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EvC Forum Science Forums Biological Evolution Explaining the pro-Evolution position

# Summations Only

Author Topic:   Explaining the pro-Evolution position
Director
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 Message 376 of 393 (792912) 10-15-2016 9:24 AM Reply to: Message 362 by Kleinman10-14-2016 6:28 PM

Re: Is it summation time?
Kleinman writes:

quote:
 All adaption by rmns requires lineages to address nested binomial probability problems.

Well, perhaps you could show us some math.

Again? That would make Percy unhappy.

I think you must have set some sort of record for repeating mathematical claims while doing so little actual math. It would make Percy very happy if you could make a mathematical presentation that supports your claims. Your very general and self evident equation doesn't do this in a way apparent to anyone.

 -- Percy EvC Forum Director

 This message is a reply to: Message 362 by Kleinman, posted 10-14-2016 6:28 PM Kleinman has not yet responded

Kleinman
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 Message 377 of 393 (792913) 10-15-2016 9:29 AM Reply to: Message 375 by Admin10-15-2016 8:48 AM

Re: Lenski
quote:
This is the only equation you've presented:

 Kleinman writes:P(−∞ < X < +∞) = P(Ad) + P(Cy) + P(Gu) + P(Th) + P(iAd) + P(iCy) + P(iGu) + P(iTh) + P(del)+… = 1

What you must do is substitute actual values into this equation demonstrating evolution impossible. If I don't see this presentation very soon I will drop this thread into summation mode.

A review: We are presenting the mathematics of the simplest case of rmns, that is a single selection pressure targeting a single gene. The derivation of the equations is done in the context of an empirical example of rmns, that of a bacteria evolving resistance to an antibiotic. This empirical example can be found at http://isites.harvard.edu/...Papers/Weinreich-et-al-2006.pdf

In the Weinreich paper he measured the mutations which evolved resistance to a particular antibiotic. There were a wide variety of variants which evolved resistance but all had in common in that it took 5 mutations to evolve high resistance to the antibiotic. The first beneficial mutation determined the evolutionary trajectory for that variant and the next 4 beneficial mutations required for that evolutionary trajectory.

The derivation for the mathematics of rmns for this problem will be done in general terms. That is that a sequence of mutations A,B,C,D and E occur where each ensuing beneficial mutation gives increasing resistance (and therefore improved fitness to reproduce) to the antibiotic selection pressure.

The first step in doing the mathematics of this stochastic process is to recognize that there are two random trials occurring in rmns. The two random trials are the replication (where the two possible outcomes are that a mutation occurs or does not occur at the particular site) and the mutation itself is a random trial (where only a particular mutation gives benefit). The possible outcomes for a mutation are written as follows:

P(-∞ < X < +∞) = P(Ad) + P(Cy) + P(Gu) + P(Th) + P(iAd) + P(iCy) + P(iGu) + P(iTh) + P(del) + … = 1

Where Ad, Cy, Gu and Th represent substitutions of the particular bases, if the base is preceded by an "i", it means the insertion of that base, "del" means deletion of the base and the "..." term represents all other mutations possible. Included in that "..." term would be the mutation that caused the Citrate metabolizer in the Lenski experiment.

We now define a term P(BeneficialA) where the value of P(BeneficialA) is determined by the particular mutation which gives benefit. If the beneficial mutation is a substitution of Ad, P(BeneficialA)=P(Ad), if the beneficial mutation is an insertion of Th, P(BeneficialA)=P(iTh) and so on.

We then define µ – the probability (frequency) that an error in replication will occur at a particular site in a single member in one replication. Then the probability that mutation A occurs in a single member in a single generation is:

P(A) = P(BeneficialA)µ

We then use the complementary rule of probabilities to compute the probability that mutation A will not occur in a single member in a single replication.

P(Ac) = 1 - P(A) = 1 - P(beneficialA)µ where P(Ac) is the probability that mutation A will not occur.

We can then define "n", the population size and using the multiplication rule of probabilities, compute the probability that mutation A will not occur in "n" replications.

