Refutation of Fred Williams

See my second rebuttal to Williams' response

ADDENDUM added 2/24/02 (see bottom)

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. He wrote what I rebut below in response to a posting that I had made to his guestbook. In the usual creationist fashion, Williams first takes good evidence for evolution and contorts it to make it look like it is actually evidence for creation. Then, as creationist writers have a distinct tendency to do, Williams takes the opportunity to disparage the authors of the papers I cite and, of course, me. This is not at all surprising, as Williams has a reputation for being extremely abrasive and insulting in his discussions on this topic. I have written my responses to his “refutation” in a point-by-point manner. Williams 'refutation' appears as normal quoted text, my responses are in bold. Any emphases in Williams' story done by me will be in red.

FRED WILLIAMS: Following is my rebuttal to a recent post that appeared in my guestbook on January 23, 2002. The guestbook entry was made by Dr. Scott Page, an associate professor at Norwich University. I will show that both papers Page cited do not support his argument. In fact, the first paper he cited actually strengthens the creationist argument against human/ape shared ancestry! I will address this paper first.

I, and a reading of the actual papers that I cite, will show that Williams does no such thing.

"Positive and Negative Selection on the Human Genome"1 In the late 50s the famous evolutionist JBS Haldane addressed the cost of substitution for mammalian species, a problem that is referred to as Haldane's Dilemma. Haldane estimated that at most, one beneficial mutation on average could become fixed in a population every 300 generations (which means that no more than 1667 beneficial mutations could have accrued in the evolution of man from an ape/man ancestor 10 million years ago)2. The genetics paper offered by Page estimates that a mere 10 generations per beneficial substitution on average is what occurred since an alleged split from old-world monkeys 30 million years ago.3

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. Famous mathematician Sir Fred Hoyle, in his book “The Mathematics of Evolution”, explains that “Haldane's so-called cost principle is an illusion." (p123). And who are we to argue with such a great mathematician?** 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.

Page takes this as a refutation of Haldane's estimate. There are several reasons why Page is mistaken: Circular Reasoning The authors of the genetics study arrive at their divergence estimate by comparing intra-species DNA sequences of humans (to determine SNP frequencies), to analogous DNA sequences of old world monkeys. They assume that "positive selection is expected to increase the number of high frequency compared to common SNPs. This effect should be stronger for A than for S". What they are essentially saying is that some proportional increase in high-frequency amino-acid-altering differences 'A' in relation to the number of synonymous differences 'S' would be evidence of positive selection at work. Synonymous differences 'S' would be expected to be neutral with no selection working on them. Deleterious mutations would be expected to persist at low frequency due to negative selection. Thus, high frequency SNPs would represent an indication that positive selection is at work, as represented by a larger A/S ratio. So what is the problem here? 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.

First, I do not take this or any one paper to 'be a refutation of Haldane's dilemma.' Indeed, I do not believe that there ever was an actual dilemma, and many professional population geneticists and evolutionary biologists seem to agree. Haldane's model certainly put a 'speed limit' on evolution, but as such, the 'dilemma' part seems to be to be the product not of Haldane's model, but of the anthropocentrism of non-evolutionists and some evolutionists alike. In fact, this anthropocentrism seems to be the only supportive evidence Walter ReMine supplies in his 1993 book “The Biotic Message”, which is the source for the bulk of Williams' writings. Second, this 'assumption' (which is not even used in the Genetics appear, by the way – Did Williams actually read it? See 'third') is warranted by actual evidence from genetics and paleontology. Even creationist attempts at analyzing genetic data- to establish the boundaries between 'kinds' place Homo in a group with Pan. This, of course, is simply rejected due to the prevailing authority of Scripture in creationist 'science.'
Nonetheless, it shows that it is not that assumption that is in error. 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. Third, Williams misrepresents the methodology employed. 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). “

Chimpanzees ('ape') are not Old World monkeys.

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.

Their DNA sequence comparison work is based on this belief.

This is utterly false, I have just shown.

If this assumption is not true, then their calculation is worthless. Haldane's estimate of 300 generations per substitution is based on a mathematical model that need not rely on such assumptions of the validity of evolution.

This demonstrates Williams' ignorance of what Haldane's paper actually says, as well as the methodology involved in the Fay, Wyckoff, and Wu paper, that he pretends to be 'refuting', and how any such models or estimates are derived. Indeed, Haldane specifically used evolutionary assumptions to formulate his model! For, what other reason would Haldane have been discussing changes in allele frequencies, gene replacements, selection, etc.?

