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Author Topic:   Population Genetics
Hyroglyphx
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Joined: 05-03-2006


Message 1 of 90 (363977)
11-15-2006 8:18 PM


Population genetics has long been a predictor for evolutionary application in any given population. The premise is simple enough, as it employs an algorithm to quantify and determine how and why adaptations and gene frequency occurs. There is, however, a problem to be dealt with, first addressed by JBS Haldane, a 19th century evolutionary biologist/geneticist. He introduced, mathematically, the maximum possible likelihood of human mutation rates. His studies were the first to calculate the finite number of possible allele frequencies caused by recurring mutations at a gene locus and introduced the idea of a "cost" function to natural selection.

While forming his thesis, he came to the revelation that there was a finite limit of possible beneficial mutations that later was coined as "The Haldane Dilemma." There exists a maximum of 1,667 beneficial substitutions over the past ten million years of the lineage that leads to modern man. The argument has been expounded by others who assert that substitutions into the population might be larger than a nucleotide. This includes insertion/deletion or inversion/duplication. Each of these count as a substitution, therefore the argument places a limit on the total number of substitutions. And this limitation has a profound impact on punctuated equilibrium, because this maximum number presents a problem for the pace at which evolution could occur.

"Several factors could reduce the 1,667 limit significantly. For example, according to Eldredge and Gould's evolutionary theory, punctuated equilibria, species are in statis at least 99% of the time, and Gould claimed punc-eq applies to human evolution. According to Gould (in his last book, The Structure of Evolutionary Theory) genetic change would typically cease during statis. If correct, this factor alone could reduce the Haldane limit by a factor of about 100, to a limit of 17 substitutions. I was the first to bring up this relationship between punc-eq and Haldane's Dilemma." -Walter Remine

"I shall investigate the following case mathematically. A population is in equilibrium under selection and mutation. One or more genes are rare because their appearance by mutation is balanced by natural selection. A sudden change occurs in the environment, for example, pollution by smoke, a change of climate, the introduction of a new food source, predator, or pathogen, and above all migration to a new habitat. It will be shown later that the general conclusions are not affected if the change is slow. The species is less adapted to the new environment, and its reproductive capacity is lowered. It is gradually improved as a result of natural selection. But meanwhile, a number of deaths, or their equivalents in lowered fertility, have occurred." -JBS Haldane

What kind of effect, if any, does the "Cost theory" or "Haldanes Dilemma" present on population genetics?


Faith is not a pathetic sentiment, but robust, vigorous confidence built on the fact that God is holy love. You cannot see Him just now, you cannot fully understand what He's doing, but you know that you know Him." -Oswald Chambers
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AdminNosy
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Message 2 of 90 (363984)
11-15-2006 9:17 PM


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RAZD
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Message 3 of 90 (363987)
11-15-2006 9:26 PM
Reply to: Message 1 by Hyroglyphx
11-15-2006 8:18 PM


False problem caused by false model.
If your mathematical model does not reflect reality IT is wrong not reality.

Enjoy.

Edited by RAZD, : opty


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This message is a reply to:
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Hyroglyphx
Member
Posts: 5637
From: Austin, TX
Joined: 05-03-2006


Message 4 of 90 (363989)
11-15-2006 9:33 PM
Reply to: Message 3 by RAZD
11-15-2006 9:26 PM


Re: False problem caused by false model.
If you mathematical model does not reflect reality IT is wrong not reality.

Did you have a specific grievance with the computation?


This message is a reply to:
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RAZD
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Message 5 of 90 (363990)
11-15-2006 9:38 PM
Reply to: Message 4 by Hyroglyphx
11-15-2006 9:33 PM


Re: False problem caused by false model.
Did you have a specific grievance with the computation?

Only one: it is refuted by the evidence.

Enjoy.


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This message is a reply to:
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Hyroglyphx
Member
Posts: 5637
From: Austin, TX
Joined: 05-03-2006


Message 6 of 90 (363994)
11-15-2006 9:54 PM
Reply to: Message 5 by RAZD
11-15-2006 9:38 PM


Re: False problem caused by false model.
ReMine has posted a challenge to question his thesis.

Answer the following questions:

    1. What is a "genetic death" physically? What does it mean?

    2. Why would a higher number of genetic deaths (of individuals containing the old-allele) lower the substitution rate (of the new-allele)? Plainly stated, this is the traditional view.

