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Haldane's Dilemma

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:* For example, the cost of substitution was often defined in terms of “genetic death” or <I>elimination</I> of the previous-type individuals. So, soft selection was claimed to reduce the problem <I>by reducing or delaying the elimination.</I> But that is wrong-headed, because the issue is not ‘elimination’ of the previous-type individuals, rather the issue is the <I>‘increase’</I> of the new-type individuals (and the reproduction rate necessary to make that happen) – and this version of soft selection does nothing whatever for that increase. (On the contrary, it keeps the previous-type individuals around <I>longer,</I> taking up resources, and slowing evolution down.) By focusing on the wrong issue, genetic death fostered this false solution to Haldane’s Dilemma.  
:* For example, the cost of substitution was often defined in terms of “genetic death” or <I>elimination</I> of the previous-type individuals. So, soft selection was claimed to reduce the problem <I>by reducing or delaying the elimination.</I> But that is wrong-headed, because the issue is not ‘elimination’ of the previous-type individuals, rather the issue is the <I>‘increase’</I> of the new-type individuals (and the reproduction rate necessary to make that happen) – and this version of soft selection does nothing whatever for that increase. (On the contrary, it keeps the previous-type individuals around <I>longer,</I> taking up resources, and slowing evolution down.) By focusing on the wrong issue, genetic death fostered this false solution to Haldane’s Dilemma.  
:* Soft selection is most commonly defined as frequency-dependent selection, or density-dependent selection. But that is not sufficient to reduce Haldane’s Dilemma, much less solve it. The total cost of substitution has an absolute minimum (that occurs when the selection coefficient approaches 0+), and rises as the selection coefficient rises. Haldane’s equations already favored evolution by granting the absolute minimum total cost of substitution – through assuming <I>consistently tiny</I> selection coefficients (approaching 0+). <B>If the selection coefficient <I>varies</I> (as in frequency- or density-dependent selection), then the total cost of substitution cannot possibly go lower than Haldane’s equations, but will surely go higher – making the problem worse than before.</B> This point is basic, yet still widely confused today, which is further evidence of evolutionist negligence.  
:* Soft selection is most commonly defined as frequency-dependent selection, or density-dependent selection. But that is not sufficient to reduce Haldane’s Dilemma, much less solve it. The total cost of substitution has an absolute minimum (that occurs when the selection coefficient approaches 0+), and rises as the selection coefficient rises. Haldane’s equations already favored evolution by granting the absolute minimum total cost of substitution – through assuming <I>consistently tiny</I> selection coefficients (approaching 0+). <B>If the selection coefficient <I>varies</I> (as in frequency- or density-dependent selection), then the total cost of substitution cannot possibly go lower than Haldane’s equations, but will surely go higher – making the problem worse than before.</B> This point is basic, yet still widely confused today, which is further evidence of evolutionist negligence.  
 +
:* Recently, evolutionists are promoting another version of soft selection. In reality, it is not a type of selection, but an illegitimate accounting trick, similar to the double-booking used in financial scams. It operates like this. In effect, the various other costs of evolution (such as the cost of continuity, the cost of mutation, the cost of segregation, the cost of random loss, and a several other costs) are collectively -- and misleadingly -- called "background mortality". Then this is claimed as an additional source to pay the cost of substitution. That is, the accounting that should go toward paying the "background mortality" is diverted to paying the cost of substitution. That leaves the other costs of evolution unpaid, which is not a plausible scenario. In effect, evolutionists are robbing Peter to pay Paul. This approach does not reduce the cost of substitution one iota, instead it attempts to increase the payment by means of misplaced accounting practices. [Note: This version of soft selection is promoted only when evolutionists are trying to solve cost-related problems, otherwise it plays no role in their evolutionary presentations.]
:* Soft selection is sometimes defined as “rank-order selection,” which is effectively just another version of truncation selection – and is not realistic, (see below). To give that an air of realism, soft selection is typically equivocated to mean “frequency-dependent or density-dependent selection.” Such equivocation (or bait-and-switch) should be rejected.  
:* Soft selection is sometimes defined as “rank-order selection,” which is effectively just another version of truncation selection – and is not realistic, (see below). To give that an air of realism, soft selection is typically equivocated to mean “frequency-dependent or density-dependent selection.” Such equivocation (or bait-and-switch) should be rejected.  
-
:* The prevalence and sufficiency of soft selection are disputed (e.g., by evolutionary geneticist, G. C. Williams).  
+
:* The prevalence and sufficiency of soft selection are disputed (e.g., by evolutionary geneticist, G. C. Williams).
=== Truncation selection ===
=== Truncation selection ===

Revision as of 20:05, 29 January 2007

J. B. S. Haldane (1892 – 1964)

Haldane's Dilemma is a severe limit on the speed of evolution, first calculated in 1957 by renowned evolutionary geneticist, J. B. S. Haldane. The limit is sufficiently slow that it calls into question the “fact” of evolution, or evolutionary genetics as an empirical science. The problem also displays various forms of long-term negligence from evolutionary leaders.

