Nunney: The Cost of Natural Selection Revisited (Haldane Dilemma)

Posted 25 February 2008 by PvM

Never too lazy to do some research when ID creationists seem to be lost for arguments I ran across a paper by Nunney in which he shows how Haldane was wrong. All ReMine supposedly was able to do was to object to the fact that Nunney refused to share the software code with ReMine and that ReMine was unable to write the necessary code himself. Haldane's dillema hardly deserves the attention it is receiving from ID creationists but then again, there is not much else for them to focus on.

Nunney's results differ markedly from those of Haldane and ReMine. Considering Nunney's reticence to have his results critiqued and the divergence from other results, his results appear to lack credibility.

Enough whine, let's look at the cheese... (see here for an earlier discussion on the non issue of Haldane's dilemma by Ian Musgrave). The paper in question: Nunney, Leonard, The cost of natural selection revisited, Ann. Zool. Fennici. 40:185-194, 2003

In a constantly changing environment, organisms must continuously adapt or face extinction. J. B. S. Haldane argued that the "cost of natural selection" (also called the cost of substitution) puts an upper limit on the rate of adaptation, and showed that the cost (C) was a decreasing function of the initial frequency of the beneficial alleles. Based on mutation-selection balance and 10% selective mortality, he suggested that the limit to adaptive evolution was about one allelic substitution per 300 generations. I have tested Haldane's results using simulations of a population limited by density-dependent regulation and subject to a constantly changing environment that affects n (= 1–7) independent survival traits, each controlled by a single locus. I investigated the influence of carrying capacity (K), mutation rate (u), number of beneficial mutations per generation (approximated by M = 2Ku) and net reproductive rate (R). Of these, M has the predominant influence. The effect of large changes in R was relatively small. The cost of selection (C) was measured as the shortest number of generations between an allelic substitution at all loci under selection that was consistent with population persistence. The results differed from Haldane's solution. Across a range of conditions, the cost of simultaneous selection at n loci was determined by the linear relationship C = C₀(M) + nC₁(M), where C₀(M) is the intercept and C₁(M) is the slope of the linear regression of C on n, for a given M. The intercept defined a positive fixed cost of substitution, that appears to reflect genetic deaths occurring during the stochastic phase when the beneficial alleles are rare. For M > 1/2, the cost of natural selection is substantially less than Haldane's estimate; however, when M < 1/2, the cost (and particularly the fixed cost) increases in an accelerating fashion as M is lowered. This result has important implications for conserved populations, since for u ~ 5 x 10^–6 the carrying capacity of the population must be 50000 for M = 1/2. To avoid low M, smaller populations should be linked together into a large metapopulation whenever possible. This large unit would be capable of adapting when the isolated parts could not. It also suggests that if M << 1, small gains in K through increases in habitat can have a very large positive influence on the future survival of the population in a changing environment.

In the conclusions Nunney mentions that

Haldane (1957) ended his paper by noting "I am quite aware that my conclusions will probably need drastic revision. But I am convinced that the quantitative arguments of the kind here put forward should play a part in all future discussions of evolution" (p. 523). The results presented here suggest that Haldane was correct that some revision of his conclusions is needed, but they also suggest that he was correct that the cost of natural selection is a real phenomenon that needs to be included in more discussions of adaptations in a changing environment. The concept is made even more relevant as we become increasingly aware of the potential for rapid environmental change, and as more and more natural populations become fragmented in many isolated units.

Perhaps it is time for ID creationists to become more familiar with the facts and depend less on hear-say? According to Scordova, Walter's research is funded by the Discovery Institute, showing once again how ID fails to provide much of any relevant scientific research. As for Walter's 'response' enjoy...

32 Comments

Bob O'H · 26 February 2008

Nunney talked about this at the ESEB last summer. Before the talk I was chatting to another guy and mentioned the ReMine incident, and his summary was "so the guy's lazy as well as stupid". It was a good talk too, tying together the AnZF work (above) and some similar quantitative genetics modelling (IIRC, Mike Lynch's) to show that they give similar results, and also that if climate change is too quick, species won't be able to keep up and will go extinct. He used the full Red Queen quote t demonstrate what he meant:

Now, here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!

caligula · 26 February 2008

ReMine's not the only lazy one. I have had it running in the background for like a year now that I should implement Nunney's simulation independently. You see, I disagree with ReMine that relevant details are somehow lacking in Nunney's paper, making it impossible to evaluate his conclusions. So far as I can see, Nunney gives pretty much enough detail for an independent implementation for anyone who can code. (I can't open the link to Walter's response, but I can guess that Walter is complaining about "not enough detail".)

