Q: If the number of ancestors you have doubles with each generation going back, you quickly get to a number bigger than the population of Earth. Does that mean we’re all a little inbred?

Physicist: In a word: yes.  But it’s not a problem in large populations.

The original questioner pointed out that in the age of Charlemagne (more or less when everybody’s 40-greats grandfolk were living) the world population was between 200 and 300 million, and yet 2^40 (the number of ancestors you would have with no overlap) is 1,099,511,627,776.  As it happens, 1.09 trillion is bigger than 300 million (math!).  That means that your average ancestor alive 1200 years ago shows up in your 40-generation-tall family tree at least around 4,000 times.  That redundancy is likely to be much higher.  Many of the people alive during the reign of Chuck the Great left no descendents, and while your family tree is probably wider than you might suspect, most of your ancestors probably came from only a few regions of the world.  Most people will start seeing redundancy in their family tree within a dozen generations (small towns and all that).  Fortunately, “redundancy” isn’t an issue as long as the genetic pool is large enough.

The biology of living things assumes that things will break and/or mess up frequently.  One of the stop-gaps to keep mistakes in the genetic code from being serious is to keep two different copies around.  This squares the chance of error (which is good).  If one strand of DNA gets things right 90% of the time, then if you have access to two strands that gets bumped up to 99% (of the 10% the first missed, the second picks up 90%).  However, if you have two identical copies, then this advantage goes away because both copies of the DNA will contain the same mistakes.  That’s a why (for example) red/green colorblindness is far more common in dudes (who have 1 X chromosome) than in ladies (who have two).  Don’t get too excited ladies; gentlemen still have two copies of all of the other chromosomes.  Also, that 90% thing is just for ease of math; if 1 in 10 genes were errors, then life wouldn’t work.

The two copies that each of us carry around are only combined together in the germline (found in our junk), and that combination is what’s passed on.  What makes the cut into the next generation is pretty random, which helps ensure genetic diversity (and is why siblings look similar, while identical twins look the same).

As long as genes have a chance to mix around, the chance of an error showing up in the same person twice is pretty low.  That said, there are a lot of things that can go “wrong” so, statistically speaking, everybody‘s got at least a few switches flipped backwards.  It happens.  If it weren’t for mistakes, biology would be pretty boring.

An impressive, but somewhat speculative computer model, says it’s likely that we all have a common ancestor (a long-dead someone who is directly related to everyone presently living) a mere few thousand years ago.  That person is very unlikely to be unique, and their genes are so watered down by now that it barely matters who/where they were.  What the computer model is saying is that, given what we know about human migration and travel, a “single drop in the human genetic pool” only takes a few thousand years to diffuse to the farthest corners of the world.

So we all have some repeated ancestry, but it’s no big deal.  You still have lots of ancestors with lots of genetic diversity.

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12 Responses to Q: If the number of ancestors you have doubles with each generation going back, you quickly get to a number bigger than the population of Earth. Does that mean we’re all a little inbred?

  1. Jackie says:

    An impressive, but somewhat speculative computer model, says it’s likely that we all have a common ancestor (a long-dead someone who is directly related to everyone presently living) a mere few thousand years ago. 

    How could this bareley be worth knowing who/where they were? Do you not think that, atleast some of the questions of our origins would be answered? Could have Theological answers as well, be it positive or negative.

  2. bitterauldqueen says:

    I have thought this for some time but was not sure until I read your article. I also believe that our indiscriminate breeding re-inforces health problems like hip dysplasia in dogs.

  3. Flavian Popa says:

    Nice post. It makes me wonder about one thing. In the past, total number of humans inhabiting Earth was very little in comparison to today’s. Nevertheless, marriages happened sometimes among related folks, even “very related” folks, and still the genetic strength was not affected at all, whereas today, if you get two cousins to marry, and the kid of a third cousin to marry the offspring of the first two, you may get the so – called genetic degeneration…any possible explanation?

