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"In my opinion the [Haldane's Dilemma] problem  was never solved, by Wallace or anyone else."     George C. Williams, a highly respected evolutionary geneticist, 1992, in his book, Natural Selection: Domains, Levels, and Challenges, p 143-144

The thrust of my argument does not speak of a limit of "1,667 gene substitutions." Rather my argument focuses on typical substitutions, which – according to evolutionists – are almost always point mutations (a single nucleotide). Yet evolutionists traditionally discussed Haldane's Dilemma in terms of "gene substitutions," which created the false impression that large blocks of new DNA are being replaced, rather than just a single mutation (typically one nucleotide). That habit further obscured the severity of Haldane's Dilemma from public view.  In fact, a well-known evolutionary genetics professor from Cornell University expressed shocked resistance when I first explained this point to him:  The 1,667 substitutions are typically single nucleotides, not 1,667 whole genes. The substituting 'thing' is a mutation, not a gene. It's a simple concept when explained clearly, though it was habitually overlooked even by professionals at the time. The traditional focus on "gene substitutions" is one of many factors that garbled Haldane's Dilemma for so long.

1/24/2005 - by Walter ReMine

Mutations to regulatory genes can sometimes have a large biological effect. So, are mutations to "regulatory genes" a solution to Haldane's Dilemma?¹  Brief answer:  It scarcely affects Haldane's Dilemma. 

Evolutionists do not get to choose the substitutions, say, as "mutations to regulatory genes" or as "mutations with a large biological effect" or as "gene clusters". Rather, evolutionists must accept what nature doles out – and we can observe what nature doles out.  The issue is fundamentally empirical and observable, not one of telling stories about regulatory genes. Take the blend of beneficial substitutions observed in nature. The coloring of melanic moths and the beak size of Galapagos finches are noted examples.  Those represent the basic building blocks that nature has to work with, the creative 'power' of nature. Leading evolutionists acknowledge (indeed most of them insist) that substitutions with small effect predominate in evolution.  Are 1,667 substitutions (like those) sufficient to create all the human adaptations?  The tripling of brain size, fully upright posture, language, speech, hand dexterity, hair distribution, and appreciation of music, to name a few. 

It scarcely matters what kind of tall-tales one can devise about regulatory genes. What matters is the blend of the beneficial substitutions observed in nature.  Are 1,667 of those sufficient for creating all the human adaptations? 

Moreover, when Haldane calculated the total cost of a substitution (=30), he assumed selection coefficients approaching zero, which gives the absolute lowest possible total cost of substitution. The figure rises for higher selection coefficients, and rises especially rapidly when selection coefficients get above one-tenth (s>0.1). Therefore, if evolutionary scenarios invoke high selection coefficients (such as mutations for antibiotic resistance or pesticide resistance), then the total cost of substitution gets quite high – and the number of substitutions (previously at 1,667) goes to a much lower limit. 

In summary, whatever the blend of substitutions, (a) they must correspond to what we observe in nature, and (b) they must meet the cost constraints, (higher selection coefficients will lower the plausible number of substitutions). 

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¹    Professor Massimo Pigliucci raised regulatory genes as a "solution" to Haldane's Dilemma during our live debate at the University of Minnesota.

1/24/2005 - by Walter ReMine

My argument is framed within a single line of inheritance.  My argument questions whether a particular number of beneficial substitutions is sufficient to create all the human adaptations starting from some alleged ape-human-like ancestor ten million years ago. This is the total number of beneficial substitutions – not the net genetic difference between the initial organism and end-point organism.¹ I cast the problem this way to make it more direct, and harder for evolutionists to finagle around.  (The reasons are technical and not necessary for this essay, which is about evolutionists misrepresenting my argument.)

My argument is not about the genetic difference between divergent organisms (organisms that do not have an ancestor-descendant relationship, sometimes called "sibling species"). If you compare divergent organisms (such as living chimps and living humans) on the basis of genetic or protein sequences, then you are misrepresenting my argument. That makes my argument less direct, more confusing, and most importantly, it grants evolutionists large fudge-factors that operate in their favor. That is why evolutionists typically  (near universally) misrepresent my argument in this manner. They are attempting to grant favors to themselves, by misrepresenting my argument. 