Furthermore, again, Haldane's model was made without the benefit of actual amino acid or nucleotide sequence data. Haldane was a brilliant population geneticist, there is little argument about that fact. However, he could only work with what he had.

Of course, if the 'assumption' of human-chimp shared ancestry is false, then Williams' “monkey-man” article is an illusion, as I refer to above. I doubt Williams would allow such a truth to be acknowledged.

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: first assume evolution is true, then arrive at an estimate that is based on this assumption, then conclude it refutes a mathematical model that contradicts evolution (Haldane's Dilemma), thus completing the circular logic.

Haldane's model did not contradict evolution. This is a common, malicious, and unwarranted misrepresentation put forth by creationists, particularly those with little or no background knowledge of the topic. Again, Haldane had the integrity to realize and admit that his conclusions would need “drastic revision.” The creationist lacks this integrity, and instead opts to cast aspersions and cling to an outdated mathematical model, which, when applied as the creationists do, seems on the surface to support their claims. The authors do not seem to think that Haldane's dilemma exists, and so there is little reason to think that Haldane's model had any bearing on their empirial evidence-based work at all.

This 'circular logic' charge is most entertaining – Williams uses publications that do the same (assume evolution) to try to support some of his claims! Which is it Mr.Williams – is the assumption a valid one or not? If it is not, then all of your 'articles' on the topic are illusory. If the assumption is valid, then the basis for your opposition to the data is unfounded.

Though Dr. Page's claim has already been refuted (circular reasoning), let's take a closer look at this paper.

Charges of circular reasoning are hardly a 'refutation', especially since the 'circularity' has not been established. The creationist is nothing if not overconfident.

The results of the genetics author's study forced them into the observation that beneficial mutations became fixed every 10 generations on average (I think it was really more of an observation on their part that they did not seek to emphasize, as it did not appear in their conclusions).

Why Williams decides to use the word “forced” is beyond me, except that the word 'forced' has certain negative connotations.

The problem is, this number flies in the face of sound reasoning. What the reader must realize is that the authors are saying that beneficial mutations that reached fixation worked their way throughout an entire population in just 10 generations on average. In this period of time, all those without the mutation, plus all their descendants who did not receive the mutation, had to be removed from the population. The replenishment of these "genetic deaths" would be governed by reproductive capacity and reproductive cycle time of primates/humans (plus the effects of recombination).

Here, Williams exhibits an ignorance of a topic that he likes to pontificate on.

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. 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. 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.' 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.

Indeed, in this scenario (since Haldane stated this, Williams must, in order to retain the appearance of an unbiased interpretation of Haldane's work, accept this as well) the 'wild type' (original, non-mutated) allele may persist in a population for a long time, while the new dominant allele is reaching fixation and beyond.

Thus, this section of Williams' 'refutation' is rendered irrelevant.

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.

Remember that for some initial number of generations half of all offspring will not even receive the mutation (unless incest takes place, which would make matters worse due to increased genetic load, more genetic deaths, etc).

If the allele is dominant, as Haldane states most evolutionarily important genes will be, then what Williams writes is clearly false. Especially if there is selection pressure that favors the mutant allele.

Of those who do receive the mutation, they must survive to pass it on to their offspring. We also know that gestation cycles are long in comparison to most other species, and reproductive capacity is smaller than most species. Considering all these roadblocks, ten generations is an awfully short amount of time for a mutation to go from few to many. This study suggests that this phenomenal rate of fixation was maintained for 30 million years! Haldane's mathematical model shows that this is nonsense.

Odd how Williams believes that actual genetic analyses have less import than a 50 year old mathematical model. Williams here shows additional ignorance of evolutionary theory. As Dr. Joseph Felsenstein (and others) pointed out as far back as 1971, the circumstances in which a mutant allele is beneficial make it such that those with the allele are the 'reproductive excess'.

