Uncommon Descent Serving The Intelligent Design Community

Lee Spetner responds (briefly) to Tom Schneider

William Dembski
November 10, 2006
Darwinism, Evolution
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Tom Schneider, “Mr. Information Theory” for the pro-Darwin side, criticized Lee Spetner (author of Not a Chance) for a probability calculation characterizing evolutionary processes. Here is a reply by Spetner that I’m posting with his permission:

Someone just brought to my attention the website http://www.lecb.ncifcrf.gov/~toms/paper/ev/AND-multiplication-error.html
which criticizes a probability calculation I made. . . .

Schneider is mistaken. He evidently did not take the trouble to understand what I was calculating. My calculation is correct. The probability 1/300,000 is the probability that a particular mutation will occur in a population and will survive to take over that population. If that mutation occurred it would have to have had a positive selective value to take over the population. If that occurred, then all members of the new population will have that mutation. Then the probability of another particular adaptive mutation occurring in the new population is again 1/300,000 and is independent of what went before – I have already taken account of the occurrence and take-over of the first mutation.

Therefore, the correct probability of both these mutations occurring and taking over their populations is the product of these two probabilities. And, as I wrote, the probability of 500 of them occurring is the probability 1/300,000 multiplied by itself 500 times. My calculation is correct and Schneider is mistaken. He is similarly mistaken about what he wrote about the article in Chance – Probability Alone Should End the Debate, http://www.windowview.org/science/06f.html, since that article relied on my calculation.

Comments
Some interesting reading: Monkey-Man Hypothesis Thwarted by Mutation Rates and updated versionJoseph
November 14, 2006
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Hello, (did you put the actual code up anywhere)? The code for the original version is here: http://www.duke.edu/~pat7/public/htm/gaWordLength.m All the code used in the second version is here: http://www.duke.edu/~pat7/public/htm/source/ The vast majority of that code is for handling the more complicated dictionary searches. The only GA-related function is here: http://www.duke.edu/~pat7/public/htm/source/gaWordLengthNewDictionaryNewCombination.m enjoy!franky172
November 14, 2006
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"I’m afraid this doesn’t obviate your problem. You’re now saying it will take 2,000 years to generate a new “species”. The Egyptians lived over 3,000 years ago, and the wild cats that lived then, are still the same today. And, yes, you’ve finally have gotten the right formula for time to fixation, but that’s not what you said before: "The chance of fixation of a selectively advantageous mutation is, regardless of the educational background of the proponent and impressiveness of their claims, 2s (2 x the selection coefficient). "" PaV, seriously, man: the chance of fixation (=2s for a beneficial mutation in a large, free-breeding population) is different from time of fixation (=(2/s)ln(2N)) which is the number of generations that it takes, on average, for a mutation that reaches fixation to do so. Go back and read what I wrote. To be explicit, just in case: a new mutation with a selection coefficient of 0.01 (small: in human terms it would mean an average of 1 more descendant over 50 generations) in a large population (say, 1,000,000 individuals) has a chance of fixation of 2%. That is, it will have to appear on average 50 times before one gets fixed. OK? Good. Now, when it gets fixed, the time it takes to reach fixation (i.e. to sweep the population) will be, on average, (2/0.01)ln(2,000,000)=~2,900 generations. Now, the evolution of cats was certainly driven by humans, and it certainly involved the fixation of many mutations affecting reproductive and behavioral features of the animal. Many genetic differences, for instance, are known to exist between domestic cats and the Ethiopian wild cat, which is thought to be their wild ancestor. That said, neither the Egyptians nor anyone else since was trying to "evolve a new species". Of course, the selection coefficients during artificial selection are much stronger. If you work on a small enough population, you can reach fixation of certain alleles in two generations. I do it in my own lab to generate purely mutant mouse strains. "If you’ll read the first post that Allen MacNeil wrote in the “We is Junk” thread,https://uncommondescent.com/archives/1777, you’ll see that evolutionary biologists have pretty much given up population genetics as a way of explaining evolution." I am sure that will come to a surprise to Dr. McNeill, and all biologists for that matter. I suggest you go read what you wrote again, paying attention to his words.Andrea
November 13, 2006
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That's: https://uncommondescent.com/archives/1777PaV
November 13, 2006
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The chance of fixation of a selectively advantageous mutation is, regardless of the educational background of the proponent and impressiveness of their claims, 2s (2 x the selection coefficient). An only slightly advantageous mutation, with a selective coefficient of 0.01 (i.e. an increase in 1% in transmission - essentially experimentally undetectable in humans) has a chance of fixation of 2%.
