The Education of a Population Geneticist

I think it’s funny that Brian Mansfield thinks I’m afraid to discuss evolution with anyone. Fine, Brian, you are herewith challenged to either a) a written debate on population genetics and neutral theory, or alternatively b) a discussion on Rebekah Davis’s channel. We’ll see who lacks what you describe as “the balls”.

“Vox Day tries to refute this on his web site but doesn’t have the balls to do it here.“

My account has been blocked on YouTube for seven years. For me to create a new account and post there would be a violation of their terms. I’m also personally banned from setting foot on Google’s Mountain View campus as it happens. So I will refute his woefully outdated critique and attempt to bring him up to date on the state of the art of his own field here. Anyone reading this is welcome to post this in its entirety in response to his comment.

“The only Kimura ‘equation’ I have mentioned is the probability of fixation of a new neutral allele — 1/2N — so he seems very confused.”

Yes, and that’s the problem. 1/2N is the fixation probability. It tells you the chance that a given neutral mutation will eventually fix, given unlimited time. It contains no time variable. It says nothing about when. The Kimura equation Brian should have used is Kimura’s equation for fixation time: 4Nₑ generations for a neutral allele, or t ≈ (2/s) × ln(2Nₑ) for a beneficial one. Without the time equation, his calculation has no temporal constraint. The fixation time equation is the Kimura equation that Brian omitted, and that’s the equation that produces the result he calls “ludicrous” because it’s the one that forces time back into a calculation from which it was omitted.

Everything Brian says depends upon k = μ applying, and he has obviously never examined the domain conditions under which that identity actually applies. It doesn’t apply over changes in either time or population. It also doesn’t apply to any sexually-reproducing species above approximately 10,000 census. Even setting aside the mathematical domain problem, comparing Bergeron’s (2023) pedigree-measured mammalian mutation rate against the required substitution rate from Yoo et al. (2025) gives k = 32.3μ, not k = μ. Brian doesn’t know the related literature and he hasn’t done the relevant math.

“For Vox Day to say that ‘genetic drift doesn’t happen in any population over 10,000’ is incomprehensibly stupid. Genetic drift happens in every population and his claim otherwise is mystifying. Population size only affects which alleles are effectively neutral.”

It’s only mystifying to those who don’t understand the relevant math and haven’t taken the limits of reproduction into account. What Brian is revealing here is that he doesn’t understand population genetics at all beyond the idealized textbook version. Population size absolutely imposes a hard limit on genetic drift. What he’s doing here is appealing to k = μ again, failing to realize it has been mathematically, empirically, and logically proven to be inapplicable to any real-world population, across more than 100 species.

“Empirically, each human zygote has about 100 new mutations. The question is how many of these are expected to drift neutrally to fixation — that is, they are neutral and they segregate independently of a selected variant.”

The question is not how many mutations are expected to appear or to drift to fixation under irrelevant steady-state assumptions. The question is how many can actually complete the journey to population-wide ubiquity within the available generations, given the actual population size and its history. Expected value under k = μ and realized completions under finite time are totally different quantities. Brian is treating the first as though it answers the second.

“If even just 2 of these 100 are neutral — which is certainly way under the actual proportion — then in a population of size N there are about 2×N new neutral alleles introduced each generation. The probability of fixation of each one is 1/2N. So, the expectation is that there will be on average 1 neutral fixation every generation if just 2% of new mutations are neutral.”

This is k = μ. Input rate × fixation probability = expected output. The algebra is correct. It is also an asymptotic steady-state identity that holds only when the fixation pipeline has been running at constant population size for at least 4Nₑ generations. For humans at variance Nₑ, that’s billions of generations. The pipeline is not full. The identity does not apply. He has derived the delivery rate of a full pipe without checking whether the pipe is full. I have actually checked the pipeline using the ancient DNA data. The empirical evidence supports my math, not his error-filled textbook assumptions. And he’s obviously not aware of Franco Chalub’s 2022 solution of the Neutral Kimura equation with two integral constraints or its implications.

“Day’s calculation of just six fixations over 9 million years is ludicrous. To get this he erroneously takes the time to fixation of a neutral allele, which is very slow. I assume this is the ‘time-related’ equation he refers to.”

The Probability Zero derivation does not use neutral fixation time. It uses Kimura’s fixation time for beneficial mutations: t ≈ (2/s) × ln(2Nₑ), at s = 0.001 (the empirical mean for beneficial mutations in humans from Zeng et al. 2021). This is faster than the neutral time of 4Nₑ, not slower. He assumed which equation was being used without reading the derivation, and he assumed incorrectly.

“This is simply incorrect. It assumes that one allele needs to get fixed before the next one can be considered. But, of course, that is nonsense and thousands of alleles are drifting around independently at the same time.”

The MITTENS calculation does not assume sequential fixation. The LTEE rate of 1,322 gen/fix is a total throughput measurement — the aggregate output of twelve independent populations running every evolutionary mechanism simultaneously, including concurrent sweeps, neutral hitchhiking, and clonal interference. It is the net output after parallel fixation has already occurred. There is no sequential assumption to remove, because the rate was never derived from one.

The Probability Zero derivation at s = 0.001 does compute a per-fixation time, but dividing total generations by per-fixation time to get maximum achievable fixations is not an assumption of sequential processing. It is also a throughput calculation, the same arithmetic you use when you ask “how many jobs can a machine complete in eight hours if each job takes twenty minutes?” The machine can run multiple jobs simultaneously, but total output is still bounded by total time divided by per-unit processing time, adjusted for parallelism. The LTEE rate is the parallelism-adjusted rate.

“His entire premise is a farce and the use of fixation time is an error. The only thing I can guess is that Day seems to think that only 1 allele can be undergoing fixation at any time because if an allele reaches fixation then there are no other alleles in the population.”

