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If not Rupe and Sanford’s presentation (8/6/13), would you believe Wiki? In this case, yes.

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Evolutionists reluctantly admit most evolution is free of selection and therefore non-Darwinian (neutral evolution). When pressed, they’ll say neutral drift is real, but they don’t like it when the dots are connected in a way that demonstrates neutral evolution refutes Darwinism, that there is a contradiction between Dawkins’ vision and neutral evolution! The way Darwinists deal with this violation of the law of non-contradiction is to pretend no contradiction exists. They’ll obfuscate and fog the issue with myriad technical terms and irrelevancies so that the illusion of non-contradiction is protected from public view. Confusion and the illusion of some higher knowledge are their friends, clarity and education of the public are their enemies.

If Dawkins had been faithful to the facts, he wouldn’t have even written The Blind Watchmaker because population genetics precludes his vision of evolution from being reality in anything but his silly Weasel simulations.

There is a simple formula from Wiki that says the rate of new mutations is the rate at which new mutations become features of every member of the population (a process called fixation).

http://en.wikipedia.org/wiki/Fixation_(population_genetics)

fixation rate

The population size is N and the Greek symbol μ (mu) is the mutation rate.

It stands to reason a slightly deleterious mutation is almost neutral, hence, approximately speaking the rate that slightly deleterious mutations become part of every member of the population is on the same order of the slightly deleterious mutation rate. That means if every human is getting 100 dysfunctional mutation per generation, about 100 dysfunctional mutations are getting irreversibly infused into humans every generation (a ratchet so to speak).

But as bad as that is, it’s actually worse in reality. Remember broken bacterial parts in anti-biotic resistance, or blindness in cave fish, or sickle cell anemia? Those are “beneficial” (in the Darwinian sense) mutations, but destructive in the functional sense. So it is actually generous the creationists are modeling the dysfunctional mutations as slightly deleterious (whereas a fair argument might actually model some of the dysfunctional mutations as “beneficial”). So the creationists are cutting Darwinists a lot of slack, and yet, even then the dysfunctional mutations will get fixed (become members of all individuals) in a population! Not to mention, lots of bad may get purged from a population only to get replaced with new generations of bad.

[ See my derivation with the Poisson distribution in Death of the Fittest to see how the bad that is purged is replaced with more bad in addition to the ratcheted mutations that never get purged! With respect to neutral evolution, I gave a little more background on this complex topic here: Most evolution is free of selection, therefore Darwinism must be false.]

But obvious math is something Darwinism hates dealing with! The above equation should be painful evidence against evolution being some process of increasing complexity from a primordial virus to incredible minds like Newton or Einstein. Darwinist won’t come to terms with it, they won’t come to terms with even a computer simulation based on population genetic models. Oh well! But anyway, Christopher Rupe and John Sanford will be presenting the results of a computer simulation that illustrates the above equation. It’s sort of like beating a dead horse or beating living puppies. It’s not very sporting, but Darwinists keep propping up that dead horse for creationists to keep beating.

Here is the presentation that will be made August 6, 2013. The link below to the 2013 International Creation Conference (ICC) can be followed for more details:

Using Numerical Simulation to Better Understand Fixation Rates, and Establishment of a New Principle – “Haldane’s Ratchet”

Christopher L. Rupe and John C. Sanford

In 1957, Haldane first described a fundamental problem with evolutionary theory. This problem eventually became widely known as “Haldane’s Dilemma”. The essence of this problem is that even given a steady supply of beneficial mutations plus deep time, the rate that such mutations reach fixation is too slow to achieve meaningful evolution. After more than 50 years, this fundamental problem remains unresolved. ReMine has gone far beyond Haldane’s original mathematical analysis, and has developed “cost theory analysis” which strongly supports Haldane’s thesis. Here we examine this long-standing problem using an entirely different approach. We employ advanced numerical simulation of the mutation/selection process to empirically measure the fixation rates of beneficial, neutral, and deleterious mutations. We do this employing both realistic and optimized population parameters. In our numerical simulations, each new mutation is tracked through time until it is either lost due to drift or becomes fixed in the population.