Contents

The Dilemma

Evolution requires the substitution of new beneficial mutation into the population, to create new biological adaptation. Haldane calculated that organisms with low reproduction rates, such as cows, could substitute a new beneficial mutation no more frequently than one per 300 generations.

The problem can only be seen through examples, and the easiest example to understand is human evolution. Start at some alleged human ancestor ten million years ago, which generously allows evolution far more time than is available. (Allegedly the last common ancestor between humans and chimps was three to five million years ago. And the human adaptations in question are alleged to have evolved mostly within the last two million years.) In ten million years, an ape-human-like lineage could substitute no more than 1667 beneficial mutations. In evolutionary genetic literature, it is undisputed that Haldane’s calculations, if correct, would indicate such a limit. (And according to evolutionary geneticists, each of those substitutions is typically one nucleotide, not thousands of nucleotide differences.)

All the necessary data, theory, and claims, come from evolutionists. The calculation is:
  • Allow 10 million years for an ape-man lineage. (This figure favors evolution by allowing far more time than is available.)
  • Divided by 20 years effective generation time. (This figure is from evolutionary geneticists, for this lineage, over this period of time.)
  • Divided by 300 generations per beneficial substitution. (This figure is from Haldane’s calculations.)
  • Equals a maximum of 1667 beneficial mutations substituted into that ape-man lineage. (Plus some limited number of neutral mutations, which do nothing to improve adaptation.)

The problem is: Can all the uniquely human adaptations be explained within that limit? Such adaptations would include: the tripling of brain size, upright posture, hand dexterity, vocal speech organs, language, distribution of hair, and appreciation of music, to name a few. That can be compared with the power of beneficial mutations observed today, such as the alleged examples in the beaks of Galapagos finches. Is a limit of 1,667 beneficial mutations sufficient to create all the uniquely human adaptations? This is Haldane’s Dilemma. The problem is deepened by the fact that Haldane’s assumptions are wildly unrealistic in favor of evolution. (See the assumptions.)

A similar problem exists for other species, especially those with low reproduction rates and long generation times, such as: whales, elephants, bears, apes, and so forth. The higher the generation time and the lower the reproduction rate, the fewer beneficial mutations are substituted over time.

Status

Haldane’s Dilemma is easy to communicate – a limit of 1,667 beneficial mutations for human evolution. Yet evolutionists never communicated any such limit to the general public. Even their technical journals strongly avoided such direct figures, and instead spoke obliquely in terms of substitution rate – such as “one gene substitution per 300 generations,” a phrase that obscures the problem from view, and may as well be in code.

Moreover, the evolutionary literature on Haldane’s Dilemma is extremely confused, contradictory, and unresolved – though evolutionists do not generally acknowledge those particulars. The confusion still permeates evolutionary literature today, and makes discussion awkward. For example, evolutionists will cite one evolutionary geneticist’s paper as true, when many other evolutionary geneticists implicitly regard it as false – and the matter remains unresolved because evolutionary leaders have not explicitly addressed such contradictions. If you enter into this controversy, be prepared for such mischief. Calls for evolutionists to clear up this topic have been ignored. (For example, see a tale of peer-review, where evolutionary leaders suppressed clarifications from their journals.) Evolutionary leaders have a lengthy record of negligence on this important problem – a record of mis-communication, a record of allowing falsehood and confusion to prevail for decades. No conspiracy is suggested, but there is long-term negligence. That negligence itself is worth studying, that we may better understand the sociology of science.

In addition, evolutionary literature has scarcely begun to discuss, much less establish, that 1,667 beneficial mutations (or any other figure) is sufficient to explain human evolution.

In short, Haldane’s Dilemma remains profoundly unsolved and under-discussed.

Despite those failures, most evolutionary geneticists regard the problem as “solved,” and largely set it aside in the 1970s. However, there exists no agreed solution to Haldane’s Dilemma. Evolutionary geneticists contradict each other not only about the solutions, but also about the basic fundamentals of the problem itself.

Evolutionary geneticist, G. C. Williams, writes:

“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.” (G. C. Williams, 1992, Natural Selection: Domains, Levels, and Challenges, p 143-144, emphasis added)

To many creationists, Haldane's Dilemma falsifies large-scale evolution. To other creationists, Haldane’s Dilemma demonstrates that evolutionary genetics cannot cope with its central issues – evolutionary genetics is theoretical castles-in-the-sky, substantially disconnected from empirical reality; amorphous and ultimately untestable; not an empirical science. As Haldane’s Dilemma moves forward, Walter ReMine predicts evolutionists will increasingly advance unfalsifiable (untestable) aspects of evolutionary theory and evolutionary genetics. This suggests the evolutionists’ explanation is either falsified, or unfalsifiable – and either way it is not scientific (using the same definition of science that evolutionists endorsed in court).

