This is where questions related to the #1 Biology, Genetics, and Evolution bestseller PROBABILITY ZERO will be posted along with their answers.
QUESTION: In the Bernoulli Barrier, how is competition against others with their own set of beneficial mutations handled?”
Category error. Drift is not natural selection. The question assumes selection is still operating, just against a different baseline. But that’s not what’s happening. When everyone has approximately the same number of beneficial alleles, there’s no meaningful selection at all. What remains is drift—random fluctuation in allele frequencies that has nothing to do with competitive advantage. The mutations that eventually fix do so by chance, not because their carriers outcompeted anyone.
This is why the dilemma in the Biased Mutation paper bites so hard. Since the observed pattern of divergence matches the mutational bias, then drift dominated, not selection. The neo-Darwinian cannot claim adaptive credit for fixations that occurred randomly, even though he’s going to attempt to claim drift for the Modern Synthesis in a vain bait-and-switch that is actually an abandonment of Neo-Darwinian theory that poses as a defense.
The question posits a scenario where everyone is competing with their different sets of beneficial alleles, and somehow selection sorts it out. But that’s not competition in any meaningful sense—it’s noise. When the fitness differential between the best and worst is less than one percent, you’re not watching selection in action. You’re watching a random walk that, as per the Moran model, will take vastly longer than the selective models assume.
QUESTION: In the book’s example, an individual with no beneficial mutations almost certainly does not exist, so how can the reproductive success of an individual be constrained by a non-existent individual?
That’s exactly right. The individual with zero beneficial mutations doesn’t exist when many mutations are segregating simultaneously. That’s the problem, not the solution. Selection requires a fitness differential between individuals. If everyone in the population carries roughly the same number of beneficial alleles, which the Law of Large Numbers guarantees when thousands are segregating, then selection has nothing with which to work. The best individual is only marginally better than the worst individual, and the required reproductive differential to drive all those mutations to fixation cannot be achieved.
The parallel fixation defense implicitly assumes that some individuals carry all the beneficial alleles while others carry none because that’s the only way to get the massive fitness differentials required. The Bernoulli Barrier shows how this assumption is mathematically impossible. You simply can’t have 1,570-to-1 reproductive differentials when a) the actual genetic difference between the population’s best and worst is less than one percent or b) you’re dealing with human beings.
QUESTION: What about non-random mutation? Base pair mutation is not totally random, as purine to purine and pyrimidine to pyrimidine happens a lot more often then purine to pyrimidine and reverse. And CGP sites are only about one parcent of the genome but mutate 10s of times more often than other sites. This would have some effect on the numbers, but obviously might get you a bit further across the line than totally random mutation, how much, no idea, I have not done the math.
Excellent catch and a serious omission from the book. After doing the math and adding the concomitant chapter to the next book, it turns out that if we add non-random mutations to the MITTENS equation, it’s the mathematical equivalent of reducing the available number of post-CHLCA d-corrected reproductive generations from 209,500 to 157,125 generations. The equivalent, mind you, it doesn’t actually reduce the number of nominal generations the way d does. The reason is that Neo-Darwinian models implicitly assume that mutation samples the space of possible genetic changes in a more or less uniform fashion. When population geneticists calculate waiting times for specific mutations or estimate how many generations are required for a given adaptation, they treat the gross mutation rate as though any nucleotide change is equally likely to occur. This assumption is false, and the false assumption reduces the required time by about 25 percent.
Mutation is heavily biased in at least two ways. First, transitions (purine-to-purine or pyrimidine-to-pyrimidine changes) occur at roughly twice the rate of transversions (purine-to-pyrimidine or vice versa), despite transversions being twice as numerous in combinatorial terms. The observed transition/transversion ratio of 2.1 represents a four-fold deviation from the expected ratio of 0.5 under uniform mutation. Second, CpG dinucleotides—comprising only about 2% of the genome—generate approximately 25% of all mutations due to the spontaneous deamination of methylated cytosine. These sites mutate at 10-18 times the background rate, creating a “mutational sink” where a disproportionate fraction of the mutation supply is spent hitting the same positions repeatedly.
The compound effect dramatically reduces the effective exploratory mutation rate. Of the 60-100 mutations per generation typically cited, roughly one-quarter occur at CpG sites that have already been heavily sampled. Another 40% or more are transitions at non-CpG sites. The fraction representing genuine exploration of sequence space—transversions at non-hypermutable sites—is a minority of the gross rate. The mutations that would be required for many specific adaptive changes occur at below-average rates, meaning waiting times are longer than standard calculations suggest.
This creates a dilemma when applied to observed divergence patterns. Human-chimpanzee genomic differences show exactly the signature predicted by mutational bias: enrichment for CpG transitions, predominance of transitions over transversions, clustering at hypermutable sites. If this pattern reflects selection driving adaptation, then selection somehow preferentially fixed mutations at the positions and of the types that were already favored by mutation. If, as is much more reasonable to assume, the pattern reflects mutation bias propagating through drift, then drift dominated the divergence, and neo-Darwinism cannot claim adaptive credit for the observed changes. Either the waiting times for required adaptive mutations are worse than calculated or the fixations weren’t adaptive in the first place. The synthesis loses either way.