He is guessing because he has not read the argument. The Hard Limits paper explicitly addresses the parallel fixation objection under the heading “The Second Objection: Fixations Run in Parallel,” devotes several pages to it, derives the transient fill fraction F(T) = exp(−π²Nₑ/T), and demonstrates that even multiplying by every mutation at every site in every individual across every generation produces an expected number of completed fixations with tens of millions of zeros after the decimal point. The objection he imagines is devastating is the one the paper conclusively refutes.

“So there can be a fixation event every generation at one of these loci, followed by another the next generation at a different locus and so on.”

Only if the pipeline is full. This is the critical point. A pipeline with a 4Nₑ-generation transit delivers one fixation per generation at steady state — that’s k = μ. But reaching steady state requires the pipeline to have been loaded for 4Nₑ generations at constant population size. For humans at variance Nₑ, the transit time is on the order of 10¹⁰ generations. The human lineage has had 252,000 generations. The pipeline isn’t partially empty. It’s functionally nonexistent and empirically confirmed to be empty. The one-per-generation delivery rate he’s invoking is the far-end output of a pipe that hasn’t been fed long enough to deliver anything.

“It would be a remarkably stupid mistake for Day to make, but it is all I can think of that would allow him to get to his impossible conclusion of 6 fixations over 9 million years.”

It is all he can think of because he isn’t aware of the problems with the textbook and he hasn’t read the paper that specifically addresses them. The six-fixation figure (now seven at updated parameters) comes from the beneficial fixation time at s = 0.001, not from neutral drift. The parallel fixation objection is addressed explicitly and closed with a quantitative proof. He has constructed his own version of the argument that would indeed be stupid, attributed it to me, and then refuted his own construction. This is textbook strawmanning.

“The real number is closer to the number I provided, but of course it depends on the real fraction that have been neutral in ancestral populations, which is certainly much higher than the low end estimate I give here.”

His number comes from k = μ. k = μ requires a full pipeline and a steady-state. The pipeline cannot fill above the drift ceiling. His number is zero at any census population above ~10,000. The fraction of neutral mutations is irrelevant to an identity that doesn’t hold.

“And his formula for the probability of 20 million changes is set up to calculate the probability of just one set of 20 million fixations, another colossal blunder on his part.”

There is no blunder at all. Either the specific fixations matter — in which case the Darwillion applies — or they’re interchangeable — in which case they’re neutral noise that can’t explain the observed functional divergence. And furthermore, the drifting of 20 million neutral substitutions is blocked by the Hard Limit and the fact that k != μ in humans.

DISCUSS ON SG

They Never Stop Lying

It’s truly remarkable how evolutionists will keep repeating obviously false statements over and over again, even after they have been a) shown that the statement was always false and b) told directly that they are repeating a false statement. A woman named Rebekah with a YouTube channel called Examining Origins has obviously read Probability Zero and challenged evolutionists to address its arguments there. The video already has 598 comments, and not one single one of them even demonstrates a basic grasp of the issues involved, let alone presents a coherent response.

Philalethist_Physikos: I respect your work, Rebekah! A quick word of caution to the audience on Vox Day’s formula in Probability Zero: his math assumes mutations fix strictly one after another in a single-file line. In real biology, sexual reproduction and recombination mean mutations sort across the genome simultaneously in parallel, so the math doesn’t hold up in population genetics. If you want rigorous mathematical challenges to evolutionary timescales, stick to researchers like Douglas Axe (coordinated mutations) or Walter ReMine and Royal Truman Haldane’s Dilemma and selection cost). They address real population genetics without making the single-file error!

No, literally none of my math assumes serial fixation. Not MITTENS, not the separate and unrelated math addressing the misapplication of Kimura’s steady-state identity, and not the separate and additionally unrelated math proving the impossibility of punctuated equilibrium. To the contrary, serial fixation with sweeps and ancestral drift are about all that is left AFTER the math eliminates various mechanisms that are not viable.

I quote from yesterday’s post: The LTEE runs twelve identical populations of bacteria in parallel from the same ancestor. Every single evolutionary mechanism from natural selection, genetic drift, mutation, hitchhiking, epistasis, compensatory mutation, and frequency-dependent selection, to clonal interference operates simultaneously in all 12 populations for 85,000 generations and counting.

Which is how we know Philalethist_Physiko isn’t merely ignorant, but dishonest. He appears to have read my post, which is why he mentions “sexual reproduction and recombination” and therefore knows that recombination isn’t included in the LTEE calculations, but he still claimed that I assumed serial fixation which is not at all the case. And he also assumes that recombination will help speed up the fixation rate, which it won’t. the recombination appeal is the signature of someone who learned evolutionary biology from the adaptive narrative rather than from the math. In the evolutionist narrative, recombination is always a good thing. In the math, recombination is a double-edged sword that also breaks linkage, imposes segregation costs, and exposes deleterious recessives. But any positive effects of recombination are massively overwhelmed by the much larger negative effects imposed by sexual reproductive limits.

To demonstrate how wildly ignorant the scientists themselves are, consider this comment from someone who claims he is a research geneticist.

brianmansfield6912: This is not ‘unresolved’. I’ve been a research geneticist for almost 40 years, perhaps I can explain the basic problem. There is a critical error in the calculations in that book. The approach he uses calculates the probability of the occurrence of the 20 million SPECIFIC substitution differences that exist between human and chimp. The correct method is to calculate the probability of ANY 20 million differences. That is, how many substitutions are expected to accumulate over 9 million years? Basic mutation rates and probability theory predict about 20 million. The problem isn’t with evolutionary theory. It would be interesting to someday find an honest creationist….

First, the Kimura equation he’s citing is inapplicable and he’s using the wrong one. The applicable Kimura equation, the time-related one, predicts six neutral mutations, not 20 million. The other Kimura equation, the steady-state identity to which he is appealing, has been mathematically and empirically proved to be irrelevant and all the calculations based upon it are totally wrong. Genetic drift simply doesn’t happen in any population over 10,000. This guy has literally no idea what he’s talking about, for all that he’s waving his credentials and Dennis McCarthy’s erroneous babblings around like a flag.

