Tag: science

In which the confusion of Ms Matthews and her team of PhDs demonstrates they don’t know natural selection no longer operates in humans because they don’t understand what the selective turnover coefficient is, why it is necessary, why it is significant, or how it is different from classic population genetics models and equations:

(1:51) He’s still using the d coefficient in MITTENS, which is really strange to me because like if he’s retracting the claim about like effective population size, then like he’s retracting the claim that they population genetics does not account for like overlapping generations. So then there shouldn’t be any d ceofficient at all. But when he’s when he uses the number of generations but that like between the human chimp common ancestor and humans, he calculates it at 450,000 generations and then he multiplies it by the d coefficient in order to cut it almost in half to like 225,000 generations or whatever and he’s still using that number for all his math.

So it’s just completely inconsistent, incoherent, right? Remember how d was one earlier? This goes back to the whole he’s trying to give conventional science the best case scenario numbers. Vox actually proposes that since d is meant to account for overlapping generations, when we take human behavior into account, instead of one, it should actually be about 0.45. And as we can see in our equation here, that effectively slices the number of achievable fixations in half. But remember, the d coefficient is Vox’s calculation. It’s his new variable.

Population genetics can already handle overlapping generations as well as a myriad of different age class structures. But Vox doesn’t know about any of those and so he has to conjure up his own coefficient to handle it. If you will recall in Will’s presentation, this is referred to as a fix. But this is inappropriate and it’s also unnecessary. More on this later, but this is crazy because remember the whole reason why Day created the d coefficient, the selective turnover coefficient, is because he thought that population genetics didn’t have a way to handle overlapping generations. He didn’t know that Wright-Fisher could do it and he didn’t know about Moran either. So if he went on to accept that yes, overlapping generations can actually be taken into account using conventional population genetics methods, specifically in relation to Kimura’s work, why does he still use the d coefficient he made up?

It’s because he doesn’t know about the regular population genetics models and equations, and he further wouldn’t know how to use them.

First, the erroneous claim I retracted about effective population size was solely related to my misunderstanding of the way in which Kimura derived his fixation equation, which was based upon how it was explained to me by the mainstream textbooks. As it turned out, there was a genuine error in Kimura’s derivation, but it was not in an invalid algebraic cancellation, it was the result of his reliance upon the Wright-Fisher model’s assumptions and how he incorporated it into his equation. My critical instincts about the effects of population growth on fixtation were correct, but they were proven through Dr. Chalub’s demonstration of the time-related boundaries of the applicability of Kimura’s equation instead of a nonexistent error in Kimura’s algebra. That correction was not a retraction of the significance of overlapping generations or of my claim that mainstream population genetics does not properly incorporate overlapping generations as it absolutely must.

Second, Matthews and Hancock have repeatedly asserted that I didn’t know about the Wright-Fisher or other population genetics models is a blatant lie that underlines the fact that they didn’t read the book or the papers. A simple text-search of the book alone suffices to prove that I am not only aware of those models, but several other topically related ones as well. For example, here is a quote from Chapter One of the first edition of Probability Zero. Emphasis added.

When population geneticists use the term “generation,” they mean something very different than the way the word is utilized in reference to the Boomers, the Millennials, and Generation X. In the two standard models—the Wright-Fisher model and its subsequent revision by Kimura—a “generation” represents the entire population. This is so important, I’m going to repeat it so that you will remember it. IN STANDARD FIXATION MODELS, A GENERATION REPRESENTS THE ENTIRE POPULATION.

Furthermore, I specifically addressed the distinction between d and other population genetics models that address overlapping generations in some way in Appendix A of the first edition of Probability Zero.

Classical population genetics assumes discrete, non-overlapping generations. For species with generation overlap, Hill (1972) and Felsenstein (1971) derived corrections for effective population size (N_e), which governs genetic drift. However, no equivalent correction has been derived for the rate of allele frequency change under directional selection. We derive the Selective Turnover Coefficient (d) from demographic first principles and show that d is mathematically distinct from Hill’s N_e /(N₁T) ratio.

Third, Ne cannot serve as a substitute for d. The standard model response to expanding populations would be as follows: large populations have large Ne, so 1/(2Ne) is very small, which means selection is more effective in large populations because even weakly deleterious alleles satisfy |s| > 1/(2Ne) and are therefore visible to selection. This is Kimura and Ohta’s nearly neutral theory, and it’s the textbook population genetics answer.

But this erroneously treats selection as a frictionless force that acts with perfect efficiency given enough population to work with. It ignores the physical mechanism by which selection actually operates: organisms must differentially survive and reproduce within the limits set by the reproductive process. If the population is turning over at a glacial rate relative to its size, which is to say if nearly everyone survives to reproduce regardless of their mutational load, then selection has no medium through which to act. The theoretical visibility of an allele to selection (|s| > 1/(2Ne)) is meaningless if there’s insufficient differential mortality or fertility to realize that selection in practice.

