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It's a very old scenario but never seems to be explored in great detail - not even in the Bible.

Two astronauts, a man and a woman, return to Earth to find that all mammals have been wiped out by a virus.

All dead bodies have been cleaned by vultures, insects and bacteria. There is no danger from pollution or from wild beasts.

There is plenty of food to be found in supermarkets and all the basic tools needed to start again can be found.

The pair decide to repopulate the Earth. That's fine, they start and by chance they have two sons and two daughters. But then what? All sperm and egg banks have long been out of action. Their only way forward is incest.

Question

How do they proceed? Who should pair with whom and in what order? You can assume that they go ahead in the most practical and beneficial way so as to make the best possible life for their descendants.

In the early days, what scientifically based marriage rules should they put in place to avoid genetic defects as much as possible? What other factors, if any, do they need to address that are specifically related to interbreeding between close relatives?

Scientifically speaking will there be sufficient genetic diversity for the human race to survive?

Additional - Religious implications

If the pair believe in Biblical teachings, which Bible passages might they use to justify their actions? Or, in order to stick with their faith, would they simply have to let the human race die out? Similarly, if they belonged to other religions of the world, what accommodation would they have to make?

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The population will not be healthy, but it will be capable of surviving as long as they produce enough offspring. Based on the genetics of the 2 founders, a certain percentage of all offspring produced by their descendants will die before reaching reproductive age or be infertile or otherwise disabled. We'll get in to how to calculate that percentage below, but the important concept is that a certain fraction of their descendants will be healthy. As long as reproductive rates are high enough to produce enough healthy individuals to expand the population, then the population will continue to grow and the rates of genetic disorders will decrease as they are negatively selected against.

Before we get into the math we need to understand why inbreeding causes problems. You may have an idea in your head like "the loss of genetic diversity", but that's really a nebulous concept that doesn't really matter. The real issue caused by inbreeding is an increase in homozygosity. Humans are diploid meaning we have two copies of each of our chromosomes, (except of course for males and their sex chromosomes) one set from each of our parents. Your chromosomes, while nearly identical, still have lots of differences between them. These different variants are called "alleles". Homozygosity means having two copies of the same allele at a given location in the genome, or put another way, your two chromosomes having the same sequence at a given location. Now, homozygosity itself isn't bad, there's nothing inherently wrong with having the same DNA sequence on both sets of chromosomes. The problem arises when you take into account mutations. Mutations can sometimes break things very badly. If they change the wrong base they can completely knockout an essential gene. Fortunately, since we have two copies of our entire genome on our two sets of chromosomes, even if a mutation breaks one copy of a gene we have another copy that still works and can compensate for it. This is called haplosufficiency. Unfortunately, this means most people carry these lethal alleles, because as long as they are compensated with a functioning copy they don't harm us and so aren't selected against. These bad alleles are known as recessively lethal.

Now we can see why homozygosity is an issue. If an individual has an increased chance of getting two copies of the same allele, then that person also has an increased chance of getting two broken copies of an allele and dying!

Finally we can get to calculating how much of the population will be affected by the genetic disorders. It all depends on how many recessive lethal mutations the 2 founders bring with them. Each recessive lethal mutation present in the founders will represent one bad allele out of a total of 4 (since each founder has 2 copies). If we assume* this allele is inherited such that its frequency doesn't change, then the population will have a 25% frequency of bad alleles for the spot in the genome. This means that a given child in the population will have a 6.25% (25% * 25%) probability of receiving two bad copies of the allele and dying. So, for each recessive lethal mutation present in the 2 founders, ~6.25 percent of the future offspring of the population are going to die. This isn't entirely accurate because the recessive lethal mutations won't be passed on by those individuals who receive two copies and die, so the frequency of those alleles will gradually decrease as they are selected against.

So, how many recessive lethal mutations are our founders likely to carry? This recent paper http://www.genetics.org/content/199/4/1243.full claims only 1 to 2 per person. Even in the worst case of both founders bringing in two recessive lethal mutations for a total of 4, each offspring has a 93.75% (100-6.25) chance of avoiding two copies of each bad allele, meaning ~77% (93.75^4) of offspring will survive. As long as each couple produces 4 or more children on average the population will grow despite the high mortality rate. With each successive generation the frequencies of the recessive lethal alleles will decrease due to natural selection.

I haven't really addressed the question of how mating should be done. There are a couple surprising attributes of this population that make mate choice interesting. First, in a normal family tree mating with a more distant relative would be vastly preferable to mating with a close one, but in this scenario the there is no out-breeding, so distant relatives are actually just as likely to be carrying the same bad alleles as close ones. It's also unclear to me whether you would even want to try to reduce the number of problematic matings. Every time two heterozygote carriers for a lethal allele reproduce 1/4 of their children will die, but 1/3 of the surviving children won't carry the lethal mutation. Every mating that results in dead children actually reduces the frequency of the bad allele that caused it. So the population has a choice. By reducing matings between carriers of bad alleles they will decrease the number of dead children early on, but increase the number of total children that will die as the population expands. If your population has a scientific mindset they could record the manner in which the diseased children died and attempt to create a pedigree of the family's different genetic disorders to inform their mating choices, but it comes at a high cost.

