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A immortal dictator controls an island with about 1,000,000 people. Apparently, he's super into eugenics and wants the population of the island to be "the ultimate humans".

Assume he can control who reproduces (and who does not).

He would want to select the "top" X% of fertile females and Y% of fertile males to produce the next generation.

Problems To Consider:

  • If X or Y are too small, there will eventually be problems with inbreeding.
  • If X or Y are too large, he won't be selecting for the "very best".
  • I assume that X will be much larger than Y, but I could be mistaken.

Problems Not To Consider:

  • How the dictator enforces this.
  • What "top" or "best" means; this is based on his subjective criteria.

Clarifications:

  • 1,000,000 is an arbitrary number and a general solution for any population size would be preferred.
  • The population of the island should remain the same.
  • "Fertile" means "can safely reproduce".
  • If a person is chosen to reproduce, their partners are chosen (semi-)randomly and outside of multiple births, no two children have the same parents.
  • Since he's immortal, the dictator wants to be able to maintain X and Y indefinitely.

What is the minimum percentage of males and females that can be allowed to reproduce without running into inbreeding problems?

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    $\begingroup$ This is a lovely problem where the expected answer is a number but the input data are such precise words as "running into problems" and "very best". $\endgroup$
    – AlexP
    Commented Apr 11, 2022 at 18:45
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    $\begingroup$ Technology level is not specified. My answer has 3 scenario's now, I'll pick one of them and work out further, when technology is specified. $\endgroup$
    – Goodies
    Commented Apr 11, 2022 at 22:17
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    $\begingroup$ VTC:Needs Details. This Q falls into my "how many angels can dance on the head of a pin?" category. Answer: "as many as wanting." One million people is well above the threshold to avoid fundamental inbreeding, meaning you'd not only have to be super limiting (only X number of people), but you'd have to choose which X people were allowed to breed to permit inbreeding. Worse, you don't explain what the goal is at all, so we can't know how many will provide best-case breeding. Conclusion: pick a number and move on. There's no science here. $\endgroup$
    – JBH
    Commented Apr 12, 2022 at 1:21
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    $\begingroup$ Also, whether you're breeding horses, wheat, or humans... the breeder is keeping meticulous records. Wouldn't that very natural, very common, and obviously beneficial characteristic of any good breeding program render this question moot? (Just to point out the fun past authors have had with this, Frank Herbert's Dune uses inbreeding to intentionally isolate and strengthen preferred traits - are you sure you don't want intentional inbreeding? How involved is your dictator in his/her own breeding program? Just how "super into eugenics" are we?) $\endgroup$
    – JBH
    Commented Apr 12, 2022 at 1:23
  • $\begingroup$ Speaking of which, OP, how long are you letting this project LAST within your story? If you're going on the suggestions noted in other answers, where "one man could impregnate 365 women in a year" and "one woman could crank out one baby a year," there's going to be a lot of protests AND a lot of extra mouths to feed. Even if you got X amount of babies from carefully-selected parents for that first year, you still have to wait twenty or so years for them to grow up. $\endgroup$
    – Jamie L.
    Commented Apr 12, 2022 at 3:10

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A woman's birthing career, if she does little else, is about a pregnancy per year for 16 years, from the age of 16 to 32. Beyond 32, you run a risk of greater genetic anomalies, nearly always not good. A male is about the same, even though males are essentially fertile for life; the same thing happens with age; a greater risk of genetic anomalies.

But one man can impregnate almost any number of women, even one per day. You don't require a lot of men.

From there, presume there are no multiple births or child deaths; each women can produce 16 adults. The replacement value for the population of X is X/16 women breeding. That is about 6.25% of carefully chosen women.

Since the proportion of men required is far smaller, we can be more selective with the men. (Nature is too; for example in horse herds nearly all foals have the same father, that impregnates 95% of mares. A few rogue non-alphas manage to impregnate the other 5% of mares.)

So say, our breeder males impregnate a woman on average once per week, which is 52 times more often than women get pregnant, so the 6.25% of women require about 1 out of 832 men. So only about 6.37% of the population is breeding; one in 15.7 people.

For any decent sized population in-breeding should not be a problem; the odds of people having the same father in a population of 1 million is about 1200 to one (1m/832). (1200 is also the number of breeding males (1m/832), while the number of breeding females is 62,500).

It should be relatively easy to ensure every coupling pair has no common parent, grandparent, or great-grandparent. I believe that is the extent of in-breeding you need to worry about.