Typically they do that by claiming I made an "invalid assumption" that they will "correct."  That is falsehood. My argument assumes humans evolved from an ape-like ancestor (as evolutionists allege), and then shows a serious problem with that. Evolutionists cannot legitimately attack that as an "invalid assumption" in need of "correction."

In an attempt to "document" their misrepresentation, some evolutionists avoided my book (where they admit they found no support for their misrepresentation), and they searched among my countless tutorial posts still available from Google (and still found no support), and apparently found from a third-party a single electronic communication alleged to be mine (but can no longer be independently authenticated), and took out-of-context a parenthetical comment (a side comment contained within parenthesis), and misrepresented it as though it were my argument.  Those several errors in scholarship are visible from what they wrote.² Moreover, those same individuals ignored my repeated notifications of their misrepresentations. Therefore, if you see anyone misrepresenting my argument, (even the occasional creationist who inadvertently absorbed the evolutionists’ line), then correct them on it and send them here.

That is:  Comparisons between living organisms (such as living chimps and humans, on the basis of genetic or protein sequences) are interesting.³ But they are not, and never were, my argument on Haldane’s Dilemma. I cast my argument specifically to give the least latitude for evolutionary finagling, fudge-factors, and story-telling.

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¹    For example, the evolution of human adaptations may likely require a series of substitutions (in a particular order) involving the same nucleotide sites.  In that case, the net genetic difference between initial and final organisms would underestimate the number of substitutions required.  

²    Robert Williams is a key example of this, but there are others too. 

³    I am not saying a comparison of living chimps and living humans is useless. (On the contrary, such a comparison is useful on many grounds, and will likely grow considerably as the data from the Chimp Genome Project comes forth.) Rather I am saying such comparison – as a means of resolving Haldane's Dilemma –  inherently favors evolutionists, and greatly caters to evolutionary story-telling. Such a comparison does not address, and does not solve, Haldane's Dilemma in its most challenging form. Haldane's Dilemma cannot be considered 'solved' until it is solved in its most challenging form. 

1/24/2005 - by Walter ReMine

Some internet evolutionists chastise me for raising Haldane's Dilemma.  They aggressively post on internet discussion groups, (typically under anonymous pen-names, such as: "Huxter," "SLP," "Gordy," "Art," "KC," or "Robert"). They suggest the 1,667 limit is "not a problem," and they try to shame me for raising the issue. They claim it is "unscientific" to raise something as a problem unless I can "prove" it. And so forth.

My immediate response is, "Who are they kidding."  I would feel differently about their posturing if the public could recall a serious history of leading evolutionists claiming a limit of 1,667 beneficial nucleotides is "not a problem." But no such history exists.  Even the 1,667 limit itself was the trade secret of evolutionary genetics.¹  I was the first to bring it to public attention.

The public can understand Haldane's Dilemma, and readily sees it as a serious problem. Everything necessary to communicate the problem (the 1,667 limit) was available in 1957 when Haldane published his paper.  Yet evolutionists did not communicate it to the public.  They still haven't.  In this matter they were grossly negligent. This is now a fact of history, and cannot be changed. 

For many decades already, evolutionary literature claimed Haldane's Dilemma was "solved." But that would require evolutionists to solve all the crucial components of the problem — including the number of substitutions needed to create all the human adaptations.  Evolutionists have scarcely begun to do that. Haldane's Dilemma was never solved. 

Haldane's Dilemma cannot be considered solved until the solution exists in ink, by capable scientists willing to put their names and reputations to it.  Evolutionary operatives posting their opinions anonymously at unreadable, internet shouting-matches, do not count as solutions. 

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¹    I am using the same wording — "trade secret" — with the same meaning as when Stephen Gould said the widespread absence of gradualism is "the trade secret of paleontology." There is no charge of conspiracy in either case. 