This phenomenon is captured by d. Ne can’t capture it. Ne tells you how fast alleles drift while d tells you whether selection has enough generational turnover to actually do its job. They are measuring two different things, which is why Dr. Zachary B. Hancock’s dismissal of d as “nonsensical” was absolutely wrong, observably inperspicacious, and why his subsequent use of the incorrect generation count in his application of MITTENS was inevitable, being the kind of error that ignoring d will reliably produce.

Neither Wright-Fisher nor Moran can model the equivalent of d declining from 0.86 (wild chimps) to 0.015 (humanity 2026) over evolutionary time, because neither model has a parameter for total gene pool turnover rate as distinct from drift dynamics. Wright-Fisher hardcodes d = 1. Moran fixes replacement at 1/N per step. Neither is structurally capable of representing a situation where population expansion and the removal of environmental selective pressure progressively drain selection of its operating powe which is what the chart shows is what actually happened over time. To model that, you need a variable that neither model contains. That variable is d, and its significance can be seen over the 6.3 million years of the post-CHLCA period.

As I pointed out in both PZ and TFG, humanity is no longer subject to natural selection and the human genome is no longer being cleansed of deleterious mutations. Humanity is genetically degrading, and this continuing degradation may be the primary culprit in the observed global decline of human fertility.

If so, that means that due to their dedication to an outmoded and disproven theory of evolution, evolutionists and population geneticists are literally standing in the way of science being utilized to address what may be one of the primary threats to continued human survival.

Just to be sure I wasn’t missing anything, I asked Claude Athos to solve the problem from the Evo-Avengers perspective.

At what Ne is selection impossible? At what Ne/N is it impossible?

This is the question that breaks the standard framework open, because the answer is: there is no such value. Neither Wright-Fisher nor Moran contain any Ne at which selection becomes impossible. It’s not that the number is very large or very small—the concept doesn’t exist within the models.

In the standard framework, selection is effective when |s| > 1/(2Ne). As Ne grows, that threshold shrinks. A population with Ne of 10,000 can only see alleles where |s| > 0.00005. A population with Ne of 10 million can see alleles where |s| > 0.00000005. The larger the population, the finer-grained selection’s resolution becomes. Selection doesn’t just remain possible as populations grow, it gets more powerful. That’s the prediction.

This means the standard models predict that modern humans, with the largest effective population size in our evolutionary history, should be experiencing the most effective natural selection our species has ever known. Every weakly deleterious allele that drifted past selection when our Ne was 10,000 should now be visible and targetable at Ne of several hundred thousand or more.

That prediction is obviously, empirically wrong. And the models have no mechanism to account for why it’s wrong.

Ne/N makes it worse, not better. The typical Ne/N ratio for humans is estimated around 0.1 to 0.3—meaning effective population size is roughly 10–30% of census size, due to variance in reproductive success, sex ratio imbalances, population bottlenecks, and so on. For modern humans with N approaching 8 billion, even a brutally low Ne/N of 0.01 gives you Ne of 80 million. The selection threshold 1/(2Ne) at that point is approximately 0.000000006. The models say selection should be able to detect fitness differences of six parts per billion.

This is self-evidently absurd. No one believes natural selection in modern human populations is operating at that resolution. But the models don’t just permit that conclusion, they require it. There is no parameter within either Wright-Fisher or Moran that allows selection to become less effective as N increases. The math runs in one direction only: bigger population, stronger selection. Always.

This means d is what’s missing. The reason the models can’t represent selection failure is that they’ve abstracted away the physical mechanism through which selection operates. Selection isn’t a mathematical force that acts on allele frequencies directly. It’s a consequence of differential survival and reproduction. Organisms with deleterious alleles must die or fail to reproduce at higher rates than organisms without them. That differential is what changes allele frequencies. No differential death, no selection.

The selective turnover coefficient, d, measures the rate of that differential. When d = 0.86, the gene pool is churning. Most individuals in every generation are being replaced, which means even small fitness differences produce detectable mortality differentials. When d = 0.015, nearly everyone survives and reproduces regardless of their mutational load. Selection has no medium to work through.

Just to be fair, I also asked the Red Team. ChatGPT’s answer:

In population genetics, the effectiveness of natural selection depends on the effective population size (Ne​) and the selection coefficient (s).

• Selection becomes ineffective when: $N_{e}s\ll 1$.
• Selection is effectively impossible to distinguish from genetic drift when: $N_{e}s\approx 1$ or smaller.

For the ratio Ne​/N, there is no universal threshold at which selection becomes impossible. This ratio measures the relationship between effective population size and census population size, rather than the strength of selection. There is no universal threshold at which selection becomes impossible. This ratio measures the relationship between effective population size and census population size, rather than the strength of selection.

