How many people are required to maintain genetic diversity?

Actually it is a very important question for laboratory animals (and, I imagine, endangered species) and was calculated to be 25 couples.

With any number of animals (including humans), there is always some inbreeding happening, but you can reduce it with the number of breeding pairs and careful pairing. When you get to 25 pairs (50 animals) and have complete control over pairing, you can sustain the genetic diversity practically infinitely (especially if you take into account spontaneous mutations).

Of course, such control over who can have children with who (plus whether one is at all allowed to procreate and what will be the sex of their children!) would be questionable morally, so in case of populating a distant planet, we would need a larger group, to provide for sexual preferences, fertility problems etc.

Some information on laboratory outbred stocks.

Inbreeding isn't negative at all, so one couple would suffice for colonization.

Inbreeding fixes recessive traits and the ones displaying unwanted traits can be culled. Actually, inbreeding is one of the most potent weapons of evolution, it speeds things up greatly. We went through a major bottleneck event ourselves and lived to tell the tale.

The exact number of individuals needed for a healthy species that will survive X number of generations depends on the species though. To maintain healthy genetic diversity and establish enough different alleles to allow for sustainability of the species. I don't remember the exact number but I think for humans it was something between 1000 or 10000, and if you get below that number the species will likely go extinct by natural causes.

Of course, everything is completely different when you have full control over who mates with who. But still, in the above example of 1 couple, they can successfully start a seemingly healthy population, but due to low genetic diversity they - as a species - won't be able to respond to, say, increased radiation, changes in atmosphere, a virus, bacteria, shortage of food, etc. That's why 1 couple is basically enough, but to ensure longetivity of the species 25 couples is far from enough.

I'm not an expert, but after reading more about it I would say between 500 - 1500 couples without trying to control the pairing.

I don't know where Dan Horvat took these assertion:

To maintain healthy genetic diversity and establish enough different alleles to allow for sustainability of the species. I don't remember the exact number but I think for humans it was something between 1000 or 10000, and if you get below that number the species will likely go extinct by natural causes.

but it seems to be supported by the evidence of past bottlenecks in human population, like the Toba Cathastrofe Theory. The human population is supposed to had a maximum of 3,000–10,000 surviving individuals. I am very optimistic and take the minimum: 1500 couples. It left to match that amount with Dan's source.

The exact answer would come by the designer of the life and DNA. ;-) That info seems to have been leaked by the creator's son in a conference. Thomas has taken note from his words:

I shall choose you, one out of a thousand, and two out of ten thousand, and they shall stand as a single one.

It seems to me that it is talking about genetic diversity, and the minimal proportions are those: 1/1000. That's why I take 500 couples as minimun.

By the way, in the previuos versicle it seems to says that that selection would be in the moment when the human race has finally ended evolving to the intended social and morphological status (very rare indeed):

When you make the two one, and when you make the inside like the outside and the outside like the inside, and the above like the below, and when you make the male and the female one and the same, so that the male not be male nor the female female; and when you fashion eyes in the place of an eye, and a hand in place of a hand, and a foot in place of a foot, and a likeness in place of a likeness; then will you enter the kingdom.

Going back to science, it seems that not to much effort should be made to control the pairing, because we seem to have a subconcient attraction for those individuals of the other sex that present better histocompatibility with us. In the case of humans given by odor and appeareance (mostly simetry).

Also the genetic diversity is supposed to be reached faster, if the environment is more aggresive. Normally a big mutation and adaptation happen after hostile and persistent environment over near 40 generations, something observed with the Peppered moth evolution

So I suppose that if you use well cared laboratory animals, the number can be 25 couples. But if you use a natural hostile enviroment the genetic diversity could be reached sooner.

It might be that if you build a nice human space station in another planet, maybe you need 25 couples, but if you let them nude with no technology and fig leaves you need fewer couples in order the species to survive more adapted (Although you might got many failed attempts)

Another point to consider, is how valuable are those animals for genetic studies?, how much is the study affected by the captivy of their population?, resembles their growing places the natural environment?, how hostile are these environment? resembles this environment the natural population dynamics ? how many generations ago their ancestors had a natural environment ?

Laboratory animals might have less genetic diversity and might need more couples.

I think the issue of epigenetics throws this answer into debate once again. This reminds me of my biggest issue with the book The Transhumanist Wager, which was centered around a very Libertarian tenant of "worth".

Without knowledge of the way in which every aspect of human genetics (including epigenetics) works, how can we possibly establish the "worth" of a given set of base allele, and thus determine minimum viable population? If such a bottleneck were forced (through disaster or "choice") would such a resultant population still be considered "human" by today's standards?

I would say that Humanity must still be defined by more than the sum of our current knowledge of genetics.

I believe these questions are something that are very often missing from the debate around The Singularity [establishing an artificial intelligence beyond the intelligence of humanity]. Most argue that such an event would be the end of humanity, but I disagree; as any intelligence created by humanity would not be so stupid as to destroy the diversity of intelligence that essentially established its baseline. In this line of thinking, personally I believe it would be more along the lines of the ideas presented in the movie Her, in which such Intelligence(s) would establish a way to remove themselves from direct human control, but ultimately observe/compare/contrast humanity as "wild stock" useful for error-correction, and a seperate line of modeling.

You only need a single female. The space ship could carry a database of genetic material in the form of frozen sperm and eggs. The first female would impregnate herself to breed and raise as many daughters as she can, using as much genetic variety as possible. The daughters would do the same once they can.