1/24/2005 - by Walter ReMine

My book had the ambitious goal of teaching this cutting-edge subject to the ordinary person. I therefore began my discussion with an uncomplicated scenario for tutorial purposes.  I discussed an ape-human-like species, with: 

• an effective generation duration of 20 years
• a population-size of 100,000
• each and every generation receives a new exceedingly beneficial mutation with selection coefficient s=1 (that is, the previous genotype immediately vanishes)
• the substitution is completed in one generation, and the cycle is ready to repeat again each and every generation
• given 10 million years, or a total of 500,000 generations
•  — for a grand total of 500,000 substitutions.

This scenario is highly unrealistic in favor of evolution, but it is useful for teaching the basic parameters of the problem and how they interact. Such as the role played by the mutation rate, the selective value of the mutation, the population size, and of course the required reproduction rate (which is a central parameter), plus how these limit the number of substitutions.  The discussion rhetorically raises questions to get my readers thinking in new terms.  Once I teach the fundamentals, I move to a more realistic scenario — Haldane's — where one substitution occurs every 300 generations, for a total of 1,667 substitutions over the same era. This teaching approach has been quite successful, and many people (who previously knew nothing of population genetics) say they are thrilled by that chapter. Considering the difficulty of the subject, I am quite pleased.

However, some of my evolutionary opponents seized that figure of "500,000 substitutions" as though it has some special role in my argument.  It has none.  It's purpose is solely tutorial, to teach, and to get the ordinary person thinking in population genetic terms — a subject most people hadn't thought about.  The example simply reveals the mechanisms behind Haldane's Dilemma as understandable to the ordinary person. That also gets readers wondering why they hadn't seen such an obviously important topic before. ............

The figure "500,000" derives solely from the example itself (10 million years / 20 year effective generation time), and my goal of dovetailing this tutorial example easily into Haldane's example. Yet evolutionists misappropriate this figure.¹ 

Throughout my book I avoid causing you to rely on my opinion, rather I cite leading evolutionists to support what I am saying.  Or, I assemble the facts from evolutionists, and let you make up your own mind.  This "de-emphasis of me," is key to making the book so compelling. This approach applies also to Haldane's Dilemma, where, for simplicity and authenticity, I advanced only one figure — Haldane's!  It is essentially Haldane's figure. The limit of 1,667 substitutions comes (in all its deepest respects) from Haldane.  I merely framed it so the ordinary person can understand, and so evolutionists would have the most difficulty finagling around.

If you see anyone mis-representing the "500,000 substitutions" figure, then correct them on it, and send them here. 

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¹    Evolutionists frequently combine two misrepresentations together:  (1) the 500,000 figure, and (2) a raw genetic comparison between living chimps and living humans  (see here). This combination doubly misrepresents me.

1/24/2005 - by Walter ReMine

Everything necessary for the 1,667 limit was known to evolutionary geneticists since 1957, but they did not communicate it to the public.  The issue ought have appeared widely (in television programs, popular science magazines and popular books).  But it didn't.  It still hasn't.  I hope the sociology of science will someday examine this remarkable history. 

But the negligence also permeates the technical literature itself. We examine that next.

After Haldane published his 1957 paper, the technical journals discussed Haldane's Dilemma from time to time, in muted tones and technical jargon.  The phrase "Haldane's Dilemma" was used, though not typically.  Typically, readers might understand the oblique references to the issue, only if they already understood the problem.  Usually no revealing figure was given.  A direct figure – such as the Haldane limit of 1,667 substitutions for human evolution – is virtually non-existent.  (That these were approximately 1,667 nucleotide substitutions was not acknowledged in print, though it should have been.)  In cases where a figure was given, it was indirect, such as "300 generations per gene substitution" – a phrase that may as well be in code, rather than revealing the problem. 

Despite the general lack of forthrightness, some leading evolutionary geneticists at least took the problem seriously. Motoo Kimura and John Maynard-Smith each cited the problem as the leading reason for their revolutionary new views of evolutionary process. They saw the problem as real, (whether or not their approach was an adequate solution). 