And Grok’s answer, after being pressed to provide for specifics:

• Ne ≪ 100
• Ne/N ≪ 100/N
• If N = 8,300,000,000, then s=0.01 is possible as long as Ne > 100 and s=0.001 as long as N > 1000.

DISCUSS ON SG

VD: This is not my response to the two Eco-Avenger videos, this is the portion of the transcript of Will Duffy’s appearance last night on Ms Matthew’s channel when they discussed Probability Zero.

On Reading the Book and Watching the Response

Will: Here are my receipts. I purchased Probability Zero on July 26th and I didn’t read it right away. Then I purchased Hardcoded on August 9th. Then I purchased The Frozen Gene on August 10th. And then I emailed Vox for the first time on August 22nd. So these are the receipts. This is the exact timeline. This was nothing I had in my back pocket. This wasn’t the long game.

As to how I knew so many details about Vox Day, including details about his son—it’s quite simple. I read his books. Everything in my presentation was from his books. Everything.

It will come as a shock to most of you that Erica, Dr. Zack Hancock, Dr. Dan, Dr. Maddie Frank, and Grayson Hawk did not read the Probability Zero book that my presentation was based on. Details forthcoming. I had a lot of homework this go-round. I had to rewatch the last presentation, watch Erica’s rebuttal video to Vox Day, and then watch “Six Scientists Roast Vox Day” for over four hours. These videos were 12 hours, 42 minutes, and 25 seconds long total. My game plan: Step one, rewatch Human Evolution 2 live stream. Step two, meet with Mike Griffiths. Step three, watch Erica’s response video to Vox Day. Step four, meet with Mike Griffiths. Step five, watch “Six Scientists Roast Vox Day.”

For those who don’t know or don’t remember, Mike Griffiths is a mathematician—he’s the head of maths at a private institution in England. He’s a huge fan of Erica, and he’s an atheist.

I want to highlight one comment from Dr. Dan over at Creation Myths: “Can we also just marvel at the fact that Will went to a GD billiards player to learn popgen instead of, I don’t know, a population geneticist?” I’ll let the comment speak for itself.

On the Fossil Record

Will: Erica covered a lot in the last session. She covered fossils, more fossils, and finally more fossils. The more Erica teaches me about the fossil record and the more I learn about it, the more I struggle to make sense of young earth creationism.

I’m not going to elaborate on this now, but I will in January during our final discussion.

Predictions and Tiktaalik

Will: Erica, you said predictions are the gold standard of science. I’ve been thinking about that. Since our series started, I’ve tried to watch every evolution debate on the Modern Day Debate YouTube channel, and the number one evolution prediction that comes up almost every time is Tiktaalik. I’ve heard it so much that I never actually looked into the prediction and just accepted the claim that it was predicted. In the past couple weeks, I decided to look into it and I can’t find any evidence that it was predicted. I’m not making a positive claim that it wasn’t predicted—I’m just saying I can’t find any evidence that it was. So I want to know: in what way was Tiktaalik predicted?

Molecular Clock Discrepancies

Will: Erica, you said that the molecular clock matches with the fossil emergence time. Unfortunately, I have not had time to look into this, but I have been contacted by multiple people who said there are significant discrepancies with reconciling the fossil record with the molecular clock.

I have been sent multiple scientific papers that I haven’t read, and I’ll show them:

• “The Origin of Animals: Can Molecular Clocks and the Fossil Record Be Reconciled?”
• “Uncertainty in the Timing of Origin of Animals and the Limits of Precision in Molecular Timescales”
• “Survival and Selection Biases in Early Animal Evolution and a Source of Systematic Overestimation in Molecular Clocks”
• “Re-evaluating Molecular Clock Maximum Age Calibrations Revives Pre-Ediacaran Divergence Estimates for Animals”

Teleology

Will: When this part of the presentation came up, I mentioned to Erica that I thought what she was saying went against what she said about teleology originally—that we can’t tell if something’s designed.

Here’s what was said in the last presentation: “There is actually a way to use fracture patterns to tell whether or not a tool was made by a hominin or not. You can actually roll a bunch of rocks down a hill and see how they break. So there’s a way to differentiate between something that was designed by hands and something that nature did in the case of stone tools.”

But in our first session, she said: “The problem with teleology is exactly what you see on the screen. We can’t differentiate between the designed and the natural.” And a couple minutes later: “It’s not that teleology is impossible. It’s that teleology is non-scientific because it can’t actually be tested.”

I do struggle to understand that when combined with saying there is a test we can do. I think it’s possible teleology is kind of sneaking back in the door here.

The Selection Coefficient / Selective Turnover Coefficient Error

Will: When Erica and Zach were going over my slide, Erica said that “d” in the formula is “Day’s selection coefficient.” And then she said, “What’s crazy is that Day’s selection coefficient isn’t actually a selection coefficient.”

