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Why fixation in gigantic but widely separated human populations doesn’t happen

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If there was any time the human population was very small, fixation was likely inevitable as discussed in Neutral Evolution for Newbies, Part 2. The time for required for fixation in a population according to standard population genetics is approximately 4 Ne, where Ne is the effective population size.

For example, for an Ne of six individuals, the approximate time to fixation using this approximation is:

4 x 6 = 24 generations

In 24 generations, assuming they don’t die from inbreeding depression, everyone will be pretty much genetically identical according to standard theory. Even if their differences were huge (maybe millions of nucleotides), they should fix in 24 generations using this approximation.

In contrast consider the current human population of 7 Billion, and suppose the effective reproductively viable population is 1.5 billion. Using the approximation, the time to fixation with Ne = 1.5 billion is

4 x 1,500,000,000 = 6 billion generations

Assuming a reproductive generation is about 20 years, that’s about 120 billion years on average to fix a new trait!

😯

Now given gametic mutation rates are estimated in the ball park of 3.0 x 10^-8 per nucleotide position per generation, let’s do some math as to how much an individual nucleotide position might get overwritten with mutations in 6 billion generations:

3.0 x 10^-8 (mutations per nucleotide position per generation) x 6,000,000,000 generations = 180 mutations per nucleotide position

Which looks non-sensical because it essentially says in the time it would have taken to fix a single point mutation in a given nucleotide position, it will have been scrambled 180 times over anyway, so again as I said before, we can’t blindly follow the formula that says fixation rate equals gametic mutation rate. I gave other conditions under which that claim cannot hold in Fixation rate, what about breaking rate?.

Now if we are dealing with selection, large populations actually help fixation of traits even under weak selection, but how long will that take, and will it even happen for geographically spread out populations that don’t migrate much?

In the case of anti-biotic resistance where a billion bacteria could be killed off for every resistant strain in the first phase of evolving a resistance, natural selection works quite well in fixing a trait. But such forms or truncation selection will not happen in the current human population barring some sort of epidemic that kills of all but a few of the 7 billion living individuals on the planet, at which point we might suppose the human race might as well be extinct should that happen.

If the fixation time under relatively constant population and weak selection takes too many generations, then for similar reasons like the neutral case, the genome would essentially be scrambled any way, so what little is gained by fixation by selection is lost by mutation accumulation. This scrambling is illustrated with the Poisson distribution in Fixation rate, what about breaking rate?.

[cross posted at CEU IDCS, Why fixation in gigantic but widely separated human populations doesn’t happen]

13 Replies to “Why fixation in gigantic but widely separated human populations doesn’t happen

  1. 1
    vjtorley says:

    Hi Sal,

    Thanks very much for your thought-provoking post. I just came across this article, which suggests that even today, with a worldwide human population of 7 billion, the effective human population size is still only 10,000. Here’s an excerpt from an article by Jef Akst, titled, “Ancient humans more diverse?” in The Scientist (January 18, 2010):

    When examining genetic diversity, scientists often use a measure called the effective population size, which describes how big a population has to be to carry its level of genetic diversity. Modern humans have an effective population size of about 10,000 — a relatively low level of diversity. Chimps and gorillas, for example, both have effective population sizes of greater than 20,000. This estimate of 10,000 has been regarded as stable for about 200,000 to 400,000, maybe “as far back as a million” years, said population geneticist Chad Huff of the University of Utah. (Emphases mine – VJT.)

    If that’s right, then it seems fixation could still occur, although it would take 40,000 generations, or 1.1 million years. What do you think, Sal?

  2. 2
    kevnick says:

    Why this fixation issue is such a big deal here @UD and on sandwalk? I admit that I don’t know much about the fixation, but it seem to me to be very speculative at best. I have read everything I could find @UD and sandwalk about the issue, and it appears to me that nobody really has any evidence to support his claims. The way I see it is this:

    Nobody knows what the genome was like of an ape-like-ancestor that chimps and human supposedly diverged from several million if not billions years ago, so how could all this speculation have any validity? I’m puzzled. Educate me, if you can please or provide some links so that I could educate myself.