But they were implicitly contradicted by numerous other evolutionary geneticists, who gave radically different definitions of the problem's central concept – known as the "cost of substitution." 

• Haldane, Kimura, Maynard-Smith, Ewens, and many others, saw that the total-cost of a single isolated substitution is 30, on average.
• Others (such as Bruce Wallace) suggested "soft selection" would reduce that figure far below Haldane's estimate of 30.
• Others (such as William Feller) suggested the total-cost is always 1.
• Others (such as Joe Felsenstein) claim the cost of beneficial substitution is zero, which would make the problem go away. 
• Others (such as Fred Hoyle) claim Haldane's cost of substitution is "an illusion". 
• Others (such as Alice Brues) claim "the cost of not evolving is greater than the cost of evolving", which would turn the issue on its head. 
• Some defined the cost of substitution in terms of "genetic death" – though there was little agreement on the physical meaning of genetic death.  Others defined cost in terms of "genetic load" – whereby the population's fitness is said to decrease during a beneficial substitution. (Indeed this was called a "fitness depression" caused by a beneficial substitution.)  There were other notions too.
• Some insisted the cost of substitution applies only to a "deteriorating environment."  While others openly applied the cost of substitution to any environment. 
• Some defined the cost of substitution in terms of extinction. Others did not. 

In other words, the technical literature become overwhelmed with contradictions and confusions – which were seldom acknowledged, nor resolved. They still exist today, virtually unchallenged by evolutionists. Yet the contradictions occur under the simplest conceivable circumstances – single, isolated substitutions in asexual haploids. In other words, the contradictions involve the most basic fundamentals. 

Of all the evolutionary authorities, Motoo Kimura was the most effective proponent of the problem, which he saw (legitimately) as a compelling limitation on selective evolution (and on Darwinian evolution).  Unfortunately, Kimura's causal account of the problem skipped key portions of the reasoning behind it.  Kimura, an evolutionist, was explaining a serious evolutionary problem to other evolutionists, perhaps without wanting to reveal too much, or be too explicit, or draw too much attention?  More significantly, other evolutionists scarcely bothered to expand Kimura's causal account.  Perhaps they too did not care to reveal too much?  Whatever the cause, this lamentable situation brought some experts (such as Fred Hoyle) to note the incomplete reasoning, and thereby cast the entire problem aside as nonsense.¹ More commonly, evolutionists amplified various confusion factors into so-called "solutions."  

This is another notable feature of Haldane's Dilemma, namely the evolutionists' lack of pursuit of clarity and resolution.  Virtually any suggestion was given a free pass, so long as it blurred, confused, or allegedly "solved" Haldane's Dilemma, regardless of the inconsistencies and contradictions raised thereby.  These tended to remain in the literature uncorrected, and even be repeated, cited, and pressed forward.  On the other hand, challenges to the confusions, contradictions and "solutions" were rare, half-hearted, usually non-explicit, and seldom cited or repeated, so these were effectively lost in the vast ocean of evolutionary literature.  The disparity is noteworthy.  Again I hope the sociology of science will someday examine this history. 

Around the mid-1970s, twenty years after Haldane's paper, evolutionists largely set the issue aside, believing it had been solved.  I say Haldane's Dilemma was never actually solved.  Instead, it was garbled, confused, and prematurely brushed aside as "solved," when it wasn't.²  

Haldane's Dilemma was already a decades-long scandal³ when I raised it in 1993.⁴  I called for evolutionists to publicly address the issue, to clean-up their confusions and contradictions, and finally to resolve Haldane's Dilemma. My calls fell on deaf ears, or more precisely, on angry ears. Evolutionists responded (not in print, but on the internet) by repeatedly maligning me personally, and misrepresenting what I wrote.  To this date (January, 2005), the evolutionary literature has responded neither to me, nor to the highly respected evolutionary geneticist, George C. Williams, who wrote: 

"In my opinion the [Haldane's Dilemma] problem was never solved, by Wallace or anyone else.  It merely faded away, because people got interested in other things.  They must have assumed that the true resolution lay somewhere in the welter of suggestions made by one or more of the distinguished population geneticists who had participated in the discussion. .... I think the time has come for renewed discussion and experimental attack on Haldane's dilemma."  (George C. Williams, 1992, Natural Selection: Domains, Levels, and Challenges, p 143-148)⁵

One would think the Internet would speed up resolution of this mess. But that has not happened. 