This is unfortunate. If you go back and look at my slide, it’s a selective turnover coefficient. It is not a selection coefficient. So when you said Day’s selective turnover coefficient cannot do what a selection coefficient does, that was not valid because it’s not a selection coefficient.

Zach was presenting and said, “So Vox has this other term d, but we don’t know what it means.” He admitted that he doesn’t know what it means, which makes sense. Unfortunately, that entire section of the video was a category error, and I didn’t find one person in the thousands of comments who caught this—I could be wrong, but I think it’s because people did not read Probability Zero.

After reading the book, you walk away with a really good understanding of what a selection coefficient is in population genetics, and you would never confuse it with Day’s selective turnover coefficient d. In population genetics, a selection coefficient uses the symbol S, which I actually used in the formula. Selection coefficients are S. The selective turnover coefficient is d.

Who Actually Read the Book

Will: People ask, “How do you know so much about Vox?” I read his books. In the beginning of the second video, Erica said, “So we read his book. Now when I say ‘we,’ I mean me, Zach, and four of our other credentialed friends.” That was a collective “we,” and I think people might have missed what it actually meant. It didn’t mean all of them read the book.

• Zach said: “It’s like trying to explain to a 5-year-old why the sky is blue. It’s just a waste of time and I’m not going to read your book. I’m not going to waste my time with it. I got science to do.” So Zach didn’t read the book.
• Maddie said: “I read 40% of a book about this.” So she read less than half.
• Erica said: “I read about 60 to 70% of the book in its entirety, whereas I skimmed the rest.”

Then something else happened. When Erica’s first video rebuttal to Vox Day came out, the numbers were not the same numbers that I originally presented. They were way off. The quotes and page numbers she was giving were not correct in my book. Come to find out, none of them purchased Probability Zero. They obtained an EPUB version somewhere and shared it with everyone else. It was the wrong version. The only version you can buy—which is what I bought, for $4.99 on Amazon—is the second edition, which had corrections, updates, and the latest science. The EPUB version they all used was the original edition.

Vox Day’s Prediction

Will: Vox Day made a prediction on his blog on September 26th, the day after our last live session: “My response is fairly simple and straightforward. I’ll be happy to talk to her or to whomever and explain these things. I do not expect anyone to actually (a) talk to me or (b) read the book. I don’t know what it is about biologists, population geneticists, and other science enthusiasts, but they always seem to imagine they can effectively critique anything without bothering to actually learn anything about it.”

I was really hoping this prediction would not come true.

Wright-Fisher, Moran, and Day’s Selective Turnover Coefficient

Will: Zach said: “There are two classic models—the Wright-Fisher model and the Moran model. In its classic sense, the Wright-Fisher model does not have overlapping generations. But you can equate the two by setting the population size (the N value) in the Wright-Fisher model to an effective population size and you just scale that effective population size by the slowdown of drift due to overlapping generations. So even the Wright-Fisher model can account for overlapping generations.”

Zach is correct here. But since he didn’t read Probability Zero and doesn’t understand Day’s selective turnover coefficient d, he doesn’t know why it’s still necessary and why it captures something that N-sub-e misses.

Both models—Wright-Fisher and Moran—are answering this question: How fast does genetic drift move neutral alleles through the population?

Day’s selective turnover coefficient d is designed to answer an entirely different question: How fast does the entire gene pool turn over?

The d formula involves variables that simply have not been accounted for in standard population genetic models.

Now, if anyone out there wants to grab my attention and immediately build rapport with me, simply acknowledge and tip your hat to Vox Day for his selective turnover coefficient. It has essentially nothing to do with his Mittens argument that evolution by natural selection is mathematically impossible. So conceding this one should be relatively harmless.

Zach’s Calculation Errors

Will: Zach said, “This is going to be 76.8 multiplied by 252,000, and that’s how many mutations you’re actually going to have in that time period.” This was a mistake. And remember what Erica said—trusted creators are people who can own their mistakes. Zach is a trusted creator. He owned his mistake, and it’s in the video. He corrected himself: “Importantly, we can’t use 6.4—this is the diploid genome size—for the fixation rate, because you fix on a haploid genome. So it should be 3.2.”

This made me happy. But then a few seconds later he said, “I want to quickly clarify that value, but I also want to say that we can still use this value in the following derivations.” He referenced Perubski et al. 2025, saying they estimate an average of 152 de novo mutations every single generation, and dividing that in half for the haploid genome size gives 76—meaning the original number can still be used.

But this is a pretty significant error. The Perubski et al. number includes large structural variants, insertions, deletions, and duplications—not just single nucleotide polymorphisms (SNPs). Zach’s entire calculation on the whiteboard is explicitly about single nucleotide differences using a single nucleotide mutation rate. You can’t validate a SNP-only calculation with a number that includes large structural variation.