SteveF · 26 February 2008

Caligula, you correctly predict ReMine's response. The link above doesn't take you to the correct part of ReMine's website (though it does include an attack on Ian Musgrave for a Pandasthumb article, essentially accusing him of quote mining - I'd like to see Ians response to that). What you need to check out is the page "Evolutionists withhold evidence", accessible via the main page. Here he says:

Starting December 19, 2006, I sent emails to Prof. Nunney, expressing my interest in his paper, and requesting access to his simulation software. After several emails, across several months, I still received no reply. Perhaps he had moved on? So on March 7th, I emailed a separate evolutionist professor in his department, again expressing the situation and requesting access to the simulation software. Again, I received no reply. I then switched away from emails, and eventually reached Professor Nunney by phone on April 5th. He acknowledged he had received my emails, and said he did had not responded because I "do not publish in peer-reviewed journals" (his words) – which is evolutionist-speak for Anti-evolutionist! I again requested his software for my examination of his published results and methods. He declined, saying he will not share his software with "people who do not publish in peer-reviewed journals."

SteveF · 26 February 2008

Pondering a little on ReMine's request from Nunney brings to my mind his involvement with another YEC, John Sanford. Sanford has written a book that basically argues that Muller's Ratchet is an insurmountable problem for evolution - genome deterioration as a result of the accumulation of deleterious mutations can't be stopped. In his view, such deterioration is a result of "the fall". Anyway, one solution to Muller's Ratchet, truncation selection, was discussed by James Crow in various papers. A neat description can be found in: Crow, J.F. (1997) The high spontaneous mutation rate: Is it a health risk? PNAS, 94, 8380-8386. and is:

Let me illustrate the consequences of truncation selection with a simple numerical example, using what seem to me to be reasonable values. I'll assume a mutation rate of one per zygote per generation and a mean persistence of 80 generations. Thus, the average fly carries 80 mutations. Assume that the population is truncated so that 10% are selectively eliminated---the 10% with the largest number of mutations. The distribution of random mutations is roughly Poisson. Actually, the variance is a little less than Poisson for the following reason. Each generation of selection reduces the variance, mainly by generating linkage disequilibrium. This is partially, but not completely, restored by recombination and mutation (ref. 45, p. 154). A Poisson distribution with a mean of 80 is essentially normal, so I shall assume a normal distribution with a standard deviation of 8. The mean number of mutations in individuals in the selected group deviates from the population mean by x = zsigma /p, where z is the ordinate at the truncation point, sigma is the standard deviation, and p is the proportion saved (ref. 46, p. 192). Thus, the mean number of mutations per individual in the selected group is 80 - (0.1755)(8)/0.9 = 80 - 1.56 = 78.44. Similarly, the mean number per individual in the eliminated group is 80 + 14.1 = 94.1 (Fig. 2). Thus, the individuals that reproduce and are represented in the next generation have 1.56 fewer mutations than the unselected population. This is more than enough to balance one new mutation per generation. I have used arbitrary numbers, but I believe they are realistic for Drosophila. They illustrate the point that truncation selection of rather small intensity is very effective in eliminating mutations. If the mutant genes act independently, 80 mutations, each causing a fitness reduction of 1/80, would reduce the population fitness to e-1 = 0.37. Thus, 10% elimination by truncation removes more mutations than 63% independent elimination.

What does this have to do with ReMine? Well, Sanford asked ReMine to develop software to do numerical simulations of Crows' model. The results of this modelling can be seen here, in a scanned copy of the relevant pages in the book (hopefully you don't need to register to see them) http://iidb.infidels.org/vbb/showpost.php?p=4570986&postcount=355 So, the above information suggests that ReMine is quite prepared to do modelling work and without any pressing need to contact the authors in question. Now, I've never modelled anything in my entire life and I'm not particularly expert on population genetics. However, looking at the Nunney paper, it strikes me that if there is sufficient information provided by Crow, then there is sufficient information provided by Nunney. Crow's model is simpler, which presumably makes it easier to deal with, but Nunney seems to provide the relevant information. What do those more knowledgable about such things think? Anyway, such musings aside, I've also turned up another relevant paper in this discussion. I think it is free access, but apologies if not: http://jhered.oxfordjournals.org/cgi/content/full/95/4/277

Woodruff, R.C. et al. (2004) Premeiotic Clusters of Mutation and the Cost of Natural Selection. Journal of Heredity, 95, 277-283. Haldane stated that there is a cost of natural selection for new beneficial alleles to be substituted over time. Most of this cost, which leads to "genetic deaths," is in the early generations of the substitution process when the new allele is low in frequency. It depends on the initial frequency and dominance value, but not the selection coefficient, of the advantageous allele. There have been numerous suggestions on how to reduce the cost for preexisting genetic variation that goes from disadvantageous, or neutral, to advantageous with a change in the environment. However, the cost of natural selection for new alleles that arise by mutation is assumed to be high, based on the assumption that new mutant alleles arise in natural populations as single events [1/(2N) of the total alleles]. However, not all mutant alleles arise as single events. Premeiotic mutations occur frequently in individuals (germinal mosaics), giving rise to multiple copies of identical mutant alleles called a "cluster" (C) with an initial allele frequency of C/(2N) instead of 1/(2N). These clusters of new mutant alleles reduce the cost of natural selection in direct proportion to the relative size of the cluster. Hence new advantageous alleles that arise by mutation have the greatest chance of going to fixation if they occur in large clusters in small populations.