We first confirm that our numerical simulations correctly tallying the fixation of neutral mutations. We show that neutral mutations go to fixation just as predicted by conventional theory (i.e., over deep time the fixation rate approached the gametic mutation rate). We also show that the reason the vast majority of neutral mutant alleles fail to go to fixation, is because they lost due to drift, and this rate of loss rapidly approached 100% as population size is increased.
We then show that given realistic distributions of mutation fitness affects, the vast majority of all mutations (including deleterious and beneficial mutations), are similarly lost due to random drift. In terms of fixations, deleterious mutations went to fixation only slightly slower, while beneficial mutations went to fixation only slightly faster, than neutral mutations.

We then perform large-scale experiments to examine the feasibility of the ape-to-man scenario over a six million year period. We analyze neutral and beneficial fixations separately (realistic rates of deleterious mutations could not be studied in deep time due to extinction). Using realistic parameter settings we only observe a few hundred selection-induced beneficial fixations after 300,000 generations (6 million years). Even when using highly optimal parameter settings (i.e., favorable for fixation of beneficials), we only see a few thousand selection-induced fixations. This is significant because the ape-to-man scenario requires tens of millions of selective nucleotide substitutions in the human lineage.
Our empirically-determined rates of beneficial fixation are in general agreement with the fixation rate estimates derived by Haldane and ReMine using their mathematical analyses. We have therefore independently demonstrated that the findings of Haldane and ReMine are for the most part correct, and that the fundamental evolutionary problem historically known as “Haldane’s Dilemma” is very real.
Previous analyses have focused exclusively on beneficial mutations. When deleterious mutations were included in our simulations, using a realistic ratio of beneficial to deleterious mutation rate, deleterious fixations vastly outnumbered beneficial fixations. Because of this, the net effect of mutation fixation should clearly create a ratchet-type mechanism which should cause continuous loss of information and decline in the size of the functional genome. We name this phenomenon “Haldane’s Ratchet”.

http://creationicc.org/more.php?pk=46

UD readers are invited to come to the presentation!

