Talk:Haldane's dilemma

Article Neglects to Mention Kimura's Resolution

First, it should be noted that many anti-evolution arguments fixate on Haldane's observations as evidence against evolution. This is visible in the references, which include some anti-evolutionary articles. I suggest moving the creatinist references into their own section explaining the importance of this topic in anti-evolutionism.

Second, this puzzle was solved by Kimura's neutral theory (https://en.wiki.x.io/wiki/The_Neutral_Theory_of_Molecular_Evolution). See also this article (https://inference-review.com/article/the-neutral-theory-of-evolution). It seems critical to include discussion of this connection in this article. — Preceding unsigned comment added by 24.207.136.42 (talk) 18:48, 7 April 2023 (UTC)

Article is written for people already possessing advanced knowledge of Haldane's Dilemma

This article is written for an audience that already possesses advanced knowledge of what Haldane's Dilemma is, when the reason people come to wikipedia is to learn what a subject is about in the first place. The article makes barely any attempt to clarify what the problem is, and what the implications are in any way that a layperson might be able to understand.

Haldane's dilemma is a limit on the speed of beneficial evolution

This is extremely vague, and immediately overshadowed by someone's unsourced ranting about creationists. Then we are quickly assured that Haldane was probably wrong, before we have any idea what he was wrong about.

The next small section is about as close as this article gets to clarifying what the actual substance of Haldane's argument:

In the introduction to The Cost of Natural Selection Haldane writes that it is difficult for breeders to simultaneously select all the desired qualities, partly because the required genes may not be found together in the stock; but, writes Haldane (p. 511) "especially in slowly breeding animals such as cattle, one cannot cull even half the females, even though only one in a hundred of them combines the various qualities desired."

That is, the problem for the cattle breeder is that keeping only the specimens with the desired qualities will lower the reproductive capability too much to keep a useful breeding stock.

This is bordering on being cryptic. A reader not already familiar with the subject of Haldane's Dilemma, will probably not even make the connection that this refers to the population cost for fixating a single genetic trait within a population.

From here on it is all mathematical formulas and pop-gen jargon. The overall substance of this subject-matter does not have to be veiled from the layperson in such complex language, does it? 71.161.201.225 (talk) 16:30, 29 December 2013 (UTC)

I would go so far as to say that the article in incomprehensible

Every symbol introduced needs to be clearly defined

One example is Ln(S0/S) Is S = 1 - S0

As for the intro to the maths !!!! — Preceding unsigned comment added by 80.4.167.103 (talk) 10:43, March 16, 2019 (UTC)

I agree that the maths sections are more or less useless as they currently stand. I think it would be nice to keep some minimal mathematical examples so that it will be clear that this limit is a quantity calculated from some model which makes some set of assumptions. But, it seems reasonable to trim the maths section back to a more useful example. LarryBoy79 (talk) 09:53, 18 March 2019 (UTC)

1992 - eminent evolutionary biologist G.C. Williams declares Haldane's Dilemma never solved

...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.

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

Why should this point of view not be reflected in the article? Why the mythology that Haldane's Dilemma was settled?

Do people defending the current version of the article not find this a bit awkward? 70.16.207.189 (talk) 15:33, 14 January 2014 (UTC)

Update, I added a reference to G.C. Williams discussion on Haldane's Dilemma to the article.

This is a mainstream scientific journal article dealing directly with the subject and it should be included.

Williams clearly views Haldane's Dilemma as a challenge, as recently as the 1990's. Anyone who is skeptical of this can read the article for themselves here: http://books.google.co.in/books?id=nTJlZ9QTssYC&pg=PA145&lpg=PA145&focus=viewport&vq=Haldane%27s+Dilemma

"I think the time has come for a renewed discussion and experimental attack on Haldane's Dilemma"

72.73.109.8 (talk) 18:20, 20 January 2014 (UTC)

There isn't much to discuss. We all make simple mistakes. Williams simply overlooked the fact mentioned in the introduction: "while sexual recombination means that two can be selected simultaneously so that both reach fixation more quickly". MvH (talk) 17:23, 13 April 2015 (UTC)MvH

Haldane's dilemma may explain why so many species use sexual reproduction

The introduction briefly mentions something that deserves far more attention: The argument in Haldane's dilemma does not apply to species that use sexual reproduction.

