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In my particular Earth, much has remained after the human-killing virus, and nature is thriving - even taking over the cities. It's beautiful. But I have separated the healthy populace in orbit until it was safe to return.

In a near-future scenario, where I have rescued only a few non-related people from Portland, Oregon (not-relevant, but I thought someone might ask), they're ready to return to Earth after 3 years or so in space.

Setting aside their trials upon return, etc., how many random people should I preserve in space when humanity is almost wiped out, for relatively clean genetics? Is there even such a thing?

I realize this is purely speculative, but I'd like the fewest possible people and would welcome some scientific reasoning so that I don't end up with genetically distressed children / population.

EDIT, as requested: Infrastructure, technology forests, roads & bridges, etc., are all only about 3 years old without people. There are many machines and materials; this question is purely for genetics-sake.

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    $\begingroup$ Related: What is minimum human population necessary for a sustainable colony $\endgroup$ – newton1212 May 31 '15 at 1:55
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    $\begingroup$ @Frostfyre It is pretty close to a duplicate, but I think the major difference here is the existence of pre-manufactured resources. The space faring individuals will have a great advantage sprouting from the long-lasting packaged food, weapons, and other consumables the conlonists would have to produce themselves. This is assuming the virus didn't somehow contaminate all food supplies. $\endgroup$ – newton1212 May 31 '15 at 2:17
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    $\begingroup$ A world of populated by descendants of Portlanders sounds like it's off to a good start. $\endgroup$ – Samuel May 31 '15 at 2:25
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    $\begingroup$ Now I want to know if there are any genetic anomalies specific to Portland... $\endgroup$ – evankh May 31 '15 at 2:25
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    $\begingroup$ Note you could reduce the number, if you had a stock of embryos | eggs | sperm (sperm would probably be easiest) So if you had time to plan, or at least make a daring raid on a fertility clinic, before the last shuttle left; you could have a small crew and a use the sample to supplement the gene pool, when you got back to earth. This could make some interesting plot elements. Sex ratios, impact on gender roles, the most valuable substance on and off earth being spunk. Don't forget to pack some contraceptives (they will be pretty valuable too) Eunuchs? $\endgroup$ – DarcyThomas May 31 '15 at 5:46

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Preface
This question is very similar (but not identical) to a previous World Builder question (What is the minimum human population to maintain a colony). If you're interested in this question and answer, I recommend reading that question and its answers for additional information.

MVP
The term you are looking for is Minimum Viable Population.

This term [MVP] is used in the fields of biology, ecology, and conservation biology. More specifically, MVP is the smallest possible size at which a biological population can exist without facing extinction from natural disasters or demographic, environmental, or genetic stochasticity. The term "population" rarely refers to an entire species.

MVP doesn't normally mean survival of a species but it can be used to calculate this too.

The reference indicates that without human management, this value averages slightly under 5,000 individuals for terrestrial vertebrates.

I do recall reading that you can make smaller numbers viable through human intervention. The following is my recollection. I no longer remember the reference I got the numbers from.

At 5000 individuals
Population is viable without human intervention.

At 500 individuals
Couples can remain monogamous but mating pairs must be approved by a genetics board to ensure genetic diversity and limit in-breeding.

At 50 individuals
Each individual must have as many babies with different partners as possible over their lifetime.

A genetics board must approve all matings. Couples may pair, but each couple could only conceive one child. Individuals that had paired would still have to mate outside their relationship until the size of the population grew larger and more diverse (probably not possible for several generations).

It looked like 50 was the absolute minimum and that if you lost very many members early (due to accident or disease) it would endanger the whole colony.

Another opinion:
A geneticist actually studied a related question, which was "what is the optimal crew size for a generation ship". The "optimum" was considered the smallest crew that maintained acceptable genetic diversity (I don't know what he deemed acceptable) during the ship's 200 year / 10 generation voyage.