P(Ac) = (1 - P(BeneficialA)µ)^n

We can then define "nGA" the number of generations the population "n" replicates for the probability of mutation A to occur. And again using the multiplication rule gives:

P(Ac) = ((1 - P(BeneficialA)µ)^n)^nGA = (1 - P(BeneficialA)µ)^(n*nGA)

And to obtain the probability of mutation A occurring in a population size "n" in "nGA replications we again use the complementary rule which gives:

P(A) = 1 - (1 - P(BeneficialA)µ)^(n*nGA)

Note that n*nGA is simply the total number of replication trials for the mutation A to occur. With sufficient numbers of trials, we finally get a reasonable probability for mutation A to occur on some member of the population. That member with mutation A is the progenitor for a new lineage who are candidates for mutation B, that is a new branch on a phylogenetic tree. However, there is only one member to start with. This member must replicate for many generations so that there are a large number of members with mutation A, then there will be a reasonable probability that one of the members with mutation A on replication will get mutation B. The mathematics is done in an analogous manner as computing the probability of mutation A occurring in a population size "n" in "nGA" generations but in this case n->nA the number of members with mutation A, nGA->nGB, the number of generations the members with mutation A replicate. The calculation goes as follows:

P(B) = P(BeneficialB)µ, complementary rule
P(Bc) = 1 - P(beneficialB)µ, multiplication rule
P(Bc) = (1 - P(BeneficialB)µ)^nA, again multiplication rule
P(Bc) = ((1 - P(BeneficialB)µ)^nA)^nGB = (1 - P(BeneficialB)µ)^(nA*nGB), and finally complementary rule
P(B) = 1 - (1 - P(BeneficialB)µ)^(nA*nGB)

And to compute the joint probability of some member of the population getting both mutation A and B, we use the multiplication rule:

P(A)P(B)= (1 - (1 - P(BeneficialA)µ)^(n*nGA))*(1 - (1 - P(BeneficialB)µ)^(nA*nGB))

The calculation for the mutations C,D and E occurring is done in the exact same manner. What is seen that in order for this evolutionary process to occur, we have a cycle of beneficial mutation followed by amplification of that mutation in order to improve the probability of the next beneficial mutation. That rate of amplification is strongly dependent on environmental conditions, that is the other selection pressures that are acting on the population at that time.

The simplest example of how this cycle of beneficial mutation followed by amplification of the mutation can be disrupted is by applying a second selection pressure simultaneous with the first selection pressure. Not only does this make the evolutionary trajectory more complex, the amplification process for any beneficial mutation for one selection pressure is interfered with by selection pressures targeting other genetic loci.

One can easily substitute values into the above equations using a spreadsheet program using different values for the mutation rates and populations sizes and determine the probabilities.

An interesting extension of this mathematics is determining the probabilities when more than a single selection pressure are acting at the same time where it requires 2 (or more simultaneous) beneficial mutations in order to improve fitness. Anyone here besides me want to try to do that computation? Perhaps you can find a way to rescue your theory of evolution from the multiplication rule of probabilities. And feel free to substitute 1 for any of the P(Beneficial) terms.

 This message is a reply to: Message 375 by Admin, posted 10-15-2016 8:48 AM Admin has responded

 Replies to this message: Message 378 by Admin, posted 10-15-2016 9:48 AM Kleinman has not yet responded Message 379 by Dr Adequate, posted 10-15-2016 9:51 AM Kleinman has not yet responded

Director
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 Message 378 of 393 (792914) 10-15-2016 9:48 AM Reply to: Message 377 by Kleinman10-15-2016 9:29 AM

Re: Lenski
Hi Kleinman,

You're repeating the same self-evident math you presented in Message 214, and you've provided no values. To repeat what I just said, you must substitute actual values into your equation demonstrating evolution impossible, and if you don't then I will drop this thread into summation mode.

 -- Percy EvC Forum Director

 This message is a reply to: Message 377 by Kleinman, posted 10-15-2016 9:29 AM Kleinman has not yet responded

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 Message 379 of 393 (792915) 10-15-2016 9:51 AM Reply to: Message 377 by Kleinman10-15-2016 9:29 AM

One More Obvious Equation, That's It?
 And to compute the joint probability of some member of the population getting both mutation A and B, we use the multiplication rule:

 What is seen that in order for this evolutionary process to occur, we have a cycle of beneficial mutation followed by amplification of that mutation in order to improve the probability of the next beneficial mutation. That rate of amplification is strongly dependent on environmental conditions, that is the other selection pressures that are acting on the population at that time.

