This will be the final response to the first Evo-Avengers video, and it’s chiefly of interest for the way it demonstrates once more that biologists simply don’t understand the concept of averages. We saw that with JF Gariepy. And now we see it demonstrated here by Dr. Hancock being mystified by the concept of an average rate of fixation.
They really are innumerate.
(1:29:30) We’re going to follow his math and I’m going to give you sort of the logic which you just saw, but we’ll do it again so that you can, you know, the more times you see it, the better it’ll cement in your in your brain. Okay, he then says fmax is equal to t over g which is the divergence time divided by generation. So we’re basically converting it to generations over k and k we’re going to call the fixation rate.
What he is what he is saying is the maximum fixation rate that has ever been observed. Right? That’s that 1400 generations. So he has this other term D, but I don’t we don’t know what it means. We don’t we don’t know how to how to correct and it’s just one in his equation anyway, so we’ll just ignore it. Um, so he then claims that this ratio is 252,000 generations over 1,400 generations to fix a mutation. So we’ve got 250,000 generations and each mutation takes 1,400 generations to fix. That’s that’s basically what he’s saying. And of course that equals 180 expected fixed differences. You follow that so far? Roger. Okay.
So that all might seem okay to you if you if like maybe you’re not like particularly mathematically minded or maybe you don’t know a ton about population genetics, but let’s break down what this actually means. Um and I think the best way to show it is actually graphically. So we’re going to we’re going to test my artistic skills here. Um so this is the frequency which we’ll call f of p the frequency of p and then here is time on the x- axis. Okay. And we have out to exactly 252,000 generations. That’s how much time that we have to to start fixing things, right? So if we start at time zero, we get a mutation. Now he claims it takes 1400 generations for that mutation to fix.
So we we go up we eventually reach fixation and then this interval here is 1,400 generations. That’s what he’s claiming, right? Yeah. So we’ve now fixed one mutation. Then we can get another mutation here and then it has to go to fixation and then this interval as well is 1,400 generations. And you just keep doing that over and over and over until you get to 250,000, right? And how many little intervals does it take to get to 250,000? It takes 180 intervals to get there. So hopefully you can see a 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. Right?
Because otherwise if you can allow multiple mutations to occur at the same time that means multiple muta multiple mutations can fix at the same time. But that is not allowed in this math. There must be these discrete intervals. And we know that because it takes 180 intervals to get to 252,000. Right? That’s literally what that math is showing. Does that make sense? Yeah. He’s defining it in with the equation he’s choosing to use. Yeah. in effect he’s he’s the the way that this equation is set up assumes that these these mutations must arise and fix sequentially. Um that’s the the basic assumption and to me that makes this whole thing preposterous, right?
The calculation T/k = 252,000/1,400 = 180 is a rate calculation. It says: given an observed fixation rate of one per 1,400 generations, how many fixations fit in 252,000 generations? The answer is 180. That’s throughput, or output per unit time.
However, Hancock somehow interprets it as a latency calculation and assumes that each fixation must complete before the next one even starts, like cars going through a single-lane tunnel one at a time. Then he triumphantly announces that mutations can fix in parallel, as if that was ever stated or successfully refutes anything.
The problem here is that observed rate already includes whatever parallelism actually occurs. Specifically, it includes, on average 5.1 neutral hitchhikers with each selective adaptation. Because that’s the primary form that “parallel fixation” takes, not multiple selection events completing at the same time, but five neutral hitchhikers being swept to fixation with the selected mutation. This boost to the throughput is already reflected in the observed fixation rate. The rate is the rate. It doesn’t matter whether it comes from one fixation at a time taking 1,400 generations or seven fixations running in parallel each taking 9,800 generations. The output is the same: 144 in 201,600 effective generations.
And here’s the irony: if he wants to argue for massive parallel fixation to increase throughput beyond the observed 144, he has to deal with Hill-Robertson interference, the fact that simultaneously segregating beneficial mutations compete with each other and slow each other’s rate of fixation down.
So what Hancock did was to draw a picture of sequential fixation on a whiteboard, falsely asserted it was my assumption, and then refuted his own drawing.

Now, what Dr. Hancock didn’t know, because he didn’t bother to read my data paper on the LTEE, is that this is neither what the experiment data shows nor does it represent my argument correctly. First, because he didn’t understand why d is necessary to correct for overlapping generations, he uses the wrong number of generations: 252,000 instead of 201,600. Second, we’re in the process of considerably increasing the accuracy of the denominator from fixation to base-pair, which is very important, but doesn’t matter for now. Third, he also didn’t know that I have independently run the LTEE data for all 723,000 generations covering all 12 populations at a much higher resolution than is published in any of the papers; 500 generations rather than 10,000 generations.
So, instead of guessing and theorizing about what sort of fixations appeared and when they appeared, I know exactly what happened. And here is what the data actually looks like for the one of the fastest of the five remaining healthy populations, Ara+4, over its 60,000 generations.

That’s not theory. That’s what actually happened. The red are the fixation events. There are 16 of them. The yellow are the 64 neutral hitchhikers that also fixed during the 11 sweep events. So what this shows is neither serial fixation nor what people usually imagine parallel fixation would look like; there was never one single overlapping fixation event in any of the 5 normal populations or the 7 hypermutating ones. Interestingly enough, the hypermutational populations actually had fewer fixation events, although the sweeps were considerably larger, as can be seen in the most active hypermutational population, Ara+6, with 9 vs 16 fixation events and 2581 hitchhikers vs 64.

It’s easy to see when Ara+6 broke down; the massive sweep that started at generation 6k and extended over 14k generations is the result of the broken DNA repair mutation; essentially, the genome developed cancer then. Notice, however, that both the normal and the cancerous population had gaps that ranged from a minimum of 1,500 generations in between sweeps up to a maximum of 7,000 generations. So the idea that there is any parallelism that can somehow magically speed up the process to a rate that could possibly account for the size of the observed divergences between all of the 7 ape species is an absolute non-starter.
In fact, the LTEE data reveals something the butterfly collectors exercising their imaginations rarely contemplate: the distinction between how often fixations complete and how long each one actually takes. Which means we can measure the parallelism of each population as their mutations rise toward fixation at the same time. Across the five non-mutator populations, an average of 18 mutations that eventually fixed were simultaneously rising through the population at any given timepoint. The all-transit depth was 43, meaning that 25 other mutations entered the 5–95% frequency zone, competed for survival, and eventually faded before they could fixate.
And the variation across populations is significant: Ara+2’s completing depth of 5.24 versus Ara−5’s 33.35 represents a sixfold difference in the degree of parallelism between populations of the same organism in the same environment. But not even the highest degree of parallelism observed is anywhere close enough to the degree envisioned to permit significantly reducing the number of generations per fixation.
