Haldane's Dilemma


In recent years, creationist Walter ReMine has been making claims that the evolution from the common ancestor of humans and other apes to humans could not have happened in five million years because of a concept known as "Haldane's Dilemma". Haldane's Dilemma is based upon the substitution cost introduced by J.B.S. Haldane in his classic 1957 paper "The Cost of Natural Selection" (Haldane, 1957). ReMine addresses these issues in his book "The Biotic Message" (ReMine, 1993). ReMine also claims that the scientific community has "brushed aside" and never properly responded to Haldane's Dilemma. The purpose of this essay is to show that ReMine's arguments are false (or at least greatly exaggerated), and were answered decades before "The Biotic Message" was even published.

Haldane calculated the substitution cost based upon a scenario where a sudden environmental change makes genes that were formerly detrimental and very rare become favorable. The genes begin the process of becoming common (because they are now favored by natural selection) and eventually are fixed in the population - present in virtually every individual). Under Haldane's deteriorating environment scenario, huge numbers of deaths will occur in the population because for most of the substitution, only a few individuals will have the beneficial genes that protect them from the environmental change.

William Feller, P.A.P. Moran, and Joe Felsenstein all proposed that Haldane's Dilemma did not apply to beneficial mutations (mutations that produce genes that benefit the organism without a change to the environment that is detrimental to all of the organisms not carrying the mutated gene). This makes perfect sense because you will not see the huge numbers of deaths (an average 30 times the population size in the case of diploids, according to Haldane) required to make the replacement of a beneficial mutation that you will see in the case Haldane describes, where there has been a deterioration in the environment. However, Motoo Kimura (who used  Haldane's Dilemma as a justification for his Neutral Theory) had a response to this claim. He pointed out that in order for beneficial mutations to explain the genetic differences seen in mammals, huge (ridiculous, like 1078 offspring per individual each generation) numbers of offspring would be required. Kimura used these arguments as part of the evidence to support his neutral theory of evolution - the idea that most (but not all) gene substitutions seen in evolution have little or no effect upon the fitness of species. In response to Kimura, Warren Ewens demonstrated that the ridiculous numbers of offspring are not required to drive the simultaneous selection of many beneficial mutations in a finite population.

What is Haldane's Dilemma?

Haldane claimed that in a fixed population (a population that is neither growing nor shrinking in the number of its member animals) of relatively slowly reproducing mammals, no more than 1 gene could be fixed per 300 generations due to the cost of substitution. Haldane assumed that the deaths caused by the newly disadvantageous gene's lower fitness (possibly due to a change in environment) would be over and above the "background" death rate - the naturally occurring deaths due to all reasons other than the lowered fitness of the gene. Haldane estimated that the substitution cost (for a diploid) would require the deaths of 30 times the population size for a single gene fixation from a very rare mutation to homozygous for the entire population. Since he claimed that the intensity of selection rarely exceeded 10%, Haldane believed a cost of 30 times the population size for the substitution would require 300 generations (30 / 0.1) to fix a single gene.

Haldane seemed satisfied that this rate of substitution was sufficient to explain theorized substitution rates at the time (see pg. 521 of "The Cost..."), but other scientists  felt this rate was  too low. The first mention of the term "Haldane's Dilemma" appears to come from paleontologist Leigh Van Valen in his 1963 paper "Haldane's Dilemma, Evolutionary Rates, and Heterosis" (Van Valen, 1963). Van Valen saw the dilemma as the observation that "for most organisms, rapid turnover in a few genes precludes rapid turnover in the others." Haldane's dilemma has come to mean this limit upon the rate of evolution.

What is the Substitution Cost?

Very simply, the substitution cost (or cost of natural selection) as defined by Haldane is the number of deaths (normalized to the population size) required for a substitution to occur. Thus, when Haldane states that a substitution cost of 30 is typical for a substitution for a diploid organism, he is saying that such a substitution would require the deaths of 30 times the population size. Therefore, if the population size was 100,000, 30 * 100,000 or 3 million deaths would be required for the substitution to occur. I have assembled a series of quotes from Haldane from "The Cost of Natural Selection" to document this definition. The fact that the substitution cost represents the number of deaths required for the substitution to occur should also be apparent from the derivations for the cost that are linked below.

 A (Somewhat) Non-Technical Description of the Substitution Cost

What Does ReMine Say About Haldane's Dilemma?