But your math doesn't model this amplification in any way. Unlike, for example, my simulation.

 Not only does this make the evolutionary trajectory more complex, the amplification process for any beneficial mutation for one selection pressure is interfered with by selection pressures targeting other genetic loci.

Again, where's the math? All your middle-school math deals with so far is the probability of two mutations arising in a given period of time, it says nothing about how they get amplified.

 This message is a reply to: Message 377 by Kleinman, posted 10-15-2016 9:29 AM Kleinman has not yet responded

Director
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 Message 380 of 393 (792916) 10-15-2016 9:54 AM

 Kleinman writes:I did the first fundamental steps of the calculation earlier in the thread but you can see the full mathematics in the publications.

You've cited these inaccessible papers too many times. Until they're made publicly available, each time you cite them henceforth I will suspend you for 24 hours.

About doing "the first fundamental steps of the calculation," you haven't made any calculations based upon the single equation you presented.

 -- Percy EvC Forum Director

 Replies to this message: Message 382 by Kleinman, posted 10-15-2016 10:29 AM Admin has acknowledged this reply

Kleinman
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 Message 381 of 393 (792917) 10-15-2016 10:11 AM Reply to: Message 373 by Modulous10-14-2016 8:00 PM

Re: the equality of pressure?
quote:
quote:
 ... What I do remember is that they listed at least 8 genes necessary to be transformed. ...

Excuse me for coming in late in the discussion. I have received your pdfs but not had time to look them over yet. Can you answer a simple question for me, even if it has already been asked?
What is the probability that a mutation will be beneficial?

If you don't know then you cannot invalidate evolution with your calculations.

 ... But this is not a number which you have to know to understand how rmns works.

Evolution works by beneficial mutations being selected by natural processes -- success in living and breeding. The probability of a mutation being beneficial would seem to be central to any mathematical approach trying to show that evolution is broken.

RAZD, which do you think will be larger, the mutation rate or the beneficial mutation rate? We know with mathematic certainty that the P(Beneficial) term can only have a value between 0 and 1. If you let P(Beneficial) = 1, you bracket the solution with the upper limit of the probability. Knowing or not knowing the exact value of P(Beneficial) does not have any mathematical significance on the physics of rmns.
quote:
 quote:I think we can all agree that mutations are random -- leaving aside for the moment that the probability of mutations varies with the section of DNA involved -- and that some are immediately deleterious or immediately beneficial, while others are immediately neutral and their relative deleterious\beneficial value can be important later.We also have cases where a mutation is somewhat deleterious but leads later to beneficial results because of changing environmental conditions.So how can we predict the probability of a mutation being beneficial?Most people say that most mutations are neutral. ...

Which leaves the door open to later mutations that can build on them.

Certainly, environmental conditions have a significant impact in determining whether a mutation is beneficial or not. But it doesn't change the physics of rmns and that physics consists of nested binomial probability problems linked by the multiplication rule of probabilities.
quote:
 ... Mutations are fairly rare to begin with. ...

Yet every individual in every species has several.

That's fine, but you need to understand that in order for a lineage to accumulate a set of beneficial mutations, it must do so by overcoming a set of binomial probability problems linked by the multiplication rule. If you have an interest in solving medical problems such as less than durable cancer treatments, you need to understand the physics you are dealing with. This will become even more important as the use of targeted cancer therapies are developed. Targeted selection pressures give the easiest binomial probability problems for a replicator to solve by rmns. If you are going to gamble with replicators, you had better learn the rules of the game if you want to shift the odds in your favor.
quote:
 ... Most DNA replication is done with high fidelity. ...

For individuals that survive from zygote to born young. All those that die from birth defects are because of less than sufficient fidelity.