One caveat of this analysis is that we are only considering recessive lethal mutations. There could be other detrimental recessive alleles that don't quite result in death, but still severely impair anyone with two bad copies. As long as they don't influence fertility they don't really impact our populations growth though, just how many issues our population is going to have.

Of course, we also aren't considering natural disasters, disease, starvation and other non-genetic factors here. If Adam gets pneumonia from wearing only a fig leaf around or Eve gets bitten by a venomous snake none of the genetics matter at all.

  • Note: this is not a safe assumption. With 4 kids there's a 1/16 chance that the mutation will never be passed to any children, a 1/4 chance it will be passed to just one of them, a 3/8 chance it will be inherited by 2 of them, a 1/4 chance it will be received by 3 of them, and a 1/16 chance that the lethal allele will be present in all 4 of them. The outcome of this genetic lottery is extremely important and to properly perform our calculations we should consider each possibility but I fear that would make this answer even longer than it is and wouldn't meaningfully change the outcome.
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    $\begingroup$ Informed mating could be very important for the first few generations as increasing the number viable will increase the population of the next generation and getting that population up fast is more important than pruning bad alleles at that point. $\endgroup$ – Tim B Aug 4 '15 at 11:13
  • $\begingroup$ Informed in what way? On the face of it, this seems to contradict what Mike Nichols says, "...I haven't really addressed the question of how mating should be done. It turns out it doesn't really matter that much..." Any thoughts on this? $\endgroup$ – chasly from UK Aug 4 '15 at 13:10
  • $\begingroup$ Wait, if one parent has a mutated allele, than 50% of the next generation will carry that allele, not 25%. Then the generation after that will have 25% x 25% = 6.25% with both bad alleles. So if there are a total of 4 fatal alleles in the parents, the probability of their grandchildren carrying at least one pair is 100% - 93.75%^4 = 24%. $\endgroup$ – Jay Aug 4 '15 at 13:48
  • $\begingroup$ Note this discussion only considers fatal mutations, and I'm accepting your cite that the average person has 1 to 2. But there are also harmful but not instantly fatal mutations. This article -- livescience.com/… -- says 60 total mutations for the average person. (The wording is a little muddled. The first paragraph seems to say 60 new mutations every generation, but I don't think that's what they meant.) Of course many of those are trivial. $\endgroup$ – Jay Aug 4 '15 at 13:54
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    $\begingroup$ @Jay You aren't considering that there is no out-breeding. Children will have a chance of receiving mutated alleles from both parents. This means the frequencies of the alleles won't halve at each generation. $\endgroup$ – Mike Nichols Aug 4 '15 at 14:34
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The good news is that with no diseases around one consequence from your low genetic diversity is reduced. The bad news is that it's unlikely humanity will survive, however it is possible.

First we need to look at generation zero (g0). Astronauts tend to be older (average age 34), and also to have spent a lot of time in space being irradiated. Lets say we get a little bit lucky and both astronauts are still fertile and are at the younger end of the spectrum with the female being aged 30.

They have around 20 years of fertility remaining, although if they get unlucky it could be as few as none or 10 years.

If they produce one child per year and we assume an average of 1 survives each birth (which is not a forgone conclusion as modern medicine is going to be hard to access) then g0 was 2 people but g1 will be 10 to 20 people.

Now there are two choices, you can either pair off those 10 to 20 people with each other or for maximum use of the original genetic variation variation the g0 male can impregnate all the g1 females. (Using artificial insemination would make this less "icky" but you're going to have some form of incest whatever you do). I'm not sure which of these approaches is going to be the most beneficial genetically speaking, I think g1<->g1 is going to have the highest individual success rate but g0<->g1 will introduce the largest overall variation into the population.

You should also consider rotating the pairs, in particular if a pair did produce a child that showed the consequences of inbreeding that pair should not mate again.

Whichever way you handle g1 you will want to create a tree mapping who is related to who and in each generation pair up the least related individuals. Any individuals born that show harmful effects of the inbreeding would not be allowed to breed themselves and both parents should be marked on the breeding chart as carrying that recessive. The parents should then be paired up with people who so far have not shown signs of carrying that recessive.

Over time genetic diversity will return and more conventional relationships can form but it will be many generations before it does.