ReMine claims that Haldane's Dilemma shows that not "enough" genes could have substituted in the human species since the last common ancestor with other apes. I shall illustrate each of these by quotes from ReMine "The Biotic Message" and from the thread "Haldane's Cost of Natural Selection" in sci.bio.evolution.

From page 209 of "The Biotic Message":
With these clarifications, let us return to the example. Take an ape-like creature from 10 million years ago, substitute a maximum of 500,000 selectively significant nucleotides and would you have a poet philosopher? How much information can be packed into 500,000 nucleotides? It is roughly one-hundredth of one percent of the nucleotide sites in each human ovum.

Is this enough to account for the significantly improved skull, jaws,teeth, feet, upright posture, abstract thought, and appreciation of music, to name just a few? If you find it doubtful, then you are beginning to understand why this is important. It sets a limit on the number of traits that can be substituted by differential survival in the available time.

This quote is taken from ReMine's post to the usenet discussion group sci.bio.evolution on 01/28/1998, Message-ID: <6anste$qd6$1@nntp6.u.washington.edu>. Here he lays out his claim that Haldane's Dilemma allows only 1,667 substitutions to occur in the last ten million years of evolution leading to the human lineage. ReMine's quote follows:

As an example my book focuses on human evolution from its presumed ancestor (whatever it might be) from, say, ten million years ago. That is twice as old as the alleged split between gorilla, chimpanzee, and man. My book cites evolutionists such as Dawkins, Stebbins, Kimura and Ohta for an estimate of the effective generation time during that era -- twenty years. That makes for 500,000 generations. Then apply the Haldane limit of one substitution per 300 generations, and apply the evolutionary model exactly as taught in the textbooks. The result: In ten million years the population could substitute no more than 1,667 beneficial nucleotides. That is not remotely enough to explain human evolution.

ReMine also implies that Haldane's Dilemma is a problem for the genetic differences seen between humans and chimpanzees in this statement attributed to ReMine  on a page maintained by creationist Ted Holden:

Imagine a population of 100,000 of those organisms quietly evolving their way to humanity.  For easy visualization, I'll have you imagine a scenario that favors rapid evolution.  Imagine evolution happens like this.  Every generation, one male and one female receive a beneficial mutation so advantageous that the 999,998 others die off immediately, and the population is then replenished in one generation by the surviving couple.  Imagine evolution happens like this, generation after generation, for ten million years.  How many beneficial mutations could be substituted at this crashing pace?   One per generation -- or 500,000 nucleotides.  That's 0.014 percent of the genome. (That is a minuscule fraction of the 2 to 3 percent that separates us from chimpanzees).
I have read "The Biotic Message", and I am aware that ReMine does not stress the issue of the "2 to 3 percent" difference that separates humans and chimps in that book. However, unless Holden has incorrectly attributed the passage above to ReMine, ReMine does try to make an issue of those differences.  Furthermore, this form of the argument is often seen on the Internet and also was printed in the creationist publication Creation Ex Nihlio 19(1):21-22, Dec. 1996-Feb. 1997.- see Does the DNA similarity between chimps and humans prove a common ancestry?. In item 6 of the essay, Batten refers to the 120 million differences between humans and chimps (because he used a difference of 4%). In footnote 7 of the article, Batten specifically refers to "The Biotic Message" and its treatment of Haldane's Dilemma as evidence that the number of differences seen between humans and chimps is impossible to explain. So even though ReMine does not stress this issue in "The Biotic Message", because creationists are in fact using the argument that a  "2 to 3 percent" genetic difference between chimps and humans is a problem for evolution because of Haldane's Dilemma, it is very important that these arguments are addressed. One important thing ignored by these claims of ReMine and other creationists is the simple fact that neutral substitutions do not add to Haldane's substitution cost and are not part of Haldane's Dilemma.

Solutions to Haldane's Dilemma

There may not be a Dilemma
There is basically a very simple solution to Haldane's Dilemma as presented by ReMine: 1 (beneficial) gene substitution per 300 generations could be enough to account for human evolution. Although 1,667 substitutions may seem like a low number, it may be sufficient to explain the differences between humans and their ancestors of 10 million years ago. There is no way to determine the genetic differences between humans and those ancestors (because the ancestors are not available for genetic testing). No scientist currently knows the number of non neutral substitutions that have occurred during this time period. (Nor does ReMine, despite his exaggerated claims to the otherwise.) In fact, evidence is beginning to accumulate that the genetic differences between related species is due to rather few genetic differences of large effect - see  The Genetic Basis of Evolution to learn more about this fascinating development. It is hard to get concerned about a dilemma when it hasn't even been shown to exist. The pertinent question to ask of ReMine and his followers is: What is the hard evidence that more than 1,667 beneficial substitutions are required between humans and chimps? Remember, only the substitution of beneficial (fitness enhancing) alleles will add to the substitution cost as defined by Haldane. Fixation of neutral alleles (the vast majority of substitutions that have occurred in the human and chimp lines since they last shared a common ancestor) does not add to the substitution cost.