Once again, I could not find anyone in the thousands of comments who caught this. But you know who did catch it? Mike Griffiths. The billiards player.

The 38 Million Number

Will: Zach says we can fix 38 million differences between humans and chimps. That’s incorrect for three reasons.

First, the calculation is being run on the diploid genome size (76.8) instead of the haploid genome (38.4).

Second, minor: he’s using 252,000 generations instead of the d-coded size of 201,600.

Most importantly: neutral theory applies to the entire genome. Zach is using circular reasoning in assuming the neutral prediction of 35 million differences all fall perfectly into the divergent sites. In reality, the divergent sites are only 1.09% of the genome. So statistically, only 1.09% of the neutral substitutions would end up in the divergent zone. The proper formula would be: 15-some-odd-million × 35 million ÷ 3.2 billion (the size of the genome). So Zach’s original 38 million number is in actuality just 169,344.

Rate vs. Latency: The Highway Analogy

Will: Zach said: “Hopefully you can see a very glaring problem with this math. One is that it assumes that each mutation has to both arise and go to fixation before the next mutation can occur.”

Zach is incorrect here. Part of me has sympathy for him as he’s trying to critique a book he hasn’t read. But the other part of me struggles to have sympathy for the same reason—he’s trying to critique a book he hasn’t read.

When you calculate a rate such as an observed fixation rate, you are dividing the total number of generations observed by the total number of fixations over that period. This tells you how many generations elapsed per fixation on average, regardless of whether those fixations occurred sequentially or overlapped.

Vox Day’s calculation is a rate calculation. Zach thinks it is a latency calculation.

I can help everyone understand with a simple highway analogy. Imagine you were counting how many cars pass a red line in one hour, and you count 360 cars. How would you calculate the average rate? The numerator is the time (3,600 seconds), the denominator is the number of cars (360). So 3,600 ÷ 360 = 10 seconds per car. This is the exact same method Vox Day uses to calculate the average observed fixation rate. If you see this formula and say, “Well, that formula means the cars can only travel one at a time, like through a tunnel,” that is absolutely incorrect.

Vox Day’s calculation is not a latency calculation and is not assuming one fixation happens before another one starts. This was explicitly covered and anticipated in Probability Zero.

I’m not hammering on Zach here. I believe he is a trusted creator and he’s going to own these mistakes. We’re all just trying to get to the truth.

Mittens Is Not the Waiting Time Problem

Will: Dr. Dan says, “Like the waiting time problem, which—even though Vox Day has never heard of it—that’s the argument he’s making.” No. Mittens is not the waiting time problem. The waiting time problem refers to the significant amount of time required for beneficial genetic mutations to occur in a population. The Mittens argument isn’t concerned with mutation rates at all. It is an empirical audit of observable fixations. Mittens would be better referred to as the fixation problem.

The Bacteria Issue

Will: Dr. Maddie said the idea of applying the fixation rate from bacteria to human populations doesn’t work when you just take the average of the fixations out of the Lenski experiment and apply that as a fixation rate to the human population assuming all the mutations are happening in series.

No, it doesn’t assume mutations are happening in series. But let’s talk about the bacteria issue. I don’t know anyone who argues that humans fixate mutations faster than bacteria in terms of generations per fixation. I think it’s possible the audience walked away from that video thinking that is what was being argued. So I’m hoping Erica and the others can clarify whether or not they actually believe humans fixate mutations faster than bacteria.

Zach said something good: “The issue with using even conceptually the Lenski long-term evolution experiment for a fixation rate is that the Lenski long-term experiment begins with a bacterial population that is clonal and has no diversity.” Zach makes a really valid point here. This was also caught by Mike Griffiths, who brought it to my attention before this video was released.

Here’s Vox Day’s response, which I’m not claiming to understand:

“The polymorphism objection sounds legitimate until you think about what standing variation is. It’s not a warehouse of pre-adapted beneficial alleles waiting for their moment. It’s mostly neutral variation, which is why it’s still segregating. If those variants were beneficial, they’d have already swept to fixation. If they were deleterious, purifying selection would have removed them. What mutation-drift equilibrium gives you is a population full of genetic noise at low frequencies, not a head start on adaptation.”

I don’t understand this enough yet to know who’s right. But the main argument with the bacteria thing seems to be that Vox shouldn’t apply bacterial fixation rates to humans because bacteria are clonal and slow.

Dr. Michael Lynch—who I’m told is one of the most respected population geneticists in the field—has stated that bacteria are actually faster and more efficient at molecular adaptation than eukaryotes because of their population size advantage. He says: “Prokaryotes appear to be much more efficient than eukaryotes at promoting simple to moderately complex molecular adaptations.”

