In which Dennis McCarthy calls me out for failing to address his challenge to my PZ argument. And he’s right, I didn’t even bother to address the one he pointed out because it was so obviously wrong and I had already pointed out in the book that genetic drift is far too slow to ever fill in the gap that natural selection couldn’t. Hence my point about having addressed “every single relevant point”. What Dennis did on the challenge that I ignored was to apply Kimura’s substitution equation to the question of fixations over time while omitting Kimura’s equation for mean time to fixation for a neutral mutation.
So, I will rectify that failure now. To put it in terms everyone should be able to understand, he pointed to the speed limit sign to determine how fast the car was going instead of looking at the speedometer. I didn’t see any reason to respond to that; no biologist or population geneticist would ever suggest that genetic drift is actually faster than natural or sexual selection.
VD: Economists, mathematicians, and physicists are inordinately skeptical about evolution, because they all understand the math that the biologists don’t. Every single one who bothers to looks into it ends up dismissing it pretty quickly. Darwin was innumerate, by his own admission. Dawkins is observably innumerate. And the Wistar Symposium demonstrated that the very best and most influential evolutionists simply can’t comprehend the math involved.
DM: I am in fact “numerate” and would be happy to compare my peer-reviewed articles employing math with yours. Regardless, my challenge of your PZ arguments are correct–and you haven’t addressed them. You have just moved onto other errors. I will be responding to those new errors shortly.
VD: That’s nonsense, Dennis. I believe I have addressed every single relevant point you raised. Feel free to identify any one I failed to address and I will certainly do so.
DM: Vox, your original argument was that Kimura’s equation could not account for the roughly 35 million single-nucleotide differences that have accumulated since the human–chimpanzee lineages diverged. Below is my rebuttal, which remains correct. I have seen no direct response to it. If you have written one, please link to it here (And please don’t just link to a book and claim it’s in there somewhere–or note the “entire book” is a rebuttal–but link to the explicit argument that discusses these numbers and equations below.)
Quoting my original rebuttal: “Here is the problem: What Vox Day calculated—(1/20,000)^20,000,000 —are the odds that a particular group or a pre-specified list of 20 million mutations (or 20 million mutations in a row) would all become fixed. In other words, his calculation would only be accurate if the human race experienced only 20 million mutations in total over the last 9 million years—and every one of them then became fixed. And, yes, hitting a lottery (with odds 1/20,000) 20 million times in a row would indeed essentially be probability zero.
“But our evolutionary history does not require that an exact group of 20 million mutations become fixed—only that some 20 million out of an enormous pool of candidate mutations become fixed.
Here’s the correct analysis. Using Vox Day’s numbers, in a population of 10,000 humans, we would expect, on average, 50,000 new mutations per year. And over the course of 9 million years, this means we would expect:
50,000 x 9 million = 450 billion new mutations altogether.
So out of 450 billion mutations, how many mutations may we expect to achieve fixation? Well, as Vox Day noted, each mutation has a probability of 1/20,000 in becoming fixed.
450 billion x 1/20,000 = 22.5 million fixed mutations.
And that is a pretty close approximation to the 20 million fixed mutations that have been observed.
VD: I dealt with this in PZ before you even raised the question in response to it. The problem is that you left Kimura’s time component out of your response. This is Kimura’s standard equation for how long it takes a neutral mutation to fixate: t̄ = 4Nₑ generations — mean time to fixation for a neutral mutation (Kimura & Ohta 1969). It’s mainstream population genetics.
With the standard human effective population size, Nₑ = 10,000. t̄ = 4 × 10,000 = 40,000 generations. At 25 years per generation, that’s 1,000,000 years per neutral fixation.
Neutral substitution is much, much slower than natural selection, which is why, in the book, I point out that genetic drift is not a defense of evolution and it can’t explain the observable genetic differences. And it’s also why I knew your response was irrelevant from the start.
Now, it’s actually a lot worse for the neutral substitution case than that, because there is a hard limit to genetic drift even being able to affect a population. In any population over 10,000, neutral substitutions will not fixate at all. And we have actually found empirical evidence for this mathematical barrier in the ancient DNA database.
So this is what I mean by evolutionary innumeracy. I’m not saying that evolutionists can’t punch the numbers into the calculator and get a correct result. I’m saying they don’t understand what the numbers represent or how the various mathematical equations necessarily interact.
UPDATE: DM’s response:
That response does not deal with your first incorrect improbability equation, but introduces yet another error in which you are incorrectly claiming only one mutation can fix at a time. Do you seriously think that? Do you seriously think that only one mutation out of many millions can sweep through a population at a time? Anway using your numbers:
Ne =10,000
Expected fixation time: 4N_e=40,000 generations
At 25 years per generation: 40,000 times 25 =1 million years
Nine million years divided by 25=360,000 generations
So neutral mutations that have occurred in the last 40,000 years have not had time to fix yet. But mutations arising during the first:
360,000-40,000=320,000 generations
did have the average 40,000 generations available to fix. That is eight million years of mutation production:
50,000 x 8,000,000=400 billion mutations
Applying the fixation probability:
400 billion x 1/20,000 =20 million fixations. So when we apply the time available to the numbers we land on the exact correct result.
Obviously, mutations, whether neutral or not, do not have to increase in frequency throughout a population one at a time.
My improbability equation is irrelevant, as it even says in the book. It’s not “wrong” because it doesn’t exist. It has absolutely nothing to do with the proven fact of the mathematical impossibility of evolution by natural selection.
Here is where DM went wrong: “400 billion x 1/20,000 =20 million fixations. So when we apply the time available to the numbers we land on the exact correct result.”
No, because that requires assuming that every mutation is neutral. It isn’t. Which doesn’t matter when I’m just pointing out the scale of the improbability, but when you’re trying to prove that yes, it is actually possible, then you have to run the real numbers.
1/2Nₑ is the fixation probability for a neutral mutation. It is not a general fixation probability that applies to all mutations. There are 3x more harmful mutations than neutral ones.
Then DM said I’d “introduced yet another error in which you are incorrectly claiming only one mutation can fix at a time.”
No, what I was citing there is what standard population genetics has known since 1969, which is that every single neutral substitution requires ~one million years apiece to fixate. What you’re referring to now is the “parallel drift” defense, which is so obvious that I devoted Chapter 10 to it.
“Drift, on the other hand, filters nothing. It preserves nothing. It adapts to nothing. It is purely random. But these defenders of non-Darwinian random evolution have nevertheless resorted to insisting that mutations can spread through populations by random chance alone, fixating 1,017 times per generation, without needing natural selection at all. This is what they mean when they invoke “neutral” or “mostly neutral” processes operating “in parallel.” Without realizing it, they’re appealing to the fixation model produced by Kimura and its subsequent revision by Tomoko Ohta, even though neither model is capable of even coming close to accomplishing what is claimed of them…. Faced with this obvious problem, some of the less intellectually gifted defenders of evolution have retreated to an imaginary mechanism of genetic change: neutral processes running in parallel.”
And from my paper on the Bernoulli Barrier, published around the time the book came out: “The parallel fixation mechanism is self-defeating: it invokes a process that eliminates the conditions necessary for its own operation.”
And drift is obviously not a viable retreat when you think through the basic logic of it:
- For neutral substitution to work to fixation at its maximum speed, natural selection cannot be operating.
- There are 3x more harmful substitutions than neutral substitutions.
So if genetic drift were capable of producing actual changes to the genome, the human species would have been rendered infertile and gone extinct within centuries. We know drift didn’t account for the 410 million base-pair differences, because both chimps and humans survived.
DISCUSS ON SG