They conclude:

An additional example of the possible high cost of natural selection is the estimation that during the evolution of humans and Old World monkeys, advantageous substitutions are estimated to have occurred at the amazing rate of one change about every 10 generations (Fay et al. 2001). There have also been about four to six amino acid substitutions per human diploid genome per generation since human divergence from chimpanzees (Eyre-Walker and Keightley 1999; Keightley and Eyre-Walker 2000). For those substitutions that arose by mutation, there was a potentially large cost of natural selection. There must have been ways to reduce this cost, including small population sizes, soft selection, epistasis, genomic duplications (Johnson et al. 2001), and as we show here, premeiotic clusters of mutation. Although premeiotic clusters of mutation do not eliminate the cost of natural selection, the occurrence of multiple copies of the same advantageous allele at one time in one place can substantially decrease this cost. Furthermore, this reduction will increase the number of favorable mutant alleles that can simultaneously go to fixation in a population. These mutation clusters may therefore increase the importance of mutation in adaptive evolution.

Joshua Zelinsky · 26 February 2008

I'm going to have to disagree somewhat; when doing any form of modeling work it is always a good idea to provide your code on request. This allows more transparency and makes it easier for people to catch possible mistakes. That's one reason some members of the open access movement have actually argued that journals should mandate open disclosure of code.

SteveF · 26 February 2008

Well, I can see where Nunney is coming from. It's his data and he has the right to do whatever he wants with it. I'd be somewhat leery about giving my work to some crank on the internet. Having said that, I do tend to be inclined to think that researchers should provide code on request (including Nunney).

However, it seems to me that this is a bit of a side issue. Reading his paper, it looks as if his model is described in a decent amount of detail. As I said in my post above, I'm not a programmer, but it strikes me that there is sufficient information for someone sufficiently qualified to make a good attempt at replicating his results (as he was perfectly happy to do with Crow's, admittedly simpler, model). If he can't replicate them, then there are some possible ways explanations leading to ways forward:

1) ReMine is wrong
2) Nunney is wrong
3) Replication requires the original code

There's also another issue here; as far as I can tell, ReMine has not attempted to deal with this paper. He has gotten around this by appealing to lack of data. However, when evaluating a studies conclusions, it is generally typical to take them at face value (e.g. the author is honest). Bearing this in mind, whilst it is not unreasonable to try and replicate the results, ReMine should also be taking the study at face value and dealing with it in these terms.

Beowulff · 26 February 2008

caligula: ReMine's not the only lazy one. I have had it running in the background for like a year now that I should implement Nunney's simulation independently. You see, I disagree with ReMine that relevant details are somehow lacking in Nunney's paper, making it impossible to evaluate his conclusions. So far as I can see, Nunney gives pretty much enough detail for an independent implementation for anyone who can code. (I can't open the link to Walter's response, but I can guess that Walter is complaining about "not enough detail".)

Your comment piqued my interest and I decided to read the article as well. Unfortunately, while I have followed an evolutionary algorithms course once, I do not have a background in genetics, or genetic simulations. Therefore, to me, the article does not contain enough information to recreate something equivalent to Nunney's software. It seems to me that he assumes the details I am missing to be common knowledge to his intended audience, or that his readers should be able to distill them from his text. The main detail I think I am missing just from reading this paper is how the mutation works in his simulations. For instance, is it only allowed to randomly change to an adjacent allele value? Or does a mutation randomly choose an allele from a particular prior distribution, say a uniform distribution with A in [1, 2, ..., MaximumNumberOfCycles]? Other details include the exact order in which he applies mutation, reproduction, and selection, or how fecundity is combined with lottery polygyny, but I think I can make a decent guess at those if needed. Since I am now bitten by the curiosity bug, I hope somebody here can enlighten me on what is commonly used in these cases, or give me some pointers on where to find it myself (I tried googling it, but I think I need better search terms). Thanks for any responses.

Reed A. Cartwright · 26 February 2008

I highly recommend reading the section about Haldane's Dilemma in WJ Ewens' Mathematical Population Genetics. In it he describes how the dilemma is an artifact caused by applying results from an infinite population model to finite population models.

SteveF · 26 February 2008

I highly recommend reading the section about Haldane’s Dilemma in WJ Ewens’ Mathematical Population Genetics. In it he describes how the dilemma is an artifact caused by applying results from an infinite population model to finite population models.

That's very interesting. Does this mean that the attempts to deal with the dilemma (e.g. the Nunney and Woodruff papers) are unecessary? I wonder what ReMine has to say about this?

Stuart Weinstein · 26 February 2008

I can see both sides of this. As a modeler (of thermal convection) I have experienced such requests myself. My answers tend to depend on who was doing the asking. If it was somebody I knew and they were competent, I'd share what code I thought was appropriate. Otherwise, I'd give them as many details as necessary, but ultimately they would have to code it themselves. I simply couldn't be drawn into the trap of providing support to help them use the code and get it compiled, etc. etc. I don't blame Nunney for not wanting to be besieged by daily phone calls troubleshooting problems for Remine. Furthermore, imagine Remine using it improperly and then Nunney having to spend more time explaining where Remine fouled up. So, no, I don't blame him for ignoring Remine. As Nunney basically put it, he had nothing to gain from giving it to Remine, other than a good case of headache.

