I will be arguing that Haldane's Dilemma is a fatal flaw in Evolutionary Theory. First round is for acceptance.
I accept the challenge and wish my opponent luck.
What is Haldane's Dilemma?
Haldane's Dilemma is a problem in Evolution first pointed out in the 1957 paper, "The Cost of Natural Selection".(1) In this paper, Haldane mathematically demonstrated that the rate of ape-to-human evolution would have been to slow to have actually occurred within accepted evolutionary timescales.
Extrapolating on Haldane's data, one finds that, in a hypothetical 10 million years of ape-to-human evolution, only ~1,600 beneficial nucleotide substitutions could have occurred.
In other words, there could only be 1,600 “letters” in human DNA that could be different than those of their ape ancestor. This means that all the remarkable adaptions humans supposedly underwent since we diverged from our great-great-great[...]-grand-ape-parent would have to be the result of only 1,600 letter substitutions in our DNA!
Supposedly, since they evolved from apes, humans tripled their brain size, gained bipedalism, physical endurance, an appreciation for music, ability to speak, perform calculus, build pyramids and fly to the moon! And all this while losing two chromosomes!
Is it possible that all of these things which distinguish us from our hypothetical ape ancestor can be explained by a mere 1,600 nucleotide replacements?
1,600 is miniscule compared to the 3 billion nucleotides we have in total.
Here is a demonstration of how one arrives at the 1,600 number:
A population of our hypothetical ape ancestors could not absorb more than 1 beneficial single-point mutation every 300 years. When I say “absorb”, I'm referring to the spread of the new mutation to every living individual of the population.
In other words, from the time the first beneficial mutation occurs to the time every living member has it, it takes at least 300 years.
Let's say it's been 10 million years since the human lineage broke off from our hypothetical ape ancestor. (I'm being generous with 10 million years since Evolutionary Theory actually posits less time for humans to evolve from apes.)
(10 million / 300) = 33,333
That would gives us enough time for 33,333 nucleotide differences, but wait, we have to account for recombination due to sexual reproduction which cuts the chance of a mutation being passed on by half! So...
33,333 / 2 = ~1,600
To resolve Haldane's Dilemma as I've presented it, my opponent must show that either
A) My math fails to account for relevant factors that would increase the number of plausible substitutions within evolutionary timescales, or
B) Argue that a mere 1,600 letter differences in DNA composed of 3 billion can account for all the differences between humans and our hypothetical ape ancestor.
If he fails to do so, the Dilemma remains unresolved as a fatal flaw in Evolutionary Theory.
Haldane died before he solved the problem, so I wish my opponent luck!
(1) J.B.S. Haldane, "The Cost of Natural Selection", Journal of Genetics, Vol. 55, 1957 p:511-524
My argument will rely on demonstrating that Haldane's calculations made a number of severely incorrect assumptions that do not accurately reflect nature nor the evolution of humans from a primate ancestor. Instead of just focusing on my opponent's calculations (I will address them in a later round if necessary), I will detail the main parts of Haldane's Dilemma and show where he went wrong. First I will detail the various assumptions Haldane made, and then proceed to refute them.
I confirmed that all of these existed in the actual document used by my opponent before using them.
1) Before Haldane begins his calculations, he states that "a sudden change occurs in the environment." The change is supposed to be detrimental and leads to a harsher, more exacting environment. At the same time he assumes a constant population.
2)At the same time he states that the "reproductive capacity is lowered."
3) Haldane generates a 'cost of substitution' which is supposed to assign a constant to the amount of individual organisms needed to produce a beneficial substitution. Although he does not clearly state what the cost represents, it can be inferred that it is the number of deaths needed before a 'good' change happens in the DNA AND becomes common in the overall gene pool. He uses the number 30, meaning that 30 times the population must die before a good change is permanently added.
Ex. Pop.=1000, Cost=30 `58; 30000 deaths before change
4)He links this substitution cost with the overall fitness of the population. This means that once a beneficial mutation first appears, the overall fitness of ALL other individuals goes down and the 'new' one stays constant.
5) His '300' number that my opponent used in his argument is not backed up by any calculations. Haldane says, "I think n=300... is a more probable figure." He does this to generate in his calculations a low intensity of selection.