Comments
Perhaps not, Sal, but I don't think your quotees are among them. The conceptual definition of fitness is perfectly clear, even if it is not always easy to measure, and thus operationalise, nor to distinguish from drift. And of course, it also gets complicated when you want to correlate a trait with fitness, which is what you normally want to do, and to do it with respect to a specific environment. There is also the question of whether you are comparing fitness within the current population, or between the fitness of an offspring relative to its parent. So slightly different operational definitions can be used, depending on the question being asked. But that is true of a great many perfectly well defined concepts in science. Your last quote is completely irrelevant. And Lewontin, like Wagner, is discussing quantitative issues. None of these people is disputing that fitness is anything other than reproductive success. They are simply discussing the best way of measuring it. And you actually omitted the sentence that precedes your quotation from Wagner, which I found by googling (sources would be nice), which is:
With respect to the first of these cardinal questions, it is clear that ultimately robustness of only one organismal feature matters: fitness--the ability to survive and reproduce.
Elizabeth B Liddle
July 29, 2013
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Elizabeth wrote: Firstly, it is isn’t that “fitness can mean anything” in evolutionary biology. Fitness has a very precise meaning, which is “reproductive success”.
I appreciate that you sincerely believe that, but first rate biologists have serious issue with such statements including Lewontin, Wagner, and to some extent Orr: https://uncommondescent.com/intelligent-design/dennetts-strange-idea-is-a-bad-idea-for-recognizing-biological-function/
However, fitness is hard to define rigorously and even more difficult to measure Andreas Wagner
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The problem is that it is not entirely clear what fitness is. Darwin took the metaphorical sense of fitness literally. The natural properties of different types resulted in their differential “fit” into the environment in which they lived. The better the fit to the environment the more likely they were to survive and the greater their rate of reproduction. This differential rate of reproduction would then result in a change of abundance of the different types. In modern evolutionary theory, however, “fitness” is no longer a characterization of the relation of the organism to the environment that leads to reproductive consequences, but is meant to be a quantitative expression of the differential reproductive schedules themselves. Darwin’s sense of fit has been completely bypassed. … How, then, are we to assign relative fitnesses of types based solely on their properties of reproduction? But if we cannot do that, what does it mean to say that a type with one set of natural properties is more reproductively fit than another? This problem has led some theorists to equate fitness with outcome. If a type increases in a population then it is, by definition, more fit. But this suffers from two difficulties. First, it does not distinguish random changes in frequencies in finite populations from changes that are a consequence of different biological properties. Finally, it destroys any use of differential fitness as an explanation of change. It simply affirms that types change in frequency. But we already knew that. Richard Lewontin
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When does adaptationism stop being a useful research strategy and start being a silly exercise? Allen Orr
I'm pointing out not every biologist will agree with that statement.scordova
July 29, 2013
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Now that comment is bizarre if you don’t appreciate the significance of preserving functional proteins. This is a completely different topic than the one you launched off on in this post. Anyway, of course evolution preserves function, all I've said is that sometimes loss of function mutations are advantageous (or neutral). In those cases functions will be lost. You have a serious problem of moving from "sometimes" to "always" in these observations. It's true that selection can sometimes favour loss of function mutations, but there is a lot of evidence that it can act to maintain function. Read a little about the dN/dS ratio if you want an idea of how pervasive stabalising and positive selection are (short answer - most genes are highly conserved, a few show evidence of recent positive selection)wd400
July 29, 2013
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Sal, I think you are inventing problems with "Darwinism" that do not in fact exist. Firstly, it is isn't that "fitness can mean anything" in evolutionary biology. Fitness has a very precise meaning, which is "reproductive success". That's it, no more, no less. If not having to drag legs around, or provide metabolic support for useless eyes in a lightless cave, increases reproductive success, then any heritable change that means less leg or less eye will make the individual more fit Secondly, you say:
Evolutionists reluctantly admit most evolution is free of selection and therefore non-Darwinian (neutral evolution). When pressed, they’ll say neutral drift is real, but they don’t like it when the dots are connected in a way that demonstrates neutral evolution refutes Darwinism, that there is a contradiction between Dawkins’ vision and neutral evolution!