For a simplified example, let us consider a small population X. Population X has 1000 individuals. 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.
[Of note – electrical engineer and creationist author Walter ReMine, whose 1993 book “The Biotic Message” book is the primary source for the bulk of Williams' writings, has accused Haldane of using an “elevated frequency” of mutation to favor evolution. Despite numerous inquiries that this charge be supported, ReMine has thus far refused to provide any actual evidence or justification for he charge. He has, however, simply reasserted his claim, and insulted those that asked him to support it.]
As mentioned above, Haldane also explains that the evolutionarily important alleles are likely to be dominant, that is, they will be preferentially expressed. When the selection pressure warrants this mutant allele's beneficience, the other alleles will need to be removed via genetic deaths (or will they?). Say the dominant allele has been passed on to just 2 offspring originally, and each of these offspring produce only a single offspring each. In this population X, the frequency of the mutant allele increases exponentially each generation.
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.

I kindly submit that perhaps Williams has not read Haldane's 1957 paper, has not read it in its entirety, or read it only to find a snippet that could be used against evolution.

The conclusions in the Genetics paper stand, as do the implications for Haldane's 'dilemma.'

In addition, the static use of gestation cycles and generation time in primates is erroneous. Longitudinal studies of baboons show that the generation times and time between estrus in these primates is significantly reduced during times of environmental stress. The very nature of an environmental stress that would provide selection pressure, it seems, also induces a speeded-up reproductive rate. [information presented at a recent conference]

The Other Side of the Coin Most importantly, Scott Page failed to recognize that the paper actually makes matters far worse for evolution: The genomic deleterious mutation rate in humans was previously estimated to be at least 1.6 on the basis of an estimate that 38% of amino acid mutations are deleterious. The genomic deleterious mutation rate is likely much larger given our estimate that 80% of amino acid mutations are deleterious and given that it does not include deleterious mutations in noncoding regions, which may be quite common. [emphasis mine]. If we use a straight extrapolation we reach a new mutation rate estimate of U=3.4. This means that 60 offspring would be required per breeding couple just to maintain genetic fitness equilibrium in the population!4. To make matters even worse, this number does not include the impact of "deleterious mutations in noncoding regions, which may be quite common."! If we add James Crow's adjustment of 1.44, the required offspring count just to maintain equilibrium goes to 243 offspring per breeding couple!!!

This line of argumentation by Williams is irrelevant and illusory. By definition, a population undergoing evolution would not be IN equilibrium !

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.

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…

This article is a clear backfire on Dr Page. I must thank him for pointing it out to me. I will reference it in the future as further support for my article that provides powerful evidence against man/ape shared ancestry.

In reality, it is nothing of the sort. What this so-called 'refutation' has shown itself to be thus far is a prime example of the dangers of arguing well outside of one's field of expertise, especially when one has an agenda to push, which makes them less concerned with the details of what they reference and more interested in 'sound bites', which, when seen out of context, can be construed to prop up their position.

"Sexual Recombination and the Power of Natural Selection"5 Now to Dr Page's 2nd citation. He cites this from the paper's concluding paragraph: "Our results experimentally verify a counteracting advantage of recombining compared to clonal lineages: reduced accumulation of harmful mutations and increased accumulation of beneficial mutations. The magnitude of this benefit will accrue over geological time and promote the superior persistence of recombining lineages at both the level of species within communities (clonal versus sexual species) and genes within chromosomes (nonrecombining Y-linked versus recombining X-linked genes)." At first glance, it would seem that this paper is saying that recombination promotes faster accumulation of beneficial mutations over clonal lineages (asexual species). I will show why Page, as well as the authors of the paper he cited, are misleading the reader with this conclusion.

To the unbiased, it seems at first glance to say exactly what it says – in sexual species, there is a reduced accumulation of deleterious mutations and an accelerated accumulation of beneficial ones. There is nothing misleading about it – another spurious charge.

The refutation is simple. The study is contrasting the impact of recombination against asexual, non-recombination species. The authors offer these hypotheses: "Nonrecombining populations experience (i) faster accumulation of small-effect deleterious mutations [e.g., Muller's ratchet], (ii) slower accumulation of beneficial mutations…, and (iii) an increased deterministic mutational load." I should first note that these hypotheses make perfect sense and are not disputed by creationists.

I should hope not, since the authors support the hypothesis with experimental data.

To understand why the authors' conclusion is misleading, we need particular emphasis on (i) and (iii). Since Accumulation of deleterious mutation is much more rapid in an asexual species, an asexual species will likely incur slower accumulation of beneficial mutations!

