Answering Evolutionist Attempts to Dismiss "Haldane's Dilemma"

 Fred Williams
October 2000

[Author's note: see update at end of article]

Introduction

In 1993 Walter ReMine’s book "The Biotic Message"1 hit the street, bringing with it several devastating arguments against evolution that are still clamoring through the halls and smoke rooms of the evolutionary faithful. One of these arguments is based on a paper by J. B. S Haldane in 19572 that showed the reproductive capacity of vertebrates was way too low to pay the costs needed to account for large-scale evolution. This problem is referred to as “Haldane’s Dilemma” (go here for an online discussion of the problem by Walter ReMine).

Refuting Robert Williams

So far I have only encountered one attack against Haldane’s Dilemma that offers any kind of sophistication, one posted on the internet by Robert Williams. It regularly shows up early in search engines when searching on “Haldane’s Dilemma”, so evolutionists often cite it or copy from it.  

There are many, many problems with Robert Williams’ article. When I first read it, I became very suspicious that he had never read ReMine's book since ReMine deals with most of Williams’ arguments in his book. I contacted Mr. ReMine, and he confirmed that Williams eventually admitted on the newsgroup sci.bio.evolution to not having read the book. On several occasions I attempted to contact Williams about this, but he did not reply. It is very unfortunate that Williams refuses to do the right thing and properly review ReMine’s book before posting a rebuttal.

Nevertheless, since so many evolutionists refer to Williams' tenuous paper, I thought I would address its arguments. Robert Williams’ comments appear in italic green.

ReMine neglects the fact that humans did not evolve from chimpanzees, rather humans and chimps evolved from a common ancestor. Therefor we have actually had two different branches each evolving independently, thus allowing for twice as many gene substitutions (3300 vs. 1700) as ReMine has allowed, even if all of the above is true.

His insinuation that ReMine believes humans evolved from chimpanzees is completely unsubstantiated (this was the first sign he had not read ReMine's book). This is a very common ploy of evolutionists, to claim that creationists don’t understand that evolutionary theory posits common decent from a shared ancestor. Regardless, this does not double the amount of substitutions that can occur from point A (man/ape ancestor) to point B (man), and this is the context of ReMine’s (and Haldane’s) argument.

ReMine assumes that all the differences between the human and chimp genomes are due to selection.

Remine makes no such assumption in his book.

This can't possibly be the case because many of the differences are known to occur at the 3rd triplet of gene codons and thus usually do not change the amino acid coded and can't affect fitness. Furthermore, since 95% of the genome is not transcribed (although that does not mean it is all non-functional ), most point mutations will not affect fitness. This reduces the number of selected substitutions by 5 x 2/3 % or from 4.8 x 107 substitutions to 1.6 x 106. Please remember that changes in the genome due to drift and other "random" processes do not add to the cost of substitution. I should add that Haldane's Dilemma has been viewed by scientists as possible evidence for the importance of Neutral Evolution as proposed by Kimura in 1967.

At this point I was very certain Williams had not read ReMine’s book, since ReMine has an entire chapter dedicated to Neutral Evolution and its inability to solve Haldane’s Dilemma. If Williams had read ReMines’ book, or even just thought about the problem logically, he would have discovered that neutral substitutions also must be substituted in! If a neutral trait (or substitution) becomes fixed, all alternative alleles at the same locus must still be removed.

In fact, neutral mutations incur a greater cost, since they will have a greater propensity to drift back and forth in frequency since they have no selective value. Every time the frequency goes down, it negates any previous payment made by reproductive excess to get it to that frequency; when it drifts back up, a new payment via excess reproduction is needed, hence net cost is increased. According to ReMine, Haldane showed that cost is minimized only when fixation moves steadily upward3.

ReMine neglects the fact that there are only 23 pairs of human chromosomes. Thus, when there are any favorable genes on the same chromosome, their substitution cost would only have to be paid one time for the chromosome as a whole, not one time for each favorable gene. This alone could falsify ReMine's whole argument if many genes are approaching fixation on a few chromosomes.


Again, ReMine's book correctly addresses this. If Williams had read it he would have been reminded of Mendelian genetics, recombination and crossover, and that humans reproduce sexually, not asexually. Diploid offspring do not inherit completely intact chromosomes from their parents. Does Williams submit that Haldane, a distinguished evolutionist, also “neglected the fact that there are only 23 pairs of human chromosomes”?

ReMine ignores the possibility of gene hitchhiking - the concept that even though some mutations are neutral, they will be carried to fixation because they are physically close to a gene that is beneficial.

ReMine does not ignore this possibility, he discusses it in the book Williams pretended to read4. ReMine also cites Haldane as addressing this possibility and that Haldane also dismissed it as very negligible5.

For linkage to pay the cost of two for the price of one, the following must occur:

a) The neutral mutation must occur about the same time as the beneficial mutation it is linked to. If it occurs say 50% into the fixation cycle of the beneficial mutation, it can’t just magically appear on all the other chromosomes in the population. It has to begin its own payment cycle when it first appears. All those without the mutation, which would be the entire population plus all descendants without the mutation, must eventually be removed.

b) the two would have to remain very tightly coupled through at least half the fixation process to give the neutral mutation an even chance to reach fixation6.

c) gene hitchhiking is very rarely found in sexually reproducing populations7.