Edit: To preserve the idea of LuizPSR: If artificial insemination is an option, then the dictator can select his ideal couples, gather sperm and eggs to produce his new genetic specimens, and force non-selected women to carry those blastocysts to term and raise the children (to which they have contributed no genetic material). The "ideal" women would never get pregnant. Just harvest an egg per month from them.

This could drastically cut the number of women required. The only worry then is management to prevent inbreeding and ensure genetic diversity. Yes, it is a brutal form of slavery, but that is the fictional premise.

So, for example, if the dictator deems only 1% of women as breedable, then each of those women must produce 100x more babies than they would have if free. But that is possible, she would have produced 2 in her lifetime, she needs to provide 200 eggs, which she can do in 16 years, 8 months of monthly egg harvesting. Thus from the age of 16 to 32 +8 months. Those would be implanted into two hundred non-breeding females, as the eggs become available, and eventually all the non-breeding females will have two children.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – L.Dutch
    Commented Apr 12, 2022 at 17:50
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    $\begingroup$ @Amadeus Fair enough, since OP did not specify the level of realism required. But even if healthy retirement after a birthing career was not a parameter, giving birth to healthy babies probably is, and babies born by a weak or ill mother have an increased chance of health problems. $\endgroup$
    – Cloudberry
    Commented Apr 12, 2022 at 18:05
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    $\begingroup$ @Cloudberry I am more on the side of LuizPSR at this point, the "ideal" mothers, as judged by the dictators, provide only eggs for implantation into the non-breeding mothers. So the breeders never actually get pregnant, the breeding males never have sex. They just have a monthly appointment for harvesting an egg or seed, and the fertilized egg is implanted in a non-breeder female that gets pregnant (twice in her life, also young), she carries the egg to term and she raises the child. After her two young birthings are complete, she is sterilized. $\endgroup$
    – Amadeus
    Commented Apr 12, 2022 at 18:11
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Your problem is not how many, but how long. Each generation in which you prevent a significant part of your people from breeding removes a proportional chunk of the genetic variability of your population. This is fine for a few generations, especially if your population is diverse to begin with (debatable, on an island) and you pick your breeders with some care for physical and genetic fitness (note that we don't really understand enough of genetics to do this even today). But keep this going for generation after generation, and you will inevitably funnel your people into a genetic bottleneck. Intuitively, your gene pool is decaying exponentially, losing the same % every generation. This is why adding selection is worse than just leaving a 1,000,000 population to breed in isolation. Sources that would increase genetic variation exist, but are much slower, and probably undesirable anyway for an eugenicist.

The other point to keep in mind is that this plan would presumably fail, if the goal is to produce "ultimate humans" (however defined). Either the dictator knows much much more about genetics than we do (in which case he'd be better off with a gene editing programme) or he doesn't (which I suspect to be the case, or he wouldn't embark in a plan like this) and therefore, like us, doesn't actually even know what to select for. You would at best produce a genetically fragile population with some unnaturally over-represented superficial trait. Eugenics, beside the moral repugnance, is just a stupid strategy.

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  • $\begingroup$ I just mentioned in some of my comments that there's gonna be 1) lots of protests and 2) a whole lot of new mouths just after Year 1. Going on how actual farmers handle livestock, the part where you'd literally "breed better humans" needs these qualifications: 1) Split the "main percentage" into subsets, so you don't have too many mouths to feed, or 2) Stagger the program in 20-year intervals, so you know which of your "improved humans" are actually improved adults. The ruler himself wouldn't mind waiting either way, but this leaves a million people a LOT of time to get angry. $\endgroup$
    – Jamie L.
    Commented Apr 12, 2022 at 3:25
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    $\begingroup$ @JamieL. agreed, any of these plans still require the willing cooperation of large sections of society (guards, doctors, breeding plant staff). Even if you intend to suppress the broader populace with brute force, these people must be convinced, or coerced, that supporting the dictator is in their interest. $\endgroup$
    – Ottie
    Commented Apr 12, 2022 at 9:50
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    $\begingroup$ We have done this kind of breeding to many animals and plants. So far it kinda works. I don't see a reason (from a genetic viewpoint) why this shouldn't work on humans. $\endgroup$ Commented Apr 12, 2022 at 15:33
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    $\begingroup$ @AlexbGoode those were never, typically, closed gene pools. If your stock grows weak, you outcross (see also, F1 hybrids). When "official" breeding populations have been kept isolated, as for some dog breeds, it has regularly led to awful genetic defects (not just those actively selected for, like breathing distress in bulldogs, but things like cancer, degenerative myelopathy, epilepsy etc.). This was acceptable to dog breeders, so it may be acceptable to our tyrant too - we don't have enough info. But it won't be viable long-term, for either the dogs or the dictator's unfortunate subjects. $\endgroup$
    – Ottie
    Commented Apr 12, 2022 at 17:36
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    $\begingroup$ @AlexbGoode Selectively breeding animals is still far from all-out eugenics, though. For horses alone, we have all manner of different breeds that specialize at certain things, but one particular breed can hardly be considered the "ultimate horse." $\endgroup$
    – Jamie L.
    Commented Apr 12, 2022 at 19:50
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This is mentioned by LuizPSR in a comment and I decided to make it full answer.