    3. From the above answers, derive the cost equations (e.g. Haldane's cost equations)

To help your discussion, start with the simplest conceivable scenario. The simpler the scenario, the more obvious will be your confusion:

    1. A haploid species (preferably asexual, for simplicity),

    2. with a constant population size,

    3. during a single isolated substitution (Thus, there are only two alleles, A and a. The new-allele A is substituting into the population; the old-allele a is being eliminated.),

    4. with pure viability selection (e.g. selection solely by elimination of juveniles containing the old-allele), and

    5. with a tiny selection coefficient (s<<1).

Focus strictly on a single generation. If you can answer the questions for a single generation, then the same logic can be applied over-and-over again, to each and every generation. But if you cannot answer the questions for even one generation, then you have no business going further.

Then answer those questions again at each step of the following ever-looser assumptions:

    6. Next break assumption #4 and allow other types of selection (such as fertility differences). In this case, some or all of the genetic deaths are 'virtual', not real, they are organisms who are never even conceived. That adds another layer of confusion. Answer the questions again. Note especially the conundrum: Why would a virtual death of the old-allele – a death that is not real – count toward reducing the substitution rate (of the new-allele)? In effect that is the traditional view, but rationalizing it is another matter.

    7. Next, also break assumption #5, and allow larger selection coefficients, which adds another layer of complication (and confusion). Note that this disallows a simplifying assumption used by Haldane, so it will require a greater level of physical understanding. Answer the questions again.

    8. Next, also break assumption #1, and allow a sexual diploid species. Note especially the conundrum: For individuals containing both the old- and new-allele (i.e. a heterozygote), where the new-allele may be dominant or recessive: What is a genetic death? Answer the questions again.

    9. Next also break assumption #3, and allow multiple concurrent substitutions (overlapping in time). Note especially the conundrum: Various individuals contain various mixes of old- and new-alleles, so What on earth is a genetic death? Remember also that when a stream of many concurrent substitutions are occurring, the optimal genotype might never actually exist in the population. Answer the questions again.

    10. For extra credit, also break assumption #2, and allow changes in population size. (Note that none of the traditional definitions allow non-constant population size.) Answer the questions again.


Faith is not a pathetic sentiment, but robust, vigorous confidence built on the fact that God is holy love. You cannot see Him just now, you cannot fully understand what He's doing, but you know that you know Him." -Oswald Chambers
This message is a reply to:
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crashfrog
Inactive Member


Message 7 of 90 (363997)
11-15-2006 10:04 PM
Reply to: Message 1 by Hyroglyphx
11-15-2006 8:18 PM


What kind of effect, if any, does the "Cost theory" or "Haldanes Dilemma" present on population genetics?

None whatsoever. Haldane himself later recognized the errors in his own model, and was more than confident that subsequent information would render his calculations pointless (he was right, of course). In particular:

quote:
Haldane's "cost of natural selection" stemmed from an invalid simplifying assumption in his calculations. He divided by a fitness constant in a way that invalidated his assumption of constant population size, and his cost of selection is an artifact of the changed population size. He also assumed that two mutations would take twice as long to reach fixation as one, but because of sexual recombination, the two can be selected simultaneously and both reach fixation sooner. With corrected calculations, the cost disappears (Wallace 1991; Williams n.d.).

ReMine himself introduces a number of errors into an already invalid model:

quote:
* The vast majority of differences would probably be due to genetic drift, not selection.
* Many genes would have been linked with genes that are selected and thus would have hitchhiked with them to fixation.
* Many mutations, such as those due to unequal crossing over, affect more than one codon.
* Human and ape genes both would be diverging from the common ancestor, doubling the difference.
* ReMine's computer simulation supposedly showing the negative influence of Haldane's dilemma assumed a population size of only six (Musgrave 1999).

from http://www.talkorigins.org/indexcc/CB/CB121.html

To assert that there's any tooth to Haldane's so-called "dilemma" is to assert that the entire field of population genetics hasn't gone anywhere since Haldane's work in the late 50's. (Where did you get the idea that Haldane was a "19th century biologist"? He was born in 1892.)

He misstates Gould as well, I suspect. Statis isn't the cessation of genetic change; it's the cessation of morphological change. Indeed, periods of rapid change are only possible because of the genetic changes occuring "under the radar" during periods of stasis.


This message is a reply to:
 Message 1 by Hyroglyphx, posted 11-15-2006 8:18 PM Hyroglyphx has responded

Replies to this message:
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RAZD
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Posts: 19839
From: the other end of the sidewalk
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Message 8 of 90 (363998)
11-15-2006 10:09 PM
Reply to: Message 6 by Hyroglyphx
11-15-2006 9:54 PM


Re: False problem caused by false model.
I repeat: the mathematical model proposed does not reflect reality, therefore it is false. It is invalid. It is wrong.

