Evolution and Probability

Hi, I am new to this website, but not the creation/evolution debate. I was wondering what you thought of Lee Spetner's probability analysis in his book "Not By Chance!" I am mainly interested with his calculation for convergent evolution. He determined that "either the probability of the horse evolving was impossibly low, or else convergent evolution cannot occur." (http://www.trueorigin.org/spetner1.asp)We know that speciation does occur, so that only rules out convergent evolution. I am not saying that Spetner is correct, but let's have a look at his analysis.He said that in order for evolution to proceed, the chance of evolving a new species must be at least 1 in a million. He says:"Richard Lewontin of Harvard University has estimated that for each species alive today that are about 1000 that went extinct [Lewontin 1978]. Shall we then say that for evolution to work, the chance of getting a new species should be one in a thousand? On the one hand, maybe it should be larger. Some of those extinct species are not without living descendants. Some of them became extinct because their descendants evolved into species that replaced them. On the other hand some species are around today that do not seem to have evolved for a long time. so maybe the chance of speciation should be smaller than one in a thousand. Some species go for a long time without changing. This is the stasis that punctuationists emphasized. So let's throw in another factor of a thousand for this effect. Let's then set the level of chance to one in a million."So in order for evolution to proceed, the chance of it doing so must be at least one in million.He tries to calculate the probability of speciation in groups of at least 10,000. This is because, "When Fisher solved for the chance of survival of a mutant he took the population to be infinite. I solved the problem of gene survival in a finite population in an approximate way by taking it to be a random walk with two absorbing barriers [Feller 1957]. I then found the chance of survival to be 2S/(1-e^-2SN), where S is the selective value and N is the population size. Note that the larger N is, the smaller is this chance. The chance is always bigger than 2S, but when SN is large, the chance is close to 2S. When SN is 1 the chance is about 16% larger than 2S. When SN is 2 it's about 2% larger. When SN is 3 it's only about .25% larger. ... If you divide a population into smaller groups you'll raise the chance that a positive mutant, if it occurs, will survive. The mutant will survive better in a small group than in a large one. That follows from the expression I gave in the previous note for the chance of survival. But as you can see from the numerical values in the previous note, reducing the population gains only a little in the chance of survival. The population has to be small to get a significant increase in the chance of survival. To get substantial benefit from this effect you have to make the population very small, but then the whole group is in danger of extinction by a minor catastrophe."It is therefore more plausible to believe that speciation took place in groups of ~10,000. This is not such a huge number. If there were 200,000 members of a species worldwide, a population of 10,000 would only represent 5% of it.Anyway, Spetner goes on to his calculations. I have readjusted some of his parameters, since his mutation rate was incorrect. He takes the horse as an example of evolution.Numbers:Mutation rate-10^-7 Steps in Speciation-50 Number of individuals per step:
( 25 billion births per species/50 steps per transition-) 500,000,000.(*I used 50 steps in a species transition because Spetner used a 500 step species transition estimated by Stebbins, Haldane, etc.. However this number is variable. Many of the evolutionists I have encountered on the internet say that speciation can take less than 500 steps. Therefore, in their favor, I assumed 90% of speciation was 1 step and the rest were 500 as Spetner described. This balances out to an average of 50. It is important to note that each step only represents 1 nucleotide.)Probability 1 nucleotide will take over a population: 500,000,000 x 10^-7 = 50. 50/1 x 1/3 (correct nucleotide) = 17/1 x 1/500 (selection coefficient) = 0.034. 