Introduction to technical details

The Cost of Substitution

Haldane’s Dilemma arises from a concept called the cost of substitution. This concept became confused in various ways, and the confusion was the source of many false “solutions.” Intelligent design theorist, Walter ReMine objects to the many confusion factors still entrenched in the literature, and has published a paper to clarify the issues. Leading evolutionary geneticists, including James Crow and Warren Ewens, peer-reviewed the paper and acknowledge it is correct.

A cost argument operates as follows. Every evolutionary scenario requires a certain level of reproduction rate – called a “cost.” A cost is a required reproduction rate for a given evolutionary scenario. If the species cannot actually produce the required reproduction rate, then the scenario is not plausible. In other words, each scenario has a requirement, and if the requirement is not met, then the scenario is not plausible. That requirement is reproduction rate.

There are various types of cost, each for a specific purpose. Such as:

  1. The cost of continuity – a reproduction rate of 1, which is required merely for continuing into the next generation.
  2. The cost of mutation – the extra reproduction rate required for preventing genetic deterioration due to harmful mutations.
  3. The cost of segregation – the extra reproduction rate required for maintaining polymorphisms in a population.
  4. The cost of random loss – the extra reproduction rate required for coping with random losses to the population, (such as fire, flood, famine, selection for non-heritable traits, and many other factors).
  5. The cost of substitution – the extra reproduction rate required specifically for making substitutions – that is, required for increasing the number of copies of the substituting mutations. [Haldane’s version of the cost concept was far more indirect and confusing, but (when correctly reinterpreted) it was effectively identical in how it operated, and in the results it produced.]

The sum of all those costs (plus a few other minor costs) is the cost of evolution: the total reproduction rate required by the scenario. Thus:

Cost of evolution = Cost of continuity + Cost of mutation + Cost of segregation + Cost of random loss + Cost of substitution + …

If the species cannot produce that required reproduction rate – in other words, if the species cannot “pay the cost” – then the scenario is not plausible. Haldane’s Dilemma merely applies that logic each generation.

Take a simple example. Suppose a scenario claims that in one generation a substituting mutation increases (in number of copies) by twenty-five percent. This will require a reproduction rate of at least 1.25, (which is a cost of continuity of 1, plus a cost of substitution of 0.25). That requirement is not reduced one iota by the following situations:

  • Changes in the environment
  • Changes in population size
  • Soft selection (or hard selection)

(Note: These three items have been falsely alleged as “solutions” to Haldane’s Dilemma. A clear understanding of the cost of substitution shows they are not.)

Add up the cost of substitution over all generations of a given substitution, to obtain a total. Then divide by the number of generations, to obtain the average. In other words, ‘adding up a total’ is merely an intermediate step in obtaining an average cost – which is the focus of concern. Over the long term, if the species cannot pay this average cost, then the given substitution rate is not plausible. Toward that end, Haldane calculated the total cost of substitution for various types of mutations, and various population sizes, as expected in nature. Averaged over those circumstances, he calculated the total cost of one substitution is 30.

Under Haldane’s pro-evolutionary assumptions, if more than one mutation is substituting, then their costs of substitution will add together. For example, in a given generation, if the cost of substitution for two mutations separately would be 0.07 and 0.03, then the cost for both simultaneously is 0.1. Since this summing applies each generation, it also applies over the long-term – so it also applies to their total cost of substitution. Therefore, regardless of whether the substitutions occur one at a time (end-to-end), or whether they overlap in time in any arbitrary fashion, their total cost of substitution is still fully required.

Several of the other costs tend to be large, (items 1, 2, 3, & 4 above), and consume almost the entire reproduction rate, leaving little leftover to pay for substitutions. Through breeding experiments on higher vertebrates, Haldane measured that they have a reproduction rate that leaves only 0.1 leftover to pay for substitutions.

In conclusion, the total cost of substitution is 30, and paid in installments of 0.1 per generation, which means, over the long term, substitutions can occur no more frequently than one per 300 generations (=30/0.1). His calculation allowed for sexual reproduction and for numerous concurrent substitutions overlapping in time in arbitrary ways.

Haldane’s Assumptions

Evolutionists often complain that Haldane’s assumptions are out-of-date or unrealistic. That is highly misleading. Haldane’s assumptions are wildly unrealistic in favor of evolution, and that makes Haldane’s Dilemma all the more potent as anti-evolutionary evidence. Haldane’s assumptions also represent the current evolutionary genetics textbooks.