Math can never prove reality wrong.

This is the essential difference between science and pseudoscience - when a concept is falsified, invalidated, it is discarded by science.

Therefore there is no need to show the thesis is invalid, rather the shoe is on the foot of those pushing the thesis to explain how it can account for reality being different than it's computation OR they change the computation until it matches.

Enjoy.


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Chiroptera
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Posts: 6562
From: Oklahoma
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Member Rating: 5.0


Message 9 of 90 (364002)
11-15-2006 10:29 PM
Reply to: Message 6 by Hyroglyphx
11-15-2006 9:54 PM


Re: False problem caused by false model.
To repeat RAZD's point, we know that the model is incorrect because in reality we do know that evolution has occurred, the evidence overwhelmingly shows that all known species share a common ancestal species, and, in particular, humans and other apes share a common ancestor that lived less than a dozen million years ago. If you want to dispute the evidence then there are threads for that, but most scientists recognize that humans and chimpanzees share a common ancestor. Therefore, any model that claims otherwise must have one or more serious flaws.


Kings were put to death long before 21 January 1793. But regicides of earlier times and their followers were interested in attacking the person, not the principle, of the king. They wanted another king, and that was all. It never occurred to them that the throne could remain empty forever. -- Albert Camus
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nwr
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Posts: 5585
From: Geneva, Illinois
Joined: 08-08-2005


Message 10 of 90 (364009)
11-15-2006 10:50 PM
Reply to: Message 1 by Hyroglyphx
11-15-2006 8:18 PM


There is an assumption in your argument (or Remine's argument), that genetic evolution ceases during the equilibrium phase of punctuated equilibria. To me, that seems most unlikely. That is, during a period of relative equilibrium, I would expect genetic evolution to continue, and to increase the amount of variation available to the population group. The punctuation part can then involve rapid phenotype evolution, precisely because it is largely selection from variation built up in the equilibrium stage.


Just say no to McCain 2008; he abandoned principle when he caved on habeus corpus
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Hyroglyphx
Member
Posts: 5637
From: Austin, TX
Joined: 05-03-2006


Message 11 of 90 (364014)
11-15-2006 11:08 PM
Reply to: Message 7 by crashfrog
11-15-2006 10:04 PM


quote:
What kind of effect, if any, does the "Cost theory" or "Haldanes Dilemma" present on population genetics?

None whatsoever. Haldane himself later recognized the errors in his own model, and was more than confident that subsequent information would render his calculations pointless (he was right, of course). In particular

quote:
Haldane's "cost of natural selection" stemmed from an invalid simplifying assumption in his calculations. He divided by a fitness constant in a way that invalidated his assumption of constant population size, and his cost of selection is an artifact of the changed population size. He also assumed that two mutations would take twice as long to reach fixation as one, but because of sexual recombination, the two can be selected simultaneously and both reach fixation sooner.

These issues are mischaracterizations of his argument. The argument is not about the genetic difference between divergent organisms. The figures were first supported by many eminent evolutionists before 1957. He is simply reiterating an argument posed by an evolutionist, Haldane, who candidly offered the theorum in the interest of scoence, not the special interest of evolution. ReMine answers his critics by stating:

"If you compare divergent organisms (such as living chimps and living humans) on the basis of genetic or protein sequences, then you are misrepresenting my argument. That makes my argument less direct, more confusing, and most importantly, it grants evolutionists large fudge-factors that operate in their favor. That is why evolutionists typically (near universally) misrepresent my argument in this manner. They are attempting to grant favors to themselves, by misrepresenting my argument.

Typically they do that by claiming I made an "invalid assumption" that they will "correct." That is falsehood. My argument assumes humans evolved from an ape-like ancestor (as evolutionists allege), and then shows a serious problem with that. Evolutionists cannot legitimately attack that as an "invalid assumption" in need of "correction."

The public can understand Haldane's Dilemma, and readily sees it as a serious problem. Everything necessary to communicate the problem (the 1,667 limit) was available in 1957 when Haldane published his paper. Yet evolutionists did not communicate it to the public. They still haven't. In this matter they were grossly negligent. This is now a fact of history, and cannot be changed.

For many decades already, evolutionary literature claimed Haldane's Dilemma was "solved." But that would require evolutionists to solve all the crucial components of the problem — including the number of substitutions needed to create all the human adaptations. Evolutionists have scarcely begun to do that. Haldane's Dilemma was never solved."