0.034^50 (steps per species) = 3.47^-74.Now, this is lower than the 1 in a million mark we have set previously. We need a number, which multiplied by itself 50 times (representing 50 steps/speciation event) will equal at least 1/1,000,000 (explained earlier). The smallest number to do this is close to 0.75.In order to raise .034 to .75 we need at least 22 mutations (0.034 x 22 = 0.748). Remember, the speciation odds were just for 1 nucleotide. However we know that there are many nucleotides, and this calculation takes this into account. This calculation also assumes that mutations that add functional information to the genome and are beneficial occur frequently. I am not saying that they do not occur, but Spetner improves the odds for evolution by doing this.A typical selective value is .1% according to evolutionist G.G. Simpson. If these beneficial mutations were each close to the same selective value, then at each step evolution can choose any one of 22 different paths. In lysozyme in langurs, 9 nucleotides converged to form the enzyme (like that in ruminants). That means that at each of these 9 steps, there were 22 different possibilities. This would be 22^-9. How much more would this number increase for other examples of convergence, like hemoglobin in earthworms and hemoglobin in humans?Some things to consider:1. More than one beneficial mutation could occur. This means that the correct 9 nucleotides could have occurred many times. However it seems that beneficial mutations would occur in other parts of the genome in proportion, so a ratio of 22 to 1 may be maintained. (Actually the number may be greater than 22).2. The lysozyme convergence doesn't necessarily have to deal with speciation. This is correct, but it may cause a change or step leading to speciation, which is included in the calculation. At any rate, if it is not competing in the small amount of mutations that cause speciation, it would be competing against a much larger amount of mutations throughout the genome that do not lead to speciation, seemingly making the probability worse.3. More than one nucleotide could be fixed. This is true, but how many beneficial nucleotides? Spetner uses his model to attack the NDT (neo-darwinian theory) of evolution. They assume that small changes add up to big changes. So Spetner assumed the smallest change possible-a single nucleotide. Even if we assume that all 9 nucleotides were fixed in 1 step, instead of the probability being 1 in 22^9, it would be 1 in 22.I want to approach this problem differently.According to Are Mutations Harmful?, "The average human being has about 50-100 mutations". I am not for sure about the langur, and I could not find the average number of mutations. However let us assume a number in range of humans-about 75. If I am not mistaking, there were 15 million yrs. for the convergent evolution of this lysozyme (I got this figure from a fellow named Thomas who posts on this board, and who I have discussed this issue with to before). If we assume a generation time of 7 years, that is 2,143,000 generations. If there are 10,000 in a population then there would be 750,000 total mutations. For the whole of langur evolution, it would be 750,000 x 2,143,000 = 1,607,250,000,000. This could overturn a genome of 3 billion nucleotides 535 times. However, we must divide this number by three to get the correct nucleotide, which would be about 179. Therefore the chance of fixation is 179/500^9, or 0.000096 (0.0096%). Even considering 5 yrs/generation and 100 mutations per individual this equals a 2% chance (0.026).I could remodel the calculation yet again. We determined earlier that there are 500,000,000 births per evolutionary step. This is not speciation, just a step in the speciation process. If there are 100 mutations per individual then that equals 500,000,000,000 billion mutations. This could overturn a genome of 3 billion nucleotides 17 times. That means at least 17 mutations in the correct spot in the genome. However you must divide this number by three to get the correct nucleotide. This would be 6. So if a beneficial mutation has on average a 1/500 chance of survival, this mutation would have a 6/500 chance. The overall probability for all nucleotides would be 6/500^9, or 0.000000000000000005159780352 (0.0000000000000005159780352 %). These odds are not very likely.The problem gets worse, because not only did the lysozyme converge, but the structure of also the structure of the stomach in the ruminants and langurs. At http://groups.yahoo.com/group/TrueOrigin/message/4350
you can find some more information on this.I would like your comments and opinions. I don't know if I can answer all of them though. If any of you get a chance, visit the NAiG message board. I post mostly on that website.

Thank you for the reply PaulK. You said,"I've discussed Spetner's analysis in the past and the version I am familiar with is mathematically erroneous, and biologically flawed.