  • He assumed the population does not get stuck on top of a local fitness peak, held there by survival of the fittest, and forever prevented from evolving.
  • His analysis assumed continual, non-stop evolution, with no stasis. (Haldane’s analysis pre-dated Gould and Eldredge and the general acceptance that fossil species almost always display stasis – or lack of change – throughout their existence.)
  • He assumed the fitness terrain offers no significant obstacles to evolution, such as impassable ‘mountains’ or deep ‘crevasses’ in the fitness terrain.
  • He assumed the fitness terrain is not maze-like – with dead ends, a labyrinth of blind alleys, and back tracking – which would make successful large-scale evolution far slower and far less probable.
  • He assumed the fitness terrain does not warp or deform in any ways unfavorable to evolution. For example, he assumed the fitness terrain does not warp so much, so often, or so rapidly, that it would turn evolution into a random process, where beneficial evolution becomes a moot point.
  • He assumed the species is not in error catastrophe (also known as mutational meltdown), where genetic deterioration occurs from generation to generation.
  • He assumed the species does not go extinct.
  • The above factors can occur in countless combinations that would prevent large-scale evolution or slow it down. But Haldane silently assumed-away any and all obstacles to evolution. (That practice is especially common in any evolutionist presentations to the general public.)
  • His analysis ignored pleiotropy – where a gene affects more than one biological trait. Pleiotropy generally makes substitutions difficult, and pleiotropy occurs frequently in life. Haldane’s analysis ignored this difficulty, and that favors evolution.
  • He ignored all ill effects of environmental change, and also assumed unrealistically favorable effects of environmental change – all of which favors evolution. (For example, he used a peculiar environmental-change scenario to artificially elevate the starting frequency of the substituting mutations, thereby lowering their total cost of substitution. And he completely ignored the overwhelmingly ill effects of that same scenario.)
  • In calculating the Haldane limit on substitution rate, all his cost equations assumed tiny selection coefficients (approaching 0+), and this favors evolution by giving the absolute smallest total cost of substitution in each case. This further favors evolution when taken together with the next assumption.
  • He assumed hundreds to thousands of substitutions occurring concurrently, which favors evolution by giving the optimally highest frequency of substitution, at the lowest cost of substitution.
  • He ignored genetic drift. Elimination by genetic drift is almost always the outcome for beneficial mutations, especially for the tiny selection coefficients used by Haldane. According to evolutionary geneticists, if a beneficial mutation has a modest selective advantage of one-tenth percent (s=0.001), then it will be eliminated 998 times out of a thousand. Haldane's calculation ignored this effect, via the following assumption.
  • He assumed a sufficiently high rate of beneficial mutation.
  • He ignored the cost of unsuccessful substitutions. Almost all beneficial mutations fail to substitute; instead they are eliminated by genetic drift. Yet they still incur a portion of the total cost of substitution. Ignoring this factor lowers the cost, thereby favoring evolution.
  • Beneficial recessive substitutions have an extremely high cost (easily in the thousands). But Haldane drastically discounted their cost, and that favors evolution. He also assumed the vast majority of beneficial recessive mutations are eliminated and completely without cost, and that further favors evolution. Moreover, since the large majority of mutations are known to be recessive, Haldane theoretically eliminated the largest source of beneficial mutations, and neither he, nor any evolutionary geneticist since, has accounted for that loss. In other words, Haldane assumed a sufficiently high rate of beneficial mutations, while simultaneously ignoring the fact that he theoretically eliminates the largest source of those. The role of beneficial recessive mutations is widely unaccounted by evolutionary geneticists. These have a cost for successful substitution, and a cost for unsuccessful substitution – and either way, these ought be accounted into some realistic view of evolutionary process, not simply assumed-away in favor of evolution.
  • He assumed classical Darwinian selection, also called individual selection, which favors evolution by incurring the lowest total cost of substitution. Rather than other forms of selection (such as kin selection, group selection, deme selection, or species selection) that incur a higher total cost of substitution.
  • He assumed the same model of genetics and selection still predominant in evolutionary genetics textbooks today – Haldane’s model is not out-of-date.
  • Haldane’s model implicitly assumes no epistasis (or complex, favorable, interactions between the substituting mutations). The vast majority of biological traits (such as brains, hearts, blood clotting, vision, motility, hair, replication, metabolism, etcetera) are products of numerous genes, whose specific combination (not just any random combination of genes) is vastly more beneficial than any of the same genes taken alone or in smaller combinations. (The whole is greater than the sum of parts.) This type of epistasis (which is ordinarily what is meant by the term epistasis) occurs abundantly in nature – yet is usually de-emphasized or ignored in evolutionary genetics textbooks because it strongly aggravates evolutionary problems. [For example, sexual reproduction (when combined with this epistasis) is widely acknowledged to dramatically slow beneficial evolution, because it breaks apart favorable combinations of genes each generation. This dramatic slowing of beneficial evolution magnifies the classic evolutionary problems with the origin and maintenance of sexual reproduction.] By assuming no such epistasis, Haldane’s model favors evolution and is consistent with most evolutionary discussions today.
  • He assumed a reasonably constant population size, though he also allowed for various population sizes, as expected in nature. He did that for mathematical and tutorial convenience, and to obtain broadly applicable results, (since there would be infinitely many ways to vary the population size relative to substitutions). (He also did that because his particular cost concept was defined only under constant population size; a shortcoming now remedied by ReMine's cost concept. There is always a cost of substitution; it is unavoidable, whether or not the population size is constant. Changing the population size complicates the analysis, without solving the problem.)

