With a group of twelve human couples stranded on a island, how many generations could they go before becoming infertile due to inbreeding?
How many generations could a small group go without suffering the effects of inbreeding
1$\begingroup$ Depends on how lucky they are, doesn't it? If they are really lucky they could grow and multiply and take over the world. $\endgroup$– AlexPJan 29 at 23:32
$\begingroup$ @AlexP explain? $\endgroup$– Bryan McClureJan 29 at 23:33
6$\begingroup$ Inbreeding in itself does not have to lead to bad effects. It's just that quite often it does result in an increased rate of genetic diseases. But it does not have to; if the population is extraordinarily lucky then none of the twelve founders carries any genetic defect. Or if they are only very but not extraordinarily lucky then none of the founders carries any seriously debilitating defect. The point being that inbreeding is bad only in the statistical sense; after all, some people do win the lottery. $\endgroup$– AlexPJan 29 at 23:36
3$\begingroup$ It may depend partly on how diverse the 12 couples are. $\endgroup$– manassehkatz-Moving 2 CodidactJan 30 at 1:58
1$\begingroup$ Inbreeding causes potential (pre-breeding age) deaths in population with bad genetic mixes. The genetic lottery will (assuming the population isn't hopelessly filled with genetic problems) have at least some babies that will mature to breeding age. Inbreeding will cause a lot of deaths, but some babies will survive to breed, and these will tend to be freer of genetic defects. This is how small breeding pools can survive; it requires an environment that allows for a lot of babies and a population that is willing to accept lots of infant mortality. $\endgroup$– Mark RipleyFeb 2 at 0:28
The big problem with inbreeding is the potential for genetic diseases to cause problems. This is usually related to the increased risk from a "bad" genetic variant which exists in a founding population. For example, suppose that a disease is tied to a single recessive allele (sickle cell anemia is, kind of, an example of this). A person who has one copy of the disease-causing allele (the "bad" variant) will be fine, while a person with two copies of the bad variant will be afflicted with the disease.
In a large population, it is likely that the prevalence of the bad variant of a gene will be relatively low (there is selective pressure which will, in general, select against the variant). As such, if two random people from a large population have children together, there is a relatively small chance of passing on a bad variant gene from both parents, and a correspondingly small chance that their children will be afflicted this recessive genetic ailment.
However (in this simplified model), any individual who has a copy of the disease-causing variant has a 50% chance of passing that variant on to their children. As such, if one sibling has the bad variant, then there is a 50/50 chance that the other will, as well. Hence there is a 25% chance that, if these siblings have children, those children will have two copies of the bad variant, and will be afflicted by this genetic disease.
Therefore having children with close relatives is risky because it increases the chance of passing on "bad" recessive genes.
However, if the founding population is free of these bad variants, or if there is significant genetic diversity in the founding population, then the chance any one individual having (and passing on) a dangerous recessive genetic ailment is relatively small. Hence population bottlenecks are not instant doom for a species (for example, it appears that every person in the Americas prior to European contact is descended from a population of around 70 people who crossed over Berengia around 15,000 years ago; 130 years ago, there were around [20 Northern elephant seals], the current population over 30k).
Thus, from a scientific standpoint, a small founder population could go on to establish a population which survives indefinitely.
As this is a question on Worldbuilding SE, rather than some other SE site, the actual question here is "In a fictional setting, how long could a population founded by a small group persist?"
The answer to that question is: it is up to the author.
If it is important for the plot that the colony is at risk of collapse due to a lack of genetic diversity, then the colony is at risk of collapse due to a lack of genetic diversity.
It is believed that every Cheetah alive today descends from a population bottleneck of at most seven individuals that lived roughly 10,000 years ago. This is far more extreme than a reduction to 12 couples, and did not result in infertility.
There are other problems that result from a lack of genetic diversity but there's no reason to believe that infertility would result.
$\begingroup$ While I'm not sure about animals. I can think of multiple examples of inbreeding resarting an infertility in humans. The Egyptian pharaohs, And of course the infamous hasburg's. $\endgroup$ Jan 30 at 15:08
2$\begingroup$ @BryanMcClure Individual cases of infertility, sure, but the whole population? No, not even in those cases. Also, infertility occurs at pretty high rates anyway so it's impossible to definitively link these cases to inbreeding. $\endgroup$ Jan 30 at 16:34
$\begingroup$ the consistent trend of infertile in Egyption pharaohs suggests otherwise. $\endgroup$ Jan 30 at 17:20
1$\begingroup$ @BryanMcClure for that to happen, it means that one pharaoh had the gene to cause infertility and it was was never selected out of that small population, not that inbreeding caused it. Incest was very common across all of Egypt for religious reasons, and that did not stop them from being one of the most densely populated regions in the ancient world. $\endgroup$ Jan 31 at 16:39
2$\begingroup$ It's also important to understand that a single line of succession isn't a population. By their very nature, infertility problems are heavily selected against and thus will always tend to be purged from a population. $\endgroup$ Feb 1 at 17:46
Assuming Stable Genetics (Biiiiiig Assumption) and no pre-existing Genetic conditions and fixed environmental conditions - there's no reason why it couldn't go on forever.
The problem is that Genetics aren't completely stable and that the Environment is never fixed - You could look at some of the European Monarchies as case-studies in in-breeding and draw some conclusions from that.