Following is my reply to Scott Page’s response to my first rebuttal. Page's comments appear in aqua. It is a fairly long rebuttal. At the end of this rebuttal I summarize my arguments and Dr Page’s errors.

Page: Creationist Fred Williams, author of what he has referred to as a “saterical” [sic] website mocking evolution , is an electrical engineer with McData Systems.  He has no education, training, or research experience in the biological sciences.

Dr Page spends quite a bit of energy in his reply focusing on my “lack of training” in “the biological sciences”. I have never claimed to be an “expert” in “the biological sciences”, but I have read a wealth of material on the subject (particularly genetics) and am quite capable of identifying obvious inconsistencies with evolution. I should note that Dr Page has admitted to me in the past that population genetics is not his area of expertise (you'll soon see this is the case, in glaring fashion), yet he insists on making a formal education on the topic an issue. He also is guilty of applying a double-standard, since in the past he has referenced evolutionist Robert Williams’ page on Haldane’s Dilemma. Robert Williams also does not have a degree in genetics or biology, yet this didn't stop Dr. Page from referencing his work. Finally, I should remind Page that Charles Lyell, 1800s champion of uniformitarianism, did not have formal training in geology, nor did Darwin in biology. 

Dr Page's objection regarding my level of education and training should be a good early indication to the reader that he was unable to answer my rebuttal effectively, as we shall soon see. Otherwise there would be no need to resort to such rhetoric. Also, I did not misspell “saterical” [sic] as he implies.

Now to Dr. Page’s rebuttal:

Page: Haldane admitted that his conclusions would probably need “drastic revision” (“The cost of natural selection”. 1957.). Indeed – Haldane's estimates were made without the benefit of actual genetic data, unlike the Genetics* paper I cite . Numerous solutions to 'Haldane's dilemma' – and we should keep in mind that that this is a mathematical model - have been proposed, despite the fact that Haldane's model had several unrealistic constraints in it, none of which have met the personal, usually arbitrary standards of the various creationists that use 'Haldane's dilemma' as the crux of their anti-evolution arguments.

This particular debate is not on the merits of Haldane’s argument. Dr Page seems to have completely missed this point. The debate is whether or not Page’s citation "Positive and Negative Selection on the Human Genome"[1] is a refutation, or for that matter has anything to say, of Haldane’s Dilemma. I could concede all the points Page made above, and his original claim that the above citation rebuts Haldane’s cost argument would still be wrong. I will repeat the key point in my original rebuttal: The paper Page cited assumes that common decent between simians and humans is true, and arrives at its 10 generation fixation time based on this assumption. 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. You cannot compare the conclusions of a mathematical model void of assumptions of the validity of evolution, to the conclusions of a study that derives its numbers on the assumption that evolution is true! I suspect this is why Dr. Page’s attempts to get the authors to support his claim were fruitless.

Page: Famous mathematician Sir Fred Hoyle, in his book “The Mathematics of Evolution”, explains that “Haldane's so-called cost principle is an illusion." (p123).

This is worth noting. Hoyle indeed made this claim in his book, but he didn’t rely on circular reasoning in his argument! Hoyle used mathematics to argue against Haldane’s mathematical model, which is a valid approach. I haven’t had an opportunity to review Hoyle’s argument in detail, though it's worth noting that evolutionist Maynard Smith was not convinced by Hoyle’s argument (see Walter Remine's review of the book at .

Regardless, I want to stress again that at least Hoyle went about attacking the argument in a proper fashion. Whether or not Hoyle is right doesn't matter, it does not vindicate Dr. Page's use of faulty logic. Dr Page engaged in circular reasoning, which rendered his argument completely spurious.

The Genetics paper I refer to does, as Williams indicates, 'estimate' the number, but again, unlike Haldane's estimates, these are inferred from analyses of actual data. This important fact is ignored by Williams.

Again, I did not ignore this “important fact”. The Genetics study conclusions are indeed inferred from analyses of actual data. But this data is derived from the initial assumption that simians and humans share a common ancestor. It is circular to use the Genetics study conclusion to argue against a mathematical model that contradicts simian/human ancestry.

Page: I do not take this or any one paper to 'be a refutation of Haldane's dilemma.'

Then why did you write: “According to an extrapolation of Haldane's 1957 paper, no more than 1667 fixed, beneficial mutations could accrue in the lineage leading to humans from an ape-like ancestor. 1667 is too few to account for this (unsupported assertion), therefore, humans must not have evolved at all. According to the first paper mentioned, the number is off - way off.” [emphasis mine]

Page: It also brings up a conundrum for Williams. In his other essays on the topic available on his web site, he uses publications that utilized evolutionary assumptions and models in their experimental methods. He usually concludes that evolution is impossible. If his conclusion is correct, then the conclusions of all such publications are moot, and Williams has no logical, scientific, or rational reason for using them – that is, if the evolution models are wrong, then so are the conclusions of the papers and they therefore cannot be used to support anything.