For a space trip of 200 years, perhaps eight to 10 generations, his calculations suggest a minimum number of 160 people are needed to maintain a stable population.

At the end of this journey, the crew must be reintroduced to a larger population with greater genetic diversity (a large destination population or fertilized egg bank to ensure genetic problems don't crop up. The article doesn't explicitly state this but it implies that without introducing this diversity, the effects of in-breeding might be large.

"The decrease in genetic variation is actually quite small and less than found in some successful small populations on Earth," he says. "It would not be a significant factor as long as the space travellers come home or interact with other humans at the end of the 200 year period."

For this question, we have to consider that these numbers are lower than the minimum required to repopulate the planet because to repopulate the planet, our population will start with all the genetic diversity it is ever going to get.

As others have suggested, you get better diversity if you hand pick the members for that diversity rather than depending upon chance. The 160 people number above considers that the members of that population were selected for diversity.

Also note that the person creating this population could use the opportunity to concentrate perceived positive traits in humans. However, many positive traits (e.g. one of the 1000 genes affecting intelligence) often carry hidden or recessive negative traits with them. The gene screening would need to be done most carefully to avoid concentrating genes which when combined cause major negative side-effects.

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    $\begingroup$ What's the sex split on the individuals? Surely it makes a big difference. $\endgroup$ – Samuel May 31 '15 at 2:48
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    $\begingroup$ Yeah, I considered this. For growing the population you are certainly right. But for genetic diversity, I'm not sure whether it helps more to increase the % of women or hurts more. $\endgroup$ – Jim2B May 31 '15 at 3:27
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    $\begingroup$ MVP is not an applicable number here. It is intended to measure the probability that a population will go extinct due to stochastic fluctuations, and random events, like a disease in the population. Basically, MVP asks "if my population gets really unlucky how many individuals are needed to make sure it doesn't go extinct?". The calculations take into account inbreeding depression (the loss of fitness caused by a small population), but inbreeding depression does not cause extinction. $\endgroup$ – Mike Nichols May 31 '15 at 4:10
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    $\begingroup$ Also (this is not my specialty) but 2 people isn't enough to continue the species. Genetic problems kill people. I've got one that would kill without modern medicine. With 2 people, every breeding is in-breeding. Any adverse mutations spread through the whole population almost immediately. I do NOT know the absolute minimum but I am sticking with 50 as that number unless I see a number from a reputable source indicating otherwise. FYI, if anyone has such a reference or different number, I'd love to read it :) $\endgroup$ – Jim2B Jun 1 '15 at 17:55
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    $\begingroup$ @Jim2B Inbreeding will result in premature death, sterility, intellectual disability, and many other issues in the population. But as long as each generation succeeds in increasing the population those inbreeding effects will gradually be purged form the population. Even if you were to imagine 50% of the population's children died before they could reproduce, as long as each couple produced an average of 6 children (so only 3 survive) the population would prosper over the long run. Now we are really discussing a very different question then the original though. $\endgroup$ – Mike Nichols Jun 1 '15 at 20:32
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People have reported, based on genetic bottleneck studies, that last time it may have been around 10000 people. Maybe not Toba's fault, but bottlenecks are part of our history. The amount of variation can be inferred, but it's hard to say how many people that means since we suppose that they were more diverse before that. Current humans might need many more individuals to achieve the same amount of diversity. If the survivors were the population of Queens NY, a small number would do. If they were an isolated village, the whole village is not enough.

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    $\begingroup$ Indeed. Interestingly there may be local bottlenecks though: leaving Africa, and passing the Bering Straight. $\endgroup$ – bilbo_pingouin Jun 1 '15 at 20:46
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In Testing migration patterns and estimating founding population size in Polynesia by using human mtDNA sequences. Murray-McIntosh R Scrimshaw B Hatfield P Penny D (1998) They have a stab at how many females initially colonised New Zealand. (Females only because they use mitochondrial DNA).