    On other note, Larry did admit at one point the he could live with it, if most of the non-coding DNA turned out to be functional in human, though he also admitted that most of his thinking would have to change. As an example, he himself provided an example of puffer fish that is lacking junk DNA and something else… Anybody read that?

  3. 3
    scordova says:

    VJ,

    Thank you for the kind words, and I’m delighted you are delving into this because now my ideas are getting free-of-charge peer review from Larry and Joe as they respond on the internet to what we write.

    Now to your question. I believe the true mechanism of fixation is special creation, and that is why there is lack genetic diversity from human to human, cattle to cattle, chimp to chimp, etc.

    The Kimrua/Nei neutral model: neutral evolution for all time, fixation due to neutral mechanisms, small amounts of selection

    ReMine/Sanford neutral model: neutral evolution after special creation, fixation due to special creation, small amounts of natural selection as described by creationist Blyth

    That article puts a spin on the facts. They are forced to admit the populations had to be tiny at some point. You will probably see for every species genome studied in detail, the genomes will indicate a recent bottle neck. That is a testable prediction by the way. 🙂 I’ve suggested we test shark genomes or any other living fossil genomes for recent bottle necks. 🙂

    Whether one believes in Noah’s story, one is still left with the problem of the first species, whether they were special creations (to use Darwin’s phrase) or evolved from progenitors. If they were special creations, then there would be fixation almost automatically unless the male and female were front loaded with some diversity and then the population exploded.

    Cattle Eve is measured to be about 10,000 years back. Human Eve, using REAL mutation rates is 6,500 years back.

    Darwin’s original question was “did species evolved or were they special creations?” If the genomes of species look like they all went through a recent bottleneck about the same time, this would lend support to special creations about the same time. This is a testable prediction.

    I should caution, many of the published mutation rates are suspect because they use the phylogeny method to estimate mutation rates rather than the direct method. And even then, the direct method may have issues. Further, I’m now suspecting mutations are focused on hot spots, not uniform in general. I think over time, these measurements will improve.

    I obviously have my biases, but it is still early in the game to forensically reconstruct the past. We have to gather more evidence and follow where it leads. Right now, we (myself included) can only offer speculations.

    Alright, here is a basic consideration from a simple solution to a differential equation. If we began with 6 individuals and grew them at rate of 0.465% per year over 4,500 years what how many would there be at the end of 4,500 years?

    6 * 1.00465^4500 = 7 billion

    The current population growth rate is more than 1% a year, in times past it was easily .5%. So the limitation is not the ability to make babies, but food sources!

    So do I think there was a recent bottle neck of even as few as 6, maybe even 2 (Adam and Eve), if one believes in miracles followed by natural processes, yes. If one only believes in natural processes, even on theoretical grounds alone, recent bottle necks are possible assuming inbreeding depression didn’t kill off the species. The solution to the differential equation above bears this out.

    Joe Felsenstein had some credible objections to recent Adam and Eve, but again, it all boils down to the mutation rates one is willing to accept. I’d suggest dropping the phylogenetically inferred mutation rates altogether, they have about as much legitimacy as evolutionary theory in general, which for me is not much more than speculation.

    PS
    Larry calls IDists Intelligent Design Creationist. That label is appropriate for me, but for someone like Michael Behe and other IDists the term Intelligent Design Evolutionist might be more appropriate.

  4. 4
    scordova says:

    Why this fixation issue is such a big deal here @UD and on sandwalk?

    It is anti-Darwinian, and thus Larry is now a frienemy, not just a plain vanilla enemy.

  5. 5
    Jehu says:

    If they were special creations, then there would be fixation almost automatically unless the male and female were front loaded with some diversity and then the population exploded.

    Or there were more than two created of each kind and they were genetically diverse?