In fact, to the best of my knowledge, only one genetic difference has been determined to date that produces a significant difference between humans and apes. This is a change in the structure of sialic acid, which is different in humans from all other mammals. These sialic acids are components of cell membranes throughout the body and are involved in brain development, messaging between cells, and are targets of disease organisms when they infect cells. You can read the original scientific paper on this "A mutation in human CMP-sialic acid hydroxylase occurred after the Homo-Pan divergence" online. Also, see the popular articles Which of Our Genes Make Us Human? by Ann Gibbons and Pinpointing how humans differ from apes. These changes were traced back to a single genetic change (a 92 base pair deletion in the gene that codes the hydroxylase enzyme that adds an oxygen atom to sialic acid). Additionally, here is a follow up paper from some members of the team that discovered the sialic acid difference between humans and apes: Genetic Differences between Humans and Great Apes. The authors have suggestions on how to proceed with determining the significant genetic differences between humans and chimps.

Just because the number of gene substitutions that have occurred in the recent human lineage is unknown doesn't mean that the issue is being ignored. The first part of answering this question is well under way. The Human Genome Project is an ongoing 15 year long mission of the scientific community to identify all human genes (approximately 35,000 of them) and sequence all 3 billion DNA base pairs. The second part to determining whether or not Haldane's Dilemma even exists will be to map the genome of our closest living relatives, the chimpanzee, the gorilla, and the orang-utan. The Chimpanzee Genome Project is being proposed (A Chimpanzee Genome Project Is a Biomedical Imperative and here) to take advantage of the new DNA chip technology and knowledge gained from the Human Genome Project to map the chimpanzee genome far more quickly and more economically than was the case for the Human Genome Project.  Once this has been done, differences between the human and chimpanzee can be identified and evaluated. A count of the non neutral substitutions that have occurred in the two lineages can then be made (although it may not be easy to determine which substitutions have a major effect upon fitness). Only at that point will we know whether or not Haldane's Dilemma is even an issue of concern for human evolution. Considering these facts, it is clear to see that ReMine and his followers are greatly exaggerating this issue.

Additionally, Project Silver is underway to sequence the ape genomes and compare them nucleotide by nucleotide to the human genome in an effort to determine "which of our genes make us human." Notice that on this Project Silver introduction page, we see speculation that the significant changes between humans and chimps may be in the neighborhood of 10,000. Although the author of the page clearly states that this is a "very rough guess", it is worth noting that this is far less than ReMine's uninformed claims that 500,000 such changes are insufficient to explain the last 10 million years of human evolution. It is also significant that the estimate of 10,000 important differences was made before the rough draft of the human genome project became available in Feb. of 2001, when it was learned that only 1.1% of the human genetic material encodes genes. The Project Silver page appears to use 5% as the estimate of gene encoding DNA, so if they scale back the number of "significant" genes that differ between  humans and chimps by this factor of 5, they are very close to the range permitted by Haldane (2,000 significant changes vs. 1,667 "permitted" by Haldane ). An important observation to make here is that while creationists like ReMine and his followers falsely charge that "Haldane's Dilemma" makes evolution impossible and evolutionists are covering up or ignoring the facts, the scientists are in reality doing everything they can to detect the genetic differences between humans and chimps and get those results published.

The Cost of Beneficial Substitutions and Soft Selection
Remember that Haldane defined the substitution cost as the number of deaths required for the substitution. He estimated that for a diploid species, that number would typically be 30 times the population size. The immediately obvious question is why is this number so high? If a trait is present in a few individuals, if all remaining members of the population (that don't have the trait) were wiped out, the substitution would occur with the death of only 1 times the population size individuals - not 30 times the population size. Admittedly, this is a little weak in that the population would still require time to build up to its former numbers, but it begins to point out the fact that the deaths of large multiples of the population size individuals is not required to drive a substitution. In fact, it has been shown that in two situations (besides the unrealistic one I have just mentioned), a single substitution can occur with the death of only 1 times the population size rather than a factor of (typically) 30.