I'm afraid this doesn't obviate your problem. You're now saying it will take 2,000 years to generate a new "species". The Egyptians lived over 3,000 years ago, and the wild cats that lived then, are still the same today. And, yes, you've finally have gotten the right formula for time to fixation, but that's not what you said before:
The chance of fixation of a selectively advantageous mutation is, regardless of the educational background of the proponent and impressiveness of their claims, 2s (2 x the selection coefficient). An only slightly advantageous mutation, with a selective coefficient of 0.01 (i.e. an increase in 1% in transmission - essentially experimentally undetectable in humans) has a chance of fixation of 2%.
If you'll read the first post that Allen MacNeil wrote in the "We is Junk" thread,https://uncommondescent.com/archives/1777, you'll see that evolutionary biologists have pretty much given up population genetics as a way of explaining evolution.PaV
November 13, 2006
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"The problem here, Andrea, is that if you really believe that these mutations travel forward in parallel, that means that in about 500 generations, a new species will appear." You are confusing the chance of appearance of a mutation with its time of fixation. The time of fixation for a new favorable mutation (in generations) is (2/s)ln(2N) (assuming a large enough, freely breeding population). For a mutation with a lowish s, say 0.01, in a population of reasonable size (1,000,000), you are talking a couple thousands generations on average. (This should also answer PaV's previous comment about favorable mutations becoming fixed since Darwin's times.)Andrea
November 13, 2006
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I suppose I'll need to take a 2nd look (did you put the actual code up anywhere)?
Also, despite the fact that I’m looking for any 10 letter word, there are only on the order of 10-20k of them (depending on how you count), and there are 26^10 or 1.4*10^14 possible 10-letter combinations, so the odds of picking any particular word of length 10 at random is still very low (about 1.4*10^-10).
That's actually why I don't find the results interesting. 1.4*10^10-10 doesn't even approach the Universal Probability Bound of 1*10^-50 proposed by French mathematician Emile Borel. As for calculating the informational bits, here is an example: “ME THINKS IT IS LIKE A WEASEL” is only 133 bits of information(when calculated as a whole sentence; the complexity of the individual items of the set is 16, 48, 16, 16, 32, 8, 48 plus 8 bits for each space). So aequeosalinocalcalinoceraceoaluminosocupreovitriolic would be 416 informational bits. Even though that's not 500 I'd still be surprised if that showed up with the way your GA is designed right now.Patrick
November 13, 2006
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Andrea:
But even if we assume (out of whatever calculation Spetner did) a rate of appearance of a specific mutation in a population of 1/600, that means that every few generations one of the 500 mutations he presupposes are necessary for the speciation would likely appear . And every new generation would be another roll, with another chance of another of the gene mutations to appear, and all of them would travel to the population in parallel, working through fixation.
