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Author Topic:   Page's misuse of Haldane's Dilemma
derwood
Member (Idle past 679 days)
Posts: 1455
Joined: 12-27-2001


Message 31 of 57 (12577)
07-02-2002 3:09 PM
Reply to: Message 29 by Fred Williams
07-02-2002 1:58 PM


quote:
Originally posted by Fred Williams:
Plug in the mutation rate, and you end up with a requirement of 60 offspring per breeding couple!!! This number is actually extremely conservative as many other factors are ignored. When more realistic (and still conservative) numbers are used, the number exceeds 200!

I have asked repeatedly for creationist supporters of this line of reasoning to explain, in clear, unambiguous terms, what, exactly, having X-number of offspriong per breeding couple actually means, and how that applies to evolution.
Additionally, does this apply to other lineaqges, or just the human-ape? That is, does the same 'conundrum' (as yet still unexplained) exist for, say, chimps and their close relatives, bonobos? Afterall, they have similar generations times and such.


This message is a reply to:
 Message 29 by Fred Williams, posted 07-02-2002 1:58 PM Fred Williams has not yet responded

  
derwood
Member (Idle past 679 days)
Posts: 1455
Joined: 12-27-2001


Message 32 of 57 (12677)
07-03-2002 10:33 AM


http://geocities.com/huxter4441/Williams3.html
Replies to this message:
 Message 33 by Fred Williams, posted 07-05-2002 11:39 AM derwood has responded

  
Fred Williams
Member (Idle past 2270 days)
Posts: 310
From: Broomfield
Joined: 12-17-2001


Message 33 of 57 (12831)
07-05-2002 11:39 AM
Reply to: Message 32 by derwood
07-03-2002 10:33 AM


I thought I’d address a few key items here from Page’s latest rebuttal.

quote:
Page: But what does "...cost of recessive mutation is exponentially higher." actually mean? According to Haldane (1957), recessive mutant alleles occur in a population at a rate some 200 times that of dominant ones (p.514). On p. 517, Haldane expands on the costs for dominant and recessive substitutions. He gives the cost D for dominants of between 9.9 and 79; for recessives, D= ~105. 105 is not an exponential increase unless one only considers his low value of 9.9, which the creationist must have done (Haldane put the average at 30). That is, he makes a worse case scenario.

What Page failed to notice is that D for a dominate is based on a starting frequency p of 5x10^-5, while p for a recessive is assumed a starting frequency of .01 (which means huge costs have already been paid to get it there)! Why did Haldane assume a much higher starting frequency for a recessive? He wanted to show that D is largely dependent on p, and wanted to start recessives at a point where they may be recognized by selection (p 514).

Haldane expands on this in his subsequent 1960 paper, “More Precise Expressions for the Cost of Natural Selection”. On p 358 Haldane writes “Thus the cost may be enormous if the gene selected is completely recessive, and it seems doubtful whether completely recessive genes are ever selected.” [emphasis mine] (Haldane goes on to say that recessives only have a chance to spread in small isolated populations)

Other things of note:

2) I think it is important to note that Page still refuses to acknowledge that the Wu study assumes human/simian (specifically OW monkeys) ancestry.

2) Page continues to insist that Haldane’s model is premised on evolution being true. This is precisely equivocation, and he is flat wrong to engage in it. Allele replacement is part of the YEC framework, as is selection (which creationists espoused even before Darwin). Page knows this, but would still try to have you believe that selection is an “evolutionary” idea, and allele replacement is exclusive to evolution. Using Page’s logic, I could just as easily write “Haldane’s model is premised on creation being true”.

What is ironic is that in the past Page has used Haldane’s model to argue against YEC rapid speciation since the flood! How can Page do this if he really believes the model is built off of evolutionary assumptions?!!! I have always said that Haldane’s model, since it is not formulated on how life originated, can be applied to the YEC framework. When Page and other evolutionists use it to argue against YEC, they are actually using valid logic. That is what led our debates in the past to such topics as adaptive mutations, among others. My point then and now is that evolution has no reasonable explanation for the Haldane problem, whereas the YEC model has several reasonable explanations available to it.

3) Page continues to claim the Rice study is evidence that sex is beneficial to evolution:

quote:
Page: The Rice study demonstrates the benefit of sex (which creationists claim is an 'enigma' and all that) - it helps to increase the accumulation of beneficial mutations while decreasing the accumulation of deleterious ones.

Despite having this pointed out to him now on numerous occasions, he continues to conveniently forget a very important factor. The above is only true when the ENVIRONMENT CONSISTS OF A HUGE FLOW OF HARMFUL MUTATIONS EACH GENERATION! Since a huge flow of harmful mutations is anti-evolution, it is very misleading to claim that the Rice study demonstrates the benefit of sex for evolution. Page’s explicit claim, and Rice’s implicit claim, is nothing short of intellectual dishonesty.

Let’s try something. I ask Page to show us how the Rice study demonstrates that sex is a benefit for evolution in an environment where there is a nominal rate of mutation per organism per generation. Feel free to use any rate that does not deteriorate a species. A rate that keeps the genetic load at equilibrium would be fine. Use their charts and data. Show the readers and I where in their data, recombination “increases beneficial mutations while decreasing harmful ones” when the rate of mutation is equilibrium. If you cannot achieve this, then your original claim that their study supports evolution is intellectual dishonesty and you should retract it.

(I’ll remind Page that anything less than equilibrium is deterioration, which is anti-evolution, which is the only section of the graph the Rice study works! For my analysis, see: http://www.evolutionfairytale.com/articles_debates/page_refutation.htm and page down to "Sexual Recombination and the Power of Natural Selection")

4) Questions from Page:

quote:
Page: Other things Williams deigned to ignore:
His erroneous defense of ReMine's claims (re: 500,000 changes...)

