I read in this question that the minimum viable population without causing large problems in genetic diversity is about 50. If we have a larger population (say a hundred) and genetic diversity becomes a problem and the effects of incest kick in, the population is not guaranteed to go extinct. This will mean that genetic problems will be inherited by most of the population very quickly. Assuming the population survives, how long will it take for this relatively monogamous society to regain the modern genetic diversity of modern America?
First off, I know you didn’t ask for a genetics lesson, but I need to explain some fundamentals. The majority of human variation occurs in the form of Single Nucleotide Polymorphisms or SNPs. A SNP is a difference in one nucleotide base of the DNA molecule. So if some people have a cytosine base at position 1,000,000 on Chromosome 1, and others have a thymine base, then the 1 millionth base on chromosome 1 is a SNP. According to wikipedia it is estimated that there are anywhere from 10 million to 30 million SNPs in the human population. This number only includes those polymorphisms which occur at at least 1% frequency in the human population, so it ignores very rare variation. The human genome has a of total of ~3 billion bases across its 24 unique chromosomes. This means that 1 out of every 100 to 300 bases in the genome is a SNP. Now, any 2 people will have the vast majority of these SNPs in common. If 2 people differed at all 30 million of them, their genomes would only be 99% similar.
On to the question at hand. Let's estimate how much of this starting variation the founder population of 100 will have. Each will bring 2 copies of the genome, so we start with a total of 200 copies of every base in our starting gene pool. I said before that each of these 30 million SNPs occurs at at least 1% frequency in the population. So each of our 200 copies of each base has at worst a 1% chance of having the less frequent variant. This means that the probability of any given SNP in the general human population having copies of both alleles in our founding population is at least ~87% (according to a binomial calculator I found online). If the frequency of the less common allele is higher than 1%, then that chance increases, so 87% is the worst case for capturing the rarest SNPs. Many SNPs will have frequencies closer to 50/50, in which case the chance of getting copies of both is nearly 100%. I would therefore estimate that ~90% of SNPs, which make up the majority of human genetic variation will be maintained in our founder population, assuming they were as genetically diverse as possible. That means we might lose 10%, or 3 million rare SNPs. Additionally, in the first few generations of the population more variation could be lost through random chance, but this could be minimized as long as the founders have lots of children. The total loss of genetic diversity probably won’t be a big deal, but in case you want to recoup those losses the wikipedia article I linked earlier estimated that 60 new mutations occur in every new human we make. To get 3 million new mutations we would need 50 thousand new humans. Again, some of those mutations will be lost randomly, but I think its a reasonable estimate.
Some caveats to this are that I am only considering Single Nucleotide Polymorphisms. There are also copy number variants and other larger features that vary between individuals, but there are far fewer of these than there are SNPs. I’m also only considering polymorphisms that occur at at least a 1% frequency, anything super rare is fairly likely to get lost, but the rare stuff will also be the first to come back with new mutations. Also, we are only considering the autosomes here. There will only be 150 X chromosomes in the starting population and only 50 Y chromosomes. The Y will lose a large percentage of its rare variants, but considering half the population does just fine without a Y it shouldn't be too bad.
- A founder population of 100 people (50 men and 50 women) with no fore-bearers in common going back at least 5 generations.
- Five children per couple per generation.
- Good records are kept and laws are enforced which forbid intermarriage/procreation with someone who you are related to for as many generations as possible.
- The founder population is as genetically diverse as possible (per Mike Nichols SNP discussion).
- Given the assumptions, at generation 0 your population is already likely more genetically diverse than the present US. This seems counter-intuitive, because the US has a high degree of cultural and racial diversity, and a large population, nearly all immigrants within the last 200 years from all corners of the globe. It is important to recognize that 'culture' and 'race' are social constructs, and genetic diversity is a crisply quantifiable scientific quality. In the Wikipedia article quoted by Mike Nichols, the greatest amount of genetic diversity occurs among and within populations in Africa, and is reduced in the migratory distance from Africa, with Europeans being less genetically diverse than Africans, and Asians being less genetically diverse than Europeans, with aboriginal North-and-South Americans being even less genetically diverse. Most African-Americans originated in West Africa, somewhat distant from the most genetically diverse section of Africa (Southern) and represent about 13% of the current population of the US.
- At generation 4 >50,000 new humans have been added and the lost 10% genetic diversity from gen0 is likely restored, though it is highly likely that the 'new' diversity is very different from the 'old' diversity.
- Somewhere after gen9 you have more people than the present US.
- Somewhere after gen11 you have more people than are currently on Earth.
- Around gen6, the laws will need to permit people to marry even if they are related at Gen 0. However as the population has grown from 100 to about 1.6 million, with a total of 1.9 million new people added, and with 3 million SNP mutations per 50,000 people, about 1.7 million new (possibly overlapping) mutations have occurred.
I would say, how long did it take the first time? I would guess it would take just as long again. It is believed we almost went extinct about 70,000 years ago, and we were reduced to approximately 3000 individuals, so I'd say between 70,000-80,000 years if it was mostly natural mutations.
Edit: If the survivors know enough about genetics and can put together a plan to get a none threatened population level up, then things could be a bit faster. Having different parents for each child is one way to speed things up and create a stronger gene base. Good records would have to be kept for several generations, if not more to try and prevent incestuous relationships that could be damaging. People would actually be the opposite of 'horny teenagers' because they likely wouldn't be picking their own sexual partners, at least not for purposes of procreation. this might bring the total time down by more than half, depending on how long the 'plan' is followed (honestly, likely much less than the first 1000 years following a 'plan')
Over short periods of time, your population's genetic diversity can only decrease. Diversity for this population can only increase by the introduction of new gene alleles (usually due to mutation). To gain diversity, you need to do one of the following:
- expose the population to conditions with high selective pressures (aka a high death rate)
- increase the mutation rate (aka a high death rate)
- use genetic engineering to artificially create more diversity
- or some combination of the above
Before pursuing either 1 or 2 you ought to get your population higher to ensure survival of the species first.
Unfortunately, this two step approach (increase population first and then increase the mutation rate) and the fact that I don't know how drastic you're willing to be about them means that I can't provide a quantitative answer.