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  • $\begingroup$ What is the mechanism by which genetic diversity returns - is it mutation? Presumably the healthy tribe members are going to look almost like clones for a long time to come (?) $\endgroup$ – chasly from UK Aug 4 '15 at 10:22
  • $\begingroup$ @chaslyfromUK Genetic mutation and selection would be the primary driver for return of genetic diversity, yes. And yes, that would take time. Compare cheetahs. $\endgroup$ – a CVn Aug 4 '15 at 11:06
  • $\begingroup$ @chaslyfromUK Not clones at all no, you still have a lot of variation in expression. Essentially the entire extended tribe will look like brothers and sisters. Mutation is the main way that genetic diversity returns, you can have some environmental factors that come into play by suppressing or activating various genes as well. $\endgroup$ – Tim B Aug 4 '15 at 11:09
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As @mikenichols points out, a big problem is going to be the passing on of harmful genetic mutations through the forced incest.

If they are so unlucky that they both carry the same defective gene, this could be devastating. 25% of their children would display the defect. Combined with other genetic defects, this could be brutal. But if they're reasonably lucky and they don't, their grandchildren will still have a high infant mortality rate -- see Mike Nichols post and my comments on it -- but enough grandchildren should survive to carry on the human race. And the deaths will slowly reduce the incidence of the defective gene.

Presumably they will have less genetic diversity than the human race as a whole does now. While they'll be carrying many recessive genes, they're not going to have the full set of all the genes that are presently out there. (Barring some extraordinary coincidence, the odds against which would have to be astounding.) The best chance would be it the two people are genetically as far apart as possible, like if one of them is a white person from Norway and the other is a black person from Nigeria or some such. Still, plenty of isolated communities manage to survive and thrive. There have been tribes on remote islands or deep in the jungle who had no contact with the outside world for centuries, and yet seemed reasonably healthy. There is no reason to believe that this of itself would be an insurmountable problem. It may be that they just wouldn't have the genes to survive in some climates, or to live off of certain foods, etc, but that wouldn't be fatal.

Again referring to my comments on Nichols post, suppose it's true that the average person carries 60 mutations. Most of these are probably trivial: a funny shaped ear, a mole, that sort of thing. Some will be serious. It is likely that some will be serious enough to be debilitating or fatal in the right (or wrong) circumstances. Some that are not fatal themselves will prove to be fatal in combination with others.

Once lost, there's no way to get genetic diversity back. Well, mutations will create genetic diversity, but not the kind you want. Mutations are random damage, and random damage does not make things better. Try turning your Honda into a Rolls by throwing it over a cliff a few times and see how that helps. No one has ever observed an unquestionably beneficial mutation. Even if you buy that crazy evolution theory, to fit the observed facts you have to concede that beneficial mutations are extremely rare, so it would take hundreds of thousands of years to accumulate even a handful.

Another big problem that comes to mind: How do you maintain any sort of civilization or economy with such a small population? Suppose each woman has 10 children who survive to adulthood. That seems very optimistic, but even then: second generation = 10, third generation = 50, fourth generation = 250. Sustaining our present technology requires many thousands of specialists. You rely on the work and knowledge of others every day. Suppose they decide that they want to make some electrical wiring. They'd have to know where to go to find copper ore and how to recognize it. Then they have to know how to smelt it into usable metal and string it into wires. Will they make the insulation out of rubber? What does a rubber tree look like, and what is the process for extracting the rubber and turning it into a usable form? Etc. Even assuming that libraries survive and they can look stuff up, there are limits to how much one person can learn. They might be able to continue to use many existing artifacts, but building new ones or even repairing the ones they have would be very difficult. And many would rust or decay over time, so that within a few generations they're probably wouldn't be much of the old technology still usable. They'd have to start over in many ways. They'd have the advantage that if they're smart enough to keep the old books, than they wouldn't have to re-discover or re-invent things. This would be like the fall of Rome and knowledge preserved by monks times a million.

RE religious implications: The immediate descendants of Adam and Eve had to reproduce by incest, as did the immediate descendants of Noah. It wouldn't take any great theological leap to say, This is an extreme situation, God will surely allow us to break a general law as the alternative is the extinction of the human race, there is no harm to anyone other than ourselves, and there is more harm by not doing it than by doing it. I might note that personally, I'd see this as very different from a situation where the only way to survive is by harming others. I suppose there could be Christians or Jews or Muslims or whatever religion you suppose these people are who would dogmatically say that all commands from God must be understood as no exceptions under any circumstances, and therefore we have no choice but to allow the human race to end.

Addendum: Rate of defects

Confer Mike Nichols post.

Consider just one gene. Let's call the "good" gene "A" and the bad, mutated gene "a". Then let's assume that one parent is AA and the other is Aa.