For example, since 1971, evolutionist Joe Felsenstein has claimed that beneficial substitutions inherently have "zero cost" – a profoundly mistaken view also embraced by many evolutionists as a "solution" to Haldane's Dilemma.  But more importantly for our analysis of history, Felsenstein is contradicted – implicitly – by other evolutionist experts on Haldane's Dilemma.  I pointed out the contradiction on the newsgroup sci.bio.evolution, and spent many months there personally pressing Felsenstein and other evolutionists to resolve the contradiction, if only among themselves.  They still haven't resolved it.  They scarcely address it. Not in the literature; not anywhere.  Either beneficial mutations have a cost of substitution, or not.  If evolutionists cannot resolve such utterly fundamental matters, then they cannot (or will not) resolve anything much about Haldane's Dilemma. Confusion reigns. 

If you advance the subject on an internet "discussion group" (a term I use with reservations), the evolutionist response tends to be exceedingly partisan, not the open-minded pursuit of truth we expect from science.  They attempt to wear readers down with many confusion factors and misrepresentations, switching from one to another and back again, until readers are exhausted – without evolutionists acknowledging (much less resolving) even one.  They will attempt to show that you, dear reader, do not understand the issue. Those tactics are cynical and insincere, when the truth is that the evolutionary literature is manifestly self-contradicted on the issue. 

Here is another example.⁶  Sir Fred Hoyle's book claims, "Haldane's cost principle is an illusion." So evolutionists began using Hoyle's statement to brush aside Haldane's Dilemma. The problem is, Hoyle is contradicted by most other evolutionary geneticists, including Haldane.  So an obvious question is: Who is right, Hoyle or Haldane?  It happens they used different definitions of "genetic death" (Hoyle used Definition 3 below, while Haldane used Definition 4) and that led to their different conclusions.  In other words, the contradiction is both obvious and fundamental, yet evolutionists do not pursue its resolution.  Internet evolutionists were using confusion (their own) to deflect Haldane's Dilemma. 

A profound example of negligence occurred January, 2005, at a leading journal of population genetics.  

Do not despair, there are many good and decent evolutionists.  They just happen to remain mostly silent on Haldane's Dilemma.  Someday they will make their voices heard. In the meantime, Haldane's Dilemma remains a monument to an unhealthy scientific environment.⁷  

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¹    Fred Hoyle (1987) rightly complains that the key expositors of the problem (Haldane, Wright, and Kimura) did a poor job explaining the basis for it. (However, nothing prevented other evolutionists from making clearer explanations widely known within their journals, which they didn't do.)

"To start with, Kimura gives no explanation, only statements, and then only on pages 26 and 30 of his book.  It seemed to me curious that, with 250 pages available, a clearer account of why the Darwinian theory was as devastatingly wrong as it is said to be shouldn't have been given.  A carefully reasoned argument, at whatever length was necessary, would have been worthwhile in establishing so profound a result." (Hoyle, 1987, 1999, Mathematics of Evolution, p 117)

"... if a logically sensible explanation of ([equation] 7.30) existed, Haldane's paper would have been written more clearly than it was, Sewall Wright would have explained ([equation] 7.30) instead of conjuring it like a rabbit out of a hat, and Kimura would not have based his book merely on the obscure remarks quoted above.  He would surely have devoted a whole chapter at least to a careful analysis of the precise argument itself." (Hoyle, 1987, 1999, Mathematics of Evolution, p 124) 

²    At this point in the discussion, evolutionists often charge that I am a "conspiracy theorist." But I never claimed such a thing, and on numerous occasions I explicitly disavowed any evolutionist conspiracy.  However, I do charge evolutionists with a robust history of negligence on Haldane's Dilemma, (and their "conspiracy theorist" charge is an attempt to smear my character and divert attention away from their history of negligence). 