For instance in the langur calculation he failed to take inot acocunt that some mutations would have higher probabilities of occurrence and/or higher selective values and they would be more likely to be found as a result."This is absolutely true. That is why I took the average mutation rate and the average selection coefficient. (G.G. Simpson said the average selective value of a mutation is 0.1%. This would mean it has a 1 in 500 chance of fixation.)"I should also add that convergent evolution usually refers to morphological similarities - which could have a quite different genetic basis - Spetner's argument only applies to convergence at the molecular level (and due to the redundancy of the genetic code even that may have more possibilities than Spetner allows)."The nine nucleotides that converged were at the molecular level. Not only did I use Spetner's calculations, but I also set up a few more on my own. The caluclations I set up did not depend upon a 50 step speciation model. It was simple and straightforward."You repeat Spetner's major error of grouping births into blocks and equating those groupings with evolutionary steps (defined by Spetner as a mutation achieving fixation) and of assuming that since evolution relies on small changes it is correct to focus on point mutations (dead wrong - a significant proportion in vertebrates involve larger changes at the genetic level)"I don't think Spetner made an error here. He merely took the total number of replications involved and divided by the number of species in the evolutionary series. He then divided this number by 500-which was Stebbins' estimate of the number of steps in speciation. I know that this number is off-that this number is variable. That is why I assumed that 90% of the changes were large one step changes, and that 10% of the changes were as Spetner described. It should also be noted that this 500 step model is only 500 nucleotides. Would you argue that a species can be separated by less than 500 nucleotides (on average)? At any rate your accusation does not affect my other probability analyses."That is completely and utterly wrong unless you assume that those mutations must each appear in a particular sequence at a particular time - ignoring the possibility that there might be a number of possible orderings for the mutations and that other mutations might occur and reach fixation between them."Not really. In all of my models any nucleotide can appear in any sequence. This especially holds true for the models I developed personally. I simply took the average selection coefficient and the figure off of the talkorigins website and calculated. What's wrong with it?Must be going. Nice talking with you.

Thank you for the reply. I like your post. You said,"All statistical calculations of this type type related to evolution are nonsense on stilts.
Probabalistic calculations can only be applied in one of two cases:1: When all the events in the chain are random and unconnected to each other. The classic example of this is in throwing a coin. The result of one throw does not affect another: regardless of the number of heads in a run, the probability of throwing a head remains 0.5. However, the probability of certain results for a number of throws can be calculated exactly."Tis is true. I merely took the average selection coefficient and worked it into my calculation. I think it would be nearly impossible to calculate the odds without the average. However we see from the average number it is highly improbable.2": When all the possible paths and their likelihood is known. This can only be done ex post facto. In this case you can analyse a past event and state the odds of having achieved the percieved event."Well, in the calculation I borrowed from Spetner I set a lower limit on what the possible paths had to be-22. The more possible paths, the less likely that two species will take the same path. However this does not affect the calculations I made personally (involving the numbers taken from talkorigins).E"volutionary events are not isolated - one event influences the possible sequence of future events, therefore statistical analysis is impossible."Again, this is true. I took the average selection coefficient. However it is probably still not accurate.T"he number of possible events is unknowable - therefore the probabilities cannot be calculated after the event."TThis was explained above.

I would first like to thank everyone for their replies. I would like to comment on some of the posts."No, Spetner made a major error there. It is simply invalid mathematically - and has no biological basis.
Try this example. If you toss a coin 10 times what is the probability that you will get at least 5 heads ?
Calculate it using Spetner's method of dividing the tosses into blocks of 2 and insisting on getting at least one head in each and the probability comes out as 0.75^5 ~= 0.237. Which is less than half the real probability - and it gets worse the more steps you use.
