Erika “math is hard” Matthews couldn’t quite manage to characterize my argument accurately or do the math correctly, despite reading both Probability Zero and the MITTENS 3.0 paper. But apparently, she gave it her best shot in the second video.
(16:30) Now, before we get started, I’m just going to give you Vox’s argument real quick taken directly from the horse’s mouth here and explain it to you so that you can understand why it’s problematic moving forward. We’re going to do this in baby steps. In essence, his argument is a waiting time problem, which is a specific category of creationist arguments against evolution, which essentially say there isn’t enough time for the differences we see between any two given pairs of organisms to emerge.
Instead of using any established equations or models in population genetics, Vox makes up his own equations to make this case. What he effectively ends up with is just a d= rt kind of equation or distance equals rate time time. Vox is using the human chimpanzeee divergence as his example here and he says that he is giving conventional science the most generous assumptions imaginable. Vox says that humans and chimpanzees differ by about 20 million base pairs in their 3 billion base pair long genomes. He also says that it’s been about 9 million years since the two species diverged. Given a human generation time of about 20 years, that gives us 450,000 generations in humans to accumulate all 20 million base pair differences. To account for the fact that generations overlap, which is something that population genetics can already do. Zach went over this extensively in the previous video, he introduces a new variable, which he calls the selective turnover coefficient. He calls this d, and he assigns it a value of one.
And finally, Vox provides us our rate by saying he is using the fastest known rate of mutational fixation, which he claims comes from the 2009 LTE Orinsky long-term evolution experiment observed in populations of E.coli. Since he says this is the fastest observed rate, he describes this as the speed limit for evolution or the ceiling, the fastest it can possibly occur. And the number he provides is 1,600. 1,600 is the number of generations it takes for one mutation to fix.
That word fix is important because the fixation rate is different from the mutation rate. The mutation rate is the rate at which mutations occur. And the fixation rate is the rate at which they come to define a population. Let’s use fur color and foxes as an example here. The fixation rate would be the rate at which a newly emerged coat color, let’s say red, comes to characterize the entire population of foxes. You can see then that the mutation rate is going to be quite different from the fixation rate with the latter being determined by a myriad of different factors within the environment. And as all sources, including Wikipedia will tell you,
fixation occurs through natural selection, genetic drift, or both. So, as Vox will tell you, his math here is pretty simple. 9 million years of divergence time 1, the selective coefficient, divided by the generation time, that’s 20 years, times the generation it takes for one mutation to fix, or 1600. And that equals 281ish. And 281 is way less than 20 million, right?So, that’s it. Evolution killed by a fraction that no one ever thought of. Well, I mean, as long as all the variables are correct and as long as the assumptions which go into this equation are met and or justified, if any of those variables are wrong, then the entire equation is bunk. And if the assumptions that go into those variables are wrong, the equation is also bunk. So, it’s got to be all right. Right? Wrong.
That’s her critique of MITTENS. I’ll now go over what she said and point out eight of her obvious errors.
ERROR 1: MITTENS is not the waiting time problem. The accounting issue I have identified is not the waiting time problem. She doesn’t understand that these are two entirely different arguments that are focused on opposite sides of the fixation process. The waiting time prolem refers to the significant amount of time required for beneficial genetic mutations to occur in a population, particularly when multiple coordinated mutations are needed for adaptation. The MITTENS argument isn’t concerned with mutation rates at all, it is an empirical audit of observable fixations. It doesn’t model theoretical waiting times; it measures observed throughput. Categorizing it as a “creationist argument” is not only false, but dishonest. The question of whether there enough time to account for the observed genetic divergences is a quantitative question that absolutely must have a specific quantitative answer.
ERROR 2: I did not make up the equation for determining an average rate” — Matthews exhibits the same inability to understand the concept of an average rate that Dr. Hanson demonstrated in the first video. I didn’t make up a new equation. I simply observed that given the amount of time, the time it takes for an event, and the number of events involved, the average rate required was improbably high to the point of effective impossibility.
