Not a need answer fast. 
With incestuous inbreeding, the children that are born are vulnerable to genetic disorders passed down because the family genes are too close. From a scientific standpoint, just how much diversity/difference is required for this problem to not be present? If two distant cousins bear children together, is that enough mixed diversity to avoid inbred issues, (and how far distant exactly?)
Genetic diseases can inherited even if there is no shared heritage between the parents.
Genetics is a probability thing. Brother/sister share on average 50% of their DNA. There is no degree of diversity that guarantees a genetic disorder (expressed or recessive) in one parent will not be present (either expressed or recessive) in their progeny.
Once the relationship is 3rd cousin then the average shared genes of 0.78% is not significantly different to that existing in the general population.
Depends on how cute he/she is
The master speaks :
“A recent review (Bennett et al, Journal of Genetic Counseling, 2002) says that, on average, offspring of first-cousin unions have a 2 to 3 percent greater risk of birth defects than the general population, and a little over 4 percent greater risk of early death.”
I suggest you look at the data in Table III, etc. in this paper (PDF).
Note that when you read something like “an increase of 2-3% of birth defects” when already there’s a 2-3% chance of such birth defects means a doubling of the odds of something bad happening.
And that’s with one-off unions. After a few generations of cousin marriage things get much worse. While a 3rd-cousin marriage is fairly safe, this should be a one-time deal. No repeats over each generation.
As Mr. thule implied in his full post, inbreeding is a matter of probability. Two parents who are almost unrelated might give their child a bad homozygous allele pair by bad luck; while an incestuous couple might “get lucky” and produce a healthy child.
Note that the chance that the offspring of a brother-sister mating inherits two copies of a particular rare allele is 0.25 (= 50% x 50%). This is the “Wright’s Inbreeding Coefficent” (WIC).
Animal breeders (dogs, etc.) will often maintain pedigrees and calculate the WIC for various proposed matings. However there is no clear answer to how high a WIC can be and still be acceptable. Some webpages imply that even 0.01 is too high (are they “protecting themselves”?), but some breeders will want a high WIC because they seek an especially “pure” breed. One common rule of thumb, I think, is that WIC shouldn’t exceed 0.05.
A first-cousin mating gives WIC=0.0625 if the ancestors are all otherwise unrelated to each other. It will be somewhat higher if several of the ancestors were themselves the results of cousin marriages. Double first-cousin mating and uncle-niece mating each have WIC=.125, which is certainly beyond the threshold of prudent risk.
At least three Kings of Spain had WICs in excess of 0.20 according to their official pedigrees. These include Carlos II ‘el Hechizado’ who had severe deformities; his grandfather Philip III; and the Bourbon King Alphonso XII. (Alphonso, however, is not cnsidered to be the product of inbreeding: despite the official pedigree it is generally accepted that his natural father was one of his mother’s several lovers.)
But that’s different from “a 2 to 3 percent greater risk”. At least, if everyone involved is using the terminology consistently and correctly, which you probably don’t want to take for granted.
I wonder - the original Easter Islanders were probably a single flotilla - one or two canoe-loads? This on top of a chain of expansion that meant the genetic diversity must have already been getting poorer and poorer as settlers moved east from island to island. Of course, these were big canoe-loads, so maybe 100 or more people? yet there do not appear to have been such problems in the Easter Island population that is believed to have peaked about 15,000.
Genetic relatedness decreases with the inverse square law, and even first cousin marriages were quite common in the US before 1900.
While I am definitely of the modern mindset that cousin marriage is wrong, the risk of a 40 year old women having a child with a genetic disorder is higher than first cousins.
Remember the risk is with recessive genetic disorders. The minimum viable population is really about risk, and with ~100-200 individuals you could, with management, repopulate the world. Lower numbers are higher risk, and at higher risk of divergence genetically but it is possible.
Also remember that in some time in the past 100,000 years there was only about 1000 humans or less worldwide for a very long time.
Now with easy movement and communication the risks aren’t worth it but we actually have real world examples with other species rebuilding with 20 individuals without controlled breeding programs. But the risk of going extinct due to a recessive genetic trait go way up with numbers that small.
Had the original settlers of Easter Island arrived with a large number of significant recessive genetic traits they would probably have gone extinct too.
Note that even at the time of Charlemagne to someone who is directly related today, the modern person will have 4,000,000,000,000 direct great-grandparents at that level, which is about 70,000% more individuals than existed in Europe at the time. So the very minor differences that are made up among all populations in Europe is mostly due to inbreeding.
What two things are related by the inverse square law, exactly?