The results are consistent with a founding population that includes' 70 women (between 50 and 100)

This doesn't give a minimum, but it does show a low number that worked.

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Let's do some actual math to try and estimate things. First, some basic genetics. Each founding member of your population brings with them 2 copies of each of their chromosomes. There are many thousands of genes on each of these chromosomes, and the vast majority of them all work perfectly in each of us. But, due to random mutations, some people have copies of genes that don't work. Often times this is fine, because you have only one broken copy, and your other copy works and is able to compensate for the broken allele. Geneticists call this haplosufficiency. What this means is that the broken gene, or bad allele, is recessive, while the working gene, or good allele, is dominant. The bad allele only causes an issue in individuals that get two broken copies. If you have one broken copy and one working copy you are heterozygous at that locus, and you are a carrier for the disease. If you have two broken copies you are homozygous for the disease and will be affected by it.

Most bad alleles are rare, because they are selected against by natural selection. A carrier for a disease gene is only at risk of having a child with the disease if they happen to mate with another carrier of the same disease. This is why inbreeding is bad. When two individuals that are closely related mate, they have a high probability of both being carriers for the same genetic disorders, and therefore of having a child with two copies of the bad allele, and therefore the disease.

So, math time. I'm going to simplify things a bit for the reader's sake as well as my own, but the results should still be reasonably close to the reality.

Let's say we begin with a population of size N. That means there will be 2*N total copies of each gene or allele in our gene pool. So if anyone in our starting population of size N is a carrier for a genetic disorder, that genetic disorder will exist within our population at a frequency of 1/(2N). The frequency of the good allele in the population will be 1 - 1/(2N). Let's call these frequencies q and p respectively. Now, there are 3 possible genotypes, or genetic combinations possible. 2 good alleles, 1 good allele and 1 bad allele, and 2 bad alleles. For any randomly shuffled population the probabilities for each of these genotypes are as follows: 2 good alleles = p^2, 1 good and 1 bad allele = 2pq, and 2 bad alleles = q^2. The reasoning behind these numbers should be fairly straightforward. The probability of having 2 bad alleles is equal to frequency of the bad allele squared. Using some simple substitution we now find that the frequency of a genetic disorder which was brought into the population will be (1/(2N))^2.

Let's try our formula out with an actual example. Let's say we have a starting population of 10. One of our 10 people happens to carry a mutation in the CFTR gene, meaning they are a carrier of Cystic Fibrosis. This means that 1/20 of all of the CFTR genes in our gene pool are broken. The chances of a child in the population receiving 2 copies of the broken CFTR gene and thereby having Cystic Fibrosis is 1/20 * 1/20 or 1/400 or 0.25%. Now, this doesn't sound all that bad right? The problem is that your starting population would be very lucky if it only had 1 carrier for 1 genetic disorder in it. A very recent paper estimated that the average person is a carrier for 1-2 recessive lethal mutations: http://www.genetics.org/content/199/4/1243.full. If each person in our starting population was a carrier for a single different recessive lethal genetic disorder, then each of those 10 diseases would kill ~0.25% of our future population (slightly less because sometimes they would co-occur).

Let's make things worse and say we only had a starting population of 2. If each of those individuals were a carrier for a single recessive lethal mutation then those bad alleles would exist in the population at a frequency of 25% and children would get 2 bad copies 6.25% of the time. With two diseases that means roughly one eight of the children would die from genetic defects.

Let's make things better and say we had a starting population of 100, each of whom bring in 1 recessive lethal allele. Each of these 100 diseases would now only occur 0.0025% of the time for a total of 0.25% child death.

However, this is only taking into account lethal mutations. There are likely many more mutations that could cause infertility, intellectual disability, and numerous other problems. I can't find any numbers on how many of these types of mutations the average person is a carrier for, but it's likely higher than the number for recessive lethal mutations as the selection against them would not be as strong.