³    I am using the same word — "scandal" — with the same meaning as when evolutionist Graham Bell wrote, "[T]he casualness of the few attempts to provide a functional account of haploidy and diploidy constitutes a major scandal." (The Masterpiece of Nature: The Evolution and Genetics of Sexuality)  In either case, there is no charge of conspiracy. 

⁴    At the time, I was unaware of evolutionist George C. Williams's similar (though more gently worded) assessment of Haldane's Dilemma.  (Creationist Paul Nelson brought it to my attention in March 1995.)  

⁵    My critique of Haldane's Dilemma and its many confusion factors is, in my opinion, considerably fuller than that of George C. Williams. 

⁶    From the ARN discussion group (July 2004).  

⁷    The brief history given here focuses mostly on the neglect, and does not attempt to cover all the history, all the contributors, or all the ideas  (good or bad). The good ideas were always attached to confusion factors, in virtually every conceivable combination, which garbled Haldane's Dilemma, rather than solved it.

1/24/2005 - by Walter ReMine

Evolutionists attempt the following argument (often on the internet, but seldom if ever in print).  They claim Haldane's Dilemma "only applies to the conditions assumed by Haldane."  They suggest Haldane's Dilemma is "solved" by breaking one of Haldane's starting assumptions.  They say Haldane used an old, unenlightened model from 1957, not a model based on modern knowledge. 

Their argument is mistaken, for the following reasons:  

1. Haldane used principles, and models of genetics and selection, that remain exceptionally predominant today in evolutionary genetics textbooks. 
2. In addition, Haldane used assumptions that favor evolution. When you 'break' such an assumption, not only do you not solve Haldane's Dilemma, you make the problem worse. 
3. Some of Haldane's assumptions were used (as still commonly done today) in order to simplify the math and generalize the results.  You cannot solve Haldane's Dilemma by breaking one of these particular assumptions, since that merely complicates the problem without solving it.  There is always a cost of substitution, no matter what model is used.  Evolutionists must identify a model that actually solves Haldane's Dilemma, while remaining plausible on other grounds.  They have not done that. 

 For example: 

Haldane's old model? – Haldane used a multiplicative-fitness model. (Moreover, for the parameters he used, it also approximates an additive-fitness model.)  Both of those fitness models are still predominantly used today.  Everything in "Haldane's model" is current with today's practice of evolutionary genetics (including Haldane's uses of fitness, fitness models, selection, alleles, genes, dominance, and Mendelian segregation).  So if evolutionists throw-out "Haldane's model" they must also throw-out the modern textbooks on evolutionary genetics. 

Small selection coefficients? – Haldane assumed selection coefficients approaching zero.  This gives the absolute minimum total-cost of substitution in each case.  If you break Haldane's assumption, and invoke higher selection coefficients, then the cost increases, resulting in fewer substitutions, and Haldane's Dilemma worsens.  

The environmental-change scenario? – Haldane assumed substitutions begin in a peculiar way, via an environmental-change scenario.  The scenario operates as follows.  Neutral and slightly harmful mutations (though almost always eliminated outright) sometimes drift upwards in frequency, to arrive at moderate frequencies.  Then, when the environment changes, one of these neutral or slightly harmful mutations is converted (it is alleged) into a beneficial mutation.  This elevated starting frequency is where Haldane begins to tally the total-cost of the substitution.  By giving the substitution a free head-start to an elevated frequency, it lowers the total cost of substitution.  This cost-reduction is the only impact of the environmental-change scenario that Haldane allowed into his calculations. If you break Haldane's assumption, then it raises the total-cost of substitution, and worsens Haldane's Dilemma.¹ 

Constant population size? – Haldane assumed the population size remains constant throughout a given substitution (though he allowed large varieties of population size, each for a different substitution).  That was done partly for mathematical simplification (in the era before computers were readily available to readers).  When evolutionists break this assumption, they do not "solve" Haldane's Dilemma.  They merely obscure it further.  There is always a cost of substitution; it is unavoidable.  It is not enough to merely object to Haldane's simplification.  Evolutionists must actually s-o-l-v-e Haldane's Dilemma. 