  4. The Physicist The Physicist says:

    @Flavian Popa
    The effect of inbreeding has been the same as long as there’s been breeding. Genetics today works the same as it always has. Individual groups may be more or less prone to certain afflictions (e.g., Martha’s vineyard) due to the prevalence of a particular block of code or other, but that’s been true essentially forever.

  5. Martin says:

    Wait Buy Why, a blog nearly as wonderful as this one, recently covered this topic as well:
    Your Family: Past, Present, and Future

  6. Dr. Doctorbee says:

    In regards to Jackie’s comment, the next sentence is very important.

    “That person is very unlikely to be unique[.]”

    That is, Jackie and I probably share a common ancestor within the last few thousand years. Let’s call them Grand-JackA.

    Similarly, Mrs. Doctorbee and I also share a common ancestor within the last few thousand years. Let’s call them Grand-JackB.

    What the sentence says, and what some statistics can show is that it is extremely unlikely that Grand-JackA and Grand-JackB are the same person. Most certainly, they are not. So searching for this “most prolific” Grand-Jack is not feasible.

  7. Pingback: Somewhere else, part 133 | Freakonometrics

  8. Elaine Puricelli says:

    Hmmmm…. I have a “disorder” caused by a “gene mutation” so I’m told.
    Don’t worry it has nothing to do with insanity. So….while one considers the
    gene pools of our ancestors let’s not forget about gene mutations.
    My doctor said it’s natures way of trying to correct a malady and sometimes
    goes awry. So instead of hemophilia, which the doctor said may have been
    manifested in one of my ancestors long ago, the genes overcorrected, “gene
    mutation” and created thrombophilia in myself and my more recent
    ancestors. Neat stuff those mutated genes. Weird. One wonders what
    signals a gene to “correct” or otherwise try to fix a genetic trait. Is it the
    water? Who knows. Maybe it’s the environment at the time that first
    gene mutation flip ancestor lived? It has to do with amino acids in the
    DNA changing out the order of that particular gene – amino acid trading
    places game. So I’m told.

  9. Daniel says:

    Since the number of ancestors doubles with each preceding generation back, how do we avoid the absurdity that none of us would exist without an astronomical number of them when the world clearly didn’t contain that many people? Overlap doesn’t help here; I myself would need over a billion ancestors as recently as the year 1000 C.E. Explain, please.

  10. Daniel G. says:

    To my homonymous above, it is simple. In a certain moment back in time, with a smaller population there must’ve been a tremendous amount of overlapping.

    The article itself says that the same person might appear more than 4000 times in a given individual’s family tree. So, you don’t have a trillion *different* people, but rather a trillion people where most of them are the same, not to mention that you have to sum up the people from different generations.

  11. Jeremy Parker says:

    I would like to see this expressed as a percentage of each generation. The industrial revolution is fairly recent in this context and before that wars, migration, etc… were fairly constant allowing for a relatively stable guestimate.

    Does the 4000 assume the breadth of our hypothetical gene pool is the human population at that time (stated as 300M)? If we look at DNA evidence we will quickly see that we should only consider regional populations for the breadth of our tree at any given point (for instance all my ancestors come from Norway, Sweden, Scotland, England, and Germany) So the North Sea region population would be the relevant breadth extreme (even assuming I am related directly to every living soul then and there). It would be interesting to study established trees to identify an approximate percentage and see how it jives with the math (whether we have to assume a decreasing redundancy with time).

  12. Matman says:

    It’s worth noting that the same process of random errors (“switch flips”) is an ongoing process, not just one that is passed on. Errors accumulate in successive generations until there are enough (or one particularly bad one) to prevent “fitness” (meaning the individual so affected doesn’t produce viable offspring to pass on the defects). Modern technology (especially medical science, but not exclusively… think about the prospects for extremely myopic individuals in a pre-historic environment) has made it possible for individuals to survive that in the past wouldn’t have, and thus pass on their defects.

    So in effect, technology leads to “devolution”, whereby humans accumulate more genetic defects. Ironically, it is also leading us to the ability to change the genes. This leads to an ethical/existential morass that no one is really talking about.

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