Here’s another demonstration of an inability to grasp what is being analyzed by someone named Taylor:

Just took the time to actually review the paper cited at the 2 minute mark (2009, Barrick et al), and the quote is a blatant lie.

By generation 20,000, that lineage had picked up 45 mutations, or about one per 440 generations. That’s roughly three times faster than the quote says. Then a mutation that sped up mutation across the whole genome appeared around generation 26,000, and the total climbed to 653 by generation 40,000. Vox Day’s own blog attributes the 1,401 figure to a 2017 paper, not the 2009 one, and counts only beneficial fixations, which is just so clearly biased it’s unthinkable that anyone would dare actually publish it. Human genes have evolved traits like near/far sightedness, derpression, anxiety, schizophrenia, endometriosis, sickle cell anemia, and a million other non-beneficial traits. Then there are our different eye colors, hair-growth rates, toe shapes, etc. that are closer to the neutral side… So counting only “beneficial” mutations is just plainly stupid.

The other side of the problem with this quote is that it’s clearly attempting to trick readers into thinking that this observation should be understood to be some kind of universal speed limit for mutations. It’s not. The fastest rate we’ve ever “observed” is hilarious because on one had, it proves that we’ve observed evolution occurring under lab controlled conditions, AND it only sets the bar for what we’ve literally observed in lab, not what we might observe in any and every other species. For example, the largest start we’d ever observed by the early 1700’s was our own, but that didn’t mean that our sun was the largest star we could ever see.
Observing mutation rates in a lab is a massive undertaking, unless you use something incredibly small that reproduces quickly, like bacteria or mice. But also, just because we don’t observe mutations under lab controlled conditions doesn’t mean we haven’t observed them. A human newborn carries about 60 new mutations. That puts the expected human rate at tens of substitutions per generation, which just so happens to be the EXACT order of magnitude that the human–chimp divergence requires.

TBH, I’d be shocked if you even take the time to read this. I’d be astounded if you listened closely enough to consider changing your mind, but I expect, like all other facts that contradict your religious beliefs, that you’ll simply ignore it and continue building your empire of willful ignorance.

It’s not “a blatant lie”. It’s a demonstration that the critic doesn’t have the first clue about the LTEE, how it works, or what it is measuring. First, the number that I have cited, 1,322 generations per fixation, is the AVERAGE number of fixations across the still-healthy populations for 60,000 generations each, confirmed directly from the lab’s raw data. This guy is citing the Barrick 2009 paper’s results for one population: Ara-1. The critic saw that there were 45 mutations detected in that lineage. But those are total mutations detected in a single lineage, not fixations across the entire population, and it doesn’t even begin to take into account what happened in the other 11 populations. The MITTENS figure of ~1,322 generations per fixation is derived from what is now the remaining five viable populations through 60,000 generations to count mutations that actually reached ≥95% frequency in any of those five populations. Taylor is comparing apples to automobiles.

UPDATE: Sometimes I can’t tell if they’re lying or if they’re just retarded as with this comment by CreationMyths.

He claimed he addressed this, but he hasn’t. His math clearly doesn’t, and apparently either Day nor anyone defending him understands that math well enough to realize that. Day says his math accounts for simultaneous mutations and recombinations but if you actually look at his math, it doesn’t. He explains that this is the case, apparently without realizing so, several times in his book. He’s very clear on this.

The math OBVIOUSLY does address this because parallel fixation is built right into the numbers being averaged due to the nature of the LTEE experiment. And it should be immediately obvious that parallel fixation is included in the math because the average includes all the different populations evolving separately at the same time! And the math also obviously does NOT account for recombinations because bacteria do not reproduce sexually. Once more, we have a would-be critic who has no idea what he’s babbling about. He literally doesn’t know what is being measured or how it is being measured.

UPDATE: Correction: CreationMyths is neither lying nor retarded, he’s merely confused MITTENS math with Bernoulli math.

Nope. He specifically explains this in the book. Several times. His math is for sequential fixation. He does not account for the the fact that recombination allows multiple beneficial alleles to fix at once, nor for the fact that selective sweeps fix multiple alleles at once (mostly neutral). For real, you’re all just repeating what he says as though that’s a response to all the reasons he’s wrong. By all means, keep taking his word for it. There’s a reason real biologists take this stuff seriously. It’s just the “waiting time problem”.

Now I understand why he’s confused. He’s confusing the math of MITTENS, which specifically includes and incorporates parallel fixation, with my subsequent disproofs of parallel fixation. Now, I can assume that you think there is somehow a contradiction there. But there isn’t for a simple, but non-obvious reason: neither the Bernoulli Barrier nor the Hard Limit on neutral drift apply to the LTEE experiment because a) the math is an average of 12 different populations and b) there is no time for neutral drift to have occured yet in the 85,000-generation time limit of the LTEE. The MITTENS generations-per-fixation rate includes parallel fixation due to the structure of the experiment. It is literally built into the structure since it utilizes 12 completely separate populations all running simultaneously in parallel. That’s not how real-world species work.

This is the section that has him confused. It’s from Appendix A and he doesn’t realize that it’s referring to different, non-MITTENS math.

The theory of evolution by natural selection fails its own quantitative test, by its own mathematics, against the data its own practitioners have produced and published. The logical structure of the result is as follows. The Bernoulli Barrier proves that parallel fixation—millions of mutations simultaneously reaching fixation—is physically impossible (pn ≈ 10−34,000,000). The Averaging Problem proves that the polygenic rescue—gradual frequency shifts at many loci under selection on aggregate fitness—is logically impossible, because the mechanism destroys the variance it requires to operate. Therefore fixation must be sequential. And sequential fixation is empirically falsified: the fastest rate ever measured in any organism, applied to the most generous generation count, yields 180 fixations where 205 million are required. The impossibility is in the structure—parallel is ruled out a priori by probability and by logic. The empirical falsification is in the throughput—sequential cannot do the work in the available time by a factor of 10⁶.