The problem here, Andrea, is that if you really believe that these mutations travel forward in parallel, that means that in about 500 generations, a new species will appear. That's 500 years for most animals. Are you aware of a new species of cat, or dog, or horse, or......well, fill in the blank. I thought evolution takes place too slowly for us to see it in action. Descriptions of cats from the Egyptians dynasties is the same as for current day species. And, please, don't appeal to this being attributable to artificial selection, because the selection pressure of artifical selection is much higher than that found in nature. And, if it takes 500 years for a new "species" to come about, then why don't we see them in the fossil record. I await your answer.PaV
November 13, 2006
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http://user.tninet.se/~ecf599g/aardasnails/java/Monkey/webpages/index.html This is interesting, and it does a good job of showing that blind search is infeasible as an approach to generating complicated text. For fun see if your program can hit upon pseudopseudohypoparathyroidism (30 letters) or aequeosalinocalcalinoceraceoaluminosocupreovitriolic (52 letters). I can pretty much guarantee you that the odds of finding any one of these particular words is vanishingly small. Of course, the odds of finding any particular 10 letter word is also very small, but not nearly as small as for the other words you suggested. I’m glad to see your program doesn’t “sneak in too much information” considering the fitness function only checks for a 10-character string, although the target is very large considering you’re looking for ANY 10-letter word. Actually, the fitness function itself is defined as: Fit(word) = length(word) iff word is in dictionary 0 otherwise I did implement a stopping criterion of "let me know when you hit 10 letter words" but that's just so I could analyze the process of the GA up to that point. It doesn't add anything to the GA itself. Also, despite the fact that I'm looking for any 10 letter word, there are only on the order of 10-20k of them (depending on how you count), and there are 26^10 or 1.4*10^14 possible 10-letter combinations, so the odds of picking any particular word of length 10 at random is still very low (about 1.4*10^-10). If we’re just considering 8-bit single-byte coded graphic character sets I’d only find your results interesting if the generated word (or set of words) came to close to 500 informational bits. I'm sorry you don't find these results interesting :). Making the assumptions I've used, do you know about how many letters would be equivalent to 500 informational bits?franky172
November 13, 2006
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franky, you might find this interesting: http://user.tninet.se/~ecf599g/aardasnails/java/Monkey/webpages/index.html https://uncommondescent.com/archives/1224 For fun see if your program can hit upon pseudopseudohypoparathyroidism (30 letters) or aequeosalinocalcalinoceraceoaluminosocupreovitriolic (52 letters). I'm glad to see your program doesn't "sneak in too much information" considering the fitness function only checks for a 10-character string, although the target is very large considering you're looking for ANY 10-letter word. If we're just considering 8-bit single-byte coded graphic character sets I'd only find your results interesting if the generated word (or set of words) came to close to 500 informational bits.Patrick
November 13, 2006
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See Schneider's: The AND-Multiplication Error at: http://www.lecb.ncifcrf.gov/~toms/paper/ev/AND-multiplication-error.html Section:
The multiplication rule does not apply to biological evolution. . . .That is, if one starts with a given amino acid string, the mutations in the genome (from which the string is derived) are sequential. A mutation occurs, perhaps changing the amino acid string. If the change is bad, which is true for the majority of changes, the organism dies and its genes are gone. (In diploids, recessive defects will be removed more slowly since they are only exposed when an organism becomes homozygous for the mutation.) If a rare lucky change occurs that has some advantage (or at best is neutral or only slightly deleterious) then the organism may survive to produce offspring. The possibility of appearance and acceptance (by natural selection processes) of mutations in the offspring therefore depends strongly on whether the previous generation survived and on the number of progeny.
Schneider appears to be describing the equivalent of a "bang-bang" controller. i.e., if a mutation has any positive selectivity then select it, if any negative selectivity, then it dies. That makes for simple calculations, but it seems to me that Schneider throws the baby out with the bath water with that statement. Realistic modeling needs realistic selection factors AND a realistic ratio of beneficial to harmful mutations. Spetner appears to have selected what evolutionists say is a realistic selection factor of 0.1% . However, I think Spetner is being overly generous in his calculations by ignoring the harmful mutations with small negative selectivity. Sanford, Genetic Entropy (2005) p 24 notes "The best estimates seem to be one million to one (Gerrish and Lenski 1998, Genetica 102/103:127-144) The Basic Problem - Princess and the Nucleotide Paradox See Sanford Genetic Entropy 2005) p 47. In realilstic conditions, there are few positive mutations and numerous negative mutations (the ratio of positive to negative is very small). Then the negative mutations swamp the positive. Sandford highlights this
The problem involves the enormous chasm that exists between genotypic change (a molecular mutation) and phenotypic selection (a whole organism's reprouction.) .. . . We start to see what a great leap of faith is required to believe that by selecting or rejecting a whole organism, Mother Nature can precisely control the fate of billions of individual misspellings within the assembly manual.
