This is my concluding response to Dr Page's latest rebuttal. I think it should be very clear to the reader that Page has run out of steam. Virtually all of Page's latest comments have absolutely nothing to do with the subject of our debate. In short, Dr. Page’s latest rebuttal is built entirely on 1) hairsplitting and semantics games, 2) equivocation of the word "evolution", and 3) numerous red-herrings that have nothing to do with the debate. I’ll address each individually. Dr Page's latest comments appear in maroon, my response in normal text, and any original comments from a prior post in blue.

Hairsplitting and semantics games

In my opening rebuttal, I mistakenly used “ape” instead of “monkey” when I wrote “The authors of the genetics study are arriving at their estimate of 10 generations by first assuming that man and ape share a common ancestor”. Page made note of this in his first rebuttal: “Chimpanzees ('ape') are not Old World monkeys”. Fine. I accommodated his nit-pick in my subsequent rebuttal by instead using the term “simian” (a more encompassing term). You would think this would be the end of it, but it became a focal point for Dr Page in his latest installment! He called it the “crux” of his dispute!!! (Wait, I thought the dispute, our debate, is whether or not Page’s citations have anything to say about Haldane’s Dilemma!) Dr. Page has now tried to shift the reader’s attention away from the debate and on to a silly nit-pick! He reminds the reader of this “ape” vs. “simian” hairsplit at least five times throughout his latest rebuttal, all the while complaining along the way about my revised use of “simian”! Note the desperation of Page’s argument when he writes:

“First, Williams refers to Old World monkeys as apes in his original rebuttal. I point out that Old World monkeys are not apes. Williams then re-writes his original 'challenge' and presents it as he did above, using the word 'simian' instead of ape. Old World monkeys are, at least by laymen, considered to be simians. Williams has reworded his claim so as to prevent it from being rendered moot and shown to be inaccurate, and now bases his 'new' argument on this reformulated claim.”

Dearest Dr. Page, I did not “re-formulate” my argument. I simply changed one word, ape, to “simian” to appease your nit-pick. A nit-pick extraordinaire indeed! Whether or not the simian used in the study was an ape or a monkey has no bearing on whether or not your use of the citation was circular reasoning. I wonder how else you think I should have responded. I suppose you would have preferred me to exclaim “Yep, I should have said monkey and not ape, so you win the debate on a technicality!”

Next, Dr. Page calls my use of the term “analogous” instead of “homologous” a “fundamental error”. This is quite an exaggeration. From a creationist perspective the sequences could be called analogous because creationists do not believe apes (oops, I mean “simians” J),  are related to humans via decent. Nevertheless, to speak in evolutionary terms “homologous” would indeed be the appropriate term. Yet another silly nit-pick on Page’s part.

Equivocation of the word "evolution"

I originally wrote:

This fixation rate is in stark contrast to Haldane's calculation of 300 generations, so that's why Dr. Page cites this study. But Haldane's cost argument is a mathematical model that is not based on the assumption that simian/man ancestry (or any other form of large-scale evolution) is true.

Page replies with:

“Williams can re-write this as many times as he wants to, and it will still be bogus. Haldane assumed evolution when he formulated his model. If Haldane had simply set out to produce a purely mathematical model, devoid of evolutionary assumptions and constraints, as Williams suggests (insists?), then one should be curious as to why the formulae employed by Haldane contain a variable called the selection coefficient. For, what good is the concept of selection except in an evolutionary context?”

 Here Dr. Page is equivocating on the definition of ‘evolution’ (see my article on this). In my preceding comment that he responded to, I explicitly stated that Haldane’s model is not based on the assumption that simian/man ancestry (or any other form of large-scale evolution) is true. I am not referring to population genetics (also called evolutionary biology) where concepts such as selection coefficients are used. Creationists have no problem with natural selection, and in fact proposed selection before Darwin1. So I ask Dr. Page yet again, to provide any evidence whatsoever that Haldane’s model requires the assumption that simian/man ancestry (or any other form of large-scale evolution) is true.

Red Herrings Galore

Following are several Red Herrings that have nothing to do with our debate:

Williams' continued claims that Haldane's model contradicts human/ape ancestry is premised on his personal disbelief that 1667 fixed beneficial mutations can account for human evolution from an ape-like ancestor. Willaims has never been able to provide a shred of evidence that that position has merit.