  6. 6
    scordova says:

    In the case of bottlenecks the more proper concept is lack of genetic diversity (lack of divergence), which is indirectly related to fixation via bottleneck, but lack of diversity is a more accurate term.

    It is possible to have fixation with lots of divergence, i.e. Panthera Genus (lion, tigers, etc.)

    No divergence implies fixation, but the converse is not necessarily true. Just mentioning this for the sake of completeness.

  7. 7
    JoeCoder says:

    Sal, what’s your source for Cow-mtEve at 10k?

  8. 8
  9. 9
    scordova says:

    Talk of cow-Eve reminds me of a pickup line that a guy supposedly used to pickup a girl:

    “If beauty were a drop of milk, you’d be a cow”.

  10. 10
    bornagain77 says:

    OT: Genetic study shows that bubonic plague (Black Death) was caused by loss of genes and streamlining (genetic entropy) of a non-pathogenic bacteria:

    The independent evolution of harmful organisms from one bacterial family – April 21, 2014
    “Before this study, there was uncertainty about what path these species took to become pathogenic: had they split from a shared common pathogenic ancestor? Or had they evolved independently” says Professor Nicholas Thomson, senior author from the Wellcome Trust Sanger Institute. “What we found were signatures in their genomes which plot the evolutionary path they took.
    For the first time, researchers have studied the Black Death bacterium’s entire family tree to fully understand how some of the family members evolve to become harmful.,,,
    The Yersinia family of bacteria has many sub species, some of which are harmful and others not. Two of the most feared members of this bacterial family are Yersinia pestis, the bacterium responsible for the bubonic plague or the Black Death, and Yersinia enterocolitica, a major cause of gastroenteritis. Previous studies of this family of bacteria have focused on the harmful or pathogenic species, fragmenting our full understanding of the evolution of these species….
    “Surprisingly they emerged as human pathogens independently from a background of non-pathogenic close relatives. These genetic signatures mark foothold moments of the emergence of these infamous disease-causing bacteria.”
    The team found that it was not only the acquisition of genes that has proven important to this family of bacteria, but also the loss of genes and the streamlining of metabolic pathways seems to be an important trait for the pathogenic species.
    By examining the whole genomes of both the pathogenic and non-pathogenic species, they were able to determine that many of the metabolic functions, lost by the pathogenic species, were ancestral. These functions were probably important for growth in a range of niches, and have been lost rather than gained in specific family lines in the Yersinia family.
    “We commonly think bacteria must gain genes to allow them to become pathogens. However, we now know that the loss of genes and the streamlining of the pathogen’s metabolic capabilities are key features in the evolution of these disease-causing bacteria,”
    http://phys.org/news/2014-04-p.....erial.html

  11. 11
    scordova says:

    kevnick,

    Hope this clarifies a little:

    http://www.uncommondescent.com.....-creation/

  12. 12
    PaV says:

    VJT:

    I consider it more than interesting that the “10,000” number for the human effective population is held on to.

    Some time ago, I did a calculation (series) to determine what was the “best” population size when it comes to fixation.

    OTOH, if the population is ‘small,’ then it takes a ‘long time’ for the initial ‘mutation’ to occur. OTOH, if the population is ‘large,’ then it takes a shorter amount of time for the initial ‘mutation’ to occur; however, the time for ‘fixation’ now becomes much longer. These two must be balanced.

    From what I can recall, the ‘best’ size for a population—i.e., so that mutation and fixation can occur in the least amount of time [IOW, ‘fast’ evolution]—was around 15,000. But it might have been 10,000. I just can’t recall exactly.

    So, I don’t think that it is a coincidence that the population size they want to attribute to humans is around this “fast evolution” size of 15,000. This is what can happen if you work from conclusions back to premises.

  13. 13
    wd400 says:

    There’s no secret to 10,000: it’s from the heterozgosity of modern populations. The census population size (the one from which we’d have to wait for new mutations) would of course have been much larger.

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