Now, perhaps I could have worded it better, but the statement is nevertheless correct because the all-cause rate is obviously faster than a sequential rate. They don’t realize that I am implicitly acknowledging the whole basis of their critique there, because it’s totally irrelevant. This is what I meant by the evolutionists not understanding that there are multiple levels to the disproof of evolution by any and all mechanisms. They’re still wrestling with stage one and trying to defend natural selection, so pulling in elements from later stages is only going to confuse them. They don’t realize that I’ve not only incorporated parallel fixation at the most naive level, I’ve subsequently demonstrated why it doesn’t operate the way they imagine it should.

Anyhow, the MITTENS 3.0 paper renders those complicating elements moot to such an extent that I omitted both the Bernoulli Barrier and the Averaging Problem, even though both of them remain entirely correct.

UPDATE: More hilarity forthcoming.

GraysonHawk: We’re all reading Vox Day’s book right now and laughing at how stupid his math is. Video incoming.

It should be amusing to catalog all of the various things this retard is going to get wrong in his desperate attempt to prove that math which has been confirmed by every major AI system and more than 10 math PhDs is “stupid”. They have absolutely no idea how far ahead of them I am; it appears they still genuinely believe that k=u over time even though it was both mathematically and empirically disproved more than a decade ago by mathematicians and scientists who are not me.

DISCUSS ON SG

Math Teacher Can’t Math

Another evolutionary retard publicly demonstrates his retardery to the world. This time it’s a math teacher who would obviously fail every single word problem on a math test.

So I’d like to go into the math of Vox day and Will Duffy. Who am I? I am a math teacher. I am a math teacher in secondary education. Now if we take the reasoning of Will Duffy he says f max that’s the total number of genes fixated over a specific period the result that he gets is in the given time frame we could only have [sighs and gasps] 180 genes mutated and changed.

And what is the time period? That’s t div time that is given. That’s 6300,000 sorry 6,300,000 years of evolution divided by the length of a generation. That’s G len here. The length of a generation for humans is 25 years times 400 generations. So he says it takes 1,400 generations to fix one gene.

Okay. So if we make this calculation times one because D is substituted by one we reach the number 180. Devastating results says Will Duffy, we can only fix and mutate one gene 180 genes over a time period of six million years. If we were to follow this reasoning, it would mean it would mean what? For one gene to mutate and fixate. Sorry, it would have to take 25 * 1,400 is 35,000 years for one gene. And [snorts] the reasoning is you can only mutate and fixate another gene when this time period is over. So we have [snorts] 6 300,000 6,300,000 divided by 80. That would mean 35,000 years for one gene to mutate and fixate.

Now the reasoning is wrong. Why? It would mean that if you have the Marathon of New York with 60,000 participants and an average length of 4 hours per marathon. If you would follow this reasoning, it would take on average 240,000 hours for the marathon to end. That’s 10,000 days. And that means 27 years for all the participants to arrive. Of course, that’s not possible. they run parallel. Well, the same goes with mutation and fixation. So that math is clearly uh wrong.

This guy should be fired from his job immediately. He’s obviously incompetent. The math is not wrong because parallel fixation is clearly and specifically included in the calculation. So are sweeps. So is neutral substitution. So are hitchhikers. So is any and every evolutionary mechanism, with the exception of three minor ones.

First to address his idiotic analogy. What he is attempting to do is add up the cumulative time of all 60,000 runners, which is 240,000 hours, and then claim that it is identical to the amount of time it took to televise the marathon. Because the number that was provided is THE AVERAGE RATE PER FIXATION of all the bacteria in all the viable populations all the time. Once more, we see that an evolutionist doesn’t understand what an “average” is. The 1,400 generations per fixation number is analogically identical to the four hours per runner number.

If he simply looked at the LTEE papers, or the data, or my papers, he would know that is true. For example, in 60,000 generations, the Ara-6 population has 35 fixations. Not in serial. That’s the total number that took place in that population over the 60,000 generations. Which is a rate of 1,715 generations per fixation, which the keenly observant will note is even slower than the average rate, which incorporates multiple populations.

Ericka, this guy, and everyone else to whom they are running to try to “correct the math” are amazingly and astonishingly stupid in their ignorant smugness. It’s obvious that this teacher never read my book or my papers. He’s also never read any of the three major LTEE papers. He’s never looked up the raw data upon which those three papers drew. Because he doesn’t even know what the number he’s trying to “correct” represents.

So for all you lazy, ignorant, and smug cretins who still believe in the mathematically impossible fairy tale of evolution, I will type very, very slowly in the hopes that you can somehow follow the facts:

  1. The LTEE runs twelve identical populations of bacteria in parallel from the same ancestor. Every single evolutionary mechanism from natural selection, genetic drift, mutation, hitchhiking, epistasis, compensatory mutation, and frequency-dependent selection, to clonal interference operates simultaneously in all 12 populations for 85,000 generations and counting.
  2. Parallel fixation, the idea that the same beneficial mutation can arise and fix independently in multiple lineages, isn’t just theoretically possible in this setup, it has been directly observed. The LTEE populations have fixed mutations in the same genes, sometimes at the precisely same nucleotide position, in different populations. That’s fixation running parallel in more ways than one.
  3. The only mechanisms the LTEE doesn’t capture are sexual recombination (bacteria don’t have sex), incomplete lineage sorting (which requires a speciation event), and horizontal gene transfer (the populations are maintained in isolation). Of those three, only recombination could even theoretically speed things up, and the reproductive constraints of sexual organisms more than compensate for it in the opposite direction.
  4. When we calculated the LTEE’s total average fixation throughput at 1,322 generations per fixation, that number already includes almost every way evolution can theoretically take place, in parallel, running flat out under ideal conditions, and it still falls short of what’s needed by six orders of magnitude. Note that the maximum speed of natural selection running in parallel alone is 4,615 generations per fixation.