ReMine himself introduces a number of errors into an already invalid model:

  • The vast majority of differences would probably be due to genetic drift, not selection.
  • Many genes would have been linked with genes that are selected and thus would have hitchhiked with them to fixation.
  • Many mutations, such as those due to unequal crossing over, affect more than one codon.
  • Human and ape genes both would be diverging from the common ancestor, doubling the difference.
  • ReMine's computer simulation supposedly showing the negative influence of Haldane's dilemma assumed a population size of only six
  • 1. Haldane used principles, and models of genetics and selection, that remain exceptionally predominant today in evolutionary genetics textbooks.

    2. In addition, Haldane used assumptions that favor evolution. When you 'break' such an assumption, not only do you not solve Haldane's Dilemma, you make the problem worse.

    3. Some of Haldane's assumptions were used (as still commonly done today) in order to simplify the math and generalize the results. You cannot solve Haldane's Dilemma by breaking one of these particular assumptions, since that merely complicates the problem without solving it. There is always a cost of substitution, no matter what model is used. Evolutionists must identify a model that actually solves Haldane's Dilemma, while remaining plausible on other grounds. They have not done that.

    As for the specious plea that genetics has developed more since the 1950's, one first has to consider that the backbone of genetics have not changed, such as Mendelian genetics. Its a simple, but elegant model that has straightfoward questions that have languished as far as being solved. ReMine lists some of the objections made by TalkOrigins and offers explanations for them.

    Haldane's Old Model: Haldane used a multiplicative-fitness model. (Moreover, for the parameters he used, it also approximates an additive-fitness model.) Both of those fitness models are still predominantly used today. Everything in "Haldane's model" is current with today's practice of evolutionary genetics (including Haldane's uses of fitness, fitness models, selection, alleles, genes, dominance, and Mendelian segregation). So if evolutionists throw-out "Haldane's model" they must also throw-out the modern textbooks on evolutionary genetics.

    Small selection coefficients?Haldane assumed selection coefficients approaching zero. This gives the absolute minimum total-cost of substitution in each case. If you break Haldane's assumption, and invoke higher selection coefficients, then the cost increases, resulting in fewer substitutions, and Haldane's Dilemma worsens.

    The environmental-change scenario?Haldane assumed substitutions begin in a peculiar way, via an environmental-change scenario. The scenario operates as follows. Neutral and slightly harmful mutations (though almost always eliminated outright) sometimes drift upwards in frequency, to arrive at moderate frequencies. Then, when the environment changes, one of these neutral or slightly harmful mutations is converted (it is alleged) into a beneficial mutation. This elevated starting frequency is where Haldane begins to tally the total-cost of the substitution. By giving the substitution a free head-start to an elevated frequency, it lowers the total cost of substitution. This cost-reduction is the only impact of the environmental-change scenario that Haldane allowed into his calculations. If you break Haldane's assumption, then it raises the total-cost of substitution, and worsens Haldane's Dilemma.

    Constant population size?Haldane assumed the population size remains constant throughout a given substitution (though he allowed large varieties of population size, each for a different substitution). That was done partly for mathematical simplification (in the era before computers were readily available to readers). When evolutionists break this assumption, they do not "solve" Haldane's Dilemma. They merely obscure it further. There is always a cost of substitution; it is unavoidable. It is not enough to merely object to Haldane's simplification. Evolutionists must actually s-o-l-v-e Haldane's Dilemma.

    Infinite population size?Evolutionists sometimes claim Haldane assumed an unrealistic "infinite population size." That is untrue. If Haldane had done that, then the total-cost of substitution would always be infinite – when Haldane calculated its average value is 30. So Haldane obviously did not use an infinite population size. Rather, Haldane used something at the other end of the spectrum. To see it, take a haploid species, and suppose there are two independent alleles, A and B (at independently segregating loci), each with a frequency of one per thousand. By random mating, the genotype AB (containing both alleles, A and B) would have a frequency of one per million. But if the population size is only one thousand individuals, then in a given generation, genotype AB cannot actually exist at a frequency of one in a million. Instead, either that genotype exists as a whole individual, or it does not exist – it either has a frequency of one per thousand, or zero. There is no 'in-between' when dealing with individuals that are quantized into whole-bodies. This difficulty is handled by Haldane, and by virtually all textbooks today, in the same way – by using non-quantized individuals. To greatly simplify the math, and to generalize the results, they allow a genotype to exist at its expected frequency (without having to quantize the genotype into, say, 1000 whole-bodies). Put simply, Haldane assumed non-quantized individuals, not infinite population size. If evolutionists want to throw-out that simplifying assumption, then they would have to throw-out virtually all of today's evolutionary genetics textbooks. And it still would not solve Haldane's Dilemma.