Infinite population size? – Evolutionists sometimes claim Haldane assumed an unrealistic "infinite population size." That is untrue.  If Haldane had done that, then the total-cost of substitution would always be infinite – when Haldane calculated its average value is 30.  So Haldane obviously did not use an infinite population size.  Rather, Haldane used something at the other end of the spectrum.  To see it, take a haploid species, and suppose there are two independent alleles, A and B (at independently segregating loci), each with a frequency of one per thousand.  By random mating, the genotype AB (containing both alleles, A and B) would have a frequency of one per million.  But if the population size is only one thousand individuals, then in a given generation, genotype AB cannot actually exist at a frequency of one in a million.  Instead, either that genotype exists as a whole individual, or it does not exist – it either has a frequency of one per thousand, or zero.  There is no 'in-between' when dealing with individuals that are quantized into whole-bodies.  This difficulty is handled by Haldane, and by virtually all textbooks today, in the same way – by using non-quantized individuals.  To greatly simplify the math, and to generalize the results, they allow a genotype to exist at its expected frequency (without having to quantize the genotype into, say, 1000 whole-bodies).  Put simply, Haldane assumed non-quantized individuals, not infinite population size.  If evolutionists want to throw-out that simplifying assumption, then they would have to throw-out virtually all of today's evolutionary genetics textbooks.  And it still would not solve Haldane's Dilemma. 

There is nothing in "Haldane's model" that evolutionists can object to, without shooting themselves in the foot. A solution to Haldane's Dilemma (if one exists at all) will require moving beyond the models, assumptions, and techniques commonly employed in evolutionary genetics today. 

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¹    My book shows that if the environmental-change scenario is fully accounted (which Haldane did not do), then it worsens Haldane's Dilemma.  In any case, Haldane's handling of the matter unrealistically favored evolution.  

1/24/2005 - by Walter ReMine

Cost theory has wide applicability.  Cost arguments can apply to any evolutionary scenario, for any species, in any environment, and even including computer simulations.  However, Haldane's calculation – 300 generations per substitution – applies to organisms with low reproduction rates in natural environments. That would include the higher vertebrates, and especially elephants, whales, apes, and humans. 

Under artificial selection – using human intervention and contrived circumstances – the population's reproduction rate can be dramatically increased. That can, and should, be accounted using cost theory.  In addition, a larger fraction of the reproduction rate can be devoted to substitutions (by artificially reducing the fraction of the reproduction normally disposed in other ways, such as random losses). Cost theory shows that these factors can dramatically increase the substitution rate under artificial circumstances, compared to the wild. 

Moreover, cost arguments put a limit on the beneficial substitution rate. For realistic species, the neutral substitution rate, and the harmful substitution rate, are unlimited by cost, and can be rapid.  (The reasons are technical, and covered in my paper.)  Therefore, when examining the results of artificial selection – such as the various breeds of dogs or chickens – keep in mind that many of the observed "changes" are unintended neutral or harmful outcomes.  These 'changes' should not be tabulated as "beneficial" substitutions. 

When correctly tallied, the results of artificial selection do not violate cost theory.  

2/03/2005 - by Walter ReMine

"Darwinian natural selection" is a a broad, ambiguous term with many various meanings. For some it means "Survival of the fittest" – period. For others, it means repeated cycles of mutation, variation, excess reproduction, and selection of individuals. For others it includes wild, exceedingly rare but exceedingly fortuitous meta-mutations (as in the Hopeful Monster hypothesis). For others it includes processes that are downright harmful to the population (such as harmful mutation and inbreeding) – needed in order to get past barriers in the fitness terrain. For others it includes mechanisms for warping and deforming the fitness terrain (such as the Red-Queen hypothesis, or the Stationary hypothesis) – needed in order to get past barriers in the fitness terrain.. Then there are others for whom that term includes other levels of selection (such as kin selection, group selection, deme selection, species selection, and gene selection), which (according to Stephen Jay Gould) have complex interactions between levels, with positive and negative feedback between levels. 