Schneider appears to ignore this effect in his page. This Princess and the Nucleotides Paradox alone I expect is "catestrophic" to Schneider's argument, his calculations and his Ev program. --------------- DaveScott - Andrea has proposed starting a new thread to pursue these issues. Propose taking my last four posts, reformatting to start a new thread: Schneider vs Spetner & Sanford PS Assume my quotes of Spetner come under fair copying as they are to justify his position. Please verify with him.DLH
November 13, 2006
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Get lost Zachriel. I gave you a second chance to mend your ways but you're still running about on the net posting trash talk about our site here. I consider that duplicitous and don't want your two-faced kind around here. Hasta la vista. I'll be deleting your previous comments along with you. Call it taking out the trash.DaveScot
November 13, 2006
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The website provided above has been updated to include the generation of 9- and 10-letter words. In at least some cases it appears 10 letter words can be found in about 10^4.5 calculations...franky172
November 12, 2006
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DLH: thanks for posting that - what a mess. Statistics and the post-hoc target issue are the least of it. Not sure we want to take this apart here, since this thread is disappearing anyway, but if the site owners are willing to start a new thread, it could be fun.Andrea
November 12, 2006
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Joseph: “To follow Spetner’s argument all you get to mutate is one bit, not a whole letter which is comprised of 8 bits.” Zachriel: Genomes are base-4 mapped to base-64. Letters can be mapped in a similar fashion. Did you have a point or do you just like to type? Joseph: “ If you want to say recombination is random then the onus is on you to demonstrate that.” Zachriel: In our model, recombination *is* random. Ummm, your model is designed. Zachriel: However, this is an important point. If Spetner argues that point-mutation is insufficient to account for biological diversity, then he is correct. Even simple recombination is not sufficient. As far as I can tell no one knows if anything is sufficient. Zachriel: The question remains. How long would it take such an algorithm to evolve ten-letter words when such words represent only 1 in 14 billion of the possible sequences of ten-letters? How long would it take even if we use only point-mutation? It all depends on the programmer- ie the parameters set, the efficiency of the algorithm. IOW it all depends on the design. Joseph: “When you demonstrate any search algorithm arising without intelligence please let us know.” Zachriel: The origin of such an algorithm is irrelevant to Spetner’s claim which concerns already existing evolutionary algorithms. The origins are very relevant. Dr Spetner is only arguing against unintelligent causes. What existing "evolutionary algorithms" are you talking about?Joseph
November 12, 2006
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Schneider notes that the combined probability of independent events is the product of their probabilities. Pa X Pb. He says that this does not apply to biology: http://www.lecb.ncifcrf.gov/~toms/paper/ev/AND-multiplication-error.html
It is inappropriate to multiply probabilities unless the two events are independent. One must account for all of the events (in other words, honor the dead). The functional amino acids in a protein are not obtained independently since many organisms die for the few that survive to reproduce. Each change to an amino acid occurs in the context of the current protein and therefore depends on the previous history of the protein. Although the amino acids may be functionally independent (allowing, for example, the computation of a sequence logo), the appearance of the selected amino acids is sequential during evolution and is, therefore, dependent on previous steps. It is invalid to directly apply the multiplication rule to computing the probability that proteins came into existence.
Schneider claims Spetner makes “the AND-multiplication error” citing Spetner p130: “The chance of 500 of these steps succeeding is 1/300,000 multiplied by itself 500 times.” etc. Spetner responds: “The probability 1/300,000 is the probability that a particular mutation will occur in a population and will survive to take over that population.” . . .“the probability of 500 of them occurring is the probability 1/300,000 multiplied by itself 500 times.” From the previous post, it appears to me that Spetner has addressed both the population & probability issues necessary to make NDT work, taking major evolutionist’s assumptions. Are there any errors in Spetner’s overall argument of what would be needed for NDT to work via those assumptions taken from evolutionists? 1) Has Schneider anywhere addressed Spetner’s overall argument and each of Spetner’s assumptions? 2) What support/objection is there for Spetner’s basis for independence between calculations if assuming a mutation takes over the population for each of the 500 steps per speciation? 3) Is Schneider correct in his AND-multiplication error critique of Spetner p130?DLH
November 12, 2006
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33 Andrea: “It would be good to have the actual derivation of the numbers from Spetner’s book.” See: Lee M. Spetner, PhD, Not by Chance, Shattering the Modern Theory of Evolution. 1998 Judaica Press ISBN 1-88-582-24-4 JudaicaPr@aol.com Steps per speciation: Spetner p 97
G. Ledyard Stebbins, one of the architects of the NDT, has estimated that to get to a new species would take about 500 steps [Stebbins 1966].