True as well. That's why any injury to cell in the embryonic state are transmitted to all the descendent cell. But even the normal cells in our body can develop minds of their own and become cancers because of the huge numbers of replication from zygote to adulthood. And these cells, if they are not driven to extinction by targeted therapy will still come back and kill the person. We see that with the use of estrogen blocking agents in the treatment of breast cancer. The cells are suppressed until a variant appears that's no longer estrogen sensitive. A second drug targeting these cells would slow if not stop this process.
quote:
 ... As you read my papers on rmns, you will see that I address the possibility that even though a mutation occurs at the correct site in a genome, it has to be the correct mutation to improve fitness. ...

This is confused. There is one mutation, it occurs randomly, and that means both location and format\type are part of the same mutation, not two separate problems. The same type in a different location would be a different mutation.

There is no "correct mutation" -- the mutation happens and then selection operates on that mutation, whether it is in location A or location B, whether it is type K or type L. Whether or not it is beneficial is that probability discussed above that you admit you don't know.

This seems to be the root of your problem, trying to make a single mutation event into a two event process.

It also seems from this that you are calculating the probability of a given mutation occurring in a second individual. Certainly when you go to two mutations occurring independently in different individuals the maths would give an extremely low probability for occurrence, but that is not how evolution works.

If you have no experience in the mathematics or probability theory, these papers will definitely confuse you. That's why when I looked for a journal to publish these papers, I wanted editors and peer reviewers who had experience with this type of mathematics. If you want to understand this mathematics, it's not that difficult but it requires a little training and some practice. If you want me to point you to sources, youtube has some good lectures on the subject. Master the mathematics of coin tossing and dice rolling and these calculations will become much clearer to you. If you have interest in improving cancer treatments and preventing antimicrobial drug resistance, learn this math.
quote:
 ... Just getting an accurate mutation rate is a challenging problem and then determining the fraction of the mutations which are beneficial, neutral and detrimental is even more challenging. ...

Yet we know that they all occur every generation of every species. All natural selection needs are some beneficial mutations and a low rate of death/fertility problems (where selection pressure enters the picture).

And these publications I sent you explains how natural selection does this. Mutations occur all the time on replication but in order to improve fitness to reproduce, it has to be the correct mutation occurring on the correct individual to accomplish that task.
quote:
 ... But the mutation rate is not the dominant factor in the rmns problem, it is the multiplication rule of probabilities that drives this phenomenon. ...

This too is confused. If I take a coin and toss it 53 times I end up with a pattern of heads and tails, and the probability of my getting that specific pattern is 1.

If I try to match that pattern with another 53 tosses the probabilities are, by the multiplication rule, extremely minute. You only use multiplication when the same steps need to be reproduced. Evolution does not work that way.

But in order to improve fitness requires specific patterns of mutations. Natural selection tries to select these pattern by a cycle of beneficial mutation followed by amplification of the beneficial mutation to improve fitness to reproduce.
quote:
 ... It is the joint probability that two or more beneficial mutation occur on a lineage which drives this problem.

Again, we get back to the question of the probability that a mutation will be beneficial, which you admitted you don't know ... certainly then you can't know the probability of a second mutation being beneficial, but that isn't the worst of your problem.

There are actual documented experiments (one involving E. coli) where a neutral mutation occurs in one generation and then in a later generation a second mutation occurs where the combination is beneficial, meaning that the original mutation is now beneficial. Calculating the probability that those two specific mutations would occur (the "correct mutations" at the "correct locations") would result in a very small number, but the probability that it occurred is 1: it happened.

Your model is wrong because there is an assumption of structure to the mutation process being necessary to evolution, and that assumption is false.