    He misstates Gould as well, I suspect. Statis isn't the cessation of genetic change; it's the cessation of morphological change. Indeed, periods of rapid change are only possible because of the genetic changes occuring "under the radar" during periods of stasis.

    How does he misstate Gould? The period of stasis is important to the pace of evolution. He is saying that, (actually, Haldane is saying, he is simply agreeing), that there is a finite number of possible mutations, whether by insertions, deleterious, or otherwise. He is also asking that the genetic load, genetic death, and selective pressures be examined and answered with any measure of credibility.


    Faith is not a pathetic sentiment, but robust, vigorous confidence built on the fact that God is holy love. You cannot see Him just now, you cannot fully understand what He's doing, but you know that you know Him." -Oswald Chambers
    This message is a reply to:
     Message 7 by crashfrog, posted 11-15-2006 10:04 PM crashfrog has responded

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    Hyroglyphx
    Member
    Posts: 5637
    From: Austin, TX
    Joined: 05-03-2006


    Message 12 of 90 (364015)
    11-15-2006 11:09 PM
    Reply to: Message 7 by crashfrog
    11-15-2006 10:04 PM


    *delete* double post

    Edited by nemesis_juggernaut, : No reason given.


    Faith is not a pathetic sentiment, but robust, vigorous confidence built on the fact that God is holy love. You cannot see Him just now, you cannot fully understand what He's doing, but you know that you know Him." -Oswald Chambers
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    AdminModulous
    Administrator (Idle past 238 days)
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    Message 13 of 90 (364032)
    11-16-2006 3:32 AM
    Reply to: Message 11 by Hyroglyphx
    11-15-2006 11:08 PM


    Large 'copy/pastes'
    Avoid lengthy cut-n-pastes. Introduce the point in your own words and provide a link to your source as a reference.

    A good deal of your reply is cut/paste from ReMine's article, which can be found here.

    The Haldane's dilemma debate can often get quite complicated. I'd feel more comfortable knowing that those that take a definitive position on it have a good understanding of the topic, and is able to understand potential rebuttals to it. As such, I'd rather see you explain your position to your opponents in your own words, rather than copy/pasting what you think might be relevant sections of ReMine's work.

    You may find that copy/pasting in this manner will mean you end up addressing a point different than that your opponent was making.

    Its not just the post I'm replying to: Message 6 is also a large copy/paste. Many people have read ReMine's work, and if they haven't they are free to read it at their leisure. What we are interested is NJs argument and debate.

    No moderator action taking place here, I just have a feeling that this thread might get bogged down in a 'rule 4' debate, which nobody wants.

    Any comments to this will be directed to the thread in my signature.


    New Members should start HERE to get an understanding of what makes great posts.

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    This message is a reply to:
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    PaulK
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    Message 14 of 90 (364037)
    11-16-2006 6:19 AM
    Reply to: Message 12 by Hyroglyphx
    11-15-2006 11:09 PM


    Can you explain why ReMine's claim of a maximum of 1667 beneifical nucleotide substitutions should be considered valid ?

    Larger mutations - transpositions, substitutions and deletions - are reasonably common and can include dozens or even hundreds of nucleotides. Why should we ignore these ?

    How do you measure the number of nucleotide changes in a substitution ? Given a polymorphic gene (multiple alleles in the pool) what is the baseline ? Does ReMine's claim even make sense ?


    This message is a reply to:
     Message 12 by Hyroglyphx, posted 11-15-2006 11:09 PM Hyroglyphx has responded

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    Modulous
    Member (Idle past 238 days)
    Posts: 7789
    From: Manchester, UK
    Joined: 05-01-2005


    Message 15 of 90 (364038)
    11-16-2006 6:57 AM
    Reply to: Message 14 by PaulK
    11-16-2006 6:19 AM



    Can you explain why ReMine's claim of a maximum of 1667 beneifical nucleotide substitutions should be considered valid ?

    There doesn't seem any reason NJ should have to do that, because it isn't his position. From the OP,

    quote:
    The argument has been expounded by others who assert that substitutions into the population might be larger than a nucleotide. This includes insertion/deletion or inversion/duplication. Each of these count as a substitution

    Does ReMine claim it is nucleotides? If he does, then an interesting question would be why NJ chooses to depart from ReMine on this issue.


    This message is a reply to:
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