ @CortAmmon As far as I can tell with my minimal genetics knowledge. It's not hard-science or reality-check, so I went on with some assumptions. I think the population will get into trouble with the caveats I presented a lot sooner than worrying about relatives inter-marriage. $\endgroup$ – adonies Jun 6 '17 at 17:32
  • $\begingroup$ Healthy populations of animals in the wild need to number in the hundreds to be sustainable. At some point the limited variability of your gene pool will become a weakness. $\endgroup$ – Isaac Kotlicky Jun 7 '17 at 0:09
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    $\begingroup$ A very interesting approach. I think the 4th generation tradition works in reality because there a lot more people out there. In your example someone's cousin will have children with their other cousin, and so there is a higher chance of genetic problems down the line. $\endgroup$ – ivbc Jun 7 '17 at 0:24
  • $\begingroup$ Fascinating. You raised several points I hadn't thought of, including the idea of a generation passing their fertile period before the previous generation has died out... I had assumed that multiple births would make up for stillbirths/child mortality, but I suppose that throws the genetic balance off a bit every time... and to be honest, I'd need to research the incidents of those types of things to know to what degree they compensate for one another, plus incorporate factors from the world where this all takes place... Clearly, I need to do more research. Thank you for your insights! $\endgroup$ – TheOneWhoWalks Jun 8 '17 at 3:55
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The answer to your question depends mostly on the prevalence of rare recessive genes that are harmful only if received from both parents. These can be engineered or bred/selected out of a population, although mutations from chemicals or radiation can re-introduce them. Even in a large population these genes will meet and cause birth defects or miscarriage occasionally.

Even with a reasonable number of defective recessives, your population can be very small if they are willing to cull the inevitable hemophiliac or Hapsburg jaw.

Almost half of our states allow first-cousin (though not double-first-cousin) marriage. You might want to check birth defect stats for these folks.

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