The probability of getting 50 heads out of 100 tosses is still better than 0.5 - but Spetner's method would produce 0.75^50 - exactly the numbers you used for your "1 in a million" calculation."This is an irrelevant analogy. Spetner shows that unless a number of mutations occur, then speciation is virtually impossible. Assuming that convergent evolution does occur, (and finding the minimum number of mutations per step-22), then evolution would have several ways to go. I do not know the selective value of all these positive mutations. However the average is 0.1, and that is the number I am using. It usually does not fluctuate too much from this value. Anyway, if there were 2 choices at each stage (as in your coin analogy), then evolution could proceed in 1 of 2 ways. If there was a convergence at three of the 5 choices, the probability of convergence would then be 1/2 x 1/2 x 1/2. It seems that you are not looking at specific changes. However you must in the examples that Spetner gives-like the lysozyme in langurs. They converged on at least 9 nucleotides, but could have converged on more."Dillan,
This has been done at NAIG, and it didn't go anywhere. It has, of course, scrolled off that board now, but Thomas showed fairly conclusively that your and Spetner's theses were non-starters. I can ask Thomas if he archived any of his rebuttals."Thomas and I did work through the problem on the NAiG board. In fact, in my original post I used one of his calculations. I took the number of mutations per individual of the talkorigins website and plugged it in. I also got my number of 15,000,000 years of evolution from him. The only problem that I had with his model is that it was almost too favorable for evolution. We know that 9 nucleotides converged. I assumed that these 9 nucleotides were beneficial. From my calculation we saw that the entire genome of the species could collectively be overturned a number of times. So therefore, how do we know that the other two nucleotides at each stage couldn't be beneficial as well? That would lower the probability to 1/3 x the original probability at each stage. At any rate, evolution is still improbable."I could not find any amino acid or nucleotide sequences for human and earthworm hemoglobin (no homologous sequences, that is - lots of hemoglobin d1 for earthworms, lots of b,c, a,g, etc. for human), so there were no means for comparison to see if convergence exists, though I suspect that the degree of conservation is closer in human and langur than either is to earthworm, where we would not be discussing convergenece anyway.
So"I know that parts of hemoglobin converged, because hemoglobin cannot be explained by common descent."Dillan, your reply shows that you've wholly missed my point.
To restate, if events in a probabalistic chain are linked - as are evolutionary eevents since every change in an organism allows certain others not previously allowable and prohibits certain other changes previously allowable - theoretical probabalistic calculations regardless of the sophistication of your mathematics and assumptions are simply not possible.All such calculations, regardless of their sophistication are invalid."I said that I realized your point in a previous post. From what we are able to calculate though, evolution is improbable.Well, I have seen no one really attack my second equation model. I noticed that someone said more than one nucleotide could be fixed per step. I took care of this in my original calculation. I found the probability of all nine nucleotides being fixed in a single step, and it is even lower than if we assume the whole of evolution (as there is more time, more mutations, and a better chance at fixation).By the way I would like to extend my gratitude to Fred for helping me out. I have read your article about evolution being thwarted by mutation rates. Has anyone totally refuted it? If it is solidified it would be very damaging to evolutionary theory.

I thank everyone for the replies. I would like to address some of them."Dillan: So therefore, how do we know that the other two nucleotides at each stage couldn't be beneficial as well? That would lower the probability to 1/3 x the original probability at each stage. At any rate, evolution is still improbable.FK: Most Creationists (and evolutionists, for that matter) say that beneficial mutations are extremely rare events. Yet you are proposing that 2 out of 3 possible point mutations at a specific site may have been beneficial. You seem to enjoy calculating probabilities. Set up that probability calculation, assuming that a beneficial mutation occurs once in every million or more mutations. I think you will see that what you are proposing is highly unlikely."Okay here is the deal. I do not assume that 2 out of there point mutations at a specific site are beneficial, just like I don't assume that 1/3 mutations at a specific site are beneficial (as someone may have inferred from my calculations). I just said that there is no way of knowing that the other two couldn't have been beneficial. This is why on the NAiG website I used Haldane's number to set an upper limit on the number of beneficial mutations. I could see where Thomas was coming from when he accused me of double-dipping in the probabilities. However I also saw my point of view."Dillan: I know that parts of hemoglobin converged, because hemoglobin cannot be explained by common descent.FK: You are definitely going to have to explain that one."Hemoglobin is supposed to have converged in several species, such as earthworms, mollusks, echinoderms, etc.. Dickerson says, "It is hard to see a common line of descent snaking in so unststematic a way through so many different phyla..."