I thought Dr Page understood this part of my argument, many others have (including Sumac, whom Page cited in his response). Re-read my article, particularly the conclusion. The only part of the evolutionist study I believe is flawed is the initial assumption that simians and humans share a common ancestry. The only other realistic possibilities are that their data gathering or posteriori mathematical analysis is flawed. But this is unlikely, especially since there have been several studies since then producing similar results.

Do I accept the conclusions of the studies, that the mutation rate is >3? No. The truth is we don’t know what the rate is. What we do know is that any study that compares two species supposedly related by common ancestry, and produces a rate >3 is very likely flawed somewhere. Such a rate is way too high for a mammalian species to tolerate. The logical conclusion is that the problem lies in the study’s core assumption that simian and man share a common ancestry. Remove this assumption, that is, stop comparing human DNA to simian DNA in an attempt to determine the mutation rate, and the problem goes away.

For the record, I have never claimed these studies demonstrate evolution is impossible. I merely provide them as solid evidence that simians & humans do not share common ancestry. What I do posit is impossible is for new information (particularly a “code”) to arise naturalistically. There are no known examples in man’s history of this occurring. To originate information in a materialistic medium is as impossible as it is to create energy from scratch. 

Page: There is no assumption – implicit or explicit – in the paper regarding the lineage leading to Homo splitting from the lineage leading to Pan. This is a complete fabrication. Indeed, the paper clearly states: “The divergence data are from 182 orthologous human and old world monkey genes (_183 kb). “

It is beyond me why Page provided this sentence to defend his claim that no assumption on ancestry has been made to arrive at a substitution rate of 200 years per beneficial mutation. Dr Page is absolutely mistaken here. If I am wrong, then it seems it would be easy for Dr Page, who has corresponded with Dr Wu regarding our discussion, to get Dr Wu to back up Page's claim. I eagerly await his reply. This is at the very crux of our dispute.

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. Hopefully Dr Page now realizes this.

Page: Furthermore, I am at a complete loss as to why someone claiming to be knowledgeable in the sciences, as Williams does, would discard current data-based conclusions in favor of a nearly 50 year old estimate, premised on unrealistic assumptions (such a s a constant population size), made using observations of phenotypic variation in Peppered moths. The answer should be fairy obvious.

The reason you are at a complete loss is because you have not understood my argument. I am discarding the current data-based conclusions of your first citation because using them to rebut Haldane's Dilemma is circular.

Regarding Haldane's observation of peppered moths, he postulated that such intense selection likely was not common during the course of evolution (Haldane 1957, p 521). What you failed to realize is that this intense selection makes the cost problem FAR worse! Haldane estimated that n=43 for peppered moths, which yields a fitness of e-.7.  By using n=300, the fitness improves to e-.1. So if anything Haldane was ignoring his observation of phenotypic variation in Peppered moths because it made the cost problem worse! He punctuates the fact that a lower n reduces fitness by closing the pertinent paragraph with this example: "Whereas, for example, n=7.5 would reduce the fitness to e-4, or 0.02, which would hardly be compatible with survival." (Haldane 1957, p521).

Page: 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.

How so? Haldane also made such an "allusion" in both his 1957 and 1960 papers on the topic. A large population is actually a favorable assumption for evolution. The smaller the population, the proportionally greater impact of genetic drift, which means proportionally greater genetic load since there are far more deleterious mutations than beneficial ones that drift can move to fixation.

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.

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

Page: In reality, a 'genetic death' does not require the actual death (i.e., removal) of the individual from the population. Rather, it means that the genome of the individual lacking the mutation/mutant allele is not 'passed on.'

What happens to this “genetic death”? Does this organism persist in the population, discoverer of some fountain of youth, or does he/she/it die? I repeat, ALL of those without the mutation must be removed from the population. It surprises me you question this fact.

Regarding your claim I don’t know what a genetic death is, I wrote the following on the Baptist board several days before you posted your rebuttal, a post you responded to. You didn’t seem to have a problem then with my interpretation of genetic death! I really think you would be better served to not resort to such rhetoric, though it does serve as an indicator that you are arguing from a losing position.

Me on Baptist board, 2/15/02: “Once this hurdle is surpassed and the plate is reached, there still are additional payments needed for those surviving organisms that may suffer subsequent genetic death due to ugliness, prude-ness, random death, etc.”