500 steps. P 97 ( citing Stebbins 1966). Acceptable probability of speciation: Spetner p 100:
Richard Lewontin of Harvard University has estimated that for each species alive today there about 1000 that went extinct [Lewontin 1978]. . . . Some apecies go for a long time without changing. . . So let's throw in another factor of a thousand for this effect. . . . Thus we we adopt the criterion that evolution can work if the chance of achieving a new species in 500 steps is at least one in a million.
Needed probability per step: Spetner p 100
The chance of a single step has to be so large that when we multiply it by itself 500 times we get at least 1/1,000,000. The smallest number that will do that is close to 0.9727, which is a chance of about 36 out of 37.
Spetner calculates the chance of one mutation appearing and then taking over the population as 1/600 x 1/500 = 1/300,000. Spetner p 103
You can now see what it will take to complete one successful step in a chain of 500. An adaptive mutation has to occur and it has to survive to take over the population. But the chance is small that a specific copying error will appear and survive. The chance that it will appear is 1/600. For a selective value of a tenth of a percent the chance that the mutation will survive, if it appears, is 1/500. The chance that the mutation will both appear and survive to take over the population is 1/600 x 1/500, or one in three hundred thousand. (1/300,000). That’s less than the chance of flipping 18 coins and having them all come up heads.
See previous post for 1/500 or 0.2% as 2x the 0.1% selective advantage. Basis for 1/600 for a mutation to appear: Number of births per step: Spetner p 122 ref 3
Number of births per evolutionary step. . . . George Gaylord Simpson . . .estimated that the whole of the horse evolution took about 65 million years. He estimated there were about 1.5 trillion births in the horse line. . . .The experts say the modern horse has evolved through some 10 to 15 genera. If we say the horse line, from Hyracotherium to the modern horse, went through about five species in each genus, then the horse line with its 1.5 trillion births went through about 60 species. . . .That would make about 25 billion births per species. If I divide 25 billion births per species by the 500 steps per species transition, I get 50 million births per step.
Mutation rate/nucleotide/birth in animals: Spetner p 92
For organisms other than bacteria, the mutation rate is between 0.01 and 1 per billion [Grosse et al. 1984]. The geometric-mean* is one per billion (10^-9) in bacteria and one per ten billion (10^-10) in other organisms.
Spetner p 100
Note that I have taken the mutation rate at each step to be a change in a single nucleotide.6. I don't know if there is always, at each stage, a single nucleotide that can change to give the organism a positive selective value and to add information to it. No one really knows. But I have to assume it if I am to get on with this study of cumulative selection. That's a pretty strong assumption to make, and there's no evidence for it. But if the assumption doesn't hold, the NDT surely won't work. Althrough we don't know if it holds, lets see if the NDT can work even with the assumption.
Net mutation rate of 1/600: Spetner p 100
The chance of a mutation in a specific nucleotide in one birth is 10^-10, and there are 50 million births in an evolutionary step. The chance of getting at least one such mutation in the whole step is about 50,000,000 times 10^-10, or one in two hundred. There is an equal chance that the base will change to any one of the other three.* Then the chance of getting a specific change in a specific nucleotide is a third of that, or one in six hundred.
* The chances aren't really equal, but assuming they are will give us a result that is close enough for our purposes.