I cannot comment on the 500,000 until my Remine book is returned to me.

quote:
His continued reliance upon papers that also assume evolution (e.g., Eyre-Walker and Keightly's paper), indicating some hypocrisy in his position

I think you are the only evolutionist biologist I’ve debated who refuses to understand my point, yet I have been debating it with you longer than any other “scientist”, so you have no excuse. I do not “rely” on Walker/Keightley paper for an accurate mutation rate. I have stated over and over again that their rate is WRONG. It MUST be wrong because it is ridiculous to assume that our alleged chimp/man ancestor produced 40+ offspring. Thus, since I conclude that their concluding rate of mutation is wrong, that something must be amiss within their study. Is it their math? No. Is it their data points from sequence gathering? I seriously doubt it. Is it their assumption that chimp and man share a distant ancestor? Yes, I think this must be where the problem lies, and why they end up with such a ridiculously high mutation rate.

quote:
My mention of his ignored Baptist Board posts, specifically, my question regarding his beloved 'X-number of offspring per couple' schtick

Time constraints. If it’s the question you asked in this thread, I’ll try to get to it shortly…

[This message has been edited by Fred Williams, 07-05-2002]


This message is a reply to:
 Message 32 by derwood, posted 07-03-2002 10:33 AM derwood has responded

Replies to this message:
 Message 34 by Admin, posted 07-05-2002 12:55 PM Fred Williams has not yet responded
 Message 35 by Percy, posted 07-05-2002 1:53 PM Fred Williams has responded
 Message 36 by derwood, posted 07-05-2002 2:22 PM Fred Williams has not yet responded

  
Admin
Director
Posts: 12504
From: EvC Forum
Joined: 06-14-2002
Member Rating: 3.4


Message 34 of 57 (12841)
07-05-2002 12:55 PM
Reply to: Message 33 by Fred Williams
07-05-2002 11:39 AM


The positive tone and on-topic focus of this post is greatly appreciated.

------------------

--EvC Forum Administrator


This message is a reply to:
 Message 33 by Fred Williams, posted 07-05-2002 11:39 AM Fred Williams has not yet responded

  
Percy
Member
Posts: 15632
From: New Hampshire
Joined: 12-23-2000
Member Rating: 4.0


Message 35 of 57 (12844)
07-05-2002 1:53 PM
Reply to: Message 33 by Fred Williams
07-05-2002 11:39 AM


Just in case I'm not alone in the difficulties I've faced attempting to following the discussion between Scott and Fred, I thought I'd respond to Fred's excellent post with what I hope will be some clarifications. Please post corrections to anything I get wrong.

The first questions has to be, "What is Haldane's Dilemma?" because I don't think it's apparent from only a reading of the dialogue between Scott and Fred.

Haldane's dilemma can be characterized through the example of man/chimp evolution. The evolutionary view is that some millions of years ago man and chimp shared a common ancestor from which both species eventually evolved, and today the difference between the chimp and man genome is around 2%. But man and chimp are both slowly reproducing species, so how could a difference of 2% occur in only 5 million years given prevailing rates of evolutionary change.

Haldane brought some mathematical rigor to this issue, characterizing it in terms of beneficial and non-beneficial allelic changes, dominant and recessive genes, rate of fixation of an gene in a population, and so forth. But one doesn't have to approach it on a mathematical level to wonder how so much change could occur in so little time, and even evolutionists must concede that biology does not as of yet have satisfactory models to explain fairly rapid species change for animals like ourselves. The fossil differences between Australopithicus afarensis and Homo habilis are enormous, and if habilis is actually a descendent of afarensis (something that can only be conjectured at this point) then we have little idea how the change from one to the other took place.

Lack of transitionals is the source of the lack of insight. This common Creationist objection to the fossil evidence has some validity. The well-documented example of horse evolution illustrates a clear and lengthy (in time) record of transition from one horse species to another, but how did the transitions between those species take place? There's no fine gradation. Is punctuated equilibrium the answer? Perhaps, but in a way this is an argument from no evidence, a charge often cast at Creationists.

So Haldane's Dilemma can in some small way be viewed as a specialized form of the question about missing transitional fossils. How did the angle of the hip joint change? What about the orientation and shape of the pelvis? How about the angle of the skull on the backbone. What about skull and brain changes? How much, when, how fast, sequentially or all at the same time? We don't know.

To evolutionists the fossil record is clear and unequivocal evidence that evolution has happened, but we must concede that we have little understanding of the actual process by which a new species with significant morphological differences evolves. To Creationists the fossil record is so clearly full of holes that it serves as very poor evidence of evolution and much better evidence of special creation. I think this skepticism is well founded, though it is scant justification for the Creationist flights of fancy that involve rejecting much of cosmology, physics, geology and biology.

Trying to imagine the detailed changes human ancestral species might have gone through on their way to evolving into us brings some helpful visualization to the more abstract details of the Haldane's Dilemma discussion, which from a Creationist standpoint merely postulates that the rate of evolutionary change is too slow for a chimp/man ancestor to have evolved into us.

If either Fred or Scott is willing, this might be a good time to summarize the current state of the Haldane's Dilemma discussion.

--Percy


This message is a reply to:
 Message 33 by Fred Williams, posted 07-05-2002 11:39 AM Fred Williams has responded

Replies to this message:
 Message 37 by derwood, posted 07-05-2002 2:54 PM Percy has not yet responded
 Message 39 by Fred Williams, posted 07-06-2002 2:30 PM Percy has not yet responded

  
derwood
Member (Idle past 679 days)
Posts: 1455
Joined: 12-27-2001


Message 36 of 57 (12846)
07-05-2002 2:22 PM
Reply to: Message 33 by Fred Williams
07-05-2002 11:39 AM


quote:
Originally posted by Fred Williams:
I thought I’d address a few key items here from Page’s latest rebuttal.

I would prefer Dr.Page, as such a courtesy seems to be typically applied to those with such credentials in a 'debate.'

quote:

quote:
----------------------------------------------------------------------
Page: But what does "...cost of recessive mutation is exponentially higher." actually mean? According to Haldane (1957), recessive mutant alleles occur in a population at a rate some 200 times that of dominant ones (p.514). On p. 517, Haldane expands on the costs for dominant and recessive substitutions. He gives the cost D for dominants of between 9.9 and 79; for recessives, D= ~105. 105 is not an exponential increase unless one only considers his low value of 9.9, which the creationist must have done (Haldane put the average at 30). That is, he makes a worse case scenario.
----------------------------------------------------------------------

What Page failed to notice is that D for a dominate[sic - the correct termis 'dominant'] is based on a starting frequency p of 5x10^-5, while p for a recessive is assumed a starting frequency of .01 (which means huge costs have already been paid to get it there)!