I'm not at all sure who you are talking about here, but I know of no "evolutionists" who is at all "reluctant" to "admit" that drift is a huge factor in evolutionary change. Indeed, the interesting thing about models that incorporate drift is that they provide pathways to adaptive function that wouldn't other wise exist. Without drift, "irreducible complexity" would be a substantial problem for Darwin's theory. However, it turns out it isn't, because there are many pathways to an adaptive function (i.e. a function that promotes reproductive success) that go via neutral or even deleterious mutations. Thirdly, you seem to think that "function" has nothing to do with fitness. It does. If a function doesn't make you fitter than you would be without it (i.e. more likely to reproduce) then it isn't very functional, any more than a computer is functional if you don't have need of it, and yet it's still occupying valuable real estate in your living room. So to say that "selection can select for broken function" is a highly complex way of saying what is really very simple: that if some function helped an ancestral population reproduce, but does hinders the descendent population, then it will start to become less prevalent. Finally: I think fixation is actually a red herring, although it's a good mathematical measure. The really important thing (which Sanford completely misses) is that it is very rare for any variant to go to fixation; what is more common is for variants to drop out of a population all together, and this is more likely in small populations than large. For large populations, the rate of near-neutral variance production is likely to exceed the rate of dropout - this means that large populations have a richer genetic pool, which means they are more likely to adapt in the face of environmental change - at which time what was neutral may become beneficial; what was beneficial may become neutral or deleterious; and what was slightly deleterious may seriously deleterious, and drop out of the population. And all kinds of combinations thereof. That's why Sanford's doomsday scenario is so mistaken. He's right about the dangers to small populations (and we are sending other populations to extinction at an alarming rate, because of environmental change), but we rather dramatically failing to show any signs of dwindling ourselves. Of course if we really mess things up, and cause catastrophic environmental change (or if it simply happens), those of us with a heavier load of slightly deleterious mutations may be the first to go, leaving a smaller, fitter (in the biological sense) population. Or we may go extinct. But I'd worry about the environment before I started worrying about genetic entropy.Elizabeth B Liddle
July 29, 2013
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What are you talking about?
You don't understand? That's obvious.
This doesn’t have anything to do with the nearly neutral mutations this post
It does, so let's see why. You seem to agree: 1. most evolution is neutral 2. selection can favor broken functioning parts (like broken proteins or protein expression) If selection can select for broken function, then it is believable broken function can also be neutral or slightly deleterious, right? There is no necessity that a broken function has to be deleterious, right? So what do we make of slightly deleterious that gets fixed in a population: 1. it can represent breaking of a function 2. it can represent improvement of a function :shock: If we assume #1 (that a deleterious mutation is a functional breakdown), then it means functional breakdowns will continually get incorporated into all members in the population at the dysfunctional-deleterious mutation rate. If we assume #2 (that a deleterious mutation is a functional improvement), then we are hoping function emerges despite natural selection. Thus natural selection will not be an explanation for the emergence of such novel functions. Darwinism fails in that case. Thus combining both cases: 1. selection fails to prevent destruction of Design, hence Darwinism is wrong for the preservation of function 2. selection has to fail for function to emerge, hence Darwinism is wrong for the evolution of such functions Ergo Darwinism is the wrong description of evolution and emergence of function. Do you have a problem with that? Even you seemed to brag you're not a Darwinist, so you should be happy I'm helping prove your viewpoint (of non Darwinian evolution). Feel free to tell the readers if you think most evolution is neutral with respect to selection. Next, feel free to explain if you believe function emerges without selection to create and maintain it. Like many evolutionary biologists, you don't seem to have much regard for function as evidenced by these statements:
Selection can sometimes favour mutations that break existing proteins. OK, so what?
Now that comment is bizarre if you don't appreciate the significance of preserving functional proteins.scordova
July 29, 2013
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What are you talking about? This doesn't have anything to do with the nearly neutral mutations this post and my comments are about. This comment is also bizarre. Selection can sometimes favour mutations that break existing proteins. OK, so what?wd400
July 28, 2013
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Again, I ask, so what? Why do you think this infinitesimally small reduction in fitness every 250 years or so, set against the evidence for positive selection in the human genome, is ta problem for evolutionary biology?
First problem, evolutionary biologists equate fitness with function, in the world of Darwin, blindness in cave fish, sickle cell anemia, broken bacterial parts are considered beneficial, and therefore fit! It means dysfunction migrates and permeates and is occasionally encouraged by accepted evolutionary mechanisms. Something could be functionally damaged and considered fit! You've just echoed what so perverse about evolutionary biology, fitness can mean anything even genomic deterioration! And then you just reinforced that with your comment. Yet you have Dawkins saying evolutionary mechanisms construct function when you have just shown evolutionary biologists don't even have a workable concept of function except in terms of selective advantage which is no concept whatsoever. You're comment just emphasizes how clueless evolutionary biology is!