My point is that the term "Darwinian natural selection" can be rather ambiguous, and thereby convey unintended meanings – which is why I sometimes avoid the term, in favor of something more specific.

In the case of population genetics or evolutionary genetics, a more specific term is needed. Indeed, I would argue that these fields do not use "Darwinian natural selection", rather they use differential survival or differential reproductive success at the genotype level (where "survival" and "reproductive success" are averaged over the entire life-cycle, which makes them two terms for the same thing). These fields rarely ever (never?) deal directly with the features and functions of organisms (the phenotype, such as what makes tigers and toads). Rather, these fields take values for "differential survival" at the genotype level and calculate the genetic outcomes of it.

In this sense, Haldane's Dilemma does not assume "Darwinian natural selection", but rather something much more modest – mutation and differential survival – both of which are observed facts. Mutation exists. And different organisms "survive and reproduce" at different rates. Those are observed facts.

Haldane's Dilemma then grants assumptions that are quite favorable to evolutionists, which makes the dilemma all the more problematic. Namely, Haldane's Dilemma assumes there are no barriers in the fitness terrain. It lets the mechanisms of mutation and differential- survival free-run at their fastest conceivable rate, unimpeded by barriers in the fitness terrain.

Recall your elementary math classes, where you can prove a new mathematical theorem by assuming something is true, and then showing the assumption leads to a contradiction – thus proving the assumption is false, and thereby establishing a new theorem. Well, that same method is also valid in empirical sciences, except that the source of a contradiction is often far less clear, and takes time to unravel. Haldane's Dilemma arises from a bundle of many assumptions, (as is universal in empirical sciences). So the source of a contradiction can be awkward to pin down. The question is: Which assumption in the 'bundle' is wrong? Which one is the source of contradiction?

"Darwinian natural selection" is not assumed within Haldane's Dilemma, so it cannot be the source of contradiction. Rather, Haldane's Dilemma assumes mutation and differential survival, both of which are observed facts, and cannot be discarded nor rejected. Other assumptions favor evolution, so rejecting those will only aggravate the contradiction. So the 'source' of the contradiction resides in the assumption that humans arose from ape-like creatures in ten million years, or in the assumption that the currently used models of genetics-selection are valid, and so forth.

The point is, Haldane's Dilemma does not test "Darwinian natural selection".

2/5/2005 - by Walter ReMine

Haldane's Dilemma is based on a technical concept known as the "cost of substitution."  All evolutionary authors define the cost of substitution in terms of at least one (and often two or more) of the following concepts: 

• Genetic death – the elimination of the previous-type individuals, which depends on:  their physical makeup, their life history, how they die, and when they die
• Genetic load – a concept that quantifies fitness differences in the population, and entails the notion that the population fitness decreases during a beneficial substitution
• Environment – particularly the role of "deteriorating environments" or "changing environments"
• Selection – the role of selection, and the type of selection process (for example, "soft selection" versus "hard selection")
• Extinction – the complete elimination of the species, and its avoidance. 

In truth, none of those concepts is essential to the cost of substitution. They are all secondary, at best.  Those confusion factors survive to this day.  When someone teaches those are the central issue, they have confused it.  

The so-called "solutions" to Haldane's Dilemma fail, in almost every case because they are built on a mistaken view of the cost of substitution.  Those failures are fundamental, due to a basic misunderstanding.  That is why I say Haldane's Dilemma was never solved, instead it was garbled into oblivion.  

Any progress toward resolving Haldane's Dilemma will require: (a) the elimination of many traditional confusion factors about the cost of substitution, and (b) the clarification of the physical meaning of the cost of substitution. My book and papers do that. 

1/24/2005 - by Walter ReMine