To see why and how this is possible, we have to look at Haldane's assumptions of how substitutions occurred in his derivations of the substitution cost.

Haldane considered the effects of a change in the environment. From page 514 of "The Cost of Natural Selection":

I shall investigate the following case mathematically. A population is in equilibrium under selection and mutation. One or more genes are rare because their appearance by mutation is balanced by natural selection. A sudden change occurs in the environment, for example, pollution by smoke, a change of climate, the introduction of a new food source, predator, or pathogen, and above all migration to a new habitat. It will be shown later that the general conclusions are not affected if the change is slow. The species is less adapted to the new environment, and its reproductive capacity is lowered. It is gradually improved as a result of natural selection. But meanwhile, a number of deaths, or their equivalents in lowered fertility, have occurred. If selection at the ith selected locus is responsible for di of these deaths in any generation the reproductive capacity of the species will be P(1 - di) of that of the optimal genotype, or exp(-Sdi ) nearly, if every di is small. Thus the intensity of selection approximates toSdi.
The interesting thing (as pointed out by Leigh Van Valen and Bruce Wallace) is to look at what happens under different conditions than those envisioned by Haldane. If one looks at the substitution of a new, beneficial allele, it is apparent that the number of genetic deaths required for the substitution is 1 (times the population size), not the large factors of the population size that Haldane calculated under the deteriorating environment scenario. The reason for this is that there is no longer the relentless culling of the vast majority of the population as is the case for the deteriorating environment. Although individuals carrying the beneficial allele will eventually eliminate the remaining population, the effects of this replacement will not be felt until the new allele has become fairly common. Some scientists (George Williams) have claimed that soft selection is not common in nature, but, beneficial mutations will always behave like soft selection. This is because whenever a beneficial allele is created (through a mutation), although the individuals carrying the new allele will have a higher fitness, the remaining members of the population will not have a large decrease in fitness. This is part of the reason that Feller and Moran rejected Haldane's high cost arguments for beneficial substitutions. See Substitution of a Beneficial Allele, Diploid for the mathematical details of how the substitution cost is lowered in the case of beneficial alleles.

Multiple Simultaneous Substitutions Lower the Cost Even Further
It is easy to see that the substitution cost is lowered when multiple substitutions are occurring in a population. The reason for this is very simple. If two beneficial mutations are moving towards fixation in a population, whenever an organism that carries neither of those mutations dies, the cost of substitution is exactly half what it would have been had the two substitutions occurred at different times from one another. One organism has died to "pay the cost" for two substitutions. If you prefer to look at the cost from the perspective of the number of individuals that must be born to carry the mutation to fixation, then one individual which is born with two beneficial genes (and survives to reproduce) pays the cost that would have been required of two organisms if the substitutions had occurred separately. As more substitutions are going on at the same time, the more the cost will be lowered (compared to what the cost would have been had the substitutions occurred separately. Evidence that this actually occurs in nature has recently been discovered. Scientists have recently determined that the genes driving the speciation of a particular group of aphids lie very close to one another on the same chromosome. When genes are closer together on a chromosome (tightly linked), they are more likely to move together as a single unit because they are not broken up by recombination. This will lower the substitution cost even more than the simultaneous substitution of unlinked genes.

Haldane did address the issue of multiple simultaneous substitutions in "The Cost of Natural Selection" (see the fifth paragraph of page 511). However, because he considered only substitutions occurring in the deteriorating environment scenario, he did not think that very many substitutions could occur simultaneously. He gave the example of  a change in the environment that suddenly favored 10 rare alleles, leaving the fitness of any individual carrying all 10 of those alleles unchanged and reducing the fitness of all individuals not carrying all 10. If each of the 10 alleles is rare, the vast majority of the population would carry none of the 10. If the fitness of an organism is reduced by 1/2 for each of the 10 beneficial alleles it does not have, then the fitness of the vast majority of the population would be reduced by a factor of 1024. Haldane pointed out that such a fitness reduction could not be tolerated by the vast majority of species in the world. However, when substitutions occur that are truly beneficial (when the environment is not deteriorating), then the fact that the vast majority of the population does not possess any of the beneficial mutations does not lead to any reduction in fitness. Individuals without the beneficial mutations have the same fitness that they did before. Individuals that do not have the beneficial mutations will only see a decrease in fitness when the individuals carrying the beneficial mutations become more common in the population and begin to out compete those without the beneficial mutations for resources.