6) Haldane assumes that changes due to genetic drift and gene changes happening simultaneously are uncommon in evolution and does not account for them in his assessment.
1) An important thing to note is that in the last 10 million years, the environment has not undergone rapid changes, such as a meteor strike or massive volcanic eruption. It has remained relatively constant, with the exception of several climate shifts and ice ages. However, Haldane assumes from the beginning a deteriorating environment. This does not accurately reflect nature, nor evolution. The majority of change occurs similarly to 'soft selection' where good genes find their way into the gene pool gradually, and do not necessarily 'compete' with others.
2) For some reason, Haldane assumes the reproductive capacity is lowered. His calculations show he placed it around 1.1, meaning each individual would produce, on average, 1.1 children. However, most mammals can sustain a stable population in an ancient (non-deteriorating) environment with a ratio of close to 2.
3) There are various issues with Haldane's substitution cost. One is that as population increases, the cost should go down. This has to do with simple probability and also increased competition that would promote widespread but slow change. Additionally, the cost does not account for sexual recombination, which causes fixation faster. This would reduce both the '30' and '300.' Finally, it doesn't account for simultaneous changes. Here, if two good changes were approaching fixation, and an organism without either dies, it would have died for two changes, not one. Therefore, the cost would be halved during simultaneous changes.
4) As previously stated, the majority of selection happens from a process similar, but not exactly, soft selection. Just because an organism has a higher chance of survival with a new gene does not mean that all the others will suddenly become less adapted to the environment. Their chance of survival remains constant, and this is not represented in Haldane's work.
5) The obvious problem here is that 300 comes from nowhere. He comes up with the number to make his calculation prettier, and in a way where he changed a dependent variable to fit an independent variable. There is absolutely no definitive scientific reason why the number should be 300.
6) Genetic drift (selection caused not by advantage, but random events) actually accounts for a more significant portion of the changes than Haldane assumed. Moreover, simultaneous fixation is, in fact, extraordinarily common. This occurs when certain genes are fixated at the time. Due to sheer amount of nucleotides, this is very common, and often occurs with more than one nucleotide. However, Haldane completely ignores it, even though it would greatly change the outcome.
1) Genes are not passed down individually. They are attached to each other, so recombination is more efficient. This means that some 'meaningless' changes would be passed on with the same efficiency as 'good' ones.
2) There is possible no dilemma at all. Because DNA decays relatively quickly, we cannot recover any from our primate/common ancestors. Even if we assume that Haldane is correct, 1667 may be enough nucleotides to cause a difference. Besides, because our other ape cousins evolved from this ancestor, their would be 3333 differences between us and them. This may be the case. The only major difference between humans and other apes is a structural difference in one acid: sialic acid, which resulted from only 92 nucleotide deletion. This acid has major roles in various developments in primates, so it could account for the majority of our difference.
My main points:
1) There is no deteriorating environment.
2) '300' has no basis.
3) The substitution cost is unreliable.
4) Haldane doesn't account for genetic drift nor simultaneous substitution.
5) There may not be a dilemma.
I mainly used this round for a general assessment of Haldane's work to show its overall unreliability. I will answer, to my best ability, any specific objections raised by my opponent in the final two rounds.
I'd like to correct a huge mathematical error I made in Round 1 that Con graciously led slide.
I carelessly presented 1,667 as being the result of [10 million years / (300 generations / 2)]. As you may have noticed, this makes no sense.
Allow me to backtrack and correct myself.
10 million years = time since human lineage broke off from ape ancestor
300 = number of generations Haldane figured, on average, would be required for a beneficial mutation to become “fixed” or “common” in the population of pre-humans
20 = number of years per generation, on average
1,667 = 10,000,000 / (20 * 300)
Now let me address Con's points.
According to Haldane, selection pressure may result because “a sudden change occurs in the environment”, but Con argues that “in the last 10 million years, the environment has not undergone rapid changes”. However, Haldane deals with Con's objection in the next sentence: “the general conclusions are not affected if the change is slow.”