How could I have failed to notice this when I explicitly account for the difference (i.e., "200 times...")? Why a 'huge cost' already paid? What 'huge cost' was paid to allow the spread of sickle cell trait, for example.

quote:

Why did Haldane assume a much higher starting frequency for a recessive? He wanted to show that D is largely dependent on p, and wanted to start recessives at a point where they may be recognized by selection (p 514).
Haldane expands on this in his subsequent 1960 paper, “More Precise Expressions for the Cost of Natural Selection”. On p 358 Haldane writes “Thus the cost may be enormous if the gene selected is completely recessive, and it seems doubtful whether completely recessive genes are ever selected.” [emphasis mine] (Haldane goes on to say that recessives only have a chance to spread in small isolated populations)

For example in a founder population, in which the population size would not be constant. Shame that you deigned to ignore the other important segments of Haldane's 1960 paper, such as where he explicates that one should be carefult not to apply his model where it does not apply.

quote:

Other things of note:

2) I think it is important to note that Page still refuses to acknowledge that the Wu study assumes human/simian (specifically OW monkeys) ancestry.


I think it is important to note that Williams still refuses to acknowledge the difference between his claims regarding 'apes' and 'simians'. Conflation of terminology makes it difficult to address issues. Perhpas if Williams would educate himself on proper terminology, such issues would not come up. Also of note is the fact that Williams seems unwilling to acknowledge that an assumption of ancestry is warranted by the evidence. I have never claimed, contrary to Williams repeated statements to the contrary, that the Wu study does not assume ancestry, rather, I have repeatedly pointed out that Williams simply mischaracterized their assumption to suit his needs.

quote:

2) Page continues to insist that Haldane’s model is premised on evolution being true. This is precisely equivocation, and he is flat wrong to engage in it.

Williams can repeat this hollow accusation os often as he wishes, and as I demonstrated in my latest refutation, he will still be wrong. Williams seems unwilling or unable to understand that 'evolution' as such is indeed assumed by Haldane. Williams seems to want to claim that Haldane was not specifically referring to evolution on the scale of humans and apes, for example, as his tacked-on criteria show. Unless Williams can show where Haldane specifically stated that he was referring to 'microevolution', Williams repeated charges are simply red herrings.

quote:

Allele replacement is part of the YEC framework, as is selection (which creationists espoused even before Darwin). Page knows this, but would still try to have you believe that selection is an “evolutionary” idea, and allele replacement is exclusive to evolution. Using Page’s logic, I could just as easily write “Haldane’s model is premised on creation being true”.

This is a truly bizarre extrapolation by Williams. How can I possibly 'know' something that has simply been co-opted? This is akin to claiming that because Newton was a creationist (of corts) that his work on gravity is the reulst of his being a creationist and that the laws of gravity were worked out by a 'creation scientist'!Are you actually trying to suggest that Haldane was using creationist assumptions? Absurd!

quote:

What is ironic is that in the past Page has used Haldane’s model to argue against YEC rapid speciation since the flood! How can Page do this if he really believes the model is built off of evolutionary assumptions?!!!

Misrepresentation. It is a shame that Williams so rapidly resorts to this sort of activity. I used Haldane's model against creationism to demonstrate the folly of using it against evolution. I have explicitly explained this on several occasions. That Williams is yet again trying to mischaracterize this is not surprising. But this passage is interesting - it seems to me that Williams is implying that only constructs built on the proper assumptions can be used when analysing issues that follow from those assumptions, i.e., only evolution-based models are useful when addressing evolutionary issues, only creationistic models are useful when evaluating creationist claims. If this is so, then Williams will need to engage in a large amount of retraction.

quote:

I have always said that Haldane’s model, since it is not formulated on how life originated, can be applied to the YEC framework. When Page and other evolutionists use it to argue against YEC, they are actually using valid logic. That is what led our debates in the past to such topics as adaptive mutations, among others.

A topic which Williams has conceded defeat in, by default.

quote:

My point then and now is that evolution has no reasonable explanation for the Haldane problem, whereas the YEC model has several reasonable explanations available to it.

One can only say this if one has completely ignored the documentation supplied to them, as ReMine has, and as Williams is doing here. This is an example of a purely hyperbolic statement. The ONLY YEC 'explanation' is 'directed mutation', a topic that Williams has been wholly unable to rationally defend, and for which I and others have already provided sound refutations of. The evolutionary 'explanations' for the Haldane issue are many, starting with the inapplicability of the model itself, as Haldane correctly pointed out. In addition, the primary reason that creationists like Williams and ReMine have latched onto this, it seems to me, is nothing more than personal incredulity. Under the unrealistic and inapplicable Haldane model, only some 1667 beneficial mutations could have become fixed in 10 million years (as I explain in my refutation of Williams). They simply do not believe that that is sufficient to explain evolution of humans from an ape-like ancestor in that amount of time. Problems: 1. they do not know what the ancestor was, therefore, they have no way of knowing how many changes would have been required 2. even if they knew what the ancestor was, they have no way of knowing how many phenotypic changes would result from the 'allowable' mutations 3. personal disbelief does not count as any sort of evidence.
oh - and miracles don't count, either.

quote:

3) Page continues to claim the Rice study is evidence that sex is beneficial to evolution:

It is, and Williams continues to fail to understand this.

quote:

quote:
----------------------------------------------------------------------
Page: The Rice study demonstrates the benefit of sex (which creationists claim is an 'enigma' and all that) - it helps to increase the accumulation of beneficial mutations while decreasing the accumulation of deleterious ones.
----------------------------------------------------------------------

Despite having this pointed out to him now on numerous occasions, he continues to conveniently forget a very important factor. The above is only true when the ENVIRONMENT CONSISTS OF A HUGE FLOW OF HARMFUL MUTATIONS EACH GENERATION! Since a huge flow of harmful mutations is anti-evolution, it is very misleading to claim that the Rice study demonstrates the benefit of sex for evolution. Page’s explicit claim, and Rice’s implicit claim, is nothing short of intellectual dishonesty.


Such charges are common coming from creationists, especially those in Williams' position of arguing on the whole from a dogmatic ignorance. Williams is fixated on the experimental conditions of the study, and seems to believe that the benefits of sex in such an environment suddenly disappear in other circumstances.
As such, I am strongly offended by Williams' charge, and demand that if he is so confident of his beliefs, that he should write up a sound rebuttal in the form of a letter and submit it to Science or send it to Rice. Accusations of dishonesty are easy to make, harder to support. And simply repeating assertions is not support.

quote:

Let’s try something. I ask Page to show us how the Rice study demonstrates that sex is a benefit for evolution in an environment where there is a nominal rate of mutation per organism per generation. Feel free to use any rate that does not deteriorate a species. A rate that keeps the genetic load at equilibrium would be fine. Use their charts and data. Show the readers and I where in their data, recombination “increases beneficial mutations while decreasing harmful ones” when the rate of mutation is equilibrium. If you cannot achieve this, then your original claim that their study supports evolution is intellectual dishonesty and you should retract it.

