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This question discusses the various steps a very small gene pool could take to avoid inbreeding however most of the answers agree that it's very unlikely that a group of 6 individuals could avoid all genetic issues.

I'm interested in exactly what those issues are.

It's my understanding that most issues arising from inbreeding are as a result of family containing similar sets of DNA. We all have recessive problems in our genome, this only becomes an issue when our partners' DNA also has the same recessive issues (because two recessive defects don't have the dominant one to correct them). Inbreeding is an issue because brothers and sisters have very similar DNA and the probability of both of them having the recessive genes is far more likely than a random person.

Assuming my understanding is correct why would a group of six unrelated people have this issue? Assuming that they all have different recessive problems their children would have a chance of inheriting the same ones however they are also almost guaranteed to have the correct dominant genes from their parents!

Given that a massive proportion of genetic issues will no longer exist (because the only ones going forward will be those present in those early progenitors) why are the probabilities any higher when starting with a smaller base?

Exactly what symptoms would a colony see if it had too few founding members?

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    $\begingroup$ The specific defect depend on what was being carried by the initial population. if all were free of recessive defects then the population will only get new mutations $\endgroup$ – ratchet freak Oct 29 '14 at 12:14
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    $\begingroup$ You may want to consider how it has turned out for the cheetah. $\endgroup$ – a CVn Oct 29 '14 at 18:53
  • $\begingroup$ There was a polish sci-fi about world like that, with many genetic defects in a small population after nuclear war. Very brutal. Individuals were evaluated on base of survival fitness, and those found lacking were dismantled for organ transplants to fix those surviving. $\endgroup$ – Peter M. Oct 30 '14 at 19:49
  • $\begingroup$ @MichaelKjörling: Or the Native Americans, for that matter. Ordinary European diseases became mega-plagues that wiped out well over 90% of the indigenous population of the Americas, because of a low degree of genetic diversity among the populace, which translates directly to a low degree of immunodiversity. (In plain English, it's far more likely that what will kill one random Native American will kill another random Native American than that what would kill one random European would kill another random European.) $\endgroup$ – Mason Wheeler Dec 21 '14 at 21:45
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So we’ve got the basics down. We all carry mutations in genes that are harmless by themselves, but if you get two broken copies of the same gene bad things happen. The answer to your question has to do with probabilities.

Let’s say you have two populations. In the first there are 100 genes with recessive lethal mutations, each at 1% frequency in the gene pool. This means that on average there are 2 recessive mutations per individual (because each individual has 2 copies of 100 genes with a 1% rate of being mutant). The probability of an individual receiving 2 copies of a single recessive mutation assuming completely random shuffling is 100 * 0.01^2 (one hundred chances of getting two copies), or 1%.

Now let’s look at a population with only 10 recessive lethal mutations, but that are now at a frequency of 10% in the population. On average there are still only 2 recessive mutations per individual, but now if we calculate the chances of a person being born with two of the same mutation we get 10 * 0.1^2 which is 10%.

The two populations have the same total number of recessive lethal mutations, but problems arise more frequently in the second population. So while a populations bottleneck will remove the vast majority of genetic issues, the ones that remain will run rampant in the remaining population.

To further illustrate how this represents a population bottleneck, imagine if you take 5 individuals from population 1 and use them to found a new population. Each of these individuals brought 2 different mutations from the original pool for a total of 10, and in the starting population there is 1 mutant copy out of 10 total (5 people, each have 2) so each mutation is at a 10% frequency. Now we have population 2.

To move away from the hypothetical and address your situation directly. It is estimated that the average person carries ~5 recessive lethal mutations. With a founder population of 6, that means you can expect ~30 total recessive lethal mutations. Each of these would exist in your population at a frequency of 1/12 or 8.3%. The first few generations would not show any issues as you are still breeding completely unrelated individuals, but once the bloodlines are sufficiently mixed each child will have a 1-(1-1/12^2)^30 ~= 19% chance of inheriting two recessive alleles and dying from a genetic defect. This chance will gradually decline over time as the children that die won't pass on those mutant alleles so the bad genes will slowly be purged from the population. Essentially for many generations the birth rate will be fairly low, but will slowly recover.

It's also important to keep in mind that the above only covers recessive lethal mutations. Plenty of recessive mutations are non-lethal and would also be frequently seen in the offspring of this population. Expect a lot of deformities and other weird stuff.