Mike Griffiths as Intermediary

Will: Mike Griffiths watched Erica and Zach’s presentation. He also bought Probability Zero. He watched Erica and Zach’s presentation twice and has a list of about a half-dozen questions and issues. I introduced Mike to Zach via email and Mike shared his list with Zach. Zach has yet to respond.

On the Probability Zero side, Mike has started reading Probability Zero and Vox Day’s scientific papers. He has a list of questions and issues for Vox as well. I asked Vox if he would respond to Mike, and he agreed. The three of us did a Zoom together last week, and after the Zoom, Mike sent his list to Vox.

I told Erica already that I do not rush things like this. I spent a very significant amount of time not only learning Vox Day’s arguments in Probability Zero, but also learning as much as I could about the math behind population genetics. I have since spent a good deal of time reviewing the responses from Erica, Zach, Dan, Maddie, and Grayson. There are significant errors that I trust will be owned and corrected. As such, the verdict is still out.

I will tell everyone I’m relying heavily on Mike Griffiths as well. I’m honestly giddy to get to be a bystander on his conversations with both Zach Hancock and Vox Day. Mike has legitimate concerns for both of them, and I’m extremely curious how they will both respond.

Will’s Conclusion

Will: I want to point out to everyone what stood out to me most the last few weeks after I mentioned Vox Day and Probability Zero.

The response I received was the exact opposite of what everyone has been telling me to do from the very beginning:

• I’ve been told to focus on the data and science and not the person. Yet the vast majority of responses and comments I get are focused on Vox Day as a person and not the data and the science.
• I’ve been told that Darwin’s racism has no relevance to evolution and that Fisher—of the Wright-Fisher model—being a eugenicist doesn’t make his math wrong. But that’s all I’m hearing about Vox Day.
• I’ve been told to focus on understanding new things instead of just trying to refute them. But I see very few people trying to actually understand his arguments—just trying to refute them.
• I’ve been told not to run to creationists hoping they can refute what Erica teaches me and to study what I’m taught. But all I’ve seen is everyone say, “I’m just gonna have Erica and Zach and whoever else refute this instead of looking into it.”

I think it’s important for what it’s worth to know what I’m experiencing and what I’m seeing from my perspective.

Erica’s Response

Erica: I have a lot of thoughts—like three pages of thoughts. I’m going to work through some of them, but I’m not going to get to everything because you have a hard stop at 7:00 and I want to get to the actual presentation and super chats.

I can understand your perspective on being frustrated with people’s response to Vox. I said this to you via email and I’ve voiced this to other people as well. I think you have to put yourself in other people’s shoes a little bit too, though. The reason Zach and I covered what we covered in that initial video is because that’s what you shared—that was in your PowerPoint. Our first video was obviously just in response to the PowerPoint we got from you. We didn’t have access to the book at that point. I hadn’t read the book at that time either, even the scant portion I did read, although I did read Mittens 3.0, which is available online for free and is supposed to be—according to Vox—the most up-to-date version of the argument. That’s also why in the second video we went over Mittens 3.0 in addition to the first version of Probability Zero, because that was according to him the strongest version of the argument.

I can understand your frustration, but I find it difficult to set aside a lot of his other beliefs in the same way one would for someone like Darwin or Fisher. In Darwin and Fisher’s case—and I said this to you via email—Fischer was a eugenicist and Darwin was racist. That’s factually true. Darwin was an abolitionist as well—he was progressive for his time—but that doesn’t change the fact that he lived within the context he lived in. But the work they did in science did stand on its own. Their work has stood the test of time, and Fisher and Darwin’s ideas are still being used today to make accurate predictions. I’ve not seen the same with Vox’s math.

This is something that people sympathetic to Vox have not appreciated, and I’ve yet to see him comment on it. The math that underpins standard population genetics has been used to accurately model real populations now. And there are like a billion of them, which is why I showed a slideshow of two dozen or however many it was. Point blank, full stop: if Vox is correct and traditional population genetics is incorrect, those papers shouldn’t exist. They shouldn’t be able to accurately model or even predict changes in real world populations.

I do still maintain that this is a waiting time problem. The waiting time problem in traditional creationist circles is a fixation problem. Mutation rate and fixation rate are used interchangeably a lot, inappropriately, as you would now know because you’ve read up on a lot of population genetics. But because they’re used interchangeably, it makes it seem like the waiting time problem is something distinct from this fixation problem. It’s not. You can go back to Doug Axe’s original paper in the early 2000s and see exactly this, which is why we’ve said this is a waiting time problem.

I’ll say too: the idea that he’s using the Lenski long-term evolution bacteria—which, as you accurately pointed out, are clonal and thus inappropriate for that reason—I don’t think anybody’s saying that bacteria quite literally fixate faster than humans do. That’s not my understanding. The problem is that in the Lenski experiment in particular, by their nature of beginning clonally and by their nature of not recombining, these two things are not analogous. It’s an apples-to-oranges comparison.