Con objects, “For some reason, Haldane assumes the reproductive capacity is lowered [when] a sudden change occurs in the environment.” Haldane meant the population's overall reproductive capacity. Haldane isn't trying to say every female suddenly lost the ability to have as many offspring, only that the majority of them are now less likely to have the usual number of babies, being less fit. The few females who do posses the beneficial genes will be able to birth the same, or even greater, number of offspring, but it won't be enough to immediately bring the entire population's overall reproductive capacity back to where it was.
I don't see the impact of Con's “mammal” point.
Con argues “There are various issues with Haldane's substitution cost. One is that as population increases, the cost should go down.” This is simply not true.
For example, imagine a population of 10 gorillas. 4 of them are pink. For the next generation to have 5 pink gorillas, the cost is a reproductive rate of 1.25.
Now, take a 2nd population of 500 gorillas with 4 pink ones. For the next generation to have 5 gorillas, the cost is still a reproductive rate of 1.25.
Con says “the cost does not account for sexual recombination, which causes fixation faster”, failing to realize that Haldane actually did account for recombination.
Con's objects, “it doesn't account for simultaneous changes. Here, if two good changes were approaching fixation, and an organism without either dies, it would have died for two changes, not one. Therefore, the cost would be halved[...]”
This is irrelephant and has no bearing on the cost. Even if an individual lacking 2 good traits dies, it won't increase the reproductive rate of those that do have the new traits.
Con says “Just because an organism has a higher chance of survival with a new gene does not mean that all the others will suddenly become less adapted to the environment. Their chance of survival remains constant, and this is not represented in Haldane's work.”
Let's assume this is true for just a second; it wouldn't damage my case in the slightest! If those individuals without the new trait maintain their fitness, instead of losing it, it only hurts the chances of the new trait getting substituted into the whole population, since those without the new trait are being stubborn and slowing the substitution of the new gene with their own old-fashion genes. Competition among members of the same species exists, so some members gaining fitness may result in a loss of fitness among other members.
Con says “His '300' number that my opponent used in his argument is not backed up by any calculations. Haldane says, "I think n=300... is a more probable figure." He does this to generate in his calculations a low intensity of selection.“
Con is not just incorrect, he contradicts himself. Haldane is not trying to account for low intensity selection, but moderate intensity selection: in other words,realisticselection, although he does point out that his estimation allows for periods of strong selection pressure (“DISCUSSION” on page 20).
Con's self-contradiction lies in the fact that here, he's claiming Haldane's number is not reasonable because it favors low intensity selection, but previously, Con tried to discredit Haldane's calculations by arguing Haldane favored strong intensity selection: “the environment has not undergone rapid changes [like Haldane says], such as a meteor strike or massive volcanic eruption. It has remained relatively constant”.
So Con is trying to undermine Haldane's paper by suggesting selection is less intense than Haldane thought, yet more intense than Haldane thought.
Con goes on, “There is absolutely no definitive scientific reason why the number should be 300.” Maybe Con didn't read page 20 of Haldane's paper.
Yes, 300 generations per fixation is an estimate, but Haldane showed the math he used to justify this number on page 20. For example, he argues 43 generations per fixation is intense selection, and rare, such as what happened to the Peppered Moth. If Con likes, he can propose a number greater than 300 number (which would help my case immensely), or a smaller number. His choice!
“The obvious problem here is that 300 comes from nowhere. “ This is simply not true, and again, I urge Con to read page 20 of Haldane's paper.
Con says “Haldane assumes that changes due to genetic drift and gene changes happening simultaneously are uncommon in evolution and does not account for them in his assessment.”
I'm not sure how Genetic Drift is relevant. Genetic Drift is, by definition, random, and Con provides no reason for us to think the randomness of Genetic Drift would hurt my case, instead of being neutral or even favorable towards it.
Con says “simultaneous fixation is, in fact, extraordinarily common. This occurs when certain genes are fixated at the time. Due to sheer amount of nucleotides, this is very common, and often occurs with more than one nucleotide. However, Haldane completely ignores it, even though it would greatly change the outcome.”
I'm not sure why Con brings this up, since it's completely neutral to both of our cases, just like Genetic Drift. It seems Con is aware of this, since he said “it would greatly change the outcome”, making sure not to claim it would sway the outcome in any specific direction.