Kimura on the Substitution Cost as Evidence for the Neutral Theory - A Fly in the Ointment?
After demonstrating that that any beneficial substitution or any substitution under the soft selection scenario would not require the death of typically 30 times the population size for a diploid organism, it is not surprising that many scientists (i.e. Van Valen, Feller, Wallace) thought Haldane's Dilemma was solved. However, Motoo Kimura, who used Haldane's arguments as evidence to support his neutral theory, had an answer for those who thought beneficial mutations or soft selection could be used to escape Haldane's Dilemma. Kimura made estimates of the substitution rate of about 1 amino acid per every 2 years (Kimura 1968), and later 6 amino acid substitutions per generation (Ewens 1979, pg. 252). Kimura based these rates upon comparisons of amino acid substitutions that had occurred among various species in the genes that code for hemoglobin, cytochrome c, and triosephosphate dehydrogenase. Note that when researchers looked at substitution rates for a wider variety of proteins and organisms, they found an amino acid substitution rate of 1 substitution per 36 years (about 1 substitution per 18 generations for most mammals), far slower than that calculated by Kimura (recounted in Spiess 1977). At any rate, based upon the rates calculated by Kimura, in order for a population to drive substitutions at the rates suggested by protein comparisons among different species, huge numbers of offspring would have to be produced by each parent. A quote from Kimura and Ohta (Ewens 1979) addresses the offspring requirements required to drive six substitution per year:

"to carry out mutant substitution at the above rate, each parent must leave e180  1078 offspring for only one of the offspring to survive. This was the main reason why random fixation of selectively neutral mutants was first proposed by one of us as the main factor in molecular evolution."
Kimura thought the huge offspring requirement generated by the substitution cost (if all substitutions were driven by natural selection) was strong evidence for his neutral theory (that a large number of amino acid substitutions was driven by random drift of selectively neutral gene variants rather than by natural selection of alleles having varying fitnesses). Kimura never thought that Haldane's Dilemma was a "problem" for evolution, only that it was good evidence that the bulk of observed substitutions between related species were neutral rather than selected. Some have argued that these huge offspring requirements are not the same as the substitution cost as defined by Haldane. Since the offspring requirement to drive a substitution is not exactly the same as the number of selective deaths required to drive the substitution (Haldane's definition of the substitution cost), these arguments may have some merit. Nonetheless, since it has already been shown that the substitution of beneficial alleles in a non-deteriorating environment will not lead to the huge costs (numbers of selective deaths) predicted by Haldane, the huge numbers of reproductive excess required by Kimura's arguments are the only way to carry Haldane's cost arguments forward into the non-deteriorating environment. If it were not for this tremendous offspring requirement, Haldane's Dilemma would have been entirely solved by the soft selection / beneficial trait arguments of Van Valen, Feller, and Walace. Regardless of where you stand on this issue, as will be shown in the next section, Warren Ewens was able to show substitutions could easily be driven at the observed rates in finite populations without the huge offspring requirements calculated by Kimura.

As an aside, if the rate of 1 substitution per 36 years (as mentioned above) is correct, this would indicate that in 10 million years, we would expect about 280,000 substitutions to occur. This rate (based upon observed amino acid differences in organisms) is slightly over half the number of substitutions (500,000) that ReMine thinks is insufficient to explain the last 10 million years of human evolution. Clearly, ReMine has no clue as to the number of selectively significant substitutions required to explain human evolution.

The Cost is So Much Lower in Finite Populations that it is Not an Issue - Ewens Answers Kimura's Objections
In two papers (Ewens 1970, Ewens 1972), Warren Ewens showed that the substitution cost was greatly reduced when realistic population sizes are considered. In fact, he showed that a finite population was capable of bearing the substitution cost required for even the highest substitution rates inferred from the sequencing of proteins across various species.