I didn't write user friendly hydrodynamics code, I wrote Stuart friendly code. Most science coders code that way; you know what works for them. Hence, its usually better to write your own stuff as you'll spend almost as much time trying to learn how to use someone else's and understand it.

That said, we did publish joint papers where we all simulated solutions to classical problems with varying difficulty, and compared the results. These papers served as benchmarks, and could be used as milestones for those writing their own code. I don't know if such things are appropriate for the population genetics community, but in the geodynamics community they did address this issue, at least with respect to code validation.

Reed A. Cartwright · 26 February 2008

I'm probably going to get half of the details wrong---save me RBH---but:

I remember when Sal (?) go a hold of the Avida code and decided that he found an error in their model---therefore evolution was false---because the program fell apart when he specified a mutation rate above 50%. Besides the fact that Sal didn't realize that such high mutation rates were not biologically relevant, what he discovered was not a problem in the model but an overflow error in the code. Apparently, the Avida programmers did not think that anyone would use such high mutation rates.

caligula · 26 February 2008

Beowulff,

Nunney's idea seems to be that the allelic values for A do form a "sequence". That is, the higher the allelic value, the farther we are, in terms of actual DNA sequence, from the starting point (A=0). I base my interpretation on how allelic values interact with the environmental change in eq. 5: at time T, where A=1 is the optimal value, A=4 would be more harmful for fitness than A=3. So, supposedly the DNA sequence for A=4 differs more from A=1 than does A=3. It also makes general sense, because after allele 1 has become fixed in the population, we are generating new mutations for allele 1, not allele 0, so value 2 is typically more than one point mutation away from value 0. This interpretation would mean, then, that the mutation rate u mentioned in the paper refers to the rate of beneficial mutations, exclusively, and that Nunney assumes only one beneficial change per each allele. (I.e. allele 3 can only experience one beneficial change: 3->4). Of course, being truly "beneficial" depends stricly on time t, i.e. the state of the environment.

I think the cycle of each generation proceeds as follows. First, the female fecundity for the entire population is calculated, based on the current density. Then, random mating occurs for female #1. The mated couple produces offspring into a newly created "population pool" according to female fecundity, each child getting her genotype according to the usual Mendelian rule for diploids (AA:2Aa:aa). Mutations are generated for each newborn child immediately after Mendelian segregation. The male returns to the "stud pool" and we move on to the next female. After completing the reproduction phase, we have a new generation in a separate population pool, and the parent populatuion is destroyed. Next, selection has its way on the new generation (juvenile deaths). Now we have completed one generation cycle.

caligula · 26 February 2008

Reed A. Cartwright: I highly recommend reading the section about Haldane's Dilemma in WJ Ewens' Mathematical Population Genetics.

I certainly agree that one should read Ewens' treatment. But, for what it's worth, here's something I wrote about it on another forum: I'm quite puzzled by Warren Ewens' idea. He seems to be claiming that substitutional load is not caused by the difference between the fitness of the theoretic optimal genotype and the average fitness of the population. Instead, he claims that substitutional load is caused by the difference between the fitness of the best actually existing genotype and the average fitness of the population. Ewens is probably right in estimating that beneficial alleles spread in the population in an even fashion, so that the fitness difference between any two living individuals tends to be relatively small. But I find Ewens' core argument questionable. Haldane's idea clearly is that we should compare the fitness of each individual to the optimal genotype, regardless of how likely such a genotype is to manifest itself in a living individual. Even if no individual ever is anywhere near the (current) optimal genotype, selective pressures apply just as mercilessly as they would if some lucky individual happened to hit the optimal genotype. Haldane's key idea seems to be that whenever we postulate the existence of a new beneficial allele, we simultaneously postulate a selection pressure which hurts the fitness of anyone lacking this allele. Ewens seems to ignore the concept of absolute fitness altogether, and only concentrate on relative fitness differences between living individuals. This seems to alter the core idea of Haldane(1957), that there is no beneficial allele without a corresponding selective pressure applied universally to the population. So far as I can tell, Ewens changes Haldane's (apparently quite reasonable) core paradigm without providing any data, or even rational persuasion, to support this assumption. While many of Haldane's assumptions, such as multiplicative fitness interaction, hard selection and omitting intraspecific competition, can reasonably be challenged, I don't think Ewens' change in core assumptions is very persuasive. Obviously, this comes from a layman to challenge an established authority.

Joe Felsenstein · 26 February 2008

No, what you really should read is my 1971 paper which really clears all this up. The load is imposed by the deterioration of the environment, and is measured by the amount of reproductive excess which it is necessary to have to prevent extinction in the face of repeated deterioration of the environment. When advantageous mutations occur in the absence of deterioration of the environment, they don't impose any load. If anything they make the population better able to bear loads.

