Neither Mathews nor any of her supporting cast of PhDs understand the basic concepts of math. For some reason, biologists are totally unable to understand the concept of “an average” or “an average rate” or even grasp the fact that if something happens multiple times over a period of time, then an average rate for that activity or process must necessarily exist.
(45:52) Maddie brings up another problem, and this one has to do with Vox’s complete lack of basic foundation in biology. So, Zach, the fundamental flaw in his logic, and this is the like what he thinks should be true of biology that simply is not, right, is he thinks that there should be some universal constant that represents fixation rate that can be applied to any species, any population at any point in time for any reason. And I make this claim out of his book, which presumably is why evolutionary biologists have operated for over 50 years without ever managing to establish the fundamental rate constants of their field. Right? He assumes that there are fundamental rate constants.
The part where he’s asking people like what is the average rate of evolution? And so that’s what he claims started the he’s he claims what started him down this entire rabbit hole is that he was asking people what is the average rate of fixation and nobody was giving him a straightforward answer and so that’s what he said well obviously they’ve all missed this or no I think what he says is they they must all not know how averages work not. Maybe my question is ill-formed or maybe I don’t understand the field at all. So to be to be clear, this is this is what he this is how he continues, right?
After saying which presumably is why evolutionary biologists have operated for over 150 years without ever managing to establish the fundamental rate constants of their field. They will tell you that evolution happens, can describe what evolution supposedly produces, can spin narratives about why certain features were selected, and will even tell you that there are no other possible alternatives to evolution by natural selection. But they cannot tell you how fast any of this occurred. And when you ask the biologists don’t say we’re not sure, or estimates vary, or that’s an active area of research. They genuinely don’t understand the question.
So let me give an example of what this made me think of out of weather that I think is pretty tangible to most folks. So if you asked me what’s a good average wind speed for planet Earth, right? I would tell you 10 meters per second because that’s like a solid order of magnitude. That’s normal, right? But what Vox is doing is saying that oh well well one that like um he would he would be saying that oh it’s 10 meters per second uh then explain how a hurricane exists right it’s like well because the winds can change right or like and so this idea that like yeah I can give you a characteristic number right that’s like if you were to go outside on a random day under average normal conditions Maybe is again order of magnitude what you’re going to find.
There just so much variance that it’s like an average rate doesn’t it’s like meaningless.
Yeah. But but telling you that is meaningless. It’s literally only useful for like order of magnitude when can we ignore certain terms in Navier Stokes, right? Like um and so yeah. So that that’s what I feel like he’s doing. I feel like this is the equivalent of him being like, “Oh, an average wind speed is 10 meters per second. Stupid meteorologists don’t know how tornadoes work. Well, it’s not it’s not as though rates for for given populations can’t be derived either. It’s not like we can’t figure out mutation rates for different groups of organisms.
This level of retardery from scientists with PhDs is genuinely painful to read, because they’re confidently asserting that the very concept they just spent the previous twenty minutes using — average fixation time — doesn’t exist. I’m not asking about some sort of universal biological constant, I am asking what is the average rate of this process taking place over time?
You said you drove the car from New York to LA last week. Fine. How fast did you drive? That is not a question about a universal automotive constant.
What do they imagine 4N_e is? It’s the average time to fixation for a neutral mutation. It’s right there in every population genetics textbook ever written. What do they think (2/s)·ln(2N_e·s) is? It’s the average time to fixation for a beneficial mutation with selection coefficient s. Kimura derived these. They are the expected values — the average rates — of stochastic processes. The entire field of population genetics is built on computing expected values for fixation times, substitution rates, and allele frequency trajectories. That’s exactly what the field does.
Their wind speed analogy is particularly self-defeating. Meteorologists absolutely use average wind speeds. They’re essential to climate modeling, building codes, wind energy engineering, and aviation. The existence of hurricanes doesn’t make the average meaningless, it just means the distribution has fat tails, which any competent scientist accounts for rather than throwing up their hands and declaring all averages to be useless. And if a meteorologist told you “the concept of average wind speed is meaningless,” you’d rightly question whether they understood their own field.
And the crazy thing is that these six ignoramuses just finished citing specific fixation times from Kimura’s formulas to argue that recombination and standing variation make human evolution faster than bacterial evolution observed in the LTEE. Those numbers they were using? Those were averages. They were using average fixation times to argue that average fixation times don’t exist. They didn’t notice the contradiction because they don’t understand the math well enough to recognize that the formulas they’re citing are the rate constants they’re claiming can’t possibly be established.
Every time you observe something taking place over time, it ABSOLUTELY WILL produce an average rate. This isn’t a biology claim. It’s arithmetic. If X events occur over Y time, then X/Y is the average rate. It doesn’t matter if the variance is enormous. It doesn’t matter if the rate fluctuates wildly. It doesn’t matter if some periods see bursts and others see nothing. The average rate exists as a mathematical certainty from the moment you have a count and a duration.
The LTEE has a count: observed fixations per population. It has a duration: generations elapsed. Divide one by the other. That’s the average rate. It’s not a philosophical position. It’s not a modeling assumption. It’s division. The human-chimp divergence has a count: 398,673,272 base-pairs observed between the two lineages. It has a duration: approximately 6.3 million years. Divide one by the other. That’s the average rate of post-CHLCA human evolution: 63.281 base-pairs per year.
We get a different rates for each of the six other great apes ranging from 37.8 to 99.4 . So we add them all together, divide by six, and we reach an average rate of human evolution based on six different speciations.
62.7 base pairs per year, or 1,958.81 base pairs per effective generation.
You can argue about the precision of the inputs, you can argue about which lineage each of those divergent base pairs should be assigned to, but you cannot argue that the quotient doesn’t exist or has no meaning. And it’s interesting to observe that the similar average holds despite the difference of 9.6 million years between the most distant and the most recent speciations.
What the Evo-Avengers are actually doing without realizing they’re doing it is confusing “the average rate varies across species and conditions” with “the average rate doesn’t exist.” Those are completely different statements. The first one is trivially true and is exactly what Probability Zero takes into account and what I have taken into account here. The second one is mathematically illiterate. And the fact that multiple PhDs in biology and meteorology and population genetics are publicly declaring the second while imagining they are asserting the first tells you everything you need to know about their total inability to comprehend the math or engage any of the unavoidable problems for evolution it creates.