Why Williams felt the need to put an exclamation point at the end is unclear to me, as all he did was restate the author's claim. The original authors did not seem to require an exclamation point. Indeed, how can this conclusion be misleading when it is just what the authors wrote?

The authors correctly note that in an asexual species, nearly all mutations will become trapped in the "living dead", as they call it. Only beneficial mutations with the highest fitness can move to fixation: In nonrecombining genomes mutations move unidirectionally from better to worse genetic backgrounds (genetic polarization) because most are trapped in low fitness genomes that are not self-sustaining and experience a net accumulation of deleterious mutations. 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.

If it is no surprise to creationists, one should wonder why then creation scientists did not discover this benefit of sexual recombination first. This is a common occurrence in the field of creationism – a co-option of evidence for evolution. This is most likely because creationists – even those claiming to be 'creation scientists' – do not actually do anything resembling actual scientific research. Rather, they wait for evolutionist publications to come out, and either nit-pick away at the research of real scientists or try to claim that the results actually support creation.

What Williams does not explain is why this is supposedly no surprise to creationists.

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.

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. Williams needs to formulate analogies with a bit more substance, consistency, and logical clarity.

But as you raise the level of harmful mutations, there is a threshold where the sexual species eventually becomes the faster environment for the fixation of a beneficial mutation, since recombination slows the spread of harmful mutation. The author's conclusion essentially is that beneficial mutations have a better chance of fixation in a sexual species over an asexual species, because the high level of harmful mutations in an asexual species wreak greater havoc than they do in a sexual species. If there were not such a powerful current of harmful to slightly harmful mutations at work, then beneficial mutations would clearly proliferate more easily in an asexual species. But the authors fail to emphasize this fact, so the reader can easily be left with the impression that recombination is an advantage to evolution (as happened to Dr Page). 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.

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 Williams says so.

Williams' pontifications notwithstanding, the conclusions of this paper in fact demonstrate just what the authors wrote. Had the authors simply sat down and written up their hypothesis on paper, contrasting a hypothetical sexual population with a hypothetical asexual one, then their conclusions would fall under Williams' umbrella denigration.

What Mr.Williams neglects to mention is that the authors verified this advantage experimentally. Williams further glosses over some important realities – as he and probably all other creationists are so fond of exclaiming, the majority of mutations are not beneficial. As such, the real mutational environment – one in which most mutations are not beneficial - was simulated in the Science paper's methods.

In other words, Williams is busily misrepresenting the conditions of the experiments and the conclusions in the paper that he claims contains misleading information.

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

In the end, this paper offers nothing more than corroborating evidence of several hypotheses, all that fit quite nicely within the creation model.

The 'creation model' is, in reality, a co-option of evolution – up to the point at which the human-ape connection comes in. Then, the 'creation model' dumps science like a hot potato and embraces the prose of Scripture as their source of scientific information.

The paper's misleading conclusions only serve to confuse, and actually have little bearing on the creation/evolution debate, other than to illustrate the huge problem high mutation rates pose for evolutionary theory.

It seems that by co-opting already-discovered realities and evolutionary hypotheses, the creationist hopes to provide some comfort to the lay creationists at large by claiming – irresponsibly – that the conclusions presented by the two cited papers are not only wrong and misleading, but at the same time supportive of creationism.

The conclusions are not misleading in the least if one considers the entirety of the experimental model employed and the hypotheses being tested. Their results were not simply some sort of comparison between asexual and sexual species as Williams implies, rather their conclusions were premised on actual data gleaned form actual experimentation. That those results support an evolutionary hypothesis should hardly be seen as a negative, as Williams does, but instead it should be seen for what it really is – an important contribution to our understanding of the benefits of recombination and the mechanisms of evolution.

Williams confuses and conflates mutation rates with mutation accumulation. I might drive my car at 100 miles per hour, but if I drove at this rate for only 10 minutes, I have not gone 100 miles. On the other hand, I can drive at 100 miles per hour for one hour and still not have traveled 100 miles away from my starting point. I could drive out 50 miles, turn around, and gone back. There is a real and obvious distinction between the two that Williams and his cohorts seem to be unwilling or unable to understand.

CONCLUSION Williams will continue to promote his misrepresentations and slanderous accusations to an uninformed lay creationist readership (of his web site). He will continue to denigrate, ignore, and minimize real research scientists, while continuing to embrace and proselytize the incoherent, illogical, evidence-less rants of fellow non-specialist creationists.