Again I ask you, which is larger, the mutation rate or the beneficial mutation rate? And before you say my model is wrong, you need to understand where it is wrong and right now you are confused. When my last paper was peer reviewed, I was asked to point out why Haldane's and Kimura's models were not correct. I studied and understood their models and calculations. In fact, I even wrote an exact solution to Haldane's model to check if his approximate solution was accurate. Haldane and Kimura don't have a problem in their mathematics, they have a problem in their physics. I explain the problem in the paper on rmns with multiple simultaneous selection pressures.
 This message is a reply to: Message 373 by Modulous, posted 10-14-2016 8:00 PM Modulous has acknowledged this reply

 Replies to this message: Message 383 by Admin, posted 10-15-2016 10:38 AM Kleinman has not yet responded

Kleinman
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 Message 382 of 393 (792918) 10-15-2016 10:29 AM Reply to: Message 380 by Admin10-15-2016 9:54 AM

Re: Mathematics cannot change reality but when done correctly can predict it
quote:
 Kleinman writes:http://www.ncbi.nlm.nih.gov/pubmed/25244620http://www.ncbi.nlm.nih.gov/pubmed/27501057http://www.ncbi.nlm.nih.gov/pubmed/25645658I did the first fundamental steps of the calculation earlier in the thread but you can see the full mathematics in the publications.

You've cited these inaccessible papers too many times. Until they're made publicly available, each time you cite them henceforth I will suspend you for 24 hours.

About doing "the first fundamental steps of the calculation," you haven't made any calculations based upon the single equation you presented.

I've posted the equations including the fundamental steps and the derivation of the equations in post 377. This is the physics and mathematics which governs rmns, it consists of nested binomial probability problems linked by the multiplication rule of probabilities. You don't need to go to the links to learn this mathematics, I've given it to you here. Now let's hear the repetitive arguments of evolutionists that it doesn't work this way despite the fact that all real, measurable and repeatable examples of rmns obeys this mathematics.

Director
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 Message 383 of 393 (792919) 10-15-2016 10:38 AM Reply to: Message 381 by Kleinman10-15-2016 10:11 AM

Re: the equality of pressure?
Hi Kleinman,

I know you sent RAZD copies of your papers, but it isn't fair to the other participants to carry on a discussion about information to which they are not privy, and in any case, here at EvC Forum one must present the information one is discussing in the thread, not just provide a link, and especially not one that's behind a paywall. When making a point that depends upon information in one of your papers, please present that information in this thread.

 Kleinman writes:Mutations occur all the time on replication but in order to improve fitness to reproduce, it has to be the correct mutation occurring on the correct individual to accomplish that task.

You do still seem to be committing the sharpshooter fallacy when you mention a "correct mutation," and you haven't made any substantive response.

Just so no one's confused let me mention that you evidently clicked the "reply" button to Modulous's Message 373, but you were actually replying to RAZD's Message 374.

 -- Percy EvC Forum Director

 This message is a reply to: Message 381 by Kleinman, posted 10-15-2016 10:11 AM Kleinman has not yet responded

Director
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 Message 384 of 393 (792920) 10-15-2016 10:45 AM

To those who would like to continue the discussion let me express my regret that I feel compelled to place this thread into summation mode. I believe that Kleinman has gone as far as he is willing, or perhaps able, in supporting his claims, and that continuing along current avenues would be antithetical to the EvC goal of constructive and informative discussion. I encourage those interested in continuing discussion to propose threads over at Proposed New Topics.

 -- Percy EvC Forum Director

Kleinman
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Posts: 136
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Joined: 10-06-2016

 Message 385 of 393 (792921) 10-15-2016 10:56 AM

Re: Mathematics cannot change reality but when done correctly can predict it
quote:
 And to compute the joint probability of some member of the population getting both mutation A and B, we use the multiplication rule:

If the subpopulation with mutation A is large enough, you may get more than one member getting mutation B. But the real amplification process starts with that progenitor(s) with mutations A and B start replicating. A single member with mutation A and B in 30 generations of doubling will e9 members in the ideal case.
quote:
 What is seen that in order for this evolutionary process to occur, we have a cycle of beneficial mutation followed by amplification of that mutation in order to improve the probability of the next beneficial mutation. That rate of amplification is strongly dependent on environmental conditions, that is the other selection pressures that are acting on the population at that time.

But your math doesn't model this amplification in any way. Unlike, for example, my simulation.

Amplification occurs when the number of replications increases for a particular variant, that doesn't necessarily happen when the relative frequency of variants in populations change. You can get fixation without any amplification just by killing off all variants except one. You need to recognize that in the stochastic process of rmns, the replication is the principle trial for this phenomenon.
quote:
 Not only does this make the evolutionary trajectory more complex, the amplification process for any beneficial mutation for one selection pressure is interfered with by selection pressures targeting other genetic loci.