In science's pecking order evolutionary biology lurks somewhere near the bottom, far closer to phrenology than to physics. Jerry Coyne
And we can say evolutionary biology lurks near the bottom in technology far closer to perpetual motion machines than to modern engineering marvels. Ironic evolutionary biologists seem qualified to lecture engineers about notions of function. Equating function to selective advantage is silly! There is some truth to the Salem hypothesis that critics of evolutionary biology have a strong engineering bias -- it begins with evolutionary biology's inability to explain function, heck you've just shown, they don't even have workable concept of function!scordova
July 28, 2013
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Which is to say, selection could “feel” the difference between a neutral mutation (with fitness equal to the wild-type) and one with only 99.9975% percent of the fitness of the wild-type.
An animal arbitrarily deciding to turn left instead of turning right would probably affect fitness orders of magnitude more than a -.0025% genetic modification. Sanford refers to this as the "Princess and the Nucleotide Paradox" The average fitness 'noise' of everyday life are like waves in an ocean. And a slight nucleotide change is like a tiny ripple within those waves. It is not going to be detected.lifepsy
July 28, 2013
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As far as I recall, I’ve never deleted yours, WD’s, Gordon’s, Jerads, KeithS, Elizabeth, Mark Frank, CLAVDIVS, Matzke’s, Ohara’s, or any evolutionist that I know of UD.
At least we know who Sal's friends are.Mung
July 27, 2013
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In his book "Why is A Fly Not A Horse?", Dr Sermonti has a chapter on proteins titled What Teaches Proteins Their Shapes? In it he pretty much destroys the notion that proteins just spontaneously find their functional spatial configuration. How are modern evolutionary biologists doing wrt answering that very basic question?Joe
July 27, 2013
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Well at least Darwinism offers a designer mimic mechanism- albeit one that has proven to be impotent. What does modern evolutionary biology have to offer for a designer mimic?Joe
July 27, 2013
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So, given about ~12% of amino-acid mutations fall in the nearly neutral zone, and there is somewhat less than 1 such mutation per birth, we end up with one fixation of mutation that reduces the host's fitness to 99.9975% of what it would otherwise be. Again, I ask, so what? Why do you think this infinitesimally small reduction in fitness every 250 years or so, set against the evidence for positive selection in the human genome, is ta problem for evolutionary biology? Everything else you've written is, typically, very confused. You don't need non-mutants in a population to get rid of "bad" mutations. Indeed, Joe Felsenstein among others have suggested sexual recombination may be maintained in poulation because it prevents what he dubbed "Mullers racthet" from accumulating mutations. Evolutionary biologists don't assume variants in all intergenic regions are selectively neutral, rather we test that idea. There is good evidence that most such regions are not maintained by selection. Some regions are. I don't know what "conserved for reasons other than purifying selection" means. Anyway, it's good that you're starting to see how rediculous it is to call modern evolutionary biology "Darwinism", but you still seem to read the literature as if looking for a chink into which you can fit your god. If you want to engage with evolutionary biology as it is practised you should read a little more widely.wd400
July 27, 2013
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Are you deleting comments, Sal?
I deleted one of mine a few minutes after posting, and revised it to a comment here: https://uncommondescent.com/genetics/rupe-and-sanford-presentation-8613-or-would-you-rather-believe-wiki-in-this-case-yes/#comment-465650 3 off topic comments by Mung were moved to the spam queue. Other off topic comments that add nothing to the topic can expect a similar fate. As far as I recall, I've never deleted yours, WD's, Gordon's, Jerads, KeithS, Elizabeth, Mark Frank, CLAVDIVS, Matzke's, Ohara's, or any evolutionist that I know of UD. Mung and Gregory are frequent off-topic offenders in my discussions and have had their off-topic posts deleted or disemvoweled. If Gregory and Mung really want to, they can post their useless garbage elsewhere, but not in these discussions. I'm happy to take reasoned criticism that has: 1. data points 2. arguments Substance-free junk can be deleted. I don't recall deleting anything you've written at UD, maybe one off topic comment by you at TSZ.scordova
July 27, 2013
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How many amino-acid changing mutations are there, per birth, do you think Sal?
Less than 1 because 2% or so is coding DNA, 3 DNA per codon, and then one includes only missense changes. A slight problem though is how is there codon bias maintained? And thus mutations that are synonymous have some importance and so do the intergenic regions. But then there is the presumption that intergenic has no selective change or is nearly neutral right? There is a reason evolutionists make this assumption.. Suppose these 100 mutations per generation mean something and are not neutral and sufficiently deleterious to require selection, you run into the U-paradox whereby cleaning out even 6 new mutations per human requires 800 kids per couple plus truncation selection. This was worked out here: https://uncommondescent.com/darwinism/darwins-delusion-vs-death-of-the-fittest/ The authors of the cited paper actually used the same formula derived from the Poisson distribution that I used in my essay. But, I'll let you answer for the readers if you think most of molecular evolution is neutral or under selection. :-) Finally, there is all this supposed purifying selection. So on the one hand neutralists know that there aren't enough population resources to support all this purifying selection to keep the conserved regions even between humans identical, thus molecular evolution must be neutral, yet we have all these conserved regions that defy neutral evolution. So evolution proceeds neutrally, is not Darwinian, but it cannot be random either. The conserved regions are conserved for other reasons than purifying selection.scordova