(I’ll remind Page that anything less than equilibrium is deterioration, which is anti-evolution, which is the only section of the graph the Rice study works! For my analysis, see: http://www.evolutionfairytale.com/articles_debates/page_refutation.htm and page down to "Sexual Recombination and the Power of Natural Selection")


Reading that article, all one sees is the original assertion which has been repeated ad nauseum. Better yet - maybe Willaims can explain why his charges have merit. From the paper, any emphases mine:

"In our experiments, we emulated feasible natural conditions by using
moderate levels of selection relative to population size and background selection
, and we experimentally verified that the constraint [equation in original] was met."
Perhaps Williams can, by using their 'charts and graphs', actually explain what he means by 'harmful mutation environment' (a phrase which does not occur in the paper and which seems to have been pulled from thin air, considering the authors' explanation of their methods).

And, best of all, perhaps Williams can provide - with evidenciary support - those 'YEC explanations for the evolution problems (e.g., chimp-bonobo issue).

quote:

4) Questions from Page:

quote:
----------------------------------------------------------------------
Page: Other things Williams deigned to ignore:
His erroneous defense of ReMine's claims (re: 500,000 changes...)
----------------------------------------------------------------------

I cannot comment on the 500,000 until my Remine book is returned to me.


I provided the quote. Stall tactic.

quote:

quote:
----------------------------------------------------------------------
His continued reliance upon papers that also assume evolution (e.g., Eyre-Walker and Keightly's paper), indicating some hypocrisy in his position
----------------------------------------------------------------------

I think you are the only evolutionist biologist I’ve debated who refuses to understand my point, yet I have been debating it with you longer than any other “scientist”, so you have no excuse.


Your implied insult is noted.

quote:

I do not “rely” on Walker/Keightley paper for an accurate mutation rate. I have stated over and over again that their rate is WRONG.

I did not say that you “rely” on Walker/Keightley paper for an accurate mutation rate. I wrote - and it is a fact - that you continue to use it in your 'articles' on your satirical website, which I understand is not meant to be taken seriously anyway, despite the fact that you claim that using papers with similar assumptions is wrong.

quote:

It MUST be wrong because it is ridiculous to assume that our alleged chimp/man ancestor produced 40+ offspring.

I have asked repeatedly what this claim actually means, and I have yet to read an answer.

quote:

Thus, since I conclude that their concluding rate of mutation is wrong, that something must be amiss within their study. Is it their math? No.

Why do you say this? Are you one of the many creationists that believe that math is the most important aspect of any pursuit, as does Dembski? What if their application of the math is off?

quote:

Is it their data points from sequence gathering? I seriously doubt it. Is it their assumption that chimp and man share a distant ancestor? Yes, I think this must be where the problem lies, and why they end up with such a ridiculously high mutation rate.

Regarding this particular paper, you at one time made much of their '90% sequencing' of loci, especially when you attempted to use it to 'insult' my data. You never did/could explain whjat the significance of that was. Perhaps you can now?

quote:

quote:
----------------------------------------------------------------------
My mention of his ignored Baptist Board posts, specifically, my question regarding his beloved 'X-number of offspring per couple' schtick
----------------------------------------------------------------------

Time constraints. If it’s the question you asked in this thread, I’ll try to get to it shortly…


Is it also a time contraint that has prevented you from writing that 'directed mutation' article, the one purporting to, among other things: provide documentation that this has occurred in multicellular eukaryotes? It seems that you had time to write what I have heard is a rather silly article on fossils, but not this one that you claimed to have been working on over a year ago?

I cannot wait to read it.

[This message has been edited by SLPx, 07-05-2002]


This message is a reply to:
 Message 33 by Fred Williams, posted 07-05-2002 11:39 AM Fred Williams has not yet responded

Replies to this message:
 Message 38 by Percy, posted 07-05-2002 5:33 PM derwood has not yet responded

  
derwood
Member (Idle past 679 days)
Posts: 1455
Joined: 12-27-2001


Message 37 of 57 (12848)
07-05-2002 2:54 PM
Reply to: Message 35 by Percy
07-05-2002 1:53 PM


quote:
Originally posted by Percipient:
Just in case I'm not alone in the difficulties I've faced attempting to following the discussion between Scott and Fred, I thought I'd respond to Fred's excellent post with what I hope will be some clarifications. Please post corrections to anything I get wrong.

The first questions has to be, "What is Haldane's Dilemma?" because I don't think it's apparent from only a reading of the dialogue between Scott and Fred.

Haldane's dilemma can be characterized through the example of man/chimp evolution. The evolutionary view is that some millions of years ago man and chimp shared a common ancestor from which both species eventually evolved, and today the difference between the chimp and man genome is around 2%. But man and chimp are both slowly reproducing species, so how could a difference of 2% occur in only 5 million years given prevailing rates of evolutionary change.


Yes and no. ReMine goes into convoluted rants when one mentions modern humans and chimps. Haldane's evolution-based model of the fixation of beneficial (adaptive) alleles put a 'speed limit' on evolution. According to ReMine's application of Haldane's model, no more than 1667 such mutations could have become fixed in 10 million years. As Haldane admitted in his 1957 paper, and alluded to in his 1960 paper, his numbers would probably require 'drastic revision', and, as he pointed out, one should not apply his model where it is not applicable. Among the constraints in Haldane's model were weak selection and a constant population size. Many evolutionary biologists (e.g., Felsenstein; Darlington) demonstrated that in many instances, the events that would lead to a speciation event would induce strong selection (as in some peppered moth populations) and a reduced population size, such that the cost would be 'paid' rapidly and the beneficial allele(s) fixed in short order. In addition, there are documented examples of organisms evolving at rates which exceed the limit imposed by Haldane's model (e.g., "Population structure in relation to cost of selection," Grant and Flake, 1974, PNAS 71(5)1670-71). Such counter-examples are mysteriously missing from ReMine's book. In my view, this is a case of data controverting the math.
At any rate, few evolutionary biologists expend much time on the issue anymore. If we are to believe the likes of ReMine, it is because of a systematic attempt by those 'evos' to hide it from the public (NOT a conspiracy, mind you...). If we are to take the actual papers and history into account, more likely it is because it was realized that as written, Haldane's model was largely inapplicable to natural populations; that some data were at odds with what the model predicted, and as such, the model needed adjusting; etc.

quote:

But one doesn't have to approach it on a mathematical level to wonder how so much change could occur in so little time, and even evolutionists must concede that biology does not as of yet have satisfactory models to explain fairly rapid species change for animals like ourselves...How did the angle of the hip joint change? What about the orientation and shape of the pelvis? How about the angle of the skull on the backbone. What about skull and brain changes? How much, when, how fast, sequentially or all at the same time? We don't know.