The cost of substitution puts a limit, or threshold, on plausible substitution rates – lower rates are plausible, but higher rates are not plausible. In addition, Haldane’s calculation made many wildly unrealistic assumptions in favor of evolution – and he made no attempt to guarantee those many favorable assumptions actually hold true. In short, the Haldane rate is an upper limit, a highly unrealistic maximum – not remotely a guaranteed ‘average rate’ of evolution.

Punctuated equilibrium

Haldane’s analysis assumed continual evolution, with no stasis. But that contradicts what is now recognized about the fossil record. Evolutionary paleontologist Stephen Jay Gould conservatively estimates that fossil species are in stasis – where change is not occurring – more than ninety-nine percent of the time. (Gould included the primate species and humans within his claims.) This predominance of stasis could reduce Haldane's limit by a factor of one-hundred – to a limit of 17 beneficial mutations for explaining human evolution.

When evolutionists eventually address this problem, ReMine predicts some of them will claim there is little or no relationship between the observed fossil stasis and genetic stasis – as though genetics and morphology are disconnected and unlinked. It is likely evolutionists will increasingly attempt that route of evasion.

But that is not the route taken by Gould and other evolutionary researchers. They suggest a broad general correlation between morphological change and genetic change – in short, a correlation between the observed fossil stasis and genetic stasis. Such a connection is central to what Gould and others call “the primary prediction of punctuated equilibrium” – which alleges to predict the relative rates of genetic change. (Gould, The Structure of Evolutionary Theory, 2002, p 812)

The connection between morphology and genetics is further strengthened by: (1) the field of evolutionary development (also called evo-devo), which claims that single beneficial mutations often have substantial effects on the organism, often visibly; and (2) the observed abundance of pleiotropy, where a given gene has more than one effect on the organism. These factors further suggest the observed fossil stasis represents genetic stasis.

Due to the observed fossil stasis, punctuated equilibrium claims that most change (including most beneficial change, or adaptation) must therefore occur at speciation events. However, leading evolutionists have long claimed that speciation is a substantially non-Darwinian process. (Because, in the Darwinian goal of “reproducing more of one’s genes into future generations,” the formation of “barriers to reproduction” is less fit.) That is, speciation events are said to be inexplicable in terms of individual selection, but are primarily due to genetic drift and inbreeding, which are non-adaptive. Altogether, those claims make adaptation and Haldane’s Dilemma even harder to solve.

To help explain adaptation, punctuated equilibrium emphasizes the role of species selection. That is, new species are said to branch-off in a random direction with respect to adaptation, then the most adapted species are selected – the entire species is selected, rather than individuals. Evolutionists made an analogy between species selection and individual selection. In individual selection, mutation randomly creates new variations of individuals (most of them unfavorable), and then the favored individuals are selected. In species selection, speciation (operating like a random mutation) randomly creates new variations of species (most of them not favorable), and then the favored species are selected. Because of this randomness, numerous speciation events would be required to obtain one that is favorable – just as countless thousands of mutations would be required to obtain one that is favorable.

Evolutionary geneticist, John Maynard-Smith, aptly argues that punctuated equilibrium is implausible because of its high cost. The species’ reproduction rate would have to replace, not just one population (as in the usual substitution process), but numerous entire species. That task requires far more reproduction (and a far higher cost of substitution), and that would slow the substitution rate. These arguments suggest that punctuated equilibrium slows beneficial evolution dramatically.

If these evolutionary leaders are correct, then beneficial evolution must be vastly slower than Haldane calculated. But these problems, like so much of Haldane’s Dilemma, have been negligently under-discussed in evolutionary literature.

The figure 1,667 is wildly unrealistic in favor of evolution: (1) by allowing far more time than is available, (2) by ignoring the large slow-down due to punctuated equilibrium and its associated claims, and (3) by numerous unrealistic assumptions in favor of evolution.

Evolutionist responses to Haldane’s Dilemma

Evolutionists must actually solve Haldane’s Dilemma – not merely confuse it into oblivion, or assume it away, or brush it aside. If a solution would require special evolutionary processes, then those ought be widely embraced as realistic and exhibited consistently as an established part of the evolutionary model. Evolutionists have not done that.