Note: It is worth pointing out that there are now six populations that were running faster than the 1,322 gens/fix rate at the 60,000-generation mark that are omitted from everyone’s calculations. By now, there may be seven or eight. This is not because anyone is hiding evidence that favors of the mathematical viability of evolution, in fact, this evidence will almost certainly prove conclusively that there can be no evolution over 120,000 generations of strong selective pressure, because the reason these populations are mutating faster is that all six have developed genomic cancer. If they weren’t bacteria, all six populations would already be dead. Hence my papers addressing punctuated equilibrium.

I’m not sure what is more pathetic, the fact that these “educators” don’t understand the first thing about what they’re “teaching” or the way in which the people who follow them are incapable of seeing their obvious blunders. Even when warned about where they are wrong, they blithely just plow forward in their admitted ignorance.

iando808: Hi Jan, note that Vox Day claims that Parallel fixation is accounted for (or at least justified to be excluded) in his work, whether you want to pursue that or not. His papers, all written using AI, are available on zenodo — lots of overlapping papers, a dispersed argument so harder to digest. He refuses or is incapable to get his work peer reviewed.

DeDzjang: Oh yeah, he rejects parallel fixation on shaky grounds. But I’m not schooled on this subject. I know babies differ in plusminus 60 genes from their parents. This alone shows mutation runs parallel, maybe not in 1 generation, but surely over a span of 1400 generations (=35 000 years). This number shows up in different independent research papers. There can not be two: babies differ from parents AND there is no parallel mutation. It’s one or the other.

iando808: DeDzjang — a welcome humility, unlike Vox Day who arrogantly assumes he knows more than anyone else…

I don’t arrogantly assume I know more than anyone else, I observably do know considerably more about the subject than any of these people who obviously don’t know anything at all about it, by their own admission. When did I ever reject parallel fixation on any grounds whatsoever? All I did was point out, correctly, that it was already included in the calculation. When did I ever reject natural selection, for that matter?

And since a) I don’t have any peers and b) the raw data is available in 500-generation slices, I’m putting together a method to determine what the rate of genuinely serial fixation is just to prevent these morons from being able to claim that a number specifically including parallel fixation is a number that excludes it.

UPDATE: The SERIAL natural selection rate for the LTEE at 60k generations is ~24,500 generations per fixation. I’ll want to dig in a little deeper to be certain of that, but that’s what happens when parallel fixation is excluded. So clearly I didn’t leave it out.

Note that now the evolutionists’ only hope is to argue that human mutations, and absolutely all sexually-reproducing animal mutations, somehow fixate much faster in the wild than mutations that appear in laboratory bacteria being subjected to sustained artificially strong selection pressure reported in the range of s ≈ 0.01. This would be a fascinating trick to see them try to pull off, considering that s = 0.001 is what the scientific literature reports as the mean selection coefficient for beneficial mutations in humans.

UPDATE: This guy is truly special.

i truly believe that’s what most people fail to understand in Motoo Kimura’s math. It is much more profound than evolution deniers will ever understand. I failed to get to know his calculations myself, but am now struck with the profundity of his observations and his formulas. Neutral, negative or positive contributions of genes in the selection process have a huge influence on reproduction and the rate of fixation (call it transfer, maybe). This tiny factor “s” in his formula has a devastating influence on how and why species evolve. And it matches the data from research up to this day. Kimuro died long before we unraveled the genome and still his findings are as relevant as they were in his day. Math has moved on, but is still based on his stochastics. Vox’ 8th grade math is a real step back. Puts us back even before Malthus’ formulas of the nineteenth century. That is so sad.

First, Kimura’s math has absolutely nothing to do with the LTEE. If the guy actually knew Kimura’s math, which he doesn’t, then he would know that 60,000 generations isn’t enough time for a single drift mutation according to Kimura’s own equation for time and neutral mutations. Second, at this point I understand Kimura’s math better than all of the population geneticists, let alone math teachers who don’t even know his calculations, because I have studied his derivations and corrected Franco Chalub’s 2012 work that identified how Kimura’s followers ignored his time calculations and misapplied what is a steady-state identity to time-sensitive applications.

Most of Kimura’s findings are no longer relevant to population genetics or the molecular clock. And I have proved that, both mathematically and empirically. But I doubt Mr. Math Teacher even knows what ancestral DNA is, much less how it falsified Kimura’s theories about genetic drift.

DISCUSS ON SG

No One is Ready For It

Sure, the papers on punctuated equilibrium and Kimura’s empty pipeline are going to shake the field of biology to its core. And sure, Castalia Unlimited is going to be the most amazing thing since The Missionaries was first bound in leather and the first Dracula was bound in pigskin at our own bindery. But never before has everything all come together like this. Yes, there is a new mix. Yes, the video is completely out of control. And yes, the funk is deeply evolved.

DISCUSS ON SG

Oligarchs Against Democracy

I don’t think the self-appointed defenders of representative democracy in Germany quite understand that it is them, and not the AfD or “right-wing extremists”, who are the real threat to democracy in Europe.

Germany’s Social Democratic Party (SPD) has called for a formal review that could pave the way for a ban on Alternative for Germany (AfD), as the right-wing party leads national polls following major regional election victories.

The push follows the AfD’s sweeping victories in Saxony-Anhalt and Mecklenburg-Western Pomerania earlier this month, where it secured 43.8% and 38.2%, respectively. German Chancellor Friedrich Merz’s Christian Democratic Union (CDU) suffered heavy losses, including failing to clear the 5% threshold in Mecklenburg-Western Pomerania.