Copying errors needed per step Spetner states on his page 104:
How many potential adaptive copying errors must there be to raise the chance of a successful step from 1/300,000 to 0.9727? A calculation shows that there must be about a million of them.7
(sic) (Reference 5 on page 123 apparently provides this detail:)
5. There have to be a million potential adaptive mutations to make the theory work. Actually the number turns out to be about 1,080,000. We can check this by verifying that at least one out of 1,080,000 possibilities will occur with probability 0.9727. We found that the chance for a particular mutation to occur and take over the population in one step is one in 300,000, or a probability of 0.000,003,333. The chance that it will not occur is one minus this number, or 0.999,996,667. The chance that none of the 1,080,000 potential mutations will occur and take over is 0.999,996,667^1,080,000. This works out to be 0.0273. The chance that at least one of the potential adaptive mutations will occur and survive is one minus this number, or 0.9727.
DLH
November 12, 2006
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29 Joseph and 34 Andrea. (To Support 30 Patrick) Spetner (p102) selects 0.001 (0.1%) as the fraction of mutations having a selective advantage, citing a “frequent value” used by George Gaylord Simpson 1953 p 119 (an NDT architect and the “dean of evolutionists”). Then Spetner states on p 101 “Fisher’s analysis shows that a mutant with a selective value of one percent has a two percent chance of survival in a large population. . . . If the selective value were a tenth of a percent, the chance of survival would be about 0.2%, or one in 500.” Citing Ronald A. Fisher (1958) The Genetical Theory of Natural Selection, Oxford. On p 102 he summarizes: “For large populations, the chance of survival turns out to be about twice the selective value.” (In populations > 10,000.)DLH
November 12, 2006
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Zachriel: The mechanism in the word experiment is random mutation/recombination along with simple selection. To follow Spetner's argument all you get to mutate is one bit, not a whole letter which is comprised of 8 bits. If you want to say recombination is random then the onus is on you to demonstrate that. Zachriel: As Spetner’s argument is strictly arithmetic, it appears it should apply to any evolutionary search algorithm. When you demonstrate any search algorithm arising without intelligence please let us know.Joseph
November 12, 2006
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"My number wasn’t 10^4, but 10^(minus) -4. Per your indication, 1/3 nucleotides produce an amino acid change, so that means 3^10-5 gene mutations (aa substitution) /generation." If you are talking per individual. But what matters is the population, so, as you stated correctly yourself the first time around: "So the number I get is: 3/30,000 , or 10^-4 mutations/gene/generation. For a population of 3 x 10^8, that means about 30,000 mutations/gene/ generation." which, corrected for aa substitutions instead of nucleotide substitutions, comes to 10,000 gene/generation (in the US). "Spetner’s numbers are 1/500 for fixation, and 1/600 for appearance. I think he was using a 1/10^5 nucleotide mutation rate, which makes my number above 1/300–about what Spetner uses. He uses 0.1 selection coefficient–very realistic. You multiply 1/600 (for the mutation to appear), and 1/500 (chance of being fixed)=1/300,000 (for each mutation)." Still doesn't make sense to me. First of all, 10^-5 mutation rate in way too high. If we had that mutation rate, we would carry 10^5 new nucleotide substitutions/generation, of which ~3% (=3,000) would be within genes, that is 1,000 new amino acid substitutions/generation (0.03/ gene). That would mean that the population in the US would sample a whopping 10^7 mutations/gene/generation. You'd pretty much saturate the possible single point mutants space each generation (a typical gene of 300 aa has ~60,000 possible single aa mutants). You'd be pretty much assured that every mutant would appear at every generation. And 0.001 is a selection coefficient that is pretty much close to neutral (it would mean, in human terms and assuming 2 children/generation, that the carriers would, on average, have an extra descendant every 500 generations - essentially negligible) But even if we assume (out of whatever calculation Spetner did) a rate of appearance of a specific mutation in a population of 1/600, that means that every few generations one of the 500 mutations he presupposes are necessary for the speciation would likely appear . And every new generation would be another roll, with another chance of another of the gene mutations to appear, and all of them would travel to the population in parallel, working through fixation. And that again is assuming you expect precisely and only those specific mutations, as opposed to any of the innumerable alternative mutation that would give rise to any of the other possible innumerable alternative species. (Which is of course the obvious conceptual flaw in the calculation.) It would be good to have the actual derivation of the numbers from Spetner's book.Andrea