This is a bit of an exaggeration - there’s no evidence for this severe a reduction for a long time. It’s true that modern human genetic diversity corresponds to a surprisingly low effective population size of the order of 10,000. But even a brief population crash wipes out genetic diversity for a long time (diversity goes with the harmonic mean). Numerous models have been proposed to explain the low diversity, including multiple bottlenecks or a somewhat larger (but still small) population for a longer time; there’s no conclusive evidence about which is correct.
Lack of genetic diversity (which reduces the pace at which continued evolution can proceed) and inbreeding are slightly different issues. Note that individuals with bad homozygous genes may be unable to reproduce, so the gene pool will gradually improve. (IIRC, a population which starts with N unrelated individuals will tend over time to a WIC of 1/N if breeding is even.)
Pitcairn Island had a very small number of initial breeders. Has there been a study of the birth defect rate there?
Do you have a cite for this? I thought there was some controversy here, and do not recall the “for a very long time” part.
(“Ninja’ed” by Riemann.)
To clarify I was not referencing the Toba theory, which is disproved.
I will not be able to provide cites until tonight, but this is related to diversity studies of other great apes etc…not the Toba catastrophe theory.
Tangential, but I’m interested in talking bottlenecks, here.
So say there WAS a bottleneck. 10,000 humans 100,000 years ago - or whatever the hypothesis is - all on the edge of extinction. Enormous pressure on the species.
That severely limits diversity. Fine. But how long should it take to reestablish a level of genetic diversity? I’m assuming that once gene lines are gone, they’re gone. The only way to introduce new genetic information - other some of the oddball ways viruses can alter DNA - is through a random level of mutation. Some sort of copying error during mitosis?
Is that correct? If so, how long, based on the numbers above, would it take to get back to a healthy level of diversity?
To explain my reference to the inverse square law.
Your number of parents follows 2[sup]n[/sup] = x, or it grows by the power. While an approximation you still need to capture the “wash out” probabilities for receiving a single copy of a gene from a parent which is not 50% from the previous generation. The easiest way to approximate this for WAGs is to add another degree of freedom which leads you to the inverse square law.
For the spherical cow case or using Perturbation theory method of finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem.
You have three degrees of freedom, which leads to the inverse square lot for the simplest case of inheriting a single segment along a line. Not exact but good for base assumptions. FWIW, that is why sound waves and light fall off with the inverse square law, it is 3 spacial degrees of freedom to expand into and thus has n[sup]3[/sup] possible directions to expand in, which on one face ends up being the n[sup]2[/sup] area.
Your chances are less but I was trying to keep the math simple.
Humans are amazingly similar even compared to other great apes. Genes wash out but I think the assumption you need to check in this case is that humans are diverse, which we are not.
The above mentioned theories are due to the mystery of the extreme lack of variety in the human genome.
But that doesn’t really answer my question, does it?
Humans are genetically not diverse. Fine. But there’s evidence other great apes are diverse. This implies that humans were more diverse in the past.
My question is how long would it take - assuming only the two systems outlined above for adding new genes to the mix - would it take to attain genetic diversity again?
You have to define what “genetic diversity” is, but the mean Minimum viable population estimates in this meta study was about 4169 individuals for a 95% chance of survival.
With human culture and an awareness of genetics 200 humans would be enough to have a 90% chance to repopulate the entire world by some accounts.
But when you have a bottle neck the “genetic diversity” is lost and wont’ be re-created, new divergences may arise. But with policies like laws against inbreeding that diversity will be slower to grow as you won’t have isolated populations.
This is all a gross simplification, but a smaller group of lets say 50 individuals may be able to re-populate the world it is just their chances of success go down. In fact a couple of family groups, if they didn’t have any major recessive genetic traits which would cause collapse may be able to repopulate the world their chances of long term success are just much lower.
To be as clear as possible, the only reason we have groups that we can even claim are distinct is due to large amounts of inbreeding in fairly modern times. The minimal amount of diversity us humans have is because our family trees don’t really branch much.
The minimal viable population could be as low as a pair of people in reproductive age if they get lucky on what genes they have and they were lucky in survival too.
To add to this, while the single migration model is in question in the Americas, the estimated effective size of the groups that peopled the New World is only around 70 individuals.
Mutations during meiosis, not mitosis, are what matters for reestablishing a diversity of alleles. Mutations during mitosis do not get passed to the next generation.
IIRC, each person has, on average, around 64 recessive alleles.
And, on average, about 70 new mutations arise per generation. But many of those new mutations are non-coding or do not alter protein synthesis due to redundancy in the genetic code. And, much more rarely, a new mutation reverts a recessive allele to the dominant type.
I was wondering about this exact OP when the North Sentinel Islanders recently came into the news again. Seems to be a fairly closed group.