On Tuesday, SPD parliamentary leaders from the Bundestag, Germany’s state legislatures and the European Parliament wrapped up a two-day summit in Bremen by again labeling the AfD a “right-wing extremist party.” They accused it of threatening democracy “from within” and “normalizing racism.” The push comes as the AfD has opened up a record polling lead over Merz’s CDU/CSU bloc. An INSA survey put the AfD at 29.5%, compared with 19% for the CDU/CSU and just 14.5% for the SPD. 

Let’s get this straight. Democracy is supposedly legitimate because it is based on the will of the people. But if the people want something that the current political elite’s don’t, or if they don’t want something that the elite is forcing on them, then their will has to be opposed and their chosen representatives banned from government.

And this is why Aristotle and Cicero described politics as a circle over time. What the SPD represents is the modern form of oligarchy.

DISCUSS ON SG

No Loans for Basket-Weaving

President Trump announces an end to student loans for make-work university degrees:

President Trump is banning students majoring in degrees that don’t make enough money from taking out college loans.

The Los Angeles Times reported Wednesday that the Education Department has finalized a rule that will force schools to prove that the loans students are taking out are paying off.

Degrees for social work, art, religious studies, teaching aides, and music, and cosmetic certification programs will be hit the hardest. For-profit programs will also be hit particularly hard.

First, all student loans should be outlawed and all student loan debt should be forgiven. It’s a predatory scam taking advantage of literal children. And the fact that these loans were being provided to obtain degrees that couldn’t reasonably expected to cover the cost of acquiring them only underlines their predatory nature.

It’s a good first step, but it shouldn’t be the last one.

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The Severing of Nine

The ill-fated JJ McCarthy experiment has ended. The former 10th pick in the draft was traded to the Giants for a 5th round pick. That he turned out to be a bust surprised very few Vikings fans, precisely ZERO of whom were happy about the draft choice in the first place. Nine actually turned out to be worse than Christian Ponder. And Christian Ponder was an equally unpopular first-round draft choice who is the icon of what passes for an unacceptable starting quarterback in Minnesota.

Consider their stats. In addition to being healthier his first two years, Ponder had better stats across the board. McCarthy had a slightly longer pass average, but his TD-INT rate was 0.92 compared to Ponder’s mediocre 1.24.

27 458 774 58.2 4,788 6.3 31 25 72 62 75.7 42.5
10 140 243 57.6 1,632 6.7 11 12 62 27 72.6 35.6

Again, not keeping Sam Darnold was not the problem. Keeping Darnold was untenable for a variety of reasons and it could have worked out well for all the parties concerned. But not keeping Daniel Jones when all they had to do was give him the chance to compete for the starting job, or even just give him the starting job in the first place, was absolutely unconscionable.

It’s a good trade for both teams. The Giants desperately need a backup and at least the Vikings got something out of the mess. And who knows, back in the day there was a young Vikings quarterback who was sent off to New York for a few years and things turned out rather well when he came back to Minnesota.

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Don’t Punctuate My Equilibrium, Bro

Punctuated equilibrium is a theory of speciation proposed by Niles Eldredge and Stephen Jay Gould in 1972. The problem it was designed to solve is straightforward: the fossil record doesn’t show what Darwin’s theory predicts. Which makes sense, of course, now that we’ve proven beyond any shadow of a reasonable doubt that evolution by natural selection is mathematically impossible, never happened, and could not possibly happen. Something that never took place doesn’t leave evidence behind.

And yet, there is obviously evidence of something. So instead of the slow, gradual transitions from one species to another that classical evolutionary theory requires, what the rocks appear to show is species appearing abruptly, persisting unchanged for millions of years, and then suddenly being replaced by other species that also appear just as quickly. Gould and Eldredge proposed that this fossil pattern is meaningful, is not just an artifact of incomplete fossilization, and that speciation happens rapidly in small, isolated populations mutating rapidly under strong natural selection pressure. The result of the rapid mutations result in a burst of dramatic change in a few thousand years, followed by millions of years of stasis when the strong selection pressure abates.

They called this process Punctuated Equalibrium and it rapidly became one of the most influential ideas in evolutionary biology. For fifty years it has served as the standard explanation for why the fossil record looks the way it does. However, in the process of analyzing the data to figure out why the scientists sequencing the E. coli generations were playing it so coy with the average number of fixations per generation for the MITTENS 3.0 paper, a thought occurred to me: if half the populations subjected to very strong artificial pressure were developing genomic cancer, then what were the probabilities required for a species under sufficient selection pressure to speciate in a punctuated manner that would avoid the cancer and the subsequent inevitable extinction?

In our first paper, Punctuated Equilibrium and the Hypermutation Hazard: The Risks of Strong Selection Pressure, Athos and I identified a hazard built into PE’s own mechanism. The same small, isolated populations that PE requires for speciation to occur are exactly the same populations where dangerous recessive genes, specifically, genes for mismatch repair deficiency that cause a massive increase in cancer rates, get exposed as active. We estimated a 2.3% probability per founder event that PE’s mechanism would produce individuals with a condition equivalent to constitutional mismatch repair deficiency, which causes over 90% cancer incidence by age 20. That may not sound like much until you realize PE require hundreds of these founder events to explain speciation patterns across major groups of animals. Across 100 such events, the probability of hitting this biological landmine at least once exceeds 90 percent.

However, the Red Team pointed out that we’d potentially missed a few things and asked for further substantiation of our estimates. It turned out that unlike MITTENS, where sexual reproduction doesn’t speed up the fixation process, it does reduce the likelihood of developing genomic cancer due to something called recombination that does not occur in the bacteria. So in the second paper, Strong Selection and the Improbability of Punctuated Equilibrium, we built the formal mathematical model — and discovered that the cancer hazard, while real and validated by our simulations, is actually the secondary problem.