Traditional confusion factors

The field is held back by traditional confusion factors, such as:
  • genetic death – which focuses on the elimination of the previous-type individuals
  • genetic load, also known as substitutional load – which focuses on the “fitness reduction” that occurs during beneficial substitutions
  • also extinction, selection intensity, fitness, fitness-renormalization, fitness-change, environmental-change and population-size-change.
The literature applies those in various combinations, to produce numerous forms of needless confusion, error, and contradiction. Some leading evolutionary geneticists have known most of those faults for decades, yet by and large, have allowed those faults to remain uncorrected in evolutionary literature. Abundant confusion is the evolutionists’ de facto main defense against Haldane’s Dilemma.

It makes “no sense,” or is “an illusion”

Such arguments (which often cite Wallace, Hoyle, Feller, Moran, or Brues) are false, and thrive on traditional confusion factors (especially genetic death and genetic load). Moreover, such arguments are implicitly contradicted by leading evolutionary geneticists – such as Crow, Ewens, Kimura, and Maynard-Smith – who all took Haldane’s cost concept seriously. Unfortunately, those contradictions are not explicitly addressed, much less resolved, in the evolutionary literature. Instead, evolutionary leaders negligently allowed those confusions to prevail – confounding generations of researchers. The continued prevalence of such arguments is evidence of evolutionist negligence.

Beneficial substitutions “pay for themselves”

That argument is most associated with Joe Felsenstein, and is still often heard today. Many evolutionary geneticists implicitly regard it as false, but have not bothered to publicly correct the falsehood. The continued prevalence of such arguments is evidence of evolutionist negligence.
The argument confuses cost versus payment. A “cost” is calculated theoretically, based upon a given evolutionary scenario. For example, if a scenario claims the mutations “increase the reproduction rate,” then that will increase the cost, but does nothing to assure the payment is made. The “payment” is the species actual reproduction rate, and is ultimately based upon observation, not storytelling or pure scenario-saying.
The cost of substitution can only be paid by an actual, real (not imaginary), reproduction rate. For example, suppose a scenario claims that, in one generation, a new beneficial mutation goes from one copy to one million copies. That would require a reproduction rate of at least one million, (that is, a cost of continuity of one, plus a cost of substitution of 999,999). That requirement is not reduced one iota by asserting, “the new substitution theoretically increases the reproduction rate to one million, thereby paying for itself!” If the species cannot actually produce the required reproduction rate (in this case, a reproduction rate of at least one million), then the scenario is not plausible. Period.

The assumptions seem “unrealistic or out-of-date”

That is highly misleading and does not even begin to solve Haldane’s Dilemma. (See here.)

Failure to pursue

The next largest source of error comes from evolutionists’ failure to pursue their own explanations to their logical conclusion. The evolutionist chooses highly peculiar circumstances favorable to evolution, and then assumes it represents a general solution to Haldane’s Dilemma. This common error occurs two ways:
  1. By ignoring the unfavorable effects of their own evolutionary scenario. (For example, by ignoring the overwhelmingly unfavorable effects of: environmental-change, barriers to gene flow, or small population size.)
  2. By mistakenly assuming the favorable effects of their scenario apply to all generations and wider circumstances in nature. Here is an example often given by evolutionists. Take a large population, where one individual has a beneficial mutation, and suppose all the disfavored individuals are eliminated in one generation – the evolutionist concludes, “The substitution occurs in one generation, not 300 generations, therefore Haldane must be wrong.” The evolutionist implies his specially chosen generation represents all evolution. But obviously, his scenario cannot work generation-after-generation over the long-term. It will require numerous generations to grow the population back to it previous size, (where it can likely receive another beneficial mutation) – and this growth, as always, is limited by the species finite reproduction rate.
These errors are basic, and their pervasiveness still today is evidence of evolutionist negligence.

Neutral evolution

Evolutionary geneticist, Motoo Kimura, saw Haldane’s Dilemma as a serious problem. In fact, Kimura cited Haldane’s Dilemma as his main reason for proposing the Neutral Theory of evolution. However, neutral evolution does not explain adaptations. And it does not change the fundamental problem – Is 1,667 beneficial mutations enough?
The Neutral Theory does not solve Haldane’s Dilemma. Instead, the Neutral Theory was proposed in order to rescue the evolutionary storyline from the jaws of falsification – which is an altogether different feat. At the time, protein sequencing (and later, gene sequencing too) was revealing numerous genetically-based differences between diverse mammals, and Kimura realized these could not be explained under the Haldane limit on beneficial substitutions. To avoid such falsification, Kimura took his only remaining avenue of escape – he proposed that most evolutionary genetic change is neutral, (and therefore not limited by Haldane’s argument).
That began the controversy between two factions of evolutionists – neutralists versus selectionists – which has lasted many decades. Selectionists claim most substitutions are due to selection (if only the selection could be measured). Neutralists claim most substitutions occur precisely because selection is absent. In other words, evolutionary theory is compatible with both outcomes – which again indicates unfalsifiability at the core of evolutionary genetic theory. As Haldane’s Dilemma moves forward, Walter ReMine predicts evolutionists will evade (rather than solve), by increasingly invoking neutral evolution.