Again, where's the math? All your middle-school math deals with so far is the probability of two mutations arising in a given period of time, it says nothing about how they get amplified.

Now Doc, I take offense to you calling this middle-school math. This is elementary school math and don't forget it.

You are correct, these are not rate equations. These equations only predict how many replications are required for a particular mutation to occur on a particular individual in the population. The rate at which these probabilities change are strongly dependent on the selection conditions. The video of bacteria evolving resistance to an antibiotic shows a rapid rmns process for a single selection pressure targeting a single gene. The Lenski experiment on the other hand takes decades to evolve because of the single selection pressure targeting multiple genetic loci. Computing rates of change of relative frequencies of variants is not going to give you the correct time relationship.

jar
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 Message 386 of 393 (792922) 10-15-2016 11:42 AM

135 Content free posts
This topic shows conclusively that it is possible to have 135 Content Free posts in one thread with zero evidence of the point asserted evolving.

My Sister's Website: Rose Hill Studios     My Website: My Website

ringo
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 Message 387 of 393 (792924) 10-15-2016 11:51 AM

You can multiply non-zero probabilities until the cows come home and you'll always get a non-zero result. That's mathematics, son!

Edited by ringo, : "never" --> "always" (sign error)

Coyote
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 Message 388 of 393 (792926) 10-15-2016 11:53 AM

Summation
This topic shows that one can use math to "prove" something that is clearly incorrect.

Evolution has been going along just fine, in its bumbling and haphazard way, for a couple of billion years--as shown by many different lines of evidence--so any mathematical model that claims otherwise is just wrong.

Religious belief does not constitute scientific evidence, nor does it convey scientific knowledge.

Belief gets in the way of learning--Robert A. Heinlein

In the name of diversity, college student demands to be kept in ignorance of the culture that made diversity a value--StultisTheFool

It's not what we don't know that hurts, it's what we know that ain't so--Will Rogers

If I am entitled to something, someone else is obliged to pay--Jerry Pournelle

If a religion's teachings are true, then it should have nothing to fear from science...--dwise1

"Multiculturalism" demands that the US be tolerant of everything except its own past, culture, traditions, and identity.

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 Message 389 of 393 (792928) 10-15-2016 12:11 PM

Well this is a wasted opportunity. Kleinman came along with a patronising teacherish attitude and stupidly extravagant claims which he refused to support.

Had he chosen to take a different route by properly explaining his ideas on his specific issue of combination therapy for HIV treatment he might have gained some traction and maybe even been able to move a little way towards a ToE discussion. Instead he chose to piss everyone off. He should have been choked off at his 3rd or 4th post that said simply this:

quote:
The answer to the question I ask you contains the reason why the theory of evolution is not true. I'm trying to get you to figure this out yourself.

That approach was never going to win him any friends.

Je suis Charlie. Je suis Ahmed. Je suis Juif. Je suis Parisien.

Life, don't talk to me about life - Marvin the Paranoid Android

"Science adjusts it's views based on what's observed.
Faith is the denial of observation so that Belief can be preserved."
- Tim Minchin, in his beat poem, Storm.

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 Message 390 of 393 (792933) 10-15-2016 8:41 PM

Parturient Montes, Nascetur Ridiculus Mus
How to summarize something so vacuous?

Kleinman promised us that his mathematics would overturn the theory of evolution, prove in particular that birds are not descended from dinosaurs, "unravel the bloody mess that evolutionists have made", overturn the theories of Haldane and Kimura, and prove the remarkable proposition that evolution slows down, rather than speeding up, as a result of additional selection pressures.

And what do we get? Over the course of his 135 posts, he has presented us with a handful of trivial equations which would meet the approval of any evolutionary biologist, or indeed any middle-schooler --- accompanied by ever more vehement repetition of his grandiose claims.

Insofar as he has gotten around to making any particular mistakes, I feel that they have been sufficiently answered in this thread, so it would be redundant to make a list; and unless he wishes to add some fresh errors in his summation, we may as well leave it at that.

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