July 27, 2013
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Are you deleting comments, Sal?Alan Fox
July 27, 2013
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Human Genetic Variation Recent, Varies Among Populations - (Nov. 28, 2012) Excerpt: Nearly three-quarters of mutations in genes that code for proteins -- the workhorses of the cell -- occurred within the past 5,000 to 10,000 years,,, "One of the most interesting points is that Europeans have more new deleterious (potentially disease-causing) mutations than Africans,",,, "Having so many of these new variants can be partially explained by the population explosion in the European population. However, variation that occur in genes that are involved in Mendelian traits and in those that affect genes essential to the proper functioning of the cell tend to be much older." (A Mendelian trait is controlled by a single gene. Mutations in that gene can have devastating effects.) The amount variation or mutation identified in protein-coding genes (the exome) in this study is very different from what would have been seen 5,000 years ago,,, The report shows that "recent" events have a potent effect on the human genome. Eighty-six percent of the genetic variation or mutations that are expected to be harmful arose in European-Americans in the last five thousand years, said the researchers. The researchers used established bioinformatics techniques to calculate the age of more than a million changes in single base pairs (the A-T, C-G of the genetic code) that are part of the exome or protein-coding portion of the genomes (human genetic blueprint) of 6,515 people of both European-American and African-American decent.,,, http://www.sciencedaily.com/releases/2012/11/121128132259.htmbornagain77
July 27, 2013
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*(it's quite a lot less than 100)wd400
July 27, 2013
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How many amino-acid changing mutations are there, per birth, do you think Sal?wd400
July 27, 2013
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Gordon,
No. That would be the fixation rate if all mutations were neutral or very very nearly neutral,
Which is the variety I was talking about, neutral or within the neutral window, as in the mutations that fit the formula quoted above. I provided some numbers from the literature. hope that gives you some of the numbers you're looking for.scordova
July 27, 2013
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For the approximation you are using to be reasonable, the “deleterious” mutations you are talking about would need to have 99.9975% of the fitness of the wildtype. Are you really trying to make something from this tiny difference?
But you have this unfortunate fact that says even if a mutation is 99.9975% of fitness, it does not mean such mutations are rare! In fact 20% of amino acid mutations in humans are supposedly in this narrow window!
20% of amino acid mutations in humans are slightly deleterious, http://mbe.oxfordjournals.org/content/19/12/2142.full
So 20% of the amino acid mutations are deleterious and fitting through that tiny little window of the neutral zone. :-) Golly, I was generous in giving my 5% estimate! And the same paper also reports:
Our results suggest that a large majority of amino acid mutations are strongly deleterious in all the species we investigated. Slightly deleterious mutations, those mutations with effects close to 1/Ne, could be a substantial fraction of fixed mutations because we found evidence for differences in selective constraint and the kinds of amino acid that are fixed between species with different recent effective population sizes.
So evolutionists agree with Rupe and Sanford as far as the bolded portion.
WD: I’m sure much of the complexity of eukaryote genomes is accumulated clutter that our relative small population sizes saved from selection. But that’s pretty much the position of mainstream evolutionary biology, what’s your point?
Say what? Most of molecular evolution "saved from selection" or can we say "not under selection" as I pointed out here: Most evolution is free of selection, therefore Darwinism is false. You call eukaryotes accumulated clutter, but what if it is mostly functional, then we have lots of designs that evolved independent of selection, thus Darwin and Dawkins are wrong wrong wrong.
WD: Of course most substitutions are neutral (that’s why molecular phylogenetics works, and especially molecular clocks work, btw).
In other words, for phylogenetics to work, Darwinism has fail. And you admit most substitutions are not the result of Darwinian evolution, hence most of what makes up human beings was constructed without the guiding hand of Darwinian evolution, hence Dawkins is wrong. Hence, Haldane's dilemma adds only insult to injury whereby only a few hundred to a few thousand mutations out of became a permanent part of the human population. This is an negligible amount when considering that the difference between Chimps and Humans could be around in the possible ball park of 200,000,000 base pairs (if we don't do the Dictionary Trick) and include the intergenic mutations and re-arrangements. Tomkins estimates only 70% similarity, and if Tomkins is correct that is about 1 giga base pairs of difference. So much for selection creating humans!