Environmental change

Environmental-change (like mutation) is random with respect to a species, and therefore it tends to harm the species. (For example, by lowering the reproduction rate, or by raising various evolutionary costs, such as the cost of random loss, or the cost of unsuccessful substitutions.) Haldane’s calculations ignored those unfavorable factors.
Haldane assumed an environmental-change scenario; therefore some evolutionists claim his argument is invalid in a constant environment. Their claim is false. Haldane’s environmental-change scenario is wildly unrealistic in favor of evolution (by lowering the cost of substitution). Under a constant environment, Haldane’s favors to evolution would not exist; therefore evolution would be slower than what Haldane calculated.
Some evolutionists (following Joe Felsenstein) claim the cost of substitution is only valid in a deteriorating environment. Their claim is false. To increase the number of copies of a substituting mutation, extra reproduction rate is required – the cost of substitution is unavoidable. (See here.) Leading evolutionary geneticists (including Crow, Ewens, Maynard-Smith, and Kimura) implicitly contradict Felsenstein’s argument, but have not publicly addressed it. Instead, they negligently allowed the confusion to prevail – confounding generations of researchers. The lingering prevalence of Felsenstein’s argument is evidence of evolutionist negligence.

Partitioned populations

Some evolutionary theorists propose a large population partitioned into many small sub-populations by intermittent barriers to gene flow. Then the barriers to gene flow are alleged to rise and fall, as needed at just the right moments, in order to solve whatever shortcoming the theorist is explaining away.
In other words, theorists attempt to choreograph nature into an intricate dance, as though nature will obey. But nature need not dance to the theorist’s tune, nor obey facile storytelling. ‘Barriers to gene flow’ generally occur randomly, and therefore will not generally help the species or evolution. Indeed, it is awkward to claim that intermittent ‘barriers to gene flow’ will speed up beneficial evolution. These proposals have not been shown to solve Haldane’s Dilemma; instead, they confused it into oblivion.

Dominance modifiers

Beneficial recessive mutations have an exceedingly high cost of substitution (easily in the thousands). In hopes of reducing that cost, some evolutionists promoted “dominance modifiers,” which would convert a beneficial recessive mutation to dominant. However:
  • These would likely be unlinked to the substituting mutation, thereby reducing effectiveness of the dominance modifier (and the random origin of “a dominance modifier already linked to the substitution that it modifies” would be exceedingly infrequent.)
  • These would likely originate too late to reduce much cost.
  • These would likely incur their own additional cost of substitution.
  • Dominance modifiers would presumably also convert harmful recessive mutations to dominant, and convert beneficial dominant genes to recessive – thereby increasing the cost of mutation.
For these reasons, dominance modifiers do not solve Haldane’s Dilemma. Moreover, they are seldom mentioned.

Soft selection

Soft selection remains ambiguous and confused in evolutionary literature. Most arguments surrounding it are based on genetic death or genetic load, which cause error.
  • For example, the cost of substitution was often defined in terms of “genetic death” or elimination of the previous-type individuals. So, soft selection was claimed to reduce the problem by reducing or delaying the elimination. But that is wrong-headed, because the issue is not ‘elimination’ of the previous-type individuals, rather the issue is the ‘increase’ of the new-type individuals (and the reproduction rate necessary to make that happen) – and this version of soft selection does nothing whatever for that increase. (On the contrary, it keeps the previous-type individuals around longer, taking up resources, and slowing evolution down.) By focusing on the wrong issue, genetic death fostered this false solution to Haldane’s Dilemma.
  • Soft selection is most commonly defined as frequency-dependent selection, or density-dependent selection. But that is not sufficient to reduce Haldane’s Dilemma, much less solve it. The total cost of substitution has an absolute minimum (that occurs when the selection coefficient approaches 0+), and rises as the selection coefficient rises. Haldane’s equations already favored evolution by granting the absolute minimum total cost of substitution – through assuming consistently tiny selection coefficients (approaching 0+). If the selection coefficient varies (as in frequency- or density-dependent selection), then the total cost of substitution cannot possibly go lower than Haldane’s equations, but will surely go higher – making the problem worse than before. This point is basic, yet still widely confused today, which is further evidence of evolutionist negligence.
  • Recently, evolutionists are promoting another version of soft selection. In reality, it is not a type of selection, but an illegitimate accounting trick, similar to the double-booking used in financial scams. It operates like this. In effect, the various other costs of evolution (such as the cost of continuity, the cost of mutation, the cost of segregation, the cost of random loss, and a several other costs) are collectively -- and misleadingly -- called "background mortality". Then this is claimed as an additional source to pay the cost of substitution. That is, the accounting that should go toward paying the "background mortality" is diverted to paying the cost of substitution. That leaves the other costs of evolution unpaid, which is not a plausible scenario. In effect, evolutionists are robbing Peter to pay Paul. This approach does not reduce the cost of substitution one iota, instead it attempts to increase the payment by means of misplaced accounting practices. [Note: This version of soft selection is promoted only when evolutionists are trying to solve cost-related problems, otherwise it plays no role in their evolutionary presentations.]
  • Soft selection is sometimes defined as “rank-order selection,” which is effectively just another version of truncation selection – and is not realistic, (see below). To give that an air of realism, soft selection is typically equivocated to mean “frequency-dependent or density-dependent selection.” Such equivocation (or bait-and-switch) should be rejected.
  • The prevalence and sufficiency of soft selection are disputed (e.g., by evolutionary geneticist, G. C. Williams).