The phenotypic characters Percy mentions are an interesting point - issues such as heterochrony are definitely at play here. Many now believe that developmental genes and regulatory sequence played as much or more of a role than those genes that control or influence morphology. Take a (hypothetical) gene that controls bone growth in the axial skeleton during fetal development, for example. If we alter the time during which this gene is turned on, we can effect substantial changes in the relative lengths/widths of bones in the axial skeleton.

quote:

To Creationists the fossil record is so clearly full of holes that it serves as very poor evidence of evolution and much better evidence of special creation. I think this skepticism is well founded, though it is scant justification for the Creationist flights of fancy that involve rejecting much of cosmology, physics, geology and biology.

I disagree with your first point. That the fossil record is not complete should actually be expected. It provides creationists with ammunition, of course - provided that their audience knows less about the fossil record than they do. As SJ Gould said at a lecture I attended, if you know a little about geology and the fossil record, what the creationists say can seem to make sense. If you know a lot, then it is just so much hogwash. The fossil record can, in my view, not in any rational way be seen as evidence for anything like the creation event(s) described in Genesis.

quote:

Trying to imagine the detailed changes human ancestral species might have gone through on their way to evolving into us brings some helpful visualization to the more abstract details of the Haldane's Dilemma discussion, which from a Creationist standpoint merely postulates that the rate of evolutionary change is too slow for a chimp/man ancestor to have evolved into us.

A belief based solely upon personal disbelief.

[This message has been edited by SLPx, 07-05-2002]


This message is a reply to:
 Message 35 by Percy, posted 07-05-2002 1:53 PM Percy has not yet responded

  
Percy
Member
Posts: 15632
From: New Hampshire
Joined: 12-23-2000
Member Rating: 4.0


Message 38 of 57 (12861)
07-05-2002 5:33 PM
Reply to: Message 36 by derwood
07-05-2002 2:22 PM


Scott's post introduced some welcome clarification for me, and I guess for me the discussion boils down to a single question for Fred.

We construct models within theoretical frameworks to help us make predictions, such as the one ReMine makes regarding human evolution. One of the inherent problems with models, however, is that they are only approximations of the reality which theory attempts to describe, and that they are constrained by the limits of human capability and understanding.

So while problems in models *can* be indications of fundamental problems with theory, in the case of Haldane's Dilemma, which is based upon a 45 year-old model not given much attention in modern biology, the model seems the obvious suspect since no significant problems with evolutionary theory have been identified. While Haldane's work in this area is instructive, I think he attempted to model that for which he had insufficient information and insight, and I think that situation still exists today.

In other words, even if Haldane's model had right up until the present been considered completely correct, and even assuming that ReMine has correctly applied Haldane's model, the wrong answers it provides only raise questions with the model and its application, and not with the theory.

--Percy


This message is a reply to:
 Message 36 by derwood, posted 07-05-2002 2:22 PM derwood has not yet responded

Replies to this message:
 Message 40 by Fred Williams, posted 07-06-2002 2:45 PM Percy has responded

  
Fred Williams
Member (Idle past 2270 days)
Posts: 310
From: Broomfield
Joined: 12-17-2001


Message 39 of 57 (12910)
07-06-2002 2:30 PM
Reply to: Message 35 by Percy
07-05-2002 1:53 PM


Haldane's Dilemma boils down to the required number of deaths that must occur in a population to fix a new allele under positive selection (beneficial mutation). Haldane showed that at best 1 substitution could become fixed in a population every 300 generations. Using conservative assumptions, he showed that the cost for allelic substitution was roughly 30 generations (and thus 30 populations). He then estimated the cost of selection per generation to be about 10% (that is, he assumed that 10% of the offspring would be available to pass on the new mutation, while the other 90% would pay for random deaths, lethal mutations, prudes, ugly ducklings, etc). With 10% of reproductive excess available for the new allele, he arrived at a total cost of 30/.1 = 300 generations per substitution.

Remine then put this figure in plain English. Assuming 10 million years for human evolution (a favorable assumption, since the current number is ~6My) this means at most only 1667 mutations under positive selection occur in 10 million years from our alleged simian/man ancestor.

Where many go astray with Haldane's Dilemma is on the cost issue. Case in point, Page recently wrote this:

quote:
Among the constraints in Haldane's model were weak selection and a constant population size. Many evolutionary biologists (e.g., Felsenstein; Darlington) demonstrated that in many instances, the events that would lead to a speciation event would induce strong selection (as in some peppered
moth populations) and a reduced population size, such that the cost would be 'paid' rapidly and the beneficial allele(s) fixed in short order.

Haldane showed that strong selection is an *enemy* of reproductive cost! (see p521, and plug in a high value for n; in the example Haldane gave, he called intense selection “hardly compatible with survival”). To illustrate this point it is convenient to go all the way to one end point. Imagine a population of 100,000 asexual animals, where a new mutation has such powerful selection that every organism without it dies. To replenish the 100,000 in one generation the organism would need to birth 99,999 offspring. Thus, the reproductive cost is huge (99,999). Apply this to any mammalian sexual species (say two receive the mutation and 99,998 die). The payment for the 99,998 deaths obviously cannot be paid in one generation (by any mammalian species I know of), but instead would require many generations to rebuild the population to 100,000 because of the reproductive limitations, provided it could even survive such an intense selection episode! (the first generations would surely be on the “endangered species” list!) By slowing the pace over time, Haldane was able to reduce the reproductive cost to a reasonable level. He showed that cost was essentially independent of selection (p 524).

One last thing regarding Page’s citation. Evolutionists always forget the other side of the coin. Small founder populations are the enemy of evolution because genetic drift will invariably work to *remove* information from the genome. In addition, genetic drift will move many of the low-frequency deleterious mutations toward higher frequencies.