In today's climate of scientific ignorance in our society, where young (and not so young) Americans are more likely to believe the propagandistic tripe they read on personal (like Wlliams') or politico-religious (like that run by the Discovery Institute) web sites than what they can be taught by degreed, legitimate scientists on this topic, we are all in a very uneasy spot.

It is simply a shame that such nonsense makes it into the halls of Congress, uncontested, for ideologues and undereducated politicians to use to pander to the religiously biased masses.

Williams' references:

1.Justin C. Fay,* Gerald J. Wyckoff* ,1 and Chung-I Wu*. Genetics 158, 1227-1234. 2001.
2.A generation period of 20 years is assumed to arrive at 1667.
3.The authors estimate "up to 1 advantageous substitution every 200 years since humans separated from old world monkeys 30 million years ago". I arrive at 10 generations by using the same generation time (20 years) used to produce the 1667 figure.
4.For specifics, see my article the mutation rate problem
5.William R. Rice* and Adam K. Chippindale 2001 Science 294:555-559

*Same as Williams' ref.1.

My reply from Dr.Wu said in part:

“I tried to read William's site but the words (and contents) are so small that I grew tired of it.”

Apparently, he didn't find much of value there.

**Hoyle is well known in anti-evolution circles, though he did not reject evolution as such. He is famous for his adage about evolution being like a tornado going through a junkyard and a 747 flying out the other side, such is its improbability. This demonstrated Hoyle's shallow understanding of evolutionary theory. Nonetheless, creationists of all sorts frequently refer to Hoyle's claims and tout his credentials.

-There are several papers available in the creationist journal CRSQ. See Baraminology.
Robinson and Cavanaugh preferentially use genetic data, until it puts humans together with chimps. They then, in a section called “Scriptural considerations”, reject the genetic analyses in deference to their interpretation of the bible.

†This was pointed out by a PhD – level immunologist/microbiologist on the OCW creation/evolution discussion board. See posts by "Sumac"

ADDENDUM 2/24/02

In an email exchange with Williams after I posted this on my web site, he implied that I had contacted the authors of the papers for ‘help’ in rebutting his charges.
I suppose that he concluded this premised on two issues:

I had written on an internet discussion board that I had contacted the authors and was waiting to hear from them, and that Williams has convinced himself that he is an expert on this topic, and that, obviously, anyone attempting to rebut him would need help. The pertinent part of our exchanges follow:

Fred wrote:

“…I suspect that is why you did not get much help from the authors of the papers. You need to go to the gym more, its a better workout than waving your hands at your computer.”

My reply to this:

“I actually had several nice exchanges with Dr.Wu, who is the chair of the ecology and evolution department at U of Chicago. He found your claims to be so unworthy of reply that he said 'my thoughts will do just fine.' “

Williams’ response:

“Wu is simply afraid, as most evos are, to admit one of their colleagues is wrong. Come on Huxy, get Wu to admit in public that his paper refutes the Haldane mathematical model. He won't because he knows it would be circular reasoning. It is you who made the simplistic error, not Wu.”

Below is the verbatim content of the email I sent to Dr. Wu. It is nearly identical to the email I sent to Dr.Rice, the only difference being that I mentioned that Williams had accused he and his coauthors of making misleading statements.

========================================================================
Dear Dr.Wu,

I have used your recent paper "Positive and Negative Selection on the Human Genome" as an example, on several occasions, of how the old estimates of mutation accumulation (e.g., Haldane) were in error.

Creationist Fred Williams took my citation of your paper and has written what he calls a 'refutation' of it on his website:

http://www.evolutionfairytale.com/

He and I have a long history of ill will between each other, so his claims against me are immaterial. However, he accuses you and your co-authors of, among other things, circular reasoning.

I am planning to write a rebuttal and post it on my own website, but I thought you or one of your co-authors might want to take a look at Williams' essay as well.
========================================================================

It is obvious that I was not asking for ‘help’, rather, I just wanted to let the authors know that they had been accused of various unsavory things. I did hold off writing my refutation until I heard form the authors, just to see if they had anything to offer. I did not hear from Dr.Rice, but as indicated in my refutation, I did get a response from Dr.Wu. He did not offer any ‘help’, but neither did I ask for any.

RESPONSE TO WILLIAMS' SECOND INSTALLMENT.
See Williams twist common English phrases to try to score points...