A few extra notes. First, these inbreeding effects will gradually decline over time. Each time a child is born with 2 bad copies of a gene and dies, those 2 bad copies are removed from the gene pool. The worse the frequency of the genetic disorders are, the faster the frequencies of the bad alleles will decrease in the population. Second, the starting population size will also determine how many generations it takes before the population is sufficiently mixed that inbreeding even begins to occur. In a starting population of 2, the first generation will need to inbreed, but in the population size of 100, many generations would go by before anyone needed to procreate with someone at all related to them. Third, when the starting population size is small the outcome will also be highly variable. The numbers I calculated above represent the average outcome assuming the population gets neither lucky nor unlucky in which alleles get passed on to the next generation, but with a small starting population size a few unlucky inheritances of bad alleles could have disastrous complications later on, whereas some lucky inheritances of good alleles could remove all the bad alleles from the population early on. Small populations would also have a high degree of chance in how bad the inbreeding becomes.

While I didn't really provide you with a concrete number, I hope the mathematics will allow you to calculate your own starting population size given your definition of "relatively clean".

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I think you could have the freedom to dictate the number, so long as you also dictated the genotypes of the would-be new population.

The problem with the human race today–from a purely natural point of view (which is unavoidably going to sound very nationalist-socialist)–is that for hundreds if not thousands of years, humanity has been fighting against natural selection. We've have been striving to preserve all human life, this includes those whose phenotypes express recessive traits that make them frail, or fragile like individuals born with physical or mental disabilities, up to and including food allergies and depression. The problem with inbreeding, is that due to the lack of variation, those recessive traits are expressed more often, which results in a genetically distressed population.

You specified random people, in your question, which would necessitate a relatively large population to ensure adequate genetics. But if the breeding population were selected, based on the strength of their genotypes, then the population could be much smaller, and the resulting human race would be much stronger, potentially free of all genetic diseases such as cancer, diabetes, and other ailments that often skip many generations until some unfortunate descendant's phenotype expresses the gene.

Creating a genetically perfect population was the premise of the James Bond film, "Moonraker". The villain in that film constructed a space station which was meant to be the home of genetically perfect couples from each race of humanity (so not totally nationalist-socialist), as well as the launch facility which would deliver a nerve toxin capable of eradicating all human life on the planet (whilst preserving animal and plant life), leaving the earth vacant, and free to be inhabited by a new "master race of human beings.

So, you have the potential to create a post-apocalyptic society that has some extremely immoral policies by todays standards, all in the name of preserving the human race and making it stronger than it was before. Think about The 100, only instead of floating people in space for being criminals, they're using methods such as serialization to preventing deleterious alleles from "infecting" the bloodlines.

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I understand that the human population dropped to a mere 600 individuals, to whom all humans are related and is why humans have relatively low genetic diversity compared to other apes.

I saw it on 'Becoming Human - episode 3' on youtube last night if you are interested in looking into it more.

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    $\begingroup$ actually, JDlugosz made a good point that the current human population may not have the genetic diversity to drop so low again. $\endgroup$ – Belverk May 31 '15 at 8:21
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    $\begingroup$ I think I saw that episode and I think they used the words "may have dropped to as low as 600" or similar. I've seen the studies referenced by @JDlugosz and it looks pretty certain that the population did drop below 10,000 individuals but the last I read (which was like 8 years ago) we didn't know how much smaller the population did get. $\endgroup$ – Jim2B Jun 1 '15 at 17:57
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    $\begingroup$ For a second I thought you were talking about "Being Human" and was wondering why a vampire, werewolf, and ghost would be talking about humanity's population dropping that far. Had to re-read :) $\endgroup$ – Paul TIKI Jan 30 '17 at 14:42
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If they're returning to Earth after the plague (or whatever) has passed, all the women in the crew (which should possibly be ALL or nearly all women) could mine the existing egg banks to obtain genetic diversity. I presume the equipment to implant the eggs would still be usable. The question of whether or not the eggs would still be frozen after three years of the refrigerator being unplugged is another thing, but this recovery seems to be planned, so maybe a UPS would help out the situation.

