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.
- “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.
- “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).
- “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.
- “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.
- 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.
- “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!