Uncommon Descent Serving The Intelligent Design Community

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

Share
Flipboard
Print
Email

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?.

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. wd400
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. PaV
kevnick, Hope this clarifies a little: https://uncommondesc.wpengine.com/genetics/cost-of-maintenance-and-construction-of-design-neutral-theory-supports-id-andor-creation/ scordova
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-plague-family-independent-evolution-bacterial.html bornagain77
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". scordova
JoeCoder, http://www.examiner.com/article/is-mitochondrial-eve-6-500-years-old scordova
Sal, what's your source for Cow-mtEve at 10k? JoeCoder
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. scordova
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? Jehu
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. scordova