Felsenstein, J. 1971. On the biological significance of the cost of gene substitution. American Naturalist 105: 1-11.

It is a very hard literature to follow, as various authors defined various costs and loads without ever making it clear what those were supposed to do for us. My paper clears this up. (OK, I'm biased).

You may also want to look at the years-long running debates between Remine and I in the Usenet newsgroup sci.bio.evolution

Paul S · 26 February 2008

caligula:

I don't think that Ewens changes Haldane's core argument. Haldane's argument is based on looking at the difference in fitness between the most fit and least fit individuals in the population (with respect to the substituting loci). Haldane argued that you couldn't expect much more than about 10% difference between these. Based on this (and I am glossing over a lot of details and subtleties), he came up with his limit of a substitution every 300 generations. Ewens shows that no individual with a fitness anywhere near this theoretical maximum will ever actually appear in a population. I don't think that the 10% was based on any hard data, but IS based roughly on what we see in real populations. That is, we don't generally see enormous variation in reproductive success in real populations. The number may not really be 10%, but it is in that ballpark. Ewen's argument is that this "obsrved" 10% is not the varation between the theoretical most fit and least fit individuals. Instead, it is the variation in individuals actually existing in the population and their range of genotypic variation is much smaller than the theoretical extremes. Thus, the limits imposed on the speed of selection are much less stringent than Haldane's argument.

SteveG · 26 February 2008

Pardon me for being naive about the requirements of professional science journals regarding what they publish. But it was my impression "from the outside" that serious research articles are in general supposed to provide enough details about the data and the research procedures so that the work and results could conceivably be replicated - or invalidated. I'm a computer programmer by profession, and while I work in business software development (design and coding of databases, and data processing applications), it really seems to me that the details of the computer programs used to model the concepts and generate the results are of criticial importance to the research articles, and the disclosure of the code should be part of the requirements of professional science journals. While I can certainly understand a professional scientist not having his time wasted by yet another creationist crackpot (there are so many - sigh), such a requirement by the professional science journals would make the issue a moot point since the program(s) used would be open viewing to anyone interested in the published research.

Ian Musgrave · 26 February 2008

though it does include an attack on Ian Musgrave for a Pandasthumb article, essentially accusing him of quote mining - I’d like to see Ian’s response to that
— SteveF

Mr. ReMine indulges in a little quote mining of his own as well as blatant misrepresentation. Let me remind you of what ReMine wrote in his book ( see my Panda’s Thumb post for more context)

In the 1950’s the evolutionary geneticist JBS Haldane, calculated the maximum rate of genetic change due to differential survival. He reluctantly concluded that there is a serious problem here, now known as Haldane’s Dilemma.” ReMine, pg 208, first para. Emphasis added by IFM.
— ReMine

Now this is what he claims his passage means

That paragraph specifically refers to Haldane's "calculations" — not his conclusions, his beliefs, or his statement of faith — and the chapter details precisely what Haldane's "calculations" refers to. That does not misrepresent Haldane. Rather it is a simple introduction to a chapter, accurately telling my readers what they are about to read.
— ReMine

Oh really, then why did Remine write ”He reluctantly concluded”? This cannot refer to Haldane’s calculations, a calculation cannot “reluctantly conclude” anything (nor can a calculation be “He”). The sentence can only make sense as a claim that Haldane himself made a reluctant conclusion. This claim is of course nonsense as any reading of the paper will show.

Unless selection is very intense the number of deaths needed to secure the substitution by natural selection, of one gene for another at a locus, is independent of the intensity of selection. It is often about 30 times the number of organisms in a generation. It is suggested that in horoletic evolution, the mean time taken for each gene substitution is about 300 generations. This accords with the observed slowness of evolution” (page 524 Haldane JBS. (1957). The cost of natural selection. J Genet, 55, 511-524) Emphasis added by IFM
— Haldane

I encourage people to read Haldane’s actual paper provided in the link (note the obsolete term “horoletic”, meaning “normal speed”), Haldane distinguished between “horoletic” evolution in slow/non changing environments and “tachytelic” (that is fast evolution) under conditions of rapid environmental change or expansion into new environments, where his calculations are not relevant (see for example pg 523 second paragraph) . ReMine’s characterisation of Haldane’s paper completely misrepresents the contents. Also note that ReMine, when quoting me, completely omits the actual paragraphs showing that Haldane regarded his calculations are compatible with “normal speed” evolution in slow changing environments (Haldane even mentions the Peppered Moths as an example of rapid selection that can occur). Indeed Remine’s ellipsis covers all of the article and most of the comments section.