Page: Since, as Haldane notes in his 1957 paper that surely Mr.Williams must have - or at least must have read - that the majority of evolutionarily important alleles are dominant or nearly so, the descendants of individuals lacking the mutant allele do in fact not have to be removed form the population.

First, Haldane assumed ALL beneficial mutations are dominant for a very good reason, because the fixation time and substitution cost of a recessive allele would obviously be vastly higher. So, this is a favorable assumption in favor of evolution. Second, Page makes no sense here. He appears to be employing a non sequitur. What does the type of mutation (dominant or recessive) have to do with whether or not someone without it need not be removed from the population?!!

Page: Williams seems to conflate 'genetic death' with an actual death of an organism. This is a common occurrence in the so-called creation/evolution debate. The creationist, spurred on by their overconfidence – their 'knowledge' of THE TRUTH – do not or cannot see that they are making claims based on an ignorance of the very topics they present themselves as being 'expert' or at least very knowledgeable in. Williams, an electrical engineer by education and profession, has a long history of making such blunders.

As I proved above with my post to Baptist board (I can provide many other examples), I knew what a genetic death was, and Page even responded to that post so he must have read it. Regarding “blunders”, Page is notorious for dwelling on mistakes, saving them on his hardisk and bringing them up over and over again, all the while forgetting the many blunders he has made, including major gaffes in this very post I am responding to. I will sum up Page’s errors at the end of this post.

Page: As Haldane explains in his 1957 paper that Williams puts much stock into and surely has read, a reasonable frequency for a mutant beneficial phenotype in a population is on the order of 0.0001. In a population of 1000, this means that 1 individual has the mutant.

A minor nit-pick. That would be a population of 10,000, not 1000.

Page: In just 9 generations, the mutant allele reaches fixation in 100% of the population, even without any physical 'removals' of the wild type allele (Keep in mind that under Haldane's model, the population size remained constant. Since Williams puts much stock into Haldane's formulation, he should not argue this point.) And since the mutant is dominant in this scenario, the wild type allele can still remain in the population, that is, it does not even have to be 'replaced' as such.

Dr Page, if a mutant allele reaches 100% fixation in a population, then THE WILD TYPE ALLELE IS GONE! I think you should spend less time talking about your education and how lowly engineers are not qualified to discuss genetics, and more time reading up on genetics! J

Page: Regardless, this brings up another interesting conundrum for Williams: ReMine indicates in his book that there must be at least “500,000 genetic changes” between humans and their ape-like ancestor, if evolution is correct.

This overstates Remine’s claim. I’ve loaned out my book, so I’ll have to revisit this. I recall Remine stating that 500,000 base pair differences does not intuitively seem to be enough given the 1-3% DNA differences between chimp/man, which amounts to 30-90 million bp.

According to the Eyre-Walker and Keightly paper that Williams refers to so endearingly, if we extrapolate their numbers, some 620,000 amino-acid altering mutations have become fixed in the lineage leading to humans in 6 million years†. Clearly, not all would be beneficial (though many deleterious ones are purged by selection, as E-W and K point out), yet ReMine says that not all changes required to account for the phenotypic differences between ancestors and descendants have to be beneficial. Is not 620,000 more than ReMine's number? Inquiring minds want to hear Williams explanation…

Page is again engaging in circular reasoning. This is the same circular argument I refuted earlier, only Page has dressed it slightly differently. The study assumes chimp/man ancestry to arrive at the 4.2 substitution rate that yields 620,000. Page then implies that since 620,000 is more than the alleged 500,000 Remine requirement, it therefore lends credence the chimp/human shared ancestry hypothesis! This is clear circular reasoning, no way around it.

Me: It is no surprise to creationists that sexual recombination, in an environment where beneficial mutations are very rare while the vast majority are deleterious to nearly neutral, would 1) reduce the accumulation of harmful mutations when contrasted to an asexual species (clonal lineages), and 2) result in an increased accumulation of beneficial mutation when contrasted to asexual species.

Page: If it is no surprise to creationists, one should wonder why then creation scientists did not discover this benefit of sexual recombination first.

What’s to "discover"? It is common sense that the spread of harmful mutation will be slower in a sexual species compared to an asexual species. This is not an earth-shattering observation.

Me: Let's assume an environment where there are no deleterious mutations, just beneficial ones. Given this scenario it is quite obvious that the mutation would spread through an asexual species much more rapidly than through a sexual species, as all of the asexual species' offspring will inherit the mutation, as opposed to only half for the sexual species.

Page: This is not obvious at all. If there were no deleterious mutations, then beneficial mutations would by necessity spread throughout a sexual species as well, since those are the only mutations available. 