I hope it is now quite apparent why linkage effects have negligible impact on cost evaluations.

Finally, ReMine ignores the fact that due to non-point mutations (deletions and insertions due to non-equal crossing over), a single mutation can affect many more than one DNA base pair. In fact, what has to be by far and away the most common mutation is the change in DNA due to the alignment mismatch mutations in mini-satellites. These mutations can affect some multiple of between 5 and 15 base pairs and have been observed in as many as 1 in 6 human sperm!

This is a completely bogus argument for several reasons. First, the must common mutations are point mutations (base pair substitutions)8. Second, even when multiple mutations occur, the harmful ones will incur an immediate reproductive cost, and any remaining neutral or “beneficial” ones must still pay their own cost if they are to reach fixation!!!  Also, it appears  Williams again forgot that humans reproduce sexually, not asexually. If multiple mutations occur, they will be divided among the offspring, and only so many of these will reproduce on to the next generation. Hence only a handful will remain, only to face the same shredding machine the next generation. Because sex continually scrambles genes every generation, population geneticist Ronald Fisher (1930) estimated that a “beneficial” mutation will have at best only a 1 in 50 chance of ever reaching fixation in a population 9.

Haldane assumed that the cost of substitution had to be paid on top of the "natural" death rate! In other words, it didn't matter that 90% of a mammal's offspring died without reproducing - any death that resulted from the substitution of one gene for another had to be additional death that the animal would not "normally" have suffered. This is known as hard selection and we can now easily see why Haldane only allowed an excess fertility of 10% to go towards the cost of substitution. However, most Biologists today consider all or some selection to occur as soft selection. In this scenario, the cost of substitution is "paid" in the natural death rate of the animal. That is, a disproportionate number of the individuals that die without reproducing in any generation are the ones that have lower fitness due to their genes. The Biologist Bruce Wallace has been the champion of soft selection, and you can learn more about this topic in his book "Fifty Years of Genetic Load - An Odyssey". 

Let me bring in another Williams to refute Williams! Highly regarded evolutionist George C. Williams wrote the following regarding Wallace and soft selection:

 “...the problem [of Haldane's dilemma] was never solved, by Wallace [soft selection] 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." 10

As we can see, Robert Williams’ last effort to soften the blow of Haldane’s Dilemma is disputed by an evolutionist of considerably more standing.

Conclusion

Despite various attempts by evolutionists over the last 40 years to soften the impact of Haldane’s Dilemma, it still remains an enormous problem for their theory. It is worth noting that Haldane's analysis even used very favorable assumptions for the evolutionary theory, such as assuming the mutations are dominant (recessive mutations pay an exponentially higher cost). Regardless, the numbers do not bode well for the evolutionists, and is very likely why the problem stays buried in back-room discussions and does not see the light of day in evolutionary textbooks.

Current molecular data is making matters even worse for the evolutionist faithful, because it makes the problem easier to see for the layman. I document this in my article Monkey-Man Hypothesis Thwarted by Mutation Rates. This article stands on its own and does not rely on the validity of Haldane’s calculations. Using a conservative estimate of mutation rates based on current studies, it shows that the ape/human line would have required at least 40 offspring per mating pair just to maintain equilibrium! This forcefully argues that the Monkey-Man shared ancestor hypothesis is simply implausible.


Update: Several months after I wrote this, Robert Williams to his credit removed most of the arguments I addressed above from his web page! (he keeps a copy of the original here). His first line of defense in his latest installment is his claim that 1667 beneficial substitutions may be enough to account for human evolution from our alleged simian ancestor! As far as I'm concerned this is a complete capitulation of the issue! Remember that this is not just a problem for human evolution, but for mammalian evolution in general.

Robert  also still defends gene hitchhiking as a cost reducer, and gives an example of it occurring in nature. I have not had a chance to confirm his example, but it doesn't really matter. It is still a rare phenomenon, as Futuyma points out in his Evolutionary Biology testbook7. A blind squirrel, well, you know the story.

Finally, Robert mentions that Haldane did address the issue of "multiple simultaneous substitutions". Haldane did indeed, but Robert's citation from Haldane's paper is completely inaccurate. In the paragraph Robert referred to, Haldane is not addressing the impact on cost of "multiple simultaneous substitutions". Where Haldane does address this is the 4th paragraph on page 522, where he explains "[for three mutants]...since the cost of selection is proportional to the negative logarithm of the initial frequency, the mean cost...would be the same as that of selection for the three mutants in series..."

 


1. Walter ReMine, The Biotic Message,  1993, St Paul Science

2. JBS Haldane, The Cost of Natural Selection, Journal of Genetics 55, pp 511-524 (1957)

3. ReMine, The Biotic Message, p 500

4. Ibid. pp 245, 503

5. Haldane, 1957, p 522

6. Douglas J. Futuyma, Evolutionary Biology, 1998, p 300

7. Ibid. p 245 (gene hitchhiking is technically referred to as linkage disequilibrium)

8. Personal correspondence with Professor James Crow

9. Futuyma, p 298

10. George C. Williams, Natural Selection: Domains, Levels, and Challenges, 1992, p 143-148

 

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