system
Given the following post, respond as if you're commenting on Reddit:
human
If Noah's Ark were real, and the entire world were reduced to three reproductive couples, how many years could humanity last until the gene mixing made us unviable as species?
gpt
One breeding pair can save a species if and only if you're lucky and deleterious recessive alleles are not present. And they don't end up doing of communicable disease or something due to extremely low genetic diversity.

Larger population helps but ultimately what has to happen at very low populations, whether 2 or 20 or 200, is inbreeding depression needs to be cancelled out by natural selection. Namely, anything that seriously hurts selective fitness that's somewhat rare and recessive needs to do enough damage that it's bred out of the population before the population goes extinct. There are many animal and probably even some small isolated human groups where this has occurred.

The next problem is that with so little population, genetic drift could wipe out most of the existing, already limited genetic diversity for no survival-important reason. This means that in  the post-bottleneck populations, you will have a less diverse genepool which gives everything the sameweaknesses. That's fine if they are in some controlled lab environment where you just make sure they never are exposed to those weaknesses, but in the real world it's quite common that a population bottleneck occurred, causing inbreeding depression, causing a second bottleneck or steepening of the first, removing the dangerous recessives, which allows the population to increase again. Then conditions change and the population goes into yet another bottleneck as they all die to exactly the same thing. So for example a particularly dangerous one is disease because once the population begins booming again it increases the odds of getting a disease, and once the disease strikes it affects every individual organism in the same way. Roll  those dice enough and the population rolls a natural 1. 


So you have:


1. Contracting population.


2. Inbreeding depression further contracts population in a vicious cycle.


3. Possible extinction if population can't pull out of the nosedive, or selective elimination of deleterious recessive alleles.


4. Genetic drift causes some alleles to be lost permanently from the population, reducing genetic diversity.


5. The now selectively fit but not diverse population booms to fill it's old niche again.


6. Extremely harsh population crashes occur due to diseases as a result of lack of genetic diversity, kicking the cycle back to stage 5 or driving it extinct.


7. Eventually the population either goes completely extinct or slowly gets new genetic diversity either from outbreeding or mutation. Bottlenecks stop.