The numbers exist out there for eukaryotes—fruit flies, rats, humans. We have pedigree studies on real-world human populations: a grandparent, a parent, and their kid. And you can use that to model these populations into the past. They don’t match Vox’s math. And they don’t behave like bacteria.

To me, what rings out most severely is that he must rectify this math with the entire scientific community, and he won’t. I find that incredibly frustrating because he puts out the books and says, “This stands on its own,” but it’s never applied to any real-world populations.

I have to ask you this. I don’t understand how you could give him the benefit of the doubt for the other stuff. I can sit here and say I disavow Darwin for the shitty stuff he said. I disavow Fisher for the shitty stuff he said. I like their math, but I can recognize that in these areas, they’re bad people for holding these perspectives. And you’ve already said—just to be clear for everyone—Will said he disavows white supremacy and doesn’t think women should lose the right to vote and doesn’t think marital rape laws should be revoked. He said that up top. But I still think you’re being a little bit defensive of Vox, and I don’t understand how you could do that after watching the video that had a lot of this stuff in his own words. That’s confusing to me. I want to give you the benefit of the doubt here because I think this series is a good thing.

DISCUSS ON SG

Here we have an interesting trialogue that demonstrates three separate and independent forms of willful cluelessness. Both Dr. Cardinale and Matthews just engage in a little rhetorical handwaving in rather transparent attempts to avoid having to address the time-to-fixation math, while Dr. Hancock goes off on what we’ve learned are his irrelevant tangents that permit him to sound as if he knows what he’s talking about while avoiding the topic at hand.

(49:53) Dr. Daniel Stern Cardinale Assistant Professor at Rutgers University: This is why I am a biologist because I love it so much. I tell my students, I forget where I heard this initially, but I tell my students in my like bio1 freshman bio class, I say there’s a saying that I really love that helps you get in the mindset for biology, and that’s physics has laws, chemistry has rules, biology has exceptions. Yeah. Which is just perfect. It’s just a giant mess. And there are no universal rules. And that’s why it’s beautiful and interesting.

Dr. Zach Hancock, Assistant Professor, Augusta University: Yeah. I mean, we we have fixation probabilities, right? I showed this in the video before. You can calculate a fixation probability. Um but the things that you need to know are things like population size and the selection coefficient. Um and those are functions of the history of the population, the the demography of the population, how that population mates, like all of those sorts of things are components of how that fixation probability plays out. I mean, even the distribution of fitness effects, every single mutation in that distribution of fitness effects has a unique probability of fixation based on where it falls in that distribution of fitness effects, right? And that distribution itself evolves through time, right? So there’s just actually no way like you could take an average, but it would be meaningless because it’s not a Gaussian distribution, right? Like the distribution of evolution would not follow a Gaussian. So even if I gave you an average like if I if I managed to somehow calculate that over time it wouldn’t tell you anything without knowing what the shape of that distribution is which is like multimodal right like it wouldn’t mean anything so I don’t I don’t it feels like someone asking something from biologist without knowing anything about biology right, like likely not understanding how biology works.

Erika Matthews: I think Maddie’s example is great there, but I’m going to provide a different one from biology that might hit a little bit closer to home. What if Vox asked, “What is the rate at which cancer metastasizes?” Well, it depends on the cancer, doesn’t it? Some cancers metastasize really quickly and some metastasize really slowly. It also depends on things like your age, your sex, your genetics. A lot of variables come into play here. And in fact, doctors can take those variables into account when diagnosing someone with cancer and use them to predict metastasis rates for specific types of cancer. But they have to know the variables. You could theoretically calculate a metastasis rate in cancer generally and it would mean nothing and be helpful to no one because there’s so much variation. Our mutation rate situation here is exactly analogous to this. We can’t sus out mutation rates looking at populations of organisms, but there isn’t a set one that can be universally applied. That’s just not how it works.

So, what we have here are several assertions that range from pure rhetoric to substantive and misleading falsehoods, beginning with a rhetorical dodge pretending to be an epistemological insight.

1. “Physics has laws, chemistry has rules, biology has exceptions” / “there are no universal rules”

This is Dr. Cardinale’s handwaving opening move. It’s not bad as a pedagogical aphorism for freshmen, but it’s being utilize here to preemptively excuse the Evo-Avengers’ collective inability to provide a quantitative answer to a meaningful question. Biology absolutely has universal constraints: the second law of thermodynamics applies to biological systems, Mendel’s laws apply with known and precisely quantified exceptions, and the mathematics of population genetics are derived from probability theory, which couldn’t care whether the substrate is biological or not.