The primary problem is obvious and more fundamental: PE’s core mechanism simply can’t do what is required of it. When you calculate the minimum selection coefficient required to fix enough new mutations to produce a recognizably new species within PE’s proposed time window, the numbers are either a) too high to be biologically real, or b) they’re low enough to be achievable only because you’ve reduced the amount of evolutionary change to something trivially small, something like a slightly different fur color, not a new species. Therefore, the PE hypothesis is caught between a rock and a hard place: either the mechanism does enough to matter, in which case it requires selection intensities that don’t exist in nature, or it operates within realistic selection paramenters, in which case it doesn’t produce speciation. The two abstracts follow:

Punctuated Equilibrium and the Hypermutation Hazard: The Risks of Strong Selection Pressure

The Long-Term Evolution Experiment (LTEE) subjected twelve Escherichia coli populations to sustained strong selection for over 60,000 generations. Six of the twelve populations independently evolved hypermutator phenotypes through destruction of DNA repair systems: four via mismatch repair defects (mutS/mutL) and two via oxidative damage repair defects (mutT). This is not a side effect. It is a central result: intense selection pressure repeatedly and independently favors the cannibalization of genome-maintenance infrastructure. Convergent evidence from clinical microbiology confirms the pattern is general: Pseudomonas aeruginosa under chronic selection in cystic fibrosis lungs shows hypermutator colonization at 36% patient incidence, while pathogenic E. coli and Salmonella under selection for host invasion show mutator incidence of 1–4%. Direct mammalian evidence establishes the cost: biallelic mismatch repair failure in humans, the homologous pathway, causes Constitutional Mismatch Repair Deficiency (CMMRD), producing cancer at greater than 90% incidence by age 20. The classical mechanism proposed for punctuated equilibrium, peripatric speciation in small, isolated founder populations under intense selection, requires precisely the conditions empirically documented to produce hypermutation, and specifically invokes the small-population dynamics that can expose heterozygous repair deficiency as homozygous repair deficiency. This paper identifies what appears to be a previously unrecognized hazard in PE’s proposed mechanism: the selection regime it requires operates in the same parameter space where DNA repair destruction is empirically favored.

Strong Selection and the Improbability of Punctuated Equilibrium

Punctuated equilibrium (PE) posits that speciation occurs rapidly in small, geographically isolated founder populations under strong selection. We ask two questions. First, can PE’s mechanism achieve its claimed adaptive throughput, the fixation of enough alleles to produce speciation-level morphological change within the punctuation window, given the reproductive and population-genetic constraints of the organisms in question? Second, does the peripatric bottleneck PE requires expose founder populations to the hypermutation hazard identified in Day and Athos (2026c)?

For the first question, we derive the minimum selection coefficient required as a function of the number of required new hard sweeps K_new, the available generations T, and the effective population size N_e, after granting reasonable contributions from standing variation and parallelism. The parameter space divides into three zones: a SAFE zone (s < 0.01) where mutator hitchhiking is improbable but adaptive capacity is limited to fewer than 10 fixations in 10,000 generations and is insufficient for speciation; a DANGER zone (0.01 ≤ s ≤ 0.10) that PE must occupy for meaningful fixation rates but where mutator dynamics become relevant; and an IMPOSSIBLE zone (s > 0.10) where no empirical evidence supports sustained selection across multiple loci. A sensitivity analysis across the standing-variation fraction and parallelism factor reveals a structural dilemma: every parameter combination that produces speciation-level morphological change requires selection coefficients in the DANGER zone or higher, and the combinations that reach safety do so only by reducing the model to standing-variation frequency shifts and a handful of new mutations, which is not PE as originally proposed by Eldredge and Gould.

For the second question, a Wright-Fisher simulation of 50,000 replicate founder events validates the published 2.3% per-event probability of producing CMMRD-equivalent homozygotes at N = 100. The risk is front-loaded, amplified by inbreeding at small population sizes, and robust to purifying selection. Across the number of founder events PE requires to explain cladogenesis, the cumulative probability of encountering the hazard approaches certainty. This pathway operates through founder sampling and drift alone and does not depend on mutator hitchhiking.

We examine mutator hitchhiking as a potential additional pathway and find that for sexual vertebrates with normal meiotic recombination, per-sweep hitchhiking probabilities are very low, orders of magnitude below the parameterized upper bounds. The hitchhiking pathway remains a genuine concern for organisms with limited recombination but is not load-bearing for the paper’s conclusions. The throughput constraint and the CMMRD homozygosity pathway are independently sufficient.

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The Road to Skepticism

A section of a rather long interview by William Dembski, a Founding and Senior Fellow with Discovery Institute’s Center for Science and Culture and a Distinguished Fellow with the Institute’s Walter Bradley Center for Natural and Artificial Intelligence.

Bill: When did you first become skeptical of neo-Darwinism? Was there a particular book, calculation, empirical result, or conversation that made you think the standard account might be mathematically inadequate? Was there a point in life when you were perfectly content to accept whatever the reigning theory of evolution happened to be?

Vox: After reading all of Richard Dawkins’s books as part of my preparation for writing The Irrational Atheist in 2008. I could not believe how stupid and incompetent the man is. He’s a wonderful writer, which is the reason no one ever notices what a vapid cretin he is or that most of his arguments aren’t even coherent. Then, after reading all of Daniel Dennett’s work, I realized that the evolutionists have no idea what they’re even trying to prove or how to prove it. I summed up the entirety of the evolutionist case thanks to Dennett’s core argument: “you can believe biologists because physicists get very accurate results.” All that evolutionary biology has ever amounted to is butterfly collectors telling fairy stories under the guise of stolen scientific valor.

Bill: What were the strongest arguments in favor of evolution that you encountered before offering your own critique of it? I’ve been able to trace blog posts by you critical of neo-Darwinism on Vox Popoli to 2012. Was this when you first officially weighed in on evolutionary theory?