This is population genetics 101. I challenge Dr Page to find any qualified population geneticist who supports his claim that a beneficial mutation will spread through a sexual species just as fast as an asexual species given the deleterious mutation free environment I specified. In a sexual species, only half the offspring will receive a new mutation. The offspring who received the mutation could suffer a genetic death and the story ends there. Population geneticists generally assign a 1 in 50 probability that a beneficial mutation will ever even reach fixation in a sexual species2. For those offspring who do not receive the mutation, at some time in the future their lineage will need to pick this mutation up. Such stringent barriers do not exist in an asexual species since ALL the offspring receive the mutation. In order for the mutation to exit the population, ALL the offspring who received it must suffer a genetic death.

Me: It is NOT an advantage to evolution. It is only an advantage when contrasted to asexual reproduction in a harmful mutation environment. Recombination remains an "enigma" to evolution.

Page: How in the world can a reduced accumulation of harmful mutations and an accelerated accumulation of beneficial ones NOT be an advantage to evolution? Why, because Wlliams the says so

Page misses my entire point, again. I will repeat, but with emphasis this time. It is only an advantage when CONTRASTED to ASEXUAL reproduction in a harmful mutation environment. Consider this analogy. You have two men who want to travel across a terrain. Both are given bikes that are the same, except for the size for the tires. Bike ‘A’ has thin “street” tires, bike ‘B’ wide “off-road” tires. The optimum surface for efficiency is a flat surface. In a race on such a surface bike ‘A’ will be have a distinct advantage every time. But as you add bumps to the surface, bike ‘A’ begins to lose ground, and bike ‘B’ starts to gain ground. As you make the surface bumpier, at some point bike ‘B’ becomes the faster and thus more efficient of the two bikes. So under bad race conditions, bike ‘B’ (analogous to a sexual species) is the better bike, under good race conditions, bike ‘A’ (the asexual species) is the better bike. But even when bike ‘B’ is the better bike, it still cannot go as fast as it would if it were racing on a smoother surface. It is still impeded in its progress, but not as much as bike B is impeded.

Page: It is not misleading when one understands the entirety of the information presented.

No, it is very much misleading, and you are a testimony to this! Your being misled resulted in you citing the paper as evidence for evolution, when it is no such thing. Essentially, the authors are implying that bike ‘B’ is the superior bike to have when crossing a terrain. This is only true if the terrain is on a bad surface. But if the terrain is smooth, you’ll be expending more energy to get from point A to point B than you would have had to if you had gone with bike ‘A’. What if the terrain is impassable except by Jeep? In either case of the smooth terrain or the impassable terrain, you would want your money back from the salesman who misled you about what the transportation vehicle he gave you could do!  J


Dr Page is incorrect to claim that the Wu paper1 refutes, or for that matter has anything to offer, the problem called Haldane's Dilemma.  You cannot use a study that assumes evolution is true to rebut a mathematical model that is void of such assumptions. Dr Page is also incorrect to imply that the Rice study3 supports the evolutionist position. The Rice study merely shows the advantage of recombination when contrasted with an asexual species in a harmful mutation environment. This is not evidence for evolution, though the paper gives some misleading statements to imply this.

Other errors Dr Page made in his post include:

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

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

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

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

* Claiming that a beneficial mutation well 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. I wonder if there is even one population geneticist in the world who would agree with him.

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

* Re-visits circular reasoning by asking why 620,000 substitutions from the Keightley study is not sufficient to account for simian/human shared ancestry, given the 500,000 he believes Remine set as a minimum. The problem is, the Keightley study also arrives at its numbers by first assuming simian/human shared ancestry. Thus, it is circular to use their numbers when contrasting against any arbitrary guestimate of mutations that would separate simian/man.


In reply to Page's addendum, I will only note that I did not accuse the authors of the Genetics paper of circular reasoning. In fact I specifically said: "I doubt if the authors of the study would agree with Page that their estimate invalidates "Haldane’s Dilemma. If they did, it would be a classic case of circular reasoning...".

Page's reply

Return to debate Table of Contents

1. Justin C. Fay,* Gerald J. Wyckoff* ,1 and Chung-I Wu*. Genetics 158, 1227-1234. 2001.

2. Evolutionary Biology, Douglas Futuyma, 1998, p 298; Not by Chance, Lee Spetner, 1998, p 55, p 80; Evolutionary Genetics, Maynard Smith, 1989, p 161-162; Theoretical Aspects of Population Genetics, Kimura & Ohta, 1971, p 3

3. William R. Rice* and Adam K. Chippindale 2001 Science 294:555-559

Haldane, J. B. S. 1960 More Precise Expressions for the Cost of Natural Selection Journal of Genetics 57:351-360

Haldane, J. B. S. 1957 The Cost of Natural Selection Journal of Genetics 55:511-524


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