November 11, 2006
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Andrea: "“For a population of 3 x 10^8, that means about 30,000 mutations/gene/ generation.” Right, but those are nucleotide substitutions. Assuming (conservatively) that 1/3 nucleotide substitutions result in amino acid substitutions (hence potential phenotypic changes), it comes to 10^4 mutations/gene/ generation in the US, 2×10^5 mutations/gene/ generation in the world, as I said." My number wasn't 10^4, but 10^(minus) -4. Per your indication, 1/3 nucleotides produce an amino acid change, so that means 3^10-5 gene mutations (aa substitution) /generation. Spetner's numbers are 1/500 for fixation, and 1/600 for appearance. I think he was using a 1/10^5 nucleotide mutation rate, which makes my number above 1/300--about what Spetner uses. He uses 0.1 selection coefficient--very realistic. You multiply 1/600 (for the mutation to appear), and 1/500 (chance of being fixed)=1/300,000 (for each mutation). Here's two other comments you made: "That means that it would take only 50 generations on average for a new selectively advantageous aa substitution to appear and “sweep” a human-size free-breeding population. And when that happens, the time to fixation is rather short - few dozens generations or so. " Along with: "For most organisms, as the example above shows, there is an enormous range of mutations sampled at each generation. The favorable ones have a very good chance of fixation. " Putting these two statements together, the only conclusion you can come to is that either one (1) beneficial mutations are extremely rare, or (2) all kinds of "beneficial" mutations have become fixed in the human population since the time of Darwin. Would you like to point out to us these "beneficial mutations", or do you want to live with the notion that "beneficial mutations" are rare? (And probably swamped by deleterious ones)PaV
November 11, 2006
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Someone previously banned a while back tried to add this comment:
Joe, Crow & Kimura (pp 418-422) show how that is figured. The assumption is that the number of offspring of a mutant follows a Poisson distribution with mean 1+s. A branching process argument then shows that the probability p of ultimate survival (meaning there is a non-zero number of mutants after a very long time) is the solution of 1-p=exp[-(s+1)p] The solution is approximately p=2s-(5/3)s^2+(7/9)s^3-(131/540)s^4 and so on, or approximately p=2s for small s.
Patrick
November 11, 2006
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Andrea: The chance of fixation of a selectively advantageous mutation is, regardless of the educational background of the proponent and impressiveness of their claims, 2s (2 x the selection coefficient). An only slightly advantageous mutation, with a selective coefficient of 0.01 (i.e. an increase in 1% in transmission - essentially experimentally undetectable in humans) has a chance of fixation of 2%. How did you figure that?Joseph
November 11, 2006
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That should have been: "no one would expect the formation of a new species to require 500 selectively disfavored mutations."Andrea
November 11, 2006
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"For a population of 3 x 10^8, that means about 30,000 mutations/gene/ generation." Right, but those are nucleotide substitutions. Assuming (conservatively) that 1/3 nucleotide substitutions result in amino acid substitutions (hence potential phenotypic changes), it comes to 10^4 mutations/gene/ generation in the US, 2x10^5 mutations/gene/ generation in the world, as I said. As to Spetner’s number of 1/300,000, he has a unique educational background, and with that background comes up with an impressive way of getting a realistic number for “fixation” (not appearance) of a mutation in a population. The chance of fixation of a selectively advantageous mutation is, regardless of the educational background of the proponent and impressiveness of their claims, 2s (2 x the selection coefficient). An only slightly advantageous mutation, with a selective coefficient of 0.01 (i.e. an increase in 1% in transmission - essentially experimentally undetectable in humans) has a chance of fixation of 2%. For most organisms, as the example above shows, there is an enormous range of mutations sampled at each generation. The favorable ones have a very good chance of fixation. Of course, unfavorable mutations won't get fixed, but no one would not expect the formation of a new species to require 500 selectively disfavored mutations. Finally, there is the usual error of painting the target around the arrow. That is, even assuming 500 mutations are required to make a