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 Message 35 by Percy, posted 07-05-2002 1:53 PM Percy has not yet responded

Replies to this message:
 Message 41 by derwood, posted 07-07-2002 2:52 PM Fred Williams has responded

  
Fred Williams
Member (Idle past 2270 days)
Posts: 310
From: Broomfield
Joined: 12-17-2001


Message 40 of 57 (12912)
07-06-2002 2:45 PM
Reply to: Message 38 by Percy
07-05-2002 5:33 PM


[QUOTE]Originally posted by Percipient:
...the model seems the obvious suspect since no significant problems with evolutionary theory have been identified... In other words, even if Haldane's model had right up until the present been considered completely correct, and even assuming that ReMine has correctly applied Haldane's model, the wrong answers it provides only raise questions with the model and its application, and not with the theory.
--Percy[/B][/QUOTE]

Where we disagree is when you say "no significant problems with evolutionary theory have been identified". We're obviously going to have our biases here. I think there is no tangible evidence whatsoever for large-scale evolution and that to me is a "significant problem!

There's the obvious design of nature, there's the fossil record that is remarkably anti-evolutionary, the mutation rate problem as described in my article (note that Hadane's model need not be correct for my article to be valid), and of course, the information problem which is a serious nail in the coffin of evolution. How did the DNA code arise by chance? Etc Etc. There are many significant problems for the theory. Again, I know we have our biases, but when I started researching this some 7 years ago I expected there to be at least some evidence, and was floored by the total lack of evidence for large-scale evolution. It amazed me that I had been brainwashed for over 30 years into believing otherwise.

I've stated before that I don't really emphasize Haldane's problem that much. It's an interesting model that could be wrong (though I have yet to see a convincing argument that it is). I instead emphasize the mutation rate problem that is somewhat related to Haldan'es model but does not rely on the model's accuracy. Current mutation rate data and statisticis 101 clearly contradict evolution in easy-to-understand terms. Here again is my article on this:

http://www.evolutionfairytale.com/articles_debates/mutation_rate.htm

Note to Page: Several studies have substiantiated the Keightley study, more reason why it is unlikely there is a flaw in their math.


This message is a reply to:
 Message 38 by Percy, posted 07-05-2002 5:33 PM Percy has responded

Replies to this message:
 Message 42 by derwood, posted 07-07-2002 3:12 PM Fred Williams has not yet responded
 Message 43 by Percy, posted 07-07-2002 7:45 PM Fred Williams has responded

  
derwood
Member (Idle past 679 days)
Posts: 1455
Joined: 12-27-2001


Message 41 of 57 (12963)
07-07-2002 2:52 PM
Reply to: Message 39 by Fred Williams
07-06-2002 2:30 PM


quote:
Originally posted by Fred Williams:
Haldane's Dilemma boils down to the required number of deaths that must occur in a population to fix a new allele under positive selection (beneficial mutation).

Clarification - the number of genetic deaths.

quote:

Haldane showed that at best 1 substitution could become fixed in a population every 300 generations.

In a population of constant size in whihc selection for the new allele is weak. Lets not forget the conditions.

quote:

Using conservative assumptions, he showed that the cost for allelic substitution was roughly 30 generations (and thus 30 populations). He then estimated the cost of selection per generation to be about 10% (that is, he assumed that 10% of the offspring would be available to pass on the new mutation, while the other 90% would pay for random deaths, lethal mutations, prudes, ugly ducklings, creationists, etc). With 10% of reproductive excess available for the new allele, he arrived at a total cost of 30/.1 = 300 generations per substitution.

Remine then put this figure in plain English. Assuming 10 million years for human evolution (a favorable assumption, since the current number is ~6My) this means at most only 1667 mutations under positive selection occur in 10 million years from our alleged simian/man ancestor.


Again I would ask for the EVIDENCE that applying Haldane's model - as electrical engineer creationist ReMine did - is justified. Specifically, you will need to provide: evidence that the ancestral primate population and all of the descendant populations were of constant size; evidence that selection was always weak. For starters.
Oh, I forgot - you will also need to supply evidence regarding the nature of the alleged ancestor and evidence as the required changes that had to have taken place in the intervenining time.
Without that information, even if Haldane's model were exactly applicable, there is no rational reason to claim that it 'contradicts evolution', as Williams is wont to do.

quote:

Where many go astray with Haldane's Dilemma is on the cost issue. Case in point, Page recently wrote this:

Among the constraints in Haldane's model were weak selection and a constant population size. Many evolutionary biologists (e.g., Felsenstein; Darlington) demonstrated that in many instances, the events that would lead to a speciation event would induce strong selection (as in some peppered
moth populations) and a reduced population size, such that the cost would be 'paid' rapidly and the beneficial allele(s) fixed in short order.

Haldane showed that strong selection is an *enemy* of reproductive cost! (see p521, and plug in a high value for n; in the example Haldane gave, he called intense selection “hardly compatible with survival”).


And yet, this is the same Haldane that ended his paper with the statement regarding the fact that his numbers would need 'drastic revision'...
"Enemy" of reproductive cost? What does that mean?

quote:

To illustrate this point it is convenient to go all the way to one end point. Imagine a population of 100,000 asexual animals, where a new mutation has such powerful selection that every organism without it dies. To replenish the 100,000 in one generation the organism would need to birth 99,999 offspring. Thus, the reproductive cost is huge (99,999).

Please provide the documentation wherein it is claimed that a population must be restored to its original size in one generation. I will be waiting with baited breath for this documentation.

quote:

Apply this to any mammalian sexual species (say two receive the mutation and 99,998 die). The payment for the 99,998 deaths obviously cannot be paid in one generation (by any mammalian species I know of), but instead would require many generations to rebuild the population to 100,000 because of the reproductive limitations, provided it could even survive such an intense selection episode!

Again, please explain why it would need to be pais in one generation.

I wonder if the creatonist has ever tried to apply this to the Flood scenario? Though the selection employed in the flood was not 'natural' - or even moral or logical or rational - we can assume that several million people were killed by the childish thug Yahweh, leaving only 8 inbreeding survivors. I don't know when YECs claim this occurred, I have heard anywhere from the ridiculously flawed 2,500 years ago to about 4,500 years ago. Let's just say that there were only 1 million people alive at the time of the flood, so the 'cost' paid for not being righteous in the eyes of the Lord was 999, 992.

How does that mesh up with population genetics, I wonder?

quote:

(the first generations would surely be on the “endangered species” list!)