And he [Haldane] concluded, "I am convinced that quantitative arguments of the kind here put forward should play a part in all future discussions of evolution."
— ReMine

ReMine trunctates this section; Here is the entire section Haldane wrote ;

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. Summary Unless selection is very intense the number of deaths needed to secure the substitution by natural selection, of one gene for another at a locus, is independent of the intensity of selection. It is often about 30 times the number of organisms in a generation. It is suggested that in horoletic evolution, the mean time taken for each gene substitution is about 300 generations. This accords with the observed slowness of evolution.
— Haldane

This is no way supports ReMine’s claim that “He [Haldane] reluctantly concluded that there is a serious problem here, now known as Haldane’s Dilemma”. And it certainly does not support ReMine’s claim that ReMine’s statement “..specifically refers to Haldane's "calculations" — not his conclusions, his beliefs, or his statement of faith — and the chapter details precisely what Haldane's "calculations" refers to..”. As I said, a calculation cannot “reluctantly conclude” anything. There are no reluctant conclusions of serious problems at all. Again, I encourage readers to read the original manuscript themselves (It can be a bit of a slog, especially with 50 year old jargon, but it is worth it, the mathematically inclined can try their hand calculating his examples). The way ReMine presents Haldane’s work seriously distorts it. The rest of ReMine’s article is a content free rant. Again, see my Panda’s Thumb post for more context and several articles looking at the supposed “dilemma”. It will soon be obvious that ReMine’s claims bear no relation to reality.

Ian Musgrave · 26 February 2008

Joe Felsenstein: No, what you really should read is my 1971 paper which really clears all this up. [snip]..... Felsenstein, J. 1971. On the biological significance of the cost of gene substitution. American Naturalist 105: 1-11. It is a very hard literature to follow, as various authors defined various costs and loads without ever making it clear what those were supposed to do for us. My paper clears this up. (OK, I'm biased). You may also want to look at the years-long running debates between Remine and I in the Usenet newsgroup sci.bio.evolution

What Joe said. I have included a link to the JSTOR copy of his article so people can access it more easily. It is hard literature to follow, especially as the usage of terms evolves along the way. But if you spend the time seriously reading and trying to understand this, you will be rewarded. ReMine seems to think that because a technically demanding conversation is going on, there is a cover-up.

Erasmus, FCD · 26 February 2008

Any chance we can get to Walt Brown some day?

Ftk I know you are waiting for it.

Joe Felsenstein · 26 February 2008

Let me give a very brief summary of different notions of substitutional load, cost of natural selection etc. and what the original debate was about. In the 1960s it was discovered that there was tons of protein variation within species. One of Motoo Kimura's arguments that most of it was neutral was that otherwise there would be too high a substitutional load. Note that this is not a concern that the rate of evolution was too high for evolution to be true -- that is how Remine describes the controversy, but I was there and I remember, and he's utterly wrong about that.

All sorts of people chimed in in the late 1960s to early 1970s with calculations of substitutional load, usually not making it clear what happened if there was too much load. There actually were at least three distinct notions:

1. That the load measured the reduction of the population size. Not widely used because it brings in all sorts of ecological issues.

2. That too high a load meant you would go extinct.

3. That too high a load meant the postulated scenario of what was happening was wrong and something else was going on.

Ewens' and Crow's loads were of type 3. They are very similar to Remine's calculation.
Haldane was unclear but basically seems to have been making a type 2 argument, as I was. Remine always ignores this distinction and just claims all the other calculations are wrong.

People also came up with schemes of gene interaction such as truncation selection that lead to lower loads. After few years everyone concluded that the substitutional load calculation didn't speak powerfully about whether variation was neutral. So shortly after I published my 1971 paper which I thought cleared things up ... the whole discussion died and everyone forgot about it. The mess was left in the literature. Remine complains that it is an unresolved mess and in that he is quite right.

I hope folks will read my paper (alas, the JSTOR link will work only for people whose institutions have a subscription to it).

Joe Felsenstein · 27 February 2008

I should add that the "original debate" I was referring to is the wave of reconsiderations of Haldane's result in the late 1960s and early 1970s. Haldane's paper was the original one, of course.

caligula · 27 February 2008

caligula: ...each child getting her genotype according to the usual Mendelian rule for diploids (AA:2Aa:aa).

Beowulff, Obviously, the example in parenthesis was for interbreeding Aa with Aa. But I'm sure that part was trivial anyway. I think it is a good idea to divide each generation into two subpopulation pools: one for males, one for females. This should save CPU clocks during mating.

caligula · 27 February 2008

Paul S: Haldane's argument is based on looking at the difference in fitness between the most fit and least fit individuals in the population (with respect to the substituting loci).

Can you explain why you find this to be Haldane's argument, preferably by quoting Haldane(1957)? I'm not quite persuaded. I interpret that paper to be very much based on the average absolute fitness of the population, not relative fitness differences between individuals. The risk of extinction is not caused by relative fitness differences, it is caused by the average absolute fitness falling so low that the female fecundity can no longer compensate for juvenile deaths. In the second paragraph of "Discussion", Haldane estimates that, when there is an environmental selection pressure compensated by optimal alleles at N loci, "the [average] fitness is reduced to MUL(1-di)", where di are the selection coefficients at loci. I think this means that the average individual has barely any of the beneficial alleles that could compensate for environmental change at that moment. I do not think that Haldane is speaking about the average individual having barely any of the beneficial alleles possessed by the most fit actually living individual. Of course, this is just the starting point: the beneficial alleles do start spreading in the population and eventually become fixed, increasing the average fitness as far as these loci and the initial environmental pressure are concerned. But during this process, supposedly new environmental changes can occur, and new loci might join the process, so that the average fitness of the population does not increase after all; the population is just successfully fighting against extinction.