Simultaneous fixation of nucleotides can happen for both favorable, neutral, and harmful mutations.
Con says “Genes are not passed down individually[...] recombination is more efficient. This means that some 'meaningless' changes would be passed on with the same efficiency as 'good' ones.”
This is not relevant... at all. I'm not sure how meaningless changes sway the facts in Con's favor.
Con says “Even if we assume that Haldane is correct, 1667 may be enough nucleotides to cause a difference.”
Considering that we differ from chimpanzees by 35,000,000 nucleotides, this isn't even slightly plausible.(2)
Perhaps my own mathematical mistakes hurt my case more Con's actual arguments. I await Con's rebuttals.
In this round I am simply going to address the points PRO has contrived.
These include the ones I made in my prior argument that I forgot to include.
Con says that “Haldane used the number 300 to account for rates that were realistic to him. Instead of using constants and solving for a variable, he used a variable to make another variable look reasonable. That is bad math.”
Bad math? No, there's nothing wrong with Haldane's math. But perhaps he should have derived the number from first principles. Let's take the number 43 instead, which we know for a fact to represent rapid fixation as in the case of the Peppered Moth.
So assuming that, on average, our ancestral population had a beneficial mutation reach fixation every 43 generations (instead of 300):
10,000,000 years / (20 years per generation * 43 generations) = ~11,000
Now all the traits that make us human, in contrast to our ape ancestor, must be accounted for by 11,000 base-pairs. This is not plausible: we differ from chimps by 35 million base-pairs, over 3,000x that number! And this is not even counting insertions or deletions.
Haldane's Dilemma remains fatal for Evolution whether you plug in 300, or 43.
Con says that “the mammal point is important in showing that human ancestors were able to sustain high reproductive rates as we are, of course mammals, but Haldane does not show this in his calculations.”
This is incorrect. Mammals do not have a high reproductive rate; in fact, they have one of the lowest in the animal kingdom: i.e. Orangutans give birth to a single offspring every 6 years.(2)
Con says that “I would like to remind PRO that the cost of substitution is "the substitution of one allele by another, if carried out by natural selection based on juvenile deaths."
This is also incorrect. The cost of substitution is the reproductive rate required to make a hypothetical scenario plausible. If the cost cannot be payed, then the scenario is not plausible, and a practical person must conclude it didn't happen. It makes no sense for Con to claim the cost of substitution is “the substitution of one allele by another”. That's like saying the cost of substitution is a substitution, or the cost of a Honda Civic is a Honda Civic.
Con says that “Obviously, with this low population, fixation would take a long time to occur. However, if the population was much higher, say, 95,000 (the current pop. of the western gorilla) fixation would happen really fast.”
This makes no sense. Population size is almost irrelevant to the cost. How in the world is a larger population going to result in the faster fixation of a mutation in the entire population?
Con has it backwards. Say I have 10 mice. 9 are black and 1 is pink. The pink phenotype can be fixated in the population by simply killing off the 9 black mice, leaving the 1 pink mouse. I'm not sure why Con thinks increasing the population size would make fixation happen faster. That means more individuals have to die for fixation to occur. You have to remember that increasing the population size increases the number of individuals that do not have the mutation to be substituted, and it's not as if increasing the number of non-mutated individuals makes the fixation of the mutation in the entire population occur any faster.
Allow me to reiterate: the cost of substitution cannot be reduced by increasing the population size.
Con says “[t]his is because as the population gets larger, more variations occur and recombination adds even more variation and causes fixation faster.”
Yes, a larger population means more variations among the population, but not in an individual. Obviously, a population of 100 will receive mutations 100x faster than a population of 1. However, it's a non-sequitur to say that more variations among a population means that any single, particular variant will get fixated in the entire population faster.
Con says “Haldane, and my opponent's calculations, only assume that one change is approaching fixation at a time. In other words, they assume that one gene change occurs, takes 300 years to successfully mix into the gene pool, and then another begins.”