This raises an interesting point, one that can be tested. Namely: if the argument in Haldane's dilemma has merit, then it implies that species with sexual reproduction can evolve much faster (counted per generation) than species without sexual reproduction.

That in turn would explain lots of things (e.g. why there are so many species that use sexual reproduction despite of the costs, why the Timeline of the evolutionary history of life seems to be faster in the last 600 M-years compared to the 3 Giga-years before that, etc.).

Rather than completely dismissing the dilemma, lets make sure that it is clear throughout the article that the dilemma (if it applies to any species at all) that it only applies to asexual species (yes, I am aware that the distinction is not quite as clear-cut as one would imagine, genetic data can still travel between members of an asexual species (e.g. through a virus), and perhaps such things may have been necessary for evolution to work in the time-scales that it did). MvH (talk) 14:00, 13 April 2015 (UTC)MvH

Sources would be needed to support this viewpoint. --Harizotoh9 (talk) 15:30, 13 April 2015 (UTC)

I don't propose to put the "may explain..." line into the article. But I think the article can be improved significantly with modest changes. The introduction says "while sexual recombination means that two can be selected simultaneously so that both reach fixation more quickly" and 3 sources are given there. This fact is crucial to understanding the dilemma, but it is completely ignored in the rest of the article. The examples (cattle, peppered moth) make matters worse because these are examples where the dilemma does not apply at all. This unnecessarily makes the article look like nonsense. MvH (talk)MvH

I believe all of Haldane's arguments apply to sexual organisms. Certainly, clonal interference exists in asexual organisms and not sexual organisms, but that is a different issue. LarryBoy79 (talk) 10:59, 8 January 2019 (UTC)

Yes. The model described in this section of the article (and on p.518 of Haldane's original paper) assumes sexual reproduction. However, when Haldane applies his argument to many loci undergoing simultaneous selection, in the discussion on p.520 and subsequent pages of his paper, he assumes that all the relevant loci are unlinked and have independent effects on fitness, and that the population is in linkage equilibrium. When many loci are involved, and all the selection coefficients are as large as Haldane had assumed were reasonably possible, these assumptions have consequences (other than the limit on the rate of substitution) which seem to me to be biologically absurd, so I doubt that they would ever be likely to hold in practice.

David Wilson (talk · cont) 12:22, 8 January 2019 (UTC)

Care to elaborate on what those consequences would be? I'd love to fill up the 'Evolution above Haldane's limit' section a little, but I don't have a ton of free time at the moment. At some point I can fill it in from some of the references that are already in the article, but more references are always welcome. Are you referring to simply unreasonably large variance in fitness between individuals or something else? LarryBoy79 (talk) 13:25, 8 January 2019 (UTC)

If L is a set of loci satisfying the three assumptions I listed, then the fitness of any genotype for L, relative to that of the fittest, is the product, over all loci in L, of the fitness of the allele of that genotype at any particular locus, relative to that of the fittest allele at that locus. Haldane considers values of up to 0.1 for his "intensity of selection" to be reasonably typical, and admits the fact that in Biston betularia, with selection on differences resulting from a single locus, it was as high as something like 0.7. For an intensity of selection of 0.1, the average fitness of the population relative to that of the fittest genotype is e^-0.1 ≈ 0.9, so the fitness of the least fit genotype relative to that of the fittest will be at most that.

Consider now a set of (say) 50 loci at each of which the fitness of the least fit allele relative to the fittest is 0.9. If the three assumptions I listed are satisfied by these loci, then the fitness of the least fit genotype relative to the fittest is 0.9⁵⁰, or, equivalently, the fitness of the fittest genotype relative to the least fit is 0.9^-50 ≈ 194. Suppose now that at the start of the the period over which the population undergoes selection, when all, or nearly all, of the population has the least fit genotype, a few individuals of the fittest genotype were to be introduced into it. We would suddenly have a set of individuals producing 194 times as many offspring that survive to reproduce as nearly all of the rest of the population. It's this sort of consequence that I was referring to as seeming to me to be biologically absurd. If the species is one whose individuals are physically incapable of producing more than (say) 20 offspring over the course of a lifetime, for instance, then the mere appearance of these fittest individuals in the population would have resulted in a disastrous drop in its absolute fitness by a factor of something like 10 or more.