Stephen Wells · 27 February 2008

It's not even clear that there is such a thing as the "theoretical optimum genome" or "absolute fitness."

caligula · 27 February 2008

Stephen Wells: It's not even clear that there is such a thing as the "theoretical optimum genome" or "absolute fitness."

At least in the sense of Haldane(1957), I think there is. It is valid to ask whether a population can survive a change for the worse in environmental pressures. This is a question based on absolute fitness, or actual chances of survival for the average individual, not relative fitness differences between individuals. If we now postulate a set of alleles capable of compensating for this change in the environment, applied in a "beanbag genetics" fashion, we also postulate a theoretical optimum genome: it is a genotype which happens to possess all of these beneficial alleles. It is theoretical in the sense that if these alleles were only made beneficial by the environmental change, they can expected to be initially marginal in frequency; this in turn makes it very, very unlikely that the optimum genome could initially manifest itself in a living individual. I'm not saying Haldane is right to restrict his model to environmental change. In fact I think he's wrong. I'm only saying that Ewens' model differs dramatically from Haldane's model, and that I find Ewens' reasons for this difference puzzling. Now, I do think that Haldane's core assumptions can be questioned, but this requires taking into account density-dependent fitness, and especially a special case of density-dependence called "intraspecifc competition". First, an environmental change might help individuals who are relatively fit compared to others, but not "optimal" -- if we take density into account. An increase in juvenile mortality makes the population size to drop below carrying capacity. This, in turn, may well make life easier for survivors (less competition for food, for starters), which gives them some extra viablity. So relatively fit individuals may not only suffer but also benefit from the environmental change. This is not taken into account in Haldane(1957). This was already a mild form of "intraspecific competition", because survivors would seem to benefit indirectly from the demise of others. But I'd like to separately emphasize a more direct and obvious type of intraspecific competition, where individuals are actively trying to beat each other in the population, in order to gain absolute fitness benefits. So: Second, not all selection pressures are environmental. Some selection pressures come from within the population, and are indeed measuring only relative fitness. With territorial animals, it may make a difference between life and death to be able to conquer a territory from the ecological niche, and a good territory at that. It is also very handy to win a mate with good genes. In these "king of the hill" type of contests, individuals are indeed compared to each other, but not to the enviroment, and relative "fitness" or competence matters. The average fitness of the population is not affected by how formidable duelists the individuals in the population are, on average. There is still the same amount of losers and winners. A pathetic conqueror gets the hill if the competition within the population is even more pathetic. (Say, close relatives of this population might look like they came from another planet when it comes to pulling each other's hair!) So, without changing the average fitness of the population one bit, we could still observe a selection force fixing alleles that make individuals better at intraspecific competition. Absolute fitness does come into play even here, because those with little intraspecific competence suffer the consequences of being unsuccessful reproducers, and those with a lot of intraspecific competence will be more successful reprocuders, but the average fitness of the population can remain constant. The rewards, in terms of absolute fitness, can remain constant while the methods of internal competition over those rewards evolve.

pwe · 27 February 2008

Oh, I have avoided ReMine for quite a long time now -- since my encounter with him on Wikipedia.

I am no biologists, and that may be why I don't get it all. I read Nunney's paper back then and Joe Felsenstein's paper -- and even ReMine's own paper -- and Joe Felsenstein's review of ReMine's paper.

But how current is Haldane's definition of evolution: the substitution of a gene (allele) for another at a locus?

And, all ReMine's tapdancing about 1667 substitutions from a simian to Mozart (or something like that), is that even woth debunking? I mean, as far as I have understood 8and that may not be very far), then gene regulation is, where it's at. I mentioned that to ReMine, bnut he only claimed that made things worth for the evolutionist side.

Oh, well, I'll probably pull the plug and go into the woods to hunt little green fairies. May you all have a nice day.

- pwe

pwe · 27 February 2008

Well, well, I followed a link on ReMine's site to a post on ARN. ReMine writes:

The latest case involves Wikipedia (the online encyclopedia), and is immediately open to your inspection (through a complete log of edits and discussion). Despite creationist efforts to make the article insightful, evolutionists repeatedly garbled the Wikipedia article, as follows:

"[C]reationist efforts to make the article insightful"? No, ReMine's attempts to advicate for his own position.

The key figure -- a limit of 1,667 beneficial mutations to explain human evolution -- was brushed aside (by falsely blaming it on creationists, instead of acknowledging that it arises solely from evolutionary theory, evolutionary genetics, and J.B.S. Haldane). This key figure was repeatedly expunged from the article, leaving readers with no idea about the severity of Haldane's Dilemma. Evolutionists suppressed this key figure. They also suppressed their history -- the fact that they never revealed any such figure to the general public.