Truncation selection

Evolutionary geneticists seldom advocate truncation selection as a wide-ranging mechanism – unless someone brings up Haldane’s Dilemma or some cost-related problem. Then, from out-of-the-woodwork, truncation selection is brought forth as a “solution.” When the discussion is over (and the problem seems “solved”), then truncation selection is silently abandoned – until the next time someone brings up these problems. Such equivocation should be condemned. Since truncation selection is not embraced as a key ingredient of the evolutionary model, evolutionists cannot claim it “solves” Haldane’s Dilemma.
For example, evolutionary geneticist, John Maynard-Smith saw Haldane’s Dilemma as a legitimate problem, and proposed truncation selection (also called threshold selection) as a solution (1968). Yet it is absent from his later textbook, Evolutionary Genetics. Likewise, Sved’s version of truncation selection (1968) is often cited as a “solution,” yet evolutionary geneticists do not otherwise embrace it.
That is because truncation selection is not realistic. In effect, it ranks individuals, say, by their number of beneficial mutations, and then eliminates individuals below a certain threshold. This process does not depend on any specific interactions between the substituting mutations. Instead, it assumes any random collection of beneficial mutations interacts (and truncates) as effectively as any other – which is not plausible.
That is quite different from the epistasis seen in nature, where highly specific genes (and their mutations) interact in highly specific combinations to produce a complex trait, such as a brain, heart, joint, blood clotting, vision, motility, hair, replication, or metabolism. Not just any random collection of genes (or mutations) will produce such spectacular advantages. This real-life epistasis makes evolutionary problems worse, which explains why evolutionary textbooks tend to de-emphasize it, or silently assume it away.

Internet tactics

  • Internet evolutionists often misrepresent their opponents. For example, see here and here. That behavior is most common on anonymous discussion groups, and especially talk.origins.
  • The name “Haldane’s Dilemma” was coined by evolutionary geneticists, and is the literature’s recognized name for this problem. However, Internet evolutionists sometimes change the name (to “ReMine’s Dilemma”): (1) which attempts to bury the problem, disconnected from evolutionary authorities and literature searches, and (2) as a sophomoric attempt to smear their opponents.
  • Evolutionary websites often misdefine Haldane’s Dilemma, and introduce confusions, irrelevant diversions, and needlessly tedious mathematical derivations – that wears down readers and obscures the problem from view. For example, see the Wikipedia article.

Related References

  • Haldane, J. B. S., 1957 The Cost of Natural Selection. J. Genet. 55:511-524. Note: Haldane’s paper is not clear or easy to understand, and has been a source for much confusion that remains to this day.
  • ReMine, W. J., 2005, Cost Theory and the Cost of Substitution — a clarification. TJ 19(1), 2005, pp. 113-125, (later renamed the Journal of Creation). See also summary by Don Batten in the same issue, pp. 20-21 Haldane’s dilemma has not been solved.
  • ReMine, W. J., 2006. More Precise Calculations of the Cost of Substitution. Creation Research Society Quarterly, Vol 43, pp. 111-120. Like ReMine's 2005 paper, this paper was submitted to the main-stream (i.e., evolutionary) journal Theoretical Population Biology, where all peer-reviewers (three in this case) found no errors. They also recognized it as new material (that does not exist in the prior literature). Nonetheless, they rejected it from publication on the grounds that it is not a “sufficient advance,” and “there is little interest in this subject today among population biologists; it is one of those subjects which has sunk almost beyond trace”.
  • The Biotic Message, by Walter ReMine, 1993, Saint Paul Science, publishers, 538 pages (pages 170-253, and 495-507) This book brought Haldane’s Dilemma to general readership.
  • Haldane's Dilemma, web updates by Walter ReMine

See Also

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