Indeed. Of course, if they were better adapted to the environemnt, they would have an advantage, wouldn't they?[/quote]

By slowing the pace over time, Haldane was able to reduce the reproductive cost to a reasonable level. He showed that cost was essentially independent of selection (p 524).[/quote]

So Haldane did this? By tweaking his mathematical model? Hmmm...

quote:

One last thing regarding Page’s citation. Evolutionists always forget the other side of the coin. Small founder populations are the enemy of evolution because genetic drift will invariably work to *remove* information from the genome. In addition, genetic drift will move many of the low-frequency deleterious mutations toward higher frequencies.

Yes, the enemy of evolution. But they are apparently the friend of creationism! For was it not you who once wrote that drift and bottlenecks (founder populations) help to explain the issues?

Convenient, that.

Of course, creationists, in my opinion purposely distort/ignore the real flip side, as for example where Haldane writes:

"Thus it is important that Kimura's theory and my own should not be extended to cover biological situations in whihc they do not apply."
(More precise expressions for the cost of natural selection. 1960.)

And what were some of those situations in which they do apply?

"...in a population of constant size... These expressions were not, however, precise unless the intensity of selection is weak."
(same)


This message is a reply to:
 Message 39 by Fred Williams, posted 07-06-2002 2:30 PM Fred Williams has responded

Replies to this message:
 Message 44 by Fred Williams, posted 07-09-2002 1:57 PM derwood has responded

  
derwood
Member (Idle past 679 days)
Posts: 1455
Joined: 12-27-2001


Message 42 of 57 (12965)
07-07-2002 3:12 PM
Reply to: Message 40 by Fred Williams
07-06-2002 2:45 PM


quote:
Originally posted by Fred Williams:
I think there is no tangible evidence whatsoever for large-scale evolution and that to me is a "significant problem!

Shame that the thousands that have relevant educational backgrounds and actually do/have done scientific research in the area don't see things your way.

quote:

There's the obvious design of nature,

Obvious to whom?

quote:

there's the fossil record that is remarkably anti-evolutionary,

Right - I mean afterall, you can find dinosaurs and humans in contemporaneous strata all over the place!

quote:

the mutation rate problem as described in my article (note that Hadane's model need not be correct for my article to be valid),

You mean the 'article' on your 'satirical' website? The one which, according to other creationists, is not to be taken seriously and is not meant to convey scientific information? The 'article' which resides solely on your website? The one that you have yet to submit to any legitimate journal for publication? That one?

quote:

and of course, the information problem which is a serious nail in the coffin of evolution. How did the DNA code arise by chance? Etc Etc.

That was quite a litany of "Gee, I can't see how evolution explains this - therewfore, it must be wrong" musings. How did it arise by chance?

Hmmm... Maybe if the creationists would stop making a caricature of science, they would stop leaving out half (or more) of the story... But i doubt it...

quote:

There are many significant problems for the theory. Again, I know we have our biases, but when I started researching this some 7 years ago I expected there to be at least some evidence, and was floored by the total lack of evidence for large-scale evolution. It amazed me that I had been brainwashed for over 30 years into believing otherwise.

And now you are brainwashed into believing that an ancient superstitious and somewhat plagiarised text written by largely unknown authors during a pre-technoological, pre-scientific time in history is inerrant and "100% true"? Wow....

This brainwashing - how did it occur? I always get a kick out of that charge. When I went to school (1970-1984), evolution was mentioned only twice that I can recall - once in sixth and slightly in 7th grade. I later took an elective course on anthropology and there was a one-week section on physical anthropology. I suspect that most curricula were similar.
Of course, we did say the Pledge everyday, during which we were coerced into 'admitting' that the God of the bible not only exists, but that it looks down on our country.
And of course there is the money issue... And the oath issue... But by golly - folks are BRAINWASHED into accepting evolution as children!

But what is 'large-scale' evolution? It seems to depend on the argument. Sometimes, it is mere speciation. Sometimes, it is the 'split' between genera or familiaes. Sometimes, it 'requires' the acquisition of a 'new body part.'

I have seen - and even generated some - data showing a relatively smooth genetic distance between species... genera... families...
But I forgot - THAT data is simply a matter of 'interpretation'...

quote:

I've stated before that I don't really emphasize Haldane's problem that much. It's an interesting model that could be wrong (though I have yet to see a convincing argument that it is).

Of course not. I wonder - have you seen convincing DATA that it is? That it is applicable in all instances?

quote:

I instead emphasize the mutation rate problem that is somewhat related to Haldan'es model but does not rely on the model's accuracy. Current mutation rate data and statisticis 101 clearly contradict evolution in easy-to-understand terms. Here again is my article on this:

http://www.evolutionfairytale.com/articles_debates/mutation_rate.htm


Yes, an amazing article. From it:

"It says that females need to produce over 10 offspring just to keep genetic deterioration near equilibrium! "

Please explain - which you do not in the article, have not in the past despite repeated requests to, and which ReMine still cannot or will not do (see: http://www.baptistboard.com/cgi-bin/ultimatebb.cgi?ubb=get_topic&f=36&t=000154&p= ) - HOW having X-number of offspring will prevent genetic deterioration. Please explain how this 'prevents' evolution.

Please do. For once.

quote:

Note to Page: Several studies have substiantiated the Keightley study, more reason why it is unlikely there is a flaw in their math.

Which studies are those?

Lets say that you inferrences' based on their paper is correct.
Mutation rates are 'too' high. Yet, here we are. What does that indicate? Does that mean that we were 'created' only a few thousand years ago by the ultimate founder population (of 2)? Or does it mean that there are mechanisms at work that we do not yet know about which counteract this mutation rate? I opt for 2. It is the rational, scientific choice.


This message is a reply to:
 Message 40 by Fred Williams, posted 07-06-2002 2:45 PM Fred Williams has not yet responded

  
Percy
Member
Posts: 15632
From: New Hampshire
Joined: 12-23-2000
Member Rating: 4.0


Message 43 of 57 (12978)
07-07-2002 7:45 PM
Reply to: Message 40 by Fred Williams
07-06-2002 2:45 PM


Hi, Fred!

I don't really have anything apropos to add at this point, but I wanted to thank you for the helpful responses. They contributed quite a bit to clarifying this discussion for me.