Vox: I never really thought about it much outside of the usual high school biology class. I was offered the opportunity to debate evolution and “be taught about it” by a science teacher who was also an evolution blogger. They love to offer to teach you. And when it became clear that he didn’t understand why “what is the average rate of evolution by natural selection” was not only a relevant question, but an absolutely necessary one, I began to notice that evolutionists are hopelessly innumerate. I mean, sure, it’s a difficult question, but by definition, there is absolutely an answer. I’ve since learned that evolutionists don’t understand the concept of an “average rate.” In fact, some of them with PhDs don’t even understand the concept of “average.” I’m not kidding.

Bill: Did your skepticism begin with natural selection, with universal common descent, with the neutral theory of molecular evolution, with philosophical naturalism more generally, or some combination of these, or none of the above? How did those concerns become connected in your thinking?

Vox: Pure natural selection. I’m not even sure what “common descent” means. I don’t think you would believe how little this stuff interests me, how unfamiliar I am with the normal buzzwords, or how obviously irrelevant the entire traditional evolutionary debate is.

Bill: Which evolutionary theorists do you regard as the strongest or most intellectually serious opponents of your position? Which do you think are fakers or poseurs?

Vox: JBS Haldane was a serious guy. EO Wilson was smart, but got too caught up in the weeds. R.A. Fisher had the right ideas, more or less, but he focused on mutations instead of fixations and set the entire field off on the wrong direction for a century as a result. Kimura was onto something, but he didn’t have the courage of his own mathematics. Ernst Mayr was a faker and a poser. Dawkins is just an innumerate moron; he genuinely believes his own nonsense. But I tend to enjoy his books; he could have been a great science fiction writer.

Bill: Is there any major aspect of contemporary evolutionary theory that you came to appreciate and embrace more fully while writing your two recent books on the topic?

Vox: I very much respect the work that the genetic scientists are doing on the various genomes. I suspect they know perfectly well what the implications and inevitable consequences of their work are, but they keep their mouths very carefully shut in order to avoid upsetting the academic apple cart.

Bill: You often use neo-Darwinism as the principal name for the theory you oppose. What exactly do you include under that term: random mutation and natural selection, the broader modern synthesis, neutral and nearly neutral evolution, or every naturalistic account of evolutionary change?

Vox: I use the term correctly. Most evolutionists don’t. Darwinism is natural selection. The Modern Synthesis is Darwinism + Mendelian genetics as per Mayr et al. Neutral and Nearly Neutral Theory are not compatible at all with Neo-Darwinism, were developed more than a decade after the Modern Synthesis, and I describe the attempt to put it all in one big Darwinian box as the Postmodern Poly-thesis. Creationists have already defeated Neo-Darwinism, which is why evolutionists immediately retreat to Kimura and various forms of neutral substitution now. Natural selection proper is dead and they know it. Even Dawkins talks about Evolution by (probably) Natural Selection now.

Bill: Which of those claims does MITTENS directly address, and which require additional arguments?

Vox: All of them. Probability Zero covers about nine stages of the evolutionist retreat from Moscow to Paris. So far, they’re just starting to touch upon stage three. The only thing that requires more work is refining the actual numbers more precisely, because the original reporting by Barrick in 2009 was sloppy and inconsistent and the later work by Goode in 2017 wasn’t quite there yet. I’ve broken their collective data down in detail in the MITTENS 3.0 paper and the detailed results are much more clear than in their papers.

Read the whole thing there. As a bonus, he also posted Chapter Six of Probability Zero, the chapter devoted to the 1966 Wistar Symposium that was so catastrophic for the biologists, at the end of the interview. If you haven’t read it yet, you really should.

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Climbing the Ladder

Arktoons has officially passed Tapas as the #2 Internet toons site. Not because we’ve grown spectacularly, but because Tapas was just shut down by its new owners:

Tapas, a popular North American comic and web novel hosting site, is shutting down. According to a report on BigGo Finance, Tapas is “a drag on earnings” for parent company Kakao Entertainment, a South Korean media company which purchased the platform in 2021 for roughly $800 million. BigGo Finance reports that Tapas was home to over “100,000 titles” from “75,000 creators” and had amassed over “10 million cumulative registered users,” many of whom are upset right now.

On social media, readers and creators alike are distressed at the news, partly because it hasn’t been officially communicated by Tapas itself. Tapas shutting down will leave many comics and writers without a place to host their work and without a potential source of revenue. Like other comic platforms, Tapas makes its money from ads and selling currency used to unlock premium stories. Creators, in turn, get a cut of that ad revenue and any currency spent on their stories.

In the Tapas Discord server, users are sharing new places to house their work while a number of commenters on social media are using the event to emphasize the need for creatives to self-host their work, as well as sharing resources to get them started. However, the appeal of Tapas was that it was a centralized location for users to access their favorite works. When the service ends, a lot of readers simply aren’t going to follow every individual creator to wherever they end up.

“I have 7k subscribers and over a half million views on Tapas,” wrote PerfectSerenad3, author of the Lucifer’s Ace comic on Tapas. “Just gonna go ‘poof’.”

Certainly those creators are welcome to come to Arktoons. It probably wouldn’t be the worst idea for the Arktoons team to reach out to some of them. I haven’t had much to do with it myself in quite some time, but it’s been quietly chugging along with a competent team and now has 7,809 episodes and 17,319,251 views.

In fact, it occurs to me that as we’re preparing the launch of Castalia Unlimited, there is no reason we shouldn’t introduce a new text series or two from our new sets of translations. It would certainly be a nice way to show off some of our first-ever English translations. And it would certainly be appropos in light of the fact that we originally stole the idea for them from Tapas in the first place.

Share your thoughts on what you’d most like to see in a text-with-pictures series on Arktoons, The Secret Scrolls of Naruto, Romance of the Three Kingdoms, or one of our other new translations?

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