Also, why off Earth? Why not stay on Earth in isolation?

And, not that it matters, but good choice on source city. We're a good bunch.

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Without being able to give you a hard number I'd say it will be very dependent on the degree of prescreening selection you can do before/during the evacuation process, the more you can screen and the more selective you can be the better off the progeny of any isolated population you create will be. I suspect that the 5000 mentioned in Jim2B's answer would be a good starting point though.

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It may not quite fit the premise of your question, but if technology levels are expected to remain about the same as they are now then it is entirely possible that a very small population could maintain some sort of genetic diversity via direct manipulation of embryonic DNA. The number of couples would not matter so much as the amount of genetic material available for splicing and the number of generations the population are expected to undergo this kind of treatment.

Obviously if the initial population were very small then 'related' individuals such as brother and sister would be required to breed. This would not hamper genetic diversity (since by design, the two individuals are sufficiently genetically different for this not to be an issue), but there could be social barriers to it depending on the cultural norms of your post-apocalyptic society.

Even in this scenario there will probably be a percentage of individuals who are made infertile or die before producing children, but this depends on environmental factors I can't hope to model here. Assuming the percentage is low then it would be possible (albeit unpleasant, as above) to repopulate with as few people as one fertile couple.

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The answer is simple. Unfortunately, since most of us already consist of some percentage of inbred genetics, it's not quite this easy, but this is the basic theory.

You need 3 females, and 3 males. They must all be removed genetically from each other enough to do this correctly, but like the colors of the rainbow, you only need 3 primary colors to produce any other color you can imagine, even black and gray. Since humans do not self-replicate, you need 6 people instead of 3. 3 males and 3 females. But because we need both male and female, we can just say that we need THREE BREEDING UNITS.

If all parents involved are removed from each other enough genetically, then theoretically it's the same as mixing those 3 colors together to get some random color, which is obviously desirable for progeny to prevent birth defects and learning disabilities.

The universe loves the number 3, and certainly, tetrahedrons (triangles) are fundamental shapes. You can't have a geometric object with less than 3 sides. Try making a tables stand with less than 3 legs. No cheating with stretched, reinforced leg bases as that counts as more than two legs. Interesting huh?

EDIT: btw the breeding PARENTS will crossbreed with the opposite breeding unit's progeny when they are old enough. Forgot to put that in there. Inbreeding will be had to some degree, but then again, if we just kept swapping out all of our genetics we wouldn't even be human. Some level of inbreeding is acceptable, we just are not adept at thinking outside of the "proper" box.

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    $\begingroup$ You did not explain where you got the number 3, and the following prose makes it sound mystical. $\endgroup$ – JDługosz Nov 29 '16 at 5:07
  • $\begingroup$ First generation: no problem. Second generation: not difficult, just avoid siblings. Third generation: first cousins marrying because everyone in that generation is either a sibling or a first cousin. And it's all downhill from there. $\endgroup$ – Brythan Nov 29 '16 at 5:20
  • $\begingroup$ We are all a little inbred, the idea that humanity sprang from 28 or so adults is perfectly fine. But where the hell did they come from? They had to have at least some inbreeding. Inbreeding isn't a problem, it's genetic frequency that's the problem. Like the colors on the the color wheel, you can't do anything without 3 of something. $\endgroup$ – Tomcat Cruiser Nov 29 '16 at 7:07
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    $\begingroup$ «the universe loves the number 3» is not a (valid, useful) explaination to why some particular question can be answered with “3”. $\endgroup$ – JDługosz Nov 29 '16 at 8:26
  • $\begingroup$ again, I explained it. You refuse to read the entire post. $\endgroup$ – Tomcat Cruiser Nov 29 '16 at 8:37

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