Our debate is not on the merits of Haldane’s Dilemma. As I stated in my previous post, even if Haldane’s model is wrong, it still doesn’t rescue Dr Page from his circular reasoning error.

Page then pulls out the chimp-bonobo red herring. What does this have to do with our debate? Absolutely nothing.

Dr Page then expands his chimp-bonobo red herring by offering several lengthy citations regarding non-random mutations. Again, what does this have to do with our debate? Again, absolutely nothing. The simple fact is, Dr Page cannot defend his use of the Genetics study, so instead tries to bury the reader with a bunch of boring and lengthy citations that have no bearing on this debate.

Revisiting Dr Page's Core Error

Page writes:

I cited the Genetics paper as recent data-based evidence that the rate of change is much faster than originally estimated by Haldane (1957). Williams expends a considerable amount of energy trying to convince the reader that 1. the authors engaged in circular reasoning (an assumption of common descent), and so 2. my citation of it and use of it is also circular and 'faulty logic.'

For the second time Dr. Page, I did not accuse the authors of circular reasoning, I accused you of circular reasoning. It is you who tried to apply a study that requires the assumption of simian/human ancestry, to a mathematical model (Haldane) that does not require the assumption of simian/human ancestry. I repeat, if the assumption of simian/human ancestry is wrong, then the Genetics study is useless. To apply such a study to a mathematical model void of assumptions about human/simian ancestry is faulty logic, plain and simple. It’s textbook circular reasoning. I will explain it again. You believe evolution. You get a rate of change from a study (Wu, et al) that begins with the assumption that evolution is true (specifically common decent, or man/simian ancestry). You contrast this rate of change to a mathematical model (Haldane) where the rate of change is so small as to make evolution untenable. Since the rates don't jive, you claim the Haldane mathematical model is refuted, and evolution is defended! The circle is complete!

More Population Genetics Errors by Dr Page

Page: Williams then writes that all those lacking the mutation and all of their descendants had to be removed from the population. As worded – and probably as understood by Williams – it sounds as though all non-mutation holding organisms must be literally removed. This is incorrect.

Me: No, it is entirely correct, unless you believe our ancestors are all still alive!

Page: How ridiculous. I was clearly referring to a time-dependant explanation.

What? Dr. Page, frankly you do not know what you are talking about. Check Futuyma, Evolutionary Biology, p 299. When an allele becomes fixed, it becomes monomorphic, its frequency is 1 (100%). That means the wild type is GONE, and ALL prior descendants who had the wild type (did not receive the new allele) over time had to be removed from the population. My statement is entirely correct, and I am surprised you would question it.

In Response to my Bike Analogy

Page responds:

In a 'harmful mutation environment', reducing the number of them that become fixed in the population, via whatever means, is a benefit, no matter how you look at it.

Notice Page switches the goal posts. He now admits it's a benefit to evolution, providing its a "harmful mutation environment"! But a harmful mutation environment is itself an obvious and huge disadvantage to evolution! Perhaps Dr Page is finally getting my point without realizing it! J

Page: I did not present it [Rice study] as “evidence for evolution” – I presented it as evidence that the typical claims of harmful mutations accumulating fast enough to prevent evolution – as is often implied by Williams and his ilk – is in error. And in this it succeeds.

No, it does not succeed. You continue to validate my claim that the Rice study is misleading, because it has surely misled you into believing something that is not true. I repeat, the Rice study merely shows the advantage of recombination when contrasted with an asexual species in a harmful mutation environment, period. Nothing more. It does nothing, I repeat, nothing to reduce the mutation problem. Here is my article on the mutation rate problem. Please explain to the audience how the Rice study has any impact whatsoever on this problem.

Dr Page's Response to List of Errors I Presented Him

(my original claim is in blue)

* [Me] Mistakenly claiming that Haldane based his substitution estimate on the observation of peppered moths (Haldane did the opposite, see Haldane 1957, p521)

Page: You sure like p.521. In my copy of Haldane's 1957 paper, on p.521. there is nothing at all about what he based his estimate on. You should notice that on the first page, p. 511, Haldane expends some time explaining the observations seen in peppered moths, and how he will attempt to estimate "the effect of natural selection in depressing the fitness of a species." I committed an error of omission, and should have included the fact that he considered some Drosophila experiments and such as well. However, your claim that he "did the opposite" seems to have no basis in reality.