ERROR 3: 410 million is not 20 million. Matthews is off by more than an order of magnitude. We know, by her own admission, that she has read MITTENS 3.0. The total divergence reported there is 410 million, with 205 million assigned to the human side. This number is slightly exaggerated because the Yoo et al 82-page supplementary spreadsheet reports three different numbers on three different pages with different denominators; a direct accounting directly from the raw data results in a total genomic human-chimp divergence of 398,673,272 base pars. She’s trying to criticize my math when she’s literally off by 95 percent on the total that must be accounted for.
ERROR 4: 9 million is not 6.3 million. She’s trying to fudge the numbers while claiming to present my argument faithfully.
ERROR 5: 20 is not 25. MITTENS uses the standard 25 years per human generation, consistent with paleodemographic reconstructions (Langergraber et al. 2012). This is another error that just happens to make the argument appear a little weaker by a) providing more generations and b) citing a different number of generations than I reported.
ERROR 6: 450,000 is not 201,600. This falls out from her false inputs (9M / 20 = 450,000). The actual number of available generations prior to the correction for generational overlap is 252,000 generations (6.3M / 25). She’s arbitrarily providing the evolutionary process more than twice as many generations as are actually contained in the argument presented, which is 201,600 effective human generations.
ERROR 7: The post-CHLCA human value of d is 0.80 not 1.0. She completely misunderstands what the Selective Turnover Coefficient is and why it is necessary. Setting d = 1 is the Wright-Fisher idealization. It’s the value for the E. coli of the LTEE, it cannot be the value for humans with overlapping generations. This is the result of Dr. Hancock’s inability to distinguish between Wright-Fisher’s and Hall’s use of overlapping generations to calculate drift and d‘s use of them to correct for the available number of effective generations over time. If humans were bacteria, there would be time for 252,000 generations. Because we are not, there was time for 201,600.
ERROR 8: 71,000x is not 1,139,000. Her own arithmetic from her wrong inputs: (9,000,000 × 1) / (20 × 1,600) = 281.25. The shortfall she calculates against 20 million (~71,000×) is actually much smaller than the MITTENS shortfall (~1,423,611×) because every one of her input errors runs in evolution’s favor. The actual calculation yields 144 fixations against 205 million required fixations. But, she’s right to observe that 281 is a small fraction of 20 million. It’s an even smaller fraction of 205 million.
ERROR 8: “If any of those variables are wrong, then the entire equation is bunk” This fails to grasp the scale of the argument’s architecture. The million-fold shortfall means it is necessary to change the inputs by orders of magnitude in order to close the gap. The margins aren’t close. There are no small corrections to a variable that will render the proof false. Only very, very large and significant structural changes are capable of showing it to be false.
Now, I’ve actively looked deep into those potential structural changes. I’ve looked into alternative evolutionary mechanisms, and thanks to correcting the application of Kimura’s time equation, actually managed to find and empirically confirm that I call “relictation” which is neither drift nor natural selection, and can, in certain circumstances, reduce the time necessary for neutral drift to fixate by cutting it in half. It’s nowhere nearly enough to render MITTENS false of course, but it is an iterative improvement in the analytical model.
However, the complete analysis of the 25,302,032,866 base pairs for the seven species of Human, Chimp, Bonobo, Gorilla, Borneo Orangutan, Sumatran Orangutan, and Siamang does open a brand new line of attack against MITTENS that will either a) potentially permit the refutation of MITTENS in one more more cases or b) weld the locked door that is already shut against evolution by natural selection, neutral drift, and relictation.
But as should be abundantly clear by now, if MITTENS is ever going to be refuted and evolution is going to be shown to be mathematically and empirically possible, it’s not going to be refuted by Erika and her innumerate Evo-Avengers. We’ll see if they managed to do any better than she did in the initial part of the video, but their collective case is obviously not off to a good start.