Hey, all I claimed was that the number 1,667 wasn't Haldane's, the number 300 (average number of generations between substitutions) was Haldane's. It is correct that the 1,667 was calculated from the 300 as 10 million years since split between apes and humans divided by 300 generations per substitution divided by 20 years between generations. But still, that calculation was not Haldane's, but ReMine's, and therefore should not be given a prominent place.

Evolutionary geneticists, James Crow and Warren Ewens, peer-reviewed my paper and acknowledge it is correct, yet they rejected it from publication, claiming they and their associates "knew" my material "in the 1970s". Nonetheless, the Wikipedia article omits all the clarifications given in my paper, and explicitly promotes the various confusion factors identified in my paper. Evolutionary geneticists (including Crow and Ewens) negligently -- and knowingly -- allowed confusion to prevail. The Wikipedia article is a vivid demonstration of it.

Ummm, well, Joe Felsenstein peer-reviewed ReMine's paper too, and he wasn't impressed.

Instead of giving real insight, the Wikipedia article wearies the reader into giving up -- through its needlessly tedious mathematical derivations, and its opaque definitions of key terms. Rather than illuminate the real problem of Haldane's Dilemma today, the article wearies the reader with a relatively fruitless and misleading journey into the "origin of the term" in 1963. The article seems intentionally designed to wear-out readers, rather than deliver understanding.

Hey, hang on there for a second, will you? As I wrote, in an encyclopedia it is common to specify the origin of a term, and I frankly can't see, why ReMine even bothers to comment on that. Isn't it of some interest in an article on 'Haldane's dilemma', who came up with the term, and what it was supposed to mean? That ReMine wants Haldane's dilemma to be an argument against human evolution from apes is a much newer issue and peculiar to ReMine. It may be worth mentioning that ReMine took refuge to CreationWiki, where he was at first greated by a fellow creationist, but later that creationist together with evolutionist Roy gave ReMine a run for his money. But I can see that ReMine has gotten his will with the CreationWiki article and with the ResearchID.org article. The first I can't do anything about, but I happen to be an editor on ResearchID.org, so let the edit war commence! - pwe

Joe Felsenstein · 27 February 2008

pwe: (snip) Ummm, well, Joe Felsenstein peer-reviewed ReMine's paper too, and he wasn't impressed.
Instead of giving real insight, the Wikipedia article wearies the reader into giving up -- through its needlessly tedious mathematical derivations, and its opaque definitions of key terms. Rather than illuminate the real problem of Haldane's Dilemma today, the article wearies the reader with a relatively fruitless and misleading journey into the "origin of the term" in 1963. The article seems intentionally designed to wear-out readers, rather than deliver understanding.

Well, that might have been an appropriate thing for me to say, but I didn't say it. I did do a peer review of Remine's paper, and I was negatively impressed. That peer review is available on line in a number of places. The above quote is not from it and not by me. It's not even a quote-mine.

Torbjörn Larsson, OM · 27 February 2008

But still, that calculation was not Haldane’s, but ReMine’s, and therefore should not be given a prominent place.

Yes, and it looks naively obvious that a biologist wouldn't come up with that number. ReMine makes what to a layman looks like a non-evolutionary prediction straight off the bat: "The origin of all the uniquely human adaptations would have to be explained within that limit." Now, I'm not a biologist, but I would assume that one compares adaptations among related species to reconstruct the differences, and the ancestral population against which one would compare adaptations. As anything "uniquely" now AFAIU depends on how all the related species evolved (losses and gains) from the common ancestor. Unless that is too simplistic. I don't know if ReMine is a creationist, but IMHO opinion (not being a biologist) he sure seems to think like one.

Ian Musgrave · 27 February 2008

Joe Felsenstein: [snip] Well, that might have been an appropriate thing for me to say, but I didn't say it.

Pwe's sentence is a comment on the quote above, not below (i'e Pwe is pointing out that while Mr. ReMine is praising his paper, and saying the Wikipedia article ignores it, ReMine's paper is omitted for good reason). The quote below this sentence is not related to Joe's work, it's quoting Remine (again the comment relating to this quote is under, not above it).

Joe Felsenstein · 27 February 2008

OK, I see the quote wasn't supposed to be me. Thanks.

caligula · 27 February 2008

By the way, I find Walter ReMine's comments on subsection "4.11 Truncation selection" rather telling, in his Creation Wiki and ResearchID.org articles.

What ReMine is complaining about truncation selection is essentially beanbag genetics, because his complaint is that the fitness interaction across loci is not epistasic. Well, Haldane was the very spokesman for "beanbag genetics", and Haldane(1957) certainly does not assume epistatic fitness interaction, as ReMine notes himself. Essentially, ReMine seems to agree that truncation selection solves the problem presented in Haldane(1957). Although the solution, too, is based on "beanbag genetics", that never was the core issue raised by ReMine. The issue was supposed to be "Haldane's dilemma", not "beanbag genetics".

ReMine of course claims that epistatic fitness interaction of a suitable kind radically slows down evolution, and that evolution is governed by just this kind of epistasis, but he has not really demonstrated his claim.