On page 521 Haldane writes: "...This represents, in my opinion fairly intense selection, of the order of that found in Biston betularia [peppered moth]... I doubt if such high intensities of selection have been common in the course of evolution. I think a more probable figure". Dr. Page, it is quite clear that Haldane did NOT base his substitution rate on the peppered moth observation (which you now implicitly admit above), and in fact did the opposite (low intensity as opposed to high intensity selection).

* [Me] Implying that a large population is a bad assumption for evolution (Haldane did the opposite; see Haldane 1960, p351)

Page: You are recklessly misrepresenting me. I claimed no such thing. Quoting from my solid refutation of your original bombast, the times I mentioned population size or Haldane's use of it: "…premised on unrealistic assumptions (such a s a constant population size), made using observations of phenotypic variation in Peppered moths." "Williams writes "entire population" for a reason - the connotation of "entire population" is that the population is extremely large, such as the human population of today. This is an unreasonable allusion." I did, however, say that a constant population size is an unrealistic assumption. But 'constant' does not mean 'large.' Misrepresentation.

I do not accept your explanation. Why did you write that an extremely large population is an "unreasonable allusion"? It sure sounds to me that you believe its a bad (unfavorable) assumption for evolution, or you would not have wrote "unreasonable allusion". It is clear you were unaware that Haldane believed it was a favorable assumption for evolution (1960, p 351).

* [Me] Claiming that a wild-type allele can still persist in a population even after its mutant allele reaches 100% fixation in the same population!

Page: I see you don't understand what fixation means, or perhaps are unaware of what a dominant allele is.

Dr. Page, I again refer you to Futuyma, Evolutionary Biology, p 299. If that is not good enough, check his glossary: "Fixation: Attainment of a frequency of 1 (ie. 100%), by an allele in a population, which thereby becomes monomorphic for the allele" [emphasis in original]. It is quite clear it is you who does not understand what fixation means.

Page continues: If 100% of a population has a DOMINANT allele, they can still be heterozygous - the individuals can still have a recessive allele for the same locus, and yet they all would exhibit the dominant phenotype.

Strawman. This is not what you claimed. Regardless, even this a very bad argument, because using your new explanation, if 100% of the population has the dominant allele, it is extremely likely that any remaining recessive alleles are by now virtually extinct, at a frequency very near zero.

* [Me] Because of his previous error, reaches the erroneous conclusion that a dominate[sic] allele does not need to be replaced, which implies it has no reproductive cost.

Page: More misrepresentation. If the members of a population are homozygous for the wild type, then the replacement of one allele with a dominant mutant will incur your beloved cost. However, the impact of the cost - under realistic assumptions - is not what you continue to claim it is.

Wrong again! Perhaps this figure from Futuyma, p 298 will help:

The diagram above should help illustrate that a new allele from a mutated wild-type, be it recessive or dominant, will have to incur reproductive costs over the life of the fixation. Haldane assumed ALL of his mutations were dominant, since the cost of recessive mutation is exponentially higher.

* [Me] Claiming that a beneficial mutation will spread through a population in a sexual species "as well" as it would in an asexual species, even given an environment free of deleterious mutations.

Page: I really wish that you would put a lid on your shameless attempts at revisionism. That or learn some common colloquial english: "as well 1 : in addition : ALSO...I am unsure whether you are purposely trying to be annoying, if you are so self-deluded that you simply ignore the context, or that your english really is that poor. Either way, all you are doing is pointing out your incompetence.

Dr Page should consider accessing a more complete dictionary next time before accusing me of "poor english" and "incompetence". Note definition #2, apparently missing from Page's dictionary, in the Webster Collegiate Dictionary:

- as well 1 : in addition : ALSO <there were other features as well> 2 : to the same extent or degree : as much <open as well to the poor as to the rich>

However, I take Dr Page at his word that his intended use was '1', so I hereby retract my original claim (stated above in blue).

* [Me] Claims that Wu's study dos *not* assume human/simian ancestry in its determination of the substitution rate.

Page: That is a fact... [NOTE ADDED HERE: Observe that Williams then changed his phrasing to “simian and human” ancestry, which is correct, then made a stink about how I was 'misrepresenting' him!] That or provide the exact quotations from their paper pointing out their assumption of human-ape ancestry - as per your ORIGINAL claim - and how it was pivotal in their mutation rate analyses.