I *did* want to make a couple comments not directly bearing on this discussion. One concerns terminology. The term "anti-evolution" doesn't really exist within biology. The process you refer to as "anti-evolution" and define as loss of information is what an evolutionist would still term evolution, since it is still a change in allele frequency over time. It might be helpful if you could find another term for evolution involving loss of information.

The other comment concerned this:

Fred Williams writes:

There's the obvious design of nature, there's the fossil record that is remarkably anti-evolutionary...Again, I know we have our biases, but when I started researching this some 7 years ago I expected there to be at least some evidence, and was floored by the total lack of evidence for large-scale evolution.

For most evolutionists, the first discovered, strongest, and most obvious evidence for evolution is the fossil record. Primary evidence from which we draw opposite conclusions probably deserves significant further discussion.

--Percy


This message is a reply to:
 Message 40 by Fred Williams, posted 07-06-2002 2:45 PM Fred Williams has responded

Replies to this message:
 Message 45 by Fred Williams, posted 07-09-2002 2:12 PM Percy has responded

  
Fred Williams
Member (Idle past 2270 days)
Posts: 310
From: Broomfield
Joined: 12-17-2001


Message 44 of 57 (13169)
07-09-2002 1:57 PM
Reply to: Message 41 by derwood
07-07-2002 2:52 PM


quote:
Originally posted by Fred Williams:
Haldane's Dilemma boils down to the required number of deaths that must occur in a population to fix a new allele under positive selection (beneficial mutation).
Page: Clarification - the number of genetic deaths.

No such clarification is required, “death” is apropos. The qualifier “genetic” is not needed.

quote:
Me: By slowing the pace over time, Haldane was able to reduce the reproductive cost to a reasonable level. He showed that cost was essentially independent of selection (p 524).
Page: So Haldane did this? By tweaking his mathematical model? Hmmm...

Page continues to demonstrate he does not have the foggiest idea what Haldane’s paper says. Page implies intense selection is a way out of the Haldane problem, and implies that Haldane ignored its impacts or was mistaken not to accommodate it. Yet Haldane recognized intense selection for what it was, an unrealistic and rare event that actually made matters worse for evolution! (specifically the cost of substitution). I again refer Page to page 520. Notice that fitness is e^(-30n^-1), and intensity is I=30n^-1. As intensity increases, n (number of generations to fix one gene) decreases, causing a logarithmic decrease in fitness! To illustrate this, Haldane gave an example of n=7.5, which represents an enormous intensity of 4. This yields a fitness of .02, which Haldane calls “hardly compatible with survival” (it means that 100 offspring are needed just to get one without a new harmful mutation). The relationship between intensity and substitution cost really only manifests itself as you start moving intensity above .1 (which is even considered atypically high selection by biologists). That is why Haldane said that cost and selection are essentially independent provided you don’t plug in ridiculously high values for selection. As I said earlier, intense selection is an enemy of reproductive cost.

Finally, Page confirms he is confused on the implications of intense selection when he takes the following quote from Haldane completely out of out-of-context:

quote:
Page: Of course, creationists, in my opinion purposely distort/ignore the real flip side, as for example where Haldane writes:
"Thus it is important that Kimura's theory and my own should not be extended to cover biological situations in whihc they do not apply."
(More precise expressions for the cost of natural selection. 1960.)
And what were some of those situations in which they do apply?
"...in a population of constant size... These expressions were not, however, precise unless the intensity of selection is weak."(same)

I hope I don’t have to scan the appropriate page (p 359) to prove Page is taking Haldane out of context. Early in the paragraph Haldane writes “The results given in 1957 are however accurate enough for most practical purposes.” Haldane then goes on to comment that Kimura’s “substitutional load” cannot be readily compensated by gene substitution, because it would require “100 of millions of years”. He proceeds to give an example of unrealistically intense selection, then notes in the sentence directly preceding Page’s quote: “Organisms which produce many offspring permit of rapid artificial selection only if they can be protected from natural causes of death.” What Haldane is saying is that in assumed scenarios of intense selection, it is unrealistic to ignore the impact of natural causes of death, which themselves incur a cost because they reduce the number of offspring available for beneficial substitution.

Page believes that Haldane is admitting that he used unrealistic assumptions, which is simply not true and actually is quite the opposite. Haldane is arguing that one should not apply his model to situations that are unrealistic (Note that Haldane actually used assumptions favorable to evolution, such as atypically high selection I=.1; What if he had used the more generally accepted value of .01? Then it would have taken 3000 generations per substitution!)

Its ironic what Page wrote regarding the above passage: “One should hope that the creationists that like to hang their hat on "Haldane's Dilemma" would have read and understood this at some point...”

Let’s hope Page finally read the passage and now understands what Haldane really was saying. I would hope a retraction from Page regarding his out-of-context quote is forthcoming…


This message is a reply to:
 Message 41 by derwood, posted 07-07-2002 2:52 PM derwood has responded

Replies to this message:
 Message 47 by derwood, posted 07-10-2002 1:32 PM Fred Williams has responded

  
Fred Williams
Member (Idle past 2270 days)
Posts: 310
From: Broomfield
Joined: 12-17-2001


Message 45 of 57 (13171)
07-09-2002 2:12 PM
Reply to: Message 43 by Percy
07-07-2002 7:45 PM


quote:
The process you refer to as "anti-evolution" and define as loss of information is what an evolutionist would still term evolution, since it is still a change in allele frequency over time.

You are actually doing me a favor here by supporting my claim that evolution is not falsifiable!

I have a short article on how the term “evolution” is equivocated to make it true by default:

http://www.evolutionfairytale.com/articles_debates/evolutiondefinition.htm

quote:
For most evolutionists, the first discovered, strongest, and most obvious evidence for evolution is the fossil record. Primary evidence from which we draw opposite conclusions probably deserves significant further discussion.

I actually started one here some time ago. It was a discussion regarding this article I wrote:

http://www.evolutionfairytale.com/articles_debates/fossil_illusion.htm

What occurred in that thread was what almost verbatim what I predicted in the sidebar in my article!

I realize the article is a bit offensive (), but it is what I truly believe, that most evolutionists both unwittingly and wittingly are employing a sleight-of-hand with the public when they try to sell the fossil record as evidence for evolution.

IMO, if the fossil record supported evolution, punctuated equilibrium would never had seen the light of day.


This message is a reply to:
 Message 43 by Percy, posted 07-07-2002 7:45 PM Percy has responded

Replies to this message:
 Message 46 by Percy, posted 07-09-2002 7:20 PM Fred Williams has not yet responded

  
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