This is incorrect, and Haldane explicitly accounted for simultaneous substitutions in his calculations. I suggest Con read page 22 of Haldane's paper, where he says:
“Can this slowness be avoided by selecting several genes at a time? I doubt it, for the
following reason. Consider clonally reproducing bacteria, in which a number of disadvan-
tageous genes are present, kept in being by mutation, each with frequencies of the order of
104. They become slightly advantageous through a change of environment or residual
genotype. Among 1012 bacteria there might be one which possessed three such mutants.
But since the cost of selection is proportional to the negative logarithm of the initial
frequency the mean cost of selecting its descendants would be the same as that of selection
for the three mutants in series[...]”(emphasis mine)
Regardless, only one beneficial mutation can be fixated at a time, for interactions between concurrent mutations which are otherwise beneficial on their own, are antagonistic.(3)
Con says, “I would like PRO to refer me to where Haldane accounts for sexual recombination, as I have read his article and cannot seem to find it.”
Haldane does not explicitly say he accounts for sexual recombination. However, contrary to what Con claims, sexual recombination does not cause fixation to happen faster. It causes it to happen twice as slow, since a beneficial mutation only has a 50% chance of being passed on from one mother to the next generation as opposed to the case in asexual organisms, where it is almost certain to be passed on. It would be better for me to say that Haldane's math actually doesn't account for sexual recombination, since his math assumes that sexual recombination doesn't reduce the speed of fixation. But this helps my case, not Con's.
Con says, “Genetic drift would increase the number of total mutations, no matter good or bad, so the net nucleotide difference would be higher. Let's say 1000 changes occurred due to drift (I am making this number up; it could be anything). This would automatically bring 1667 up to 2667.”
Haldane's cost of substitution applies both to beneficial mutations, and neutral mutations which spontaneously accumulated in the population and later became beneficial due to environmental change. It's not reasonable to suggest neutral mutations would bring the 1667 number up any higher, since it's extraordinaryly unlikely for neutral mutations to get fixated in a population. And the 1667 number only applies to fixated mutations. Natural Selection cannot pressure a neutral mutation to get fixated, so Con is appealing to mathematically implausible absurdities to raise the 1667 number. Con's appealing to the chance of a particular, neutral mutations to spontaneously make its way into every single individual in a population, even while faced with factors that actively seek to prevent this from happening, like genetic drift. That's not reasonable.
Con says, “Considering the average difference between humans is up to 30 million nucleotides (and this is just a count of single nucleotide polymorphisms), my point still stands.”
This is irrelevant. All that matters is the fixated mutations in the human population, because that is what distinguishes us as humans from our supposed ape ancestors.
PRO calculates that Haldane's dilemma applies whether 300 or 43 is used. I did mention how this number means absolutely nothing in the previous round. It must be noted that this number stems directly from the substitution cost, where Intensity of Selection = Substitution cost/number of generations. Therefore, if I can show that the cost was wrong, this entire point will not matter. Haldane's entire argument would be rendered useless. Since this debate was over Haldane's Dilemma as a whole, as long as I can demonstrate the invalidity of Haldane's paper, this individual point should not matter.
Additionally, it still may just be 1667 or 11000 differences that account for our descent, as I previously pointed out that only one major difference, the production of sialic acid, exists between us and other primates. This is only caused be 92 base pairs. My opponent only makes an argument from disbelief saying that it is not plausible without any scientific studies on significant genetic differences between humans and primates.
It does not matter how fast mammals produce offspring, but how many they do. Orangutans, the primate used by my opponent, has the longest time-span between children of ALL great apes. Plus, since they mature at age 15 and live up to 40, this rate is certainly enough for the approx. reproductive rate of 2 I gave earlier. PRO does not reconcile this would the fact I mentioned earlier that Haldane accounts for a rate of only 1.1.
"The cost of substitution...plausible."
I'm not even sure where PRO came up with this. I took the disputed quote straight from Haldane's paper. It is not the reproductive rate, it is the number times the number of generations needed for an allele to fixate. PRO completely ignored the second clause of my excerpt which stated "if carried out by natural selection based on juvenile deaths."
"How in the world...population?"