A Darwin saw all that was made by Darwinian evolution, and Darwin said, "it is good".
scordova
July 27, 2013
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If the effective population was 10,000, and a gametic mutation rate of 100 per individual, that means there are 10,000 * 100 = 1,000,000 new mutations in the pool for that generation. From this pool of 1,000,000, 100 will go to fixation, or 1 out of 10,000 from the entire pool of 1 million.
No. That would be the fixation rate if all mutations were neutral or very very nearly neutral, but that is not the case. Some mutations are significantly non-neutral, and this will throw your calculation off. Also, the total population (N) is what's relevant here, not the effective population (Ne); the prehistoric human population probably averaged around 50,000, so the overall mutation rate (but not the fixation rate) will be about 5x higher. I don't know what the actual statistics are, but let me make some simple assumptions and see what they lead to. Assume that 95% of those mutations are exactly neutral (s=0). With N=50,000, that's 4,750,000 mutations/generation, of which 1/50,000 eventually become fixed, so the population accumulates 95 truly neutral mutations per generation. Of the non-neutral mutations, assume 50% (that's 2.5% of the overall mutations, or 125,000 mutations/generation) are immediately lethal (that is, s=1). None of these are fixed. Assume another 40% of the non-neutral mutations are significantly deleterious (but not immediately lethal), that is s is beween 0.000025 and 1). That's 2% of the overall mutations, or 100,000 mutations/generation. Since these mutations are not nearly neutral, selection will still prevent them from being fixed (although some of them may persist for a while in the population as part of the genetic load). (And actually, if some of them are near the s=0.000025 level, there's a chance that they may become fixed anyway. The cutoff is not sharp...) Of the remaining non-neutral mutations (0.5% of the total, or 25,000 mutations/generation), assume 99% (24,750) are in the slightly deleterious range, that is s is between 0 and 0.000025. These are close enough to neutral that selection does not remove them effectively, so they get fixed at approxamately the neutral (1/50,000) rate. That means on average one of these slightly neutral mutations gets fixed about every other generation. But since they're only slightly deleterious, that means they decrease overall fitness by only 0.0025%/mutation, or 0.00125%/generation. What about the remaining 250 mutations/generation that I haven't counted? They're beneficial, of course. They don't all get fixed; some are eliminated by drift before selection can sweep them to fixation. In fact, the probability that a bebeficial mutation will become fixed is about -s, i.e. a mutation that increases fitness by 1% has about a 1% chance of being fixed and one that increases fitness by 10% has about a 10% chance of being fixed. Lets assume that of these beneficial mutations, 99% are only very slightly beneficial, i.e. less than 1%. That means that only about 2.5 mutations per generation increase fitness by 1% or more (and I'll assume it's just 1%). Each of these mutations has a 1% chance of being fixed, meaning that on average one beneficial mutation gets fixed every 40 generations. This increases fitness by 0.025%/generation. Which is 20 times as fast as the slightly deleterious mutations were decreasing it. Net result: each generation, an average of about 95 truly neutral nutations, 0.5 very slightly deleterious mutation, and 0.025 significantly beneficial mutations are fixed; overall fitness increases by an average of 0.024% per generation. Now, all of the numbers in the above were completely made up; I have no real basis at any for them (and I can't even promise not to have botched the math, as it's getting past my bedtime). But if you want to do a more realistic analysis, you need more realistic numbers; you can't just assume that the neutral fixation rate holds overall (it doesn't), and backfill from that faulty assumption. You need to know the fraction of mutations that have the various ranges of selection coefficients in order to get meaningful results.Gordon Davisson
July 26, 2013
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For the approximation you are using to be reasonable, the "deleterious" mutations you are talking about would need to have 99.9975% of the fitness of the wildtype. Are you really trying to make something from this tiny difference? Of course most substitutions are neutral (that's why molecular phylogenetics works, and especially molecular clocks work, btw). And I'm sure much of the complexity of eukaryote genomes is accumulated clutter that our relative small population sizes saved from selection. But that's pretty much the position of mainstream evolutionary biology, what's your point?wd400
July 26, 2013
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selection could “feel” the difference between a neutral mutation (with fitness equal to the wild-type) and one with only 99.9975% percent of the fitness of the wild-type.
If the effective population was 10,000, and a gametic mutation rate of 100 per individual, that means there are 10,000 * 100 = 1,000,000 new mutations in the pool for that generation. From this pool of 1,000,000, 100 will go to fixation, or 1 out of 10,000 from the entire pool of 1 million.
Which is to say, selection could “feel” the difference between a neutral mutation (with fitness equal to the wild-type) and one with only 99.9975% percent of the fitness of the wild-type.