So:

Generation 0: 1 AA + 1 Aa

Generation 1: 50% AA + 50% Aa

Generation 2: 25% will be children of AA+AA, 50% of AA+Aa, and 25% of Aa+Aa

Of the AA+AA, 100% are AA Of the AA+Aa, 50% are AA and 50% Aa Of the Aa+Aa, 25% are AA, 50% Aa, and 25% aa

Summing this up gives:

AA=25% x 100% + 50% x 50% + 25% x 25% = 25% + 25% + 6.25% = 56.25%

Aa=25% x 0% + 50% x 50% + 25% x 50% = 0 + 25% + 12.5% = 37.5%

aa=25% x 0% + 50% x 0% + 25% x 25% = 0 + 0 + 6.25%

So the grandchildren will have 6.25% incidence of a pair of bad genes, and thus show the recessive characteristic.

Assuming that each parent has 2 such bad genes, with no overlap of the 2, then there are 4 total bad genes, each of which will show up in 6.25% of the grandchildren. The probability of a child not having any one of these is 100 - 6.25 = 93.75. The probability of having none of the four is thus 93.75 ^ 4 = 77.25%. So -- assuming we are talking about fatal mutations here -- about 23% of the grandchildren will have at least one of the 4 fatal mutations, and die.

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  • $\begingroup$ I ask having no idea. Wouldn't the best genetic pairing be an Aboriginal Australian and a Native South American? $\endgroup$ – billpg Aug 4 '15 at 16:58
  • $\begingroup$ @billpg The best pairing would presumably be two people as genetically distant as possible. As the prevailing theories are that both native Americans and Australian aborigines are descended from people living in Asia, yes, they split off a long time ago so they'd be distant, but I think they'd be closer to each other than either would be to a white European or a black African. I'm happy to yield on this to anyone who wants to argue strongly for a contrary theory on the origin of either. $\endgroup$ – Jay Aug 4 '15 at 18:49
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    $\begingroup$ Re the last statement: If (as in any of the Abrahamitic religons) one of the commands is "multiply" and one is "no incest", they may be in logical trouble $\endgroup$ – Hagen von Eitzen Aug 4 '15 at 19:50
  • $\begingroup$ @HagenvonEitzen True. I think most people accept that every law -- God-given or man-made -- has exceptions in extreme cases. If you rushed into a burning building to save a baby, I sincerely doubt that either God or the law would condemn you for trespassing, even if you didn't first get permission to enter that building. If a crazed gunman was holding hostages and killing them one by one, and in a moment of carelessness he put down the gun and one of the hostages grabbed it from him, I can't imagine that God or the law would condemn that person for stealing the gunman's property. Etc. $\endgroup$ – Jay Aug 4 '15 at 21:04
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It's unlikely that they would be able to repopulate, since they're starting with such a limited amount of genetic diversity.

If they wanted to try, though, the wisest thing would be for them to pair off the children and have each set produce one or more kids, then mate the cousins and go from there. The initial couple would need to try to produce as many children of their own as possible.

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  • $\begingroup$ I think it's just flat-out impossible, even. $\endgroup$ – Erik Aug 4 '15 at 7:52
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Just as an alternate possibility: using your specific scenario, if they return to earth and there is still food available in supermarkets (so it's not something like a century later) - why not look for sperm samples in sperm banks?

I'm obviously not an expert when it comes to actually using such samples, but as astronauts they would probably have enough scientific knowledge to read informations about the procedures to do so. They have enough time to learn about it. If they still manage to conserve those samples for future generations, genetic diversity wouldn't be an issue.

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  • $\begingroup$ If everyone is dead, power generation would end almost immediately, thus sperm banks would thaw out pretty quickly. $\endgroup$ – bowlturner Aug 4 '15 at 15:02
  • $\begingroup$ @bowlturner That's true, but I'm not sure if those systems have some sort of emergency generators or are already stored in cool areas (where thawing would take a long time). My assumption is based on the mentioned part that the food in supermarkets didn't go bad yet ;) But I guess that colder areas (arctic) also have sperm banks - wouldn't that stuff survive there? $\endgroup$ – Katai Aug 4 '15 at 15:45
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    $\begingroup$ it might. The food thing I was expecting mostly to be canned goods. You also have to think that there are two people, how do they travel, would they go far? Would they think of sperm banks before it's two late? Would they be able to find them? No internet, not quick google. Survival would be paramount. $\endgroup$ – bowlturner Aug 4 '15 at 15:47
  • $\begingroup$ @bowlturner Yeah, that's only asuming they'ld realize that they HAVE to reproduce to save humanity - but if all those informations are missing, how can they even know that they're the last human beings? They'ld have to assume that some group of humans survived somewhere on the world - in other words, they might don't even think about the whole recreation thing then. But yeah, the idea has some flaws, it's just intended as an alternative approach to the whole incest problem ;) I think getting 1 kid per year wouldn't be much more pleasant than a long travel (cars still exist!). $\endgroup$ – Katai Aug 4 '15 at 15:55

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