Of course, in Haldane's model this scenario is ruled out by his (certainly very reasonable) assumption that the overall intensity of selection is generally at most around 0.1, which, under the three assumptions I listed, limits the sum of all the selection coefficients to be no greater than that. Thus while it's possible for the selection coefficient at any single locus to be as high as 10%, this can only be true if the selection coefficients at all the other loci are very small. However, if you drop the assumption that all the loci have independent effects on fitness (for example), then the bound on the intensity of selection no longer imposes any obvious limit on the sum of the selection coefficients, merely on each of the individual selection coefficients separately.

The upshot of all this is that the three assumptions I listed play just as crucial a role in Haldane's argument as his estimated bound on the intensity of selection. Without them, even when the overall intensity of selection is no more than about 0.1, a much greater rate of substitution than Haldane's 1 per 300 generations is possible.

David Wilson (talk · cont) 23:08, 9 January 2019 (UTC)

It doesn't really strike me as reasonable to allow selection intensities of 0.995 and say that precluding such selection intensities is a flaw in the model. I would tend to think that such high selection intensities result in extinction, just as Haldane said. Even if the event didn't result in extinction it would eliminate virtually all variation from the genome, dropping the effective population size to mid to low tens, and would be exceedingly obvious in any modern studies. While I won't rule out that some organisms somewhere has undergone such an extreme event, it certainly hasn't happened in any species I've ever looked at. Regardless, this discussion is moot unless you can point to a paper making this argument. If you can I would be happy to summarize it and put it in the appropriate section. LarryBoy79 (talk) 09:12, 10 January 2019 (UTC)

It looks like my attempted elaboration wasn't at all clear, since the first sentence of your response indicates to me that you have misunderstood it. But to indulge in further elaboration would have little or no relevance to ways of improving the article, and so wouldn't be appropriate for this talk page. I'm thus unwilling to discuss the matter further. I will however make the following brief points:

• The main point of my initial comment (and probably the only one of any relevance to improving the article) was that Haldane explicitly covered the case of sexual reproduction in his original paper, so the article should definitely not say or imply that his argument "does not apply to species that use sexual reproduction", as asserted in the post at the top of this thread.
• I'm fairly sure the definition of "intensity of selection" you're using is different from Haldane's. The quantity Haldane referred to by that term is I = ln (s₀⁄S ) , where s₀ is the fitness of the fittest individual, and S is the population mean fitness. So, for my contrived example, Haldane's intensity of selection would be I = ln(194⁄1) ≈ 5.27 . Your value of 0.995 looks to me like it's 193⁄194 rounded to 3 decimal places, so I'm guessing it's probably 1 - S⁄s₀ = 1 - e^-I in terms of Haldane's , to which it's nearly equal whenever it's close to zero.

My assertion that dropping the assumption of multiplicative fitnesses allows you to keep the intensity of selection within reasonable bounds without imposing an obvious limit on the sum of the selection coefficients was inferred from the following paper:

• Ewens, Warren (1972), "The Substitutional Load in a Finite Population", The American Naturalist, 273 (949): 273–82

I should stress that Ewens himself does not draw that inference, and I don't know of any other reliable source that does so either, so it's not an assertion I regard as being suitable for inclusion in the article. Ewens does point out, however, that Haldane's model assumes an effectively infinite population size, and argues that in finite populations, the substitution rate can greatly exceed Haldane's limit without imposing a severe genetic load on the population. His actual conclusions would therefore be suitable for inclusion in the article's section on Evolution above Haldane's limit.

David Wilson (talk · cont) 01:45, 11 January 2019 (UTC)