Let me explain this. I shouldn't have said faster, I should have said at a higher rate. If the population is low, yes, fixation can occur quicker. But there is also a MUCH higher chance that it never occurs. In a group of 10, where 2 carry a mutation, only those two have to die. In a group of 100, with 20 mutations, all 20 have to die. It is unlikely that a greater number would die, so that allele would spread much faster. Of course, these numbers are extremely exaggerated but the concept still applies. A larger population would be able to sustain more changes because it is, quite simply, larger. A wider gene pool would develop more mutations. More variation would occur in recombination. All of these factors would lead to a healthier gene pool with more room for development and sustained improvement. The cost is reduced by healthier fixation rates and more variations leading to more fixations. That's why genetic bottlenecks generally result in a species' decline.
"However, it's a non-sequitur...faster."
That's the point, I'm not saying a SINGLE variant will fixate faster. MORE variants would fixate in the end, though.
In the highlighted portion of my opponent's argument, he left out the crucial last phrase of Haldane's sentence. It reads, "the mean cost of selecting its descendants would be the same as that of selection for the three mutants in series, though the process may be quicker. Of course the total number of deaths would have to go up, it has to do with the size of the population being larger. The larger the population, the more mutations. More deaths would occur to account for it, but they would be in a shorter time span. If 100 organisms had to die, the deaths would happen faster in a constant population of 50 than in one of 10.
"only one beneficial mutation...antagonistic."
One, this only deals with beneficial mutations. Like I said before, not all changes have to be good. Two, simultaneous substitutions don't have to be always antagonistic, as they can be tightly linked and not separate during recombination. In fact, most speciation occurs because of mutations on key genes that are tightly linked on chromosomes. This generates bigger changes that fixate faster. Three, many other studies have shown that simultaneous substitutions are quite common (sources 2, 3).
"Haldane does not explicitly say he accounts for sexual recombination."
This contradicts PROS prior assertion that "Haldane actually did account for recombination."
"sexual recombination does not cause fixation to happen faster."
First, as most mammals have about 2 kids per organism, or 4 per 'couple,' and population remains constant, recombination will not reduce the appearance in the gene pool. It will either stay constant or increase. In fact, since most beneficial changes occur in important genes (ones that control central cell functions, etc), and these genes appear at the center of the chromosome, a process known as hitch-hiking ensures they almost certainly will be carried on to the next generation. If the voters need more evidence on how recombination speeds up fixation and lowers the substitution cost, they can visit sources 4 and 5.
"Haldane's cost of substitution...neutral mutations"
Haldane said, incorrectly, on genetic drift, "such events are not perhaps very frequent even on an evolutionary time scale"
So he didn't account for drift.
"it's extraordinaryly unlikely...to get fixated"
Correct, but recombination can. Hitchhiking allows neutral alleles to fixate as quickly as good alleles. A random change can occur in a central gene, but have no effect on the organism, and may approach fixation. This is not uncommon, since 1% of our nucleotides are inactive. That's 30000000. It's not a mathematical implausibility that some of these have changed and fixated due to recombination.
"All that matters...population"
My point here that huge variation exists even between humans. Considering that only two amino acids make up a difference between us and chimpanzees, a large number of our differences can easily be a result of random changes and mutations.
Over this debate, I have raised a number of objections to Haldane's argument. All that is required to discredit it entirely is one valid issue. Deciding whether any of my points was strong enough to do so is for the voters to decide. Over the course of the debate, my opponent has dismissed 6 of my arguments as irrelevant, hardly hesitating to justify. He has failed to properly address the following issues:
1) Haldane's mistake in saying the environment underwent rapid changes in every part of the last 10 million years. He merely wrote it off by quoting Haldane saying that the conclusions are unaffected.
2) Haldane's failure to address reproductive rates properly. He clarified (unnecessarily) what Haldane meant by reduced reproductive rates, then by citing a fact about chimpanzees.
3) Haldane's failure to even mention the effects of sexual recombination in his argument. PRO argued that recombination would have a negative impact on fixation, without citing sources explaining why, when virtually the entire scientific community agrees that recombination speeds up fixation.
4) Haldane's ignorance of the process of soft selection. Haldane incorrectly assumes that a beneficial gene in one organism would lower the fitness of others, and my opponent uses circular reasoning and argues for hard selection (natural selection in its most theoretical form) with a hypothetical scenario.
I hope this and all prior arguments are enough to convince voters.
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