If the setting is about same technology as ours, instead of impregnating chosen women, you collect eggs, fertilize and implant into foster mothers. This allows women to produce slightly less than one offspring per month. With this you can reduce the breeding population (down to maybe 5k) close to a level where only problem is to avoid in breeding.

With this method every couple will receive their own children to look after if your villan desires, reducing uprising chances and not birthing 10+ children will allow breeding population to live healthy lives.

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A few assumptions:

1). gender ratio close to 50:50.

2). a female can "safely" bear 4 children (theoretically allowing the population to double every generation - classic exponential growth).

3). reproduction via biological methods rather than IVF or other technological approaches.

Parameters:

1). As few people as possible should reproduce.

2). The initial population of 1x10^6 should be maintained.

Therefore at least half the females need to reproduce, just to replace the existing population.

As other answers have pointed out, the number of males required is smaller. How much smaller depends on how your dictator is running the breeding program.

The large number of females means inbreeding is less of an issue, although there are risks of gender linked issues in the males due to the smaller number of Y chromosomes.

However, if the tech level is up to genetic testing then these could be screened for.

At that point it would also be easy to tell when females were close to ovulation giving increased chances of success at achieving pregnancy over random copulation.

How dehumanised do you want the breeding program to be? In this scenario it would be possible for an eligible ovulating female to be required to report to a stud facility for copulation. Exactly how many males you need in this scenario depends on a whole bunch of other assumptions, but between one and five thousand seems a reasonable number.

If we assume that genetic screening/fertility detection is not available or that the dictator is not literally monstrous enough to breed people like cattle, the perhaps a hareem system may work.

Selected males are given high status, and eligible females are at least free to select among the males looking to add to their households. At this point you are probably looking at around 25,000 - 50,000 reproducing males. More than sufficient to avoid any problems with inbreeding, although you have other huge problems with societal stability. (Namely half a million males competing for the affections of only a quarter of a million females).

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(I took a qualitative approach, this percentage you ask for could be anywhere from "small minority" to "relevant part of the population", depending on the means your dictator has to control the process. You do have a dictator, that comes in handy.. suppose the population is obedient..)

Prevent inbreeding ? Eugenics ? depends on coordination

"Fertile" means "can safely reproduce" you say, that does not hold and will not help your dictator's eugenics project. My intuition says it would depend on technological level, which is not specified.

Don't hesitate to fillin the dots and specify technology, I'll focus below answer,

With high tech medical devices, it won't be a problem at all. You start out with a million people, that gives sufficient diversity to start with. Just sequence all of your population's genomes and regulate such that you get 1) max distance between the genomes that mate and 2) mix certain properties required by the eugenics project. This procedure does not need family checkups, the minimal allowed genome distance can be set to a certain value, by law. That minimal genome distance will determine the percentage allowed to have kids.

With your average 19th century doctor present, and a population that is obedient, you could regulate pregnancies, by letting the doctor assert family relations and health risk. You could "breed" a very healthy population, if you have a registration of family relations in place, which could be done in the 19th century. But I doubt your dictator would have the patience to wait for the result. And very few members of the population can take part. Your doctor travel around on the island, arranging the marriages across villages and using local municipality archives to check things. If that check is accurate, no inbreeding will occur.

In a medieval society, starting out with one million people, any attempt in eugenics would become a mess, whatever your dictator tries to regulate. He could try.. say, a very limited, selected part of the population would be isolated in "breeding houses". Issue is, you can't select these people safely, because there is no accurate family registration. Probably, cultural preferences would cause inbreeding, especially in these breeding houses. A 1M population may survive - many modern societes started with far less - but the eugenics project will fail. In order to prevent inbreeding, the dictator could set a rule by law: inhabitants of the same village can't mate. This would circumvent inbreeding, but only statistically. It would occur.

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