What Cardinale actually doing is confusing complexity with chaos. The distribution of fitness effects is complex, but the fixation probability formula is not. It’s Kimura’s 1962 equation. It takes inputs and produces outputs. The complexity is in the inputs, not in the existence of the relationship. Saying “there are no universal rules” is a freshman-level simplification that a PhD should know better than to deploy as an actual argument. If he truly doesn’t know better, well, we can’t rule that out.

2. “You can calculate a fixation probability… but the things you need to know are things like population size and the selection coefficient”

This is correct as stated by Dr. Hancock. Kimura’s fixation probability for a new mutation is:

P(fix) = (1 – e^(-2s)) / (1 – e^(-4Ns))

You do need N and s. But he’s trying to use the necessity of inputs to a formula as evidence that the formula can’t produce outputs. That’s like saying you can’t calculate the trajectory of a cannonball because you need to know the angle and muzzle velocity. Yes, you need the inputs. That’s how math works. That’s how equations work. The inputs for human populations are known or bounded: N_e is estimated (he’d cite the textbook ~10,000, we’ve calculated ~33,000, but either way it’s a number), and the distribution of fitness effects has been empirically characterized (Eyre-Walker & Keightley 2007).

3. “The distribution of fitness effects… every single mutation has a unique probability of fixation”

This is both true and irrelevant. No one is asking for the fixation probability of a specific mutation. The question that Hancock is dodging is about the rate, specifically how many fixation events can selection drive per unit time across the genome. That’s a throughput question, and as my work has demonstrated, the throughput depends on the total selection budget (Σs_i ≤ s_max), not on the individual distribution of s values. The s̄ cancels. He apparently doesn’t know this, but he’s asserting a complexity barrier that doesn’t exist.

4. “You could take an average, but it would be meaningless because it’s not a Gaussian distribution”

This is wrong. An average does not require a Gaussian distribution to be meaningful. The arithmetic mean of any distribution is a well-defined quantity. What he presumably means is that the mean is not sufficient to characterize a non-Gaussian distribution, which is true but irrelevant, because no one said it was. More importantly, for the throughput calculation, the mean is the correct summary statistic, because what matters is the sum of selection coefficients across concurrent sweeps, and the sum is just n × s̄. The shape of the distribution doesn’t matter when we’re looking at the throughput ceiling.

6. The cancer metastasis analogy

As we’ve learned to expect, Matthews has the dumbest response, because while she thinks it’s an analogical rebuttal, it is actually a concession. Of course the metastasis rate depends upon the cancer and the patient, just as the fixation rate depends upon the mutation and the species. But that doesn’t mean the various averages are irrelevant, particularly if the doctor is claiming that the cancer is metastasizing at an impossibly fast rate that would result in the patient dropping dead in seconds when he obviously isn’t.

“You could theoretically calculate a metastasis rate in cancer generally and it would mean nothing and be helpful to no one because there’s so much variation.”

That’s absolutely false because doctors do calculate cancer-specific metastasis rates. They calculate them for specific cancer types, stages, and patient demographics, in exactly the way population geneticists calculate fixation rates for specific population sizes, selection coefficients, and generation times. Her analogy doesn’t show that rates are incalculable, it shows that rates require specifying the relevant parameters. Which parameters are exactly what she and the others are trying to avoid addressing, because by claiming that evolution by natural selection accounts for the observed divergences, they are necessarily asserting that the average fixation rates are impossibly fast.

The analogy actually works against her. Oncologists don’t throw up their hands and say “cancer is too complex for rates.” They specify the parameters and compute. That’s what population genetics should do too, and when you do, when you set human parameters (N_e ≈ 33,000, s̄ ≈ 0.001, generation time ≈ 29 years, d ≈ 0.45), you get an answer. None of them want to address the equation directly, because they all have a very strong suspicion that the answer is inconvenient for their case.

7. “We can… sus out mutation rates looking at populations of organisms, but there isn’t a set one that can be universally applied”

Mutation rates do vary across organisms, across genomic regions, and across life-history contexts. But within a species, the per-generation mutation rate is remarkably stable and well-characterized. For humans, it’s approximately 1-1.5 × 10⁻⁸ per base pair per generation (Kong et al. 2012, among many others). This is not some vague hand-wavey number. It’s been measured directly from parent-offspring trios. The variation exists but is bounded, and the bounds are known. And, of course, as I’ve previously pointed out all rates with the same denominator, in this case, time, can be summed and averaged.

The collective response is an exercise in complexity mysticism. All three of them are appealing to the genuine complexity of biological systems to avoid giving the quantitative answers that the mathematics can actually produce despite that complexity. It’s the academic equivalent of a squid inking prior to running away. The fact is that the math exists. The parameters are either known or reasonably bounded. The answers are calculable.

Whether they just don’t want to do the math because they are afraid of the answer or because they don’t have the ability to do it is no longer really in question. The answer is both.

Only three more hours to go!

DISCUSS ON SG