Ewens showed that a significant amount of the cost of natural selection was due to differences between the fittest members of a population and the mean. To get at the mathematics of multiple substitutions, Ewens described a scenario where alleles begin moving towards fixation at regular intervals. For example, in a particular generation, one allele begins moving toward fixation (because of natural selection), and 10 generations later a second allele (at a different position than the first allele - on a different gene) begins moving towards fixation, and 10 generations later a third allele begins moving towards fixation, etc. To make it possible to do the math, each of these alleles have the same parameters (selection coefficient, coefficient of dominance, starting frequency, and ending frequency). If it takes say 200 generations for each substitution to complete, then there will be 20 substitutions going on at any one time (after the process has been going on long enough for 20 to have started). Ewens showed that the substitution load for a single generation (which he and Kimura identify as being the same as the substitution cost and the cost of natural selection) is given by the difference between the optimal genotype (the genotype that has all 20 of the favored alleles) and the average genotype. The problem that Ewens pointed out is that it is highly unlikely that any individuals of the optimal genotype will even exist in a finite population. This is due to the fact of the rarity of some of the favored alleles in the population because they have only recently started moving towards fixation. Notice that half of the favored alleles will have frequencies of 50% or less, making it highly unlikely that even one individual will exist with all or even a very large majority of the favored alleles in a finite population.

Ewens then used the statistics of extreme values to determine that it was unlikely that any individual would exist with a fitness more than 4 standard deviations above the average fitness in a finite population (a population of 100,000). He then showed that this fact greatly reduced the substitution load for multiple substitutions in a finite population. Ewens showed that a diploid animal species could drive up to 6 beneficial substitutions per generation with a reproductive output of 1.98 children per parent (meaning that each couple needs to have about 4 children - something even the most slowly reproducing mammalian species are capable of). There is at least one possible criticism of Ewens' demonstration that 2 offspring per parent is sufficient to drive the number of substitutions actually observed in genetic comparisons of various animals. This is the fact that the reproductive excess of 0.98 offspring per parent to drive the substitution, while well within the capabilities of even the most slowly reproducing species, is nonetheless higher than the amount estimated by Haldane (0.1 or 10%). There are several answers to this objection. The first is that Haldane did not make a very good case for the 10% reproductive excess limit. Haldane makes no case for this figure in "The Cost..." other than to note that the selection intensity on babies born in London (in the late 1940's, I believe - not exactly the most selective environment in the world, to say the least) demonstrated a selection intensity of 3% based upon birth weight (pg. 512). In fact, Haldane later mentions that the selection intensity in the peppered moth (Biston betularia) around 0.5 (50%) on pg. 521. Therefor it is not terribly surprising that some find Haldane's claim that the intensity of natural selection rarely exceeds 10% to be questionable (and at least worthy of further investigation). Another consideration that must be made is that the reproductive excess requirement predicted by Ewens is dependent upon the selection coefficient.

For more of the mathematical details of Ewens' work, see Ewens' on the Substitutional Load.

Quotes from Sewall Wright and Others that Support Ewens' Claims

Future Directions
There is still much to be learned about the process of natural selection and genome changes over time. Creationists like Walter ReMine seem to operate under the mistaken impression that scientists are engaged in a gigantic conspiracy to "obscure" and "brush aside" Haldane's Dilemma and other problems with the theory of evolution. In order to know whether or not the the substitution cost even has the potential to be an issue in real world evolution, there is still much to learn. One thing that has to be determined is the number of genetic differences between humans and chimps that were actually driven by natural selection. The first step will be to identify the genetic differences between humans and chimps. Then those differences will have to be evaluated to determine which of those genetic differences have any effect upon human or chimp fitness - these are the only ones that may have been driven by natural selection. Only when we have some kind of idea of the number of substitutions that actually affect fitness will we even know whether or not "Haldane's Dilemma" is even an issue for human evolution. If the number of substitutions is less than Haldane's limit (1,667 for the human / chimp lines), then Haldane's Dilemma is not an issue at all. If the number is greater than 1,667 fitness enhancing substitutions, then the nature of natural selection as it actually occurs in the wild will need to be examined carefully. Is the hard selection, deteriorating environment scenario as envisioned by Haldane always (or mostly) the case, or is the environment always deteriorating but selection is soft, or will the fixation of positive, fitness enhancing mutations be common? Each of these scenarios play a role in how high the substitution cost is, and we will never have any idea of whether or not the cost is really a factor in human evolution without a detailed understanding of how natural selection actually operates in nature. Scientists are currently working on the answers to most (if not all) of these questions.


Remember, Haldane's 1957 paper was a theoretical treatise on the cost of natural selection. Here is Haldane's conclusion, which is correct in both points:
"To conclude, I am quite aware that my conclusions will probably need drastic revision. But I am convinced that quantitative arguments of the kind here put forward should play a part in all future discussions of evolution."

Please e-mail me (Robert Williams rwms@gate.net) with suggestions, comments, or criticisms.

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