Edit: A recently published paper (http://www.genetics.org/content/199/4/1243.full) has estimated that the average person only carries around 1 or 2 recessive lethal mutations. If this is true then a founder population of 6 that each brought a single mutation would only create a population with 1-(1-1/12^2)^6 ~= 4% recessive lethal mutations.

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    $\begingroup$ Combining probabilities by adding them rarely works. To get the chance that none of the bad combinations are present you want (1-1/6^2)^30 ~= 43% - or a ~57% chance of badness $\endgroup$ – Tim B Oct 30 '14 at 16:42
  • $\begingroup$ You are correct. (1 - probability of 2 bad alleles)^(number of total possible bad alleles) is the right formula. You did make a small mistake though in that 1/6 is the probability of a parent having the bad allele of a given gene. 1/12 is the probability of the child receiving it. So I believe the final number is (1-1/12^2)^30 ~= 81% or a ~19% chance of badness. Thank you for the correction. $\endgroup$ – Mike Nichols Oct 30 '14 at 18:56
  • $\begingroup$ Also, keep in mind that selection works very slowly on recessives. After all, most recessive carriers are heterozygous, and the allele is not expressed, or selected against, in those carriers. $\endgroup$ – WhatRoughBeast May 31 '15 at 11:43
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One particular illness which was common in European nobility exactly because of inbreeding is haemophilia. Note that there were many more than six nobles, and yet you had a direct effect.

To see the problem in its purest form, take the most extreme case: Just one man, and one woman. And now assume one of them, let's say the man, has a recessive genetic defect. He's healthy (because he has a dominant healthy gene to compensate), and of course the woman is healthy because they don't have the defect.

Now they have children. All of their children have a healthy gene from the mother, therefore not a single of them is ill. However half of them will have the defective gene.

Now their children again have children. Now it gets a bit more complicated.

There's a chance of 1/4 that both don't have the gene. In which case neither will their children.

Moreover there's a chance of 1/2 that one of them has the gene. Again, all of their children will be healthy (because each one got a healthy gene from the other parent), but half of them will carry that gene.

Remains the 1/4 chance that both carry the defective gene. Then only 1/4 of their children will not carry it, 1/2 of them will carry one copy (and thus still be healthy), and 1/4 will have two copies of the defective gene, and therefore will be ill.

So together we have that 9/16 of the grandchildren will not have the gene, 3/8 will carry the gene but not be ill, and 1/16 of the grandchildren will have the illness.

Now take Mike Nichols' number that each human has on average about 5 defective recessive genes. That is, the original parents will together have 10 such genes. Assuming each of those genes is inherited independently, the change that a grandchild is healthy is $(15/16)^{10} \approx 52\%$. In other words, about half of the grandchildren will have some inheritable illness.

Now with three pairs, clearly the probability of getting two defective copies of one gene will go down, however you will still want to actively minimize it by ensuring that people who mate are as genetically different as possible.

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Not sure if you can pick out specific defects in general...more of an amplification of shared defects. Think of a coin flip...if you flip it 10'000 times, there is relatively low chances of getting 10'000 heads for results. Flipping the coin 6 times however, and you have a 3% chance of all the same result. Do this 6 person coinflip for each recessive gene and you are going to have a few of these results where all 6 members are carriers of some defect (admittadely it isn't all 50/50 coinflips...but rolling dice 6 times will also have a probability of all 6's)

Hemochromatosis is a good example. It's a two part gene, one from each parent. If both genes are positive, then you have Hemochromatosis and do not process iron correctly. If you have a single positive, then you are a carrier that has a 50/50 chance of passing it to a child, but the one negative gene prevents you from having any effects yourself.

There are a lot of genetic disorders out there that operate on this scale. If there is a common defect amoungst them (flip the coin 6 times) and this defect will amplify through the population. Hemochromatosis has a 5 in 1000 positive in the Caucasian population and a 10% chance of being a carrier. Not likely, but there is such a number of these defects that are possible that odds are one of these disorders are going to be common between them (or at very least, be carries of the same disorder).

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In addition to the active problems of lethal or (in many ways worse) deleterious recessive genes, you also have the problem of limited genetic diversity in other genes, leading to long term brittleness of the population.

Immunodiversity was mentioned above, but there are other examples, mostly dealing with flexibility in adapting to change. See http://en.wikipedia.org/wiki/Genetic_Diversity for more info.

Pity the world with only 6 basic types of human intelligence...

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