I already did, in my previous post in this debate. I'll copy it here:

Let’s look at an important passage from the study, emphasis mine. Particularly note the word “divergence”, which refers to the monkey/man split, and “positive selection” which is derived from the “divergence” data:

A common test for positive selection is a comparison of the A/S ratio of polymorphism and divergence (MCDONALD and KREITMAN 1991 ; SAWYER and HARTL 1992 ; TEMPLETON 1996 ). Since mutations under positive selection spread through a population quickly, they are not well represented in polymorphism but should have a cumulative effect on divergence. The A/S ratio from divergence is estimated from 182 orthologous human and old world monkey genes (Table 1). To avoid the confounding effects of deleterious mutations, which do not contribute to divergence but do make a significant contribution to polymorphism, the A/S ratio from divergence is compared to that of common SNPs (Table 1). The difference in the A/S ratio of common SNPs combined from both surveys compared to divergence is significant (2 = 8.14, P < 0.01) and can be explained by positive selection, assuming the average constraint on the divergence and polymorphism genes is the same.

The large number of amino acid substitutions suggests a high rate of adaptive evolution in primates. The expected number of amino acid substitutions is 2382 (4151 x 70/122) based on the A/S ratio of common polymorphism and the excess is 1278. Therefore, a large proportion, 35%, of amino acid substitutions between humans and old world monkeys are estimated to have been driven by positive selection. Extrapolating this proportion to the total amount of coding DNA in the genome (5 x 107 bp) yields an estimate of up to 1 advantageous substitution every 200 years since humans separated from old world monkeys 30 million years ago (LI 1997 ).

If Dr Wu has arrived at this substitution rate of 1 per 200 years without contrasting DNA between old-world monkeys and humans, as Dr Page is essentially saying, then Dr. Wu needs to re-write his study. But I suspect he will not need to re-write it, because he is indeed contrasting simian/human DNA, and hence assuming simian/man ancestry to arrive at this rate.

Dr. Page, you are simply in error here. If not, then get Dr. Wu, whom you admit to have contacted regarding this debate, to substantiate your claim! This is key to the entire debate! This is your only hope, that Dr Wu engaged in poor writing skills when he wrote his paper and that his estimate really did not rely on simian/man ancestry. Come on, you and I and every reader can clearly see from the excerpt above that simian/man ancestry is an important assumption in the study!


To conclude, I have clearly shown in this debate that Dr. Page was mistaken to cite the Genetics study (Wu, et al) and the Science article (Rice, et al) as implied refutations of Haldane’s Dilemma. In the Genetics study he clearly engaged in circular reasoning. To make matters worse for Dr. Page, the study actually worsens the mutational cost problem! (required offspring per breeding couple increases to at least 60 instead of 40; see first post in debate, and my article on the mutation problem for evolution). In the Rice study, Page admitted that the evolutionary "benefit" described by the study pertains to a "harmful mutation environment", which by its very description is a huge disadvantage to evolution!

This did not leave Dr Page with anything substantive to offer in his latest rebuttal, so the recourse he chose was to distract the reader with  1) hairsplitting (ape vs monkey), 2) equivocation of the definition of evolution, and 3) numerous red-herrings.

I truly believe Dr Page now knows, or at least suspects, his citations are not valid weapons against the Haldane substitution problem, nor do they support the theory of evolution in any way  (as I mentioned earlier, the Wu study in fact provides evidence against evolution).  Certainly the authors of these studies did not think their findings had a bearing on such an important issue as Haldane's Dilemma, or you would think they would have mentioned it. Despite direct correspondence with at least one of the authors, Page was unable to get any of them to join him in his circular reasoning foray.

To Page's credit, I have not seen him trumpeting on the net either study since our debate began. Unfortunately however, there are several other evolutionists on the net who have now picked up his flawed nugget and are running with it. I ask Dr Page to take the time to correct the error he started whenever it re-appears on the net.


Fred Williams

1. Evolutionist Stephen Jay Gould notes that many creationists before Darwin advocated natural selection. S.J. Gould, "Darwinism and the Expansion of Evolutionary Theory, Science, 1982, Vol 216, p 380 (original source: Modern Creation Trilogy, Vol II, 1996, p 34).


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