But selection doesn't feel these one out of 10,000 that go to fixation does it? We don't know what fraction of these these 100 are dysfunctional, but suppose 5% are dysfunctional and slightly deleterious, that means 5 dysfunctional mutation per generation goes to fixation, which means over 300,000 generations, that's 1,500,000 dysfunctional mutations that were in the neutral zone that were slightly deleterious, that's not even counting the dysfunctional mutations that could be labeled "beneficial" in the Darwinian sense that went to fixation! And that doesn't even count the mutations that don't go to fixation but still plague large fractions of the population (i.e. large fractions of the human population have diabetes, myopia, allergies, high cholesterol, and so many genetically inherited diseases I can't even begin to list them all). As far as we can tell some of these have persisted before industrialization, and we have evidence of decline in intelligence while at the same time the population has exploded. So its not just the problem of fixation but the lack of purifying selection that can't seem to purge things out like myopia and allergies or loss of intelligence.
Talking above drivel, the historical human effective population size is generally agreed to be about 10,000. Which is around the norm for a vertebrate. Which is to say, selection could “feel” the difference between a neutral mutation (with fitness equal to the wild-type) and one with only 99.9975% percent of the fitness of the wild-type.
Which is pretty much irrelevant given we have dysfunctional mutations that are "beneficial" in the Darwinian sense, so how much more reasonable is it to suppose there are dysfunctional slightly deleterious mutations that can fit in the neutral zone. Given your parameters and given the generous assumption that only 5% of the 100 fixed are dysfunctional, there will be a pool of 1,000,000 of which 5 can qualify as: 1. slightly deleterious 2. fitting in the neutral zone 3. dysfunctional 4. eventually fixed into every member of the population This is predicted by the formula above, or are you going to insist most fixation is via selection, or that 100% of the mutations that go to fixation are not dysfunctional? scordova
July 26, 2013
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Talking above drivel, the historical human effective population size is generally agreed to be about 10,000. Which is around the norm for a vertebrate. Which is to say, selection could "feel" the difference between a neutral mutation (with fitness equal to the wild-type) and one with only 99.9975% percent of the fitness of the wild-type.wd400
July 26, 2013
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How do we define nearly neutral such that it qualifies for the above formula from Wiki? Ohta made a determination. Here is (gasp) Larry Moran writing about Ohta: http://sandwalk.blogspot.com/2012/08/tomoko-ohta-and-nearly-neutral-theory.html The level selection is defined by "S" coeficients. A trait that has a near zero S-coefficient makes it effectively neutral. So how close to zero do we have to be? Ohta describes it as S much less than 1/N where N is the population size. How much less? We see it listed in Kondrashov's paper:
s < 1/4Ne
where Ne is the effective population size (the effective population size is smaller than the total population size). http://www.ncbi.nlm.nih.gov/pubmed/7475094scordova
July 26, 2013
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Well, you know, lads, it's not a matter of them dragging their feet on the logic. I expect it's just that they find it... kind of... counter-intuitive, ye ken? And therefore fuzziness is well... kind of appropriate. NO! Logical! That's it! It's only logical!Axel
July 26, 2013
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But, as you can see, the formula has to do with the rate of fixation not subject to selection being equal to the neutral mutation rate.
But Jerad postures as if I didn't say what I said even when it's right under his nose! Slightly deleterious means effectively neutral, and I said with respect to slightly deleterious mutations:
That means if every human is getting 100 dysfunctional mutation per generation, about 100 dysfunctional mutations are getting irreversibly infused into humans every generation (a ratchet so to speak).
Ergo, if the mutation rate is 100 per human per generation, the fixation rate approximately is 100 per human per generation. :roll:scordova
July 26, 2013
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But, as you can see, the formula has to do with the rate of fixation not subject to selection being equal to the neutral mutation rate.
That's what I said! And slightly deleterious means approximately not being subject to selection. Read more carefully before you post drivel on my discussions.scordova
July 26, 2013
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Umm Sal, Jerad said "not subject to selection". However no one has ever put the equation to the test. That is no one knows if the mutation rate = fixation rate (neutral theory).Joe
July 26, 2013
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Ahem, I think you've misrepresented what the Wikipedia article says:
For a diploid population of size N and neutral mutation rate mu, the initial frequency of a novel mutation is simply 1/(2N), and the number of new mutations per generation is 2Nxmu. Since the fixation rate is the rate of novel neutral mutation multiplied by their probability of fixation, the overall fixation rate is (2Nxmu) x 1/(2N) = mu. Thus, the rate of fixation for a mutation not subject to selection is simply the rate of introduction of such mutations.
Pardon my having to interpret the formatting for this comment. Please check the original if there is any confusion. But, as you can see, the formula has to do with the rate of fixation not subject to selection being equal to the neutral mutation rate. Please work harder at using references correctly.Jerad
July 26, 2013
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