new species, it is only in retrospect that it had to be that species. Going forward, evolution could have just as easily generated a different species using different mutations. In other words, while the chances of evolving one specific species are indeed low, the number of species that evolved is a minuscule fraction of the number of potential new species which could have evolved. (It's like saying that the chance of an individual with my - or your - DNA sequence coming from the mating of my or your parents are essentially zero, but once thy got to it, someone had to be born. ) One should of course correct for that when talking probabilities. Basically, I am just trying to understand how Spetner got to 1/300,000, because I can't find a solid justification in the links provided.Andrea
November 11, 2006
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Zachriel: "Illuminating work, Franky172. Apparently, the evolutionary algorithm is far more efficient than random search. " This shouldn't be surprising since most, if not all, evolutionary algorithms "sneak in" information; and "information" is always directed towards a target. And only knowing where a target is will, per NFL theorems, improve your chances over a simple random search.PaV
November 10, 2006
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Andrea:
Chance is a minor component because for most populations, a very large sequence space is sampled at each generation. For instance, each newborn human is generally estimated to carry about 1 new gene mutation. That means that 300,000,000 Americans will display 10,000 new mutations/gene/generation (ballparking at 30,000 genes). 6 billion humans will sample 2×10^5 variants/gene/generation. That’s a lot of variation!
I'm not sure how you arrived at your numbers. The mutation rate of genomes is generally considered to be about 1^10-8/nucleotide. There's about 10^10 nucleotides in the human genome. That means about 100 mutations/generation. But the percentage of the genome that is "coding" for genes is about 3%. That means about 3 mutations occuriing, on average, in "genes". There are about 30,000 genes/genome in humans. So the number I get is: 3/30,000 , or 10^-4 mutations/gene/generation. For a population of 3 x 10^8, that means about 30,000 mutations/gene/ generation. Taking 20 years as an average time per generation, that means 1500 mutations per year/gene. (How many of these are "beneficial"? ) As to Spetner's number of 1/300,000, he has a unique educational background, and with that background comes up with an impressive way of getting a realistic number for "fixation" (not appearance) of a mutation in a population.PaV
November 10, 2006
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Andrea: Chance is a minor component because for most populations, a very large sequence space is sampled at each generation. For instance, each newborn human is generally estimated to carry about 1 new gene mutation. That means that 300,000,000 Americans will display 10,000 new mutations/gene/generation (ballparking at 30,000 genes). 6 billion humans will sample 2×10^5 variants/gene/generation. That’s a lot of variation! But variation just leads to wobbling stability.; Which isn't a good thing for evolutionism. Andrea: That’s also why the 1/300,000 number claimed by Spetner seems way too low, by the way. (I wonder whether he confused mutation rate with the chance of a mutation appearing in a population. ) It is probably too high. Becoming fixed takes quite ba bit of luck or intention. The larger the population, ie those over 1000 and NS is pratically nill. For populations under 1000 Mayr assures us any mutation will get lost just by random effects. ------------------------------------------------------------ Zachriel: I note that no one has yet attempted to use Spetner’s methodology to calculate how word evolution should progress. And for good reason. And that reason would be very apparent to anyone who has read his book. Also "evolution" isn't the issue. It is the mechanism that is being debated.Joseph
November 10, 2006
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Mea culpa Following Zachriel's explanation, I formally withdraw my comments at 8 and apologize to Tom for misreading his example. Better get some more sleep and good probability book. (PS I still believe is his application to nature does not follow from reasons such the probability of selection as reviewed in Stanford' Genetic Entropy etc. )DLH
November 10, 2006
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“Americans will display 10,000 new mutations/gene/generation (ballparking at 30,000 genes). 6 billion humans will sample 2×10^5 variants/gene/generation. That’s a lot of variation!” Even if this is correct (I just don’t know the stats) it’s amazing that we all somehow remain human. Think we would have seen some hip new macro-change by now. New body plan maybe?shaner74
November 10, 2006
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