Richard Dawkins seems to agree. In an internet article Dawkins said, "The dozen or so different globins inside you are descended from an ancient globin gene which, in a remote ancestor who lived about half a billion years ago, duplicated, after which both copies stayed in the genome.‘There were then two copies of it, in different parts of the genome of all descendant animals. One copy was destined to give rise to the alpha cluster (on what would eventually become Chromosome 11 in our genome), the other to the beta cluster (on Chromosome 16)...‘We should see the same within-genome split if we look at any other mammals, at birds, reptiles, amphibians and bony fish, for our common ancestor with all of them lived less than 500 million years ago. Wherever it has been investigated, this expectation has proved correct.""You are easily impressed by Creationists arguments it seems. Maybe you should apply the same type of skepticism you seem to apply toward evolutionist’s arguments.FK"So you can read minds, eh? Must be a neat party trick. No, actually I know that there is a lot of creationist garbage out there. However, I do think that creationists devastate evolution at some points.
"
"This was pointed out to him at NAIG. He replied with something along the lines of "Spetner's calculation disproved either speciation or convergent evolution. Since speciation has been observed, that means convergent evolution is disproven". I can honestly say that this didn't make a lick of sense to me.
The funny thing is, though, if you follow Spetner's calculation, he does mathematically "disprove" the possibility of speciation. Since speciation has been observed, that pretty much nullifies Spetner's approach, which was a multi-level straw man anyway.FK"Apparently you haven't read Spetner's book, or you wouldn't have made such an elementary error. First Spetner uses a calculation to arrive at the probability of 1 nucleotide appearing and taking over the population. We see from this that speciation is impossible. However speciation has been observed. What is the answer? To assume (well it is not really an assumption, since we know it happens) that many mutations are acting together, thus increasing the probability. How many mutations are needed? My calculation said at least 22. However when this happens convergent evolution has a number of paths to take. This means that the probability that two species will take the same path is very slim."No it is neither. It is proof that Spetner's calculation makes assumptions that need to be SHOWN to be valid. You cannot - as Spetner does refuse to count any steps after the first if they occur within the blocks Spetner has artificially created. As I have pointed out elsewhere this manouevre artificially assumes that maximum rate of evolution to that required to account for the observed speciations - can't you actually see that by applying Spetner's technique you can never produce more than the number of steps you are supposedly trying to account for ? No matter HOW many births you allow per step, or whaat probabilities you use ?"I am kind of confused here. Please elaborate."I also note that you have not explained why your calculation of the probability of the langur convergence relies on assumptions you insist are not included in your model. As I have stated you need to allow for variations in the order of the sequence and for the sequence being interrupted by other beneficial mutations arrving and eaching fixation (strictly speaking you would need to show that the horse and langur would have the same number of possible beneficial mutations - I have skipped that because your number is relatively low, but it is certainly necessary for Spetner's numbers)."I am not sure that I understand you here. I am only calculating the odds of the langur convergence. I thus only need to know the # of mutations in the whole of langur evolution. All we really need to know is that 9 nucleotides converged. I used some numbers from horse evolution, but I assumed a mutation rate of 10^-7, not too far off. I also used 50 steps per speciation sequence. I freely admit that my probability analysis can be improved upon-because we do not know the exact numbers. I try to take a collective average, but that still does not yield completely accurate results."Spetner appears to look at gene survival as a randomprocess ... that neglects natural selection, which is a
prime component of ToE."Nope-he includes a selection coefficient."There are two significant problems here, and this does not speak well toward your motives. I saw the exchange at NAIG. When Thomas did the calculation, he assumed a generation time of 5 years. In fact, langurs are sexually mature at the age of 3 or 4. Yet you have increased it to 7 years for a generation. I think the reason is quite obvious."The reason I used 7 is because I searched for the relevant material on the internet but could not find any information on the generation time. I didn't know if Thomas had made an error or not. However, I used 5 yrs. below. If you want I can recalculate using 3 or 4.
"
2nd, you were shown recent estimates of mutation rates in humans. They range from 100 to about 175. Thomas used a recent estimate of 128. Yet you went with 75, from an outdated Talk.origins FAQ. Again, I think we can all see why."Nope, actually I went with 100-(me) "Even considering 5 yrs/generation and 100 mutations per individual this equals a 2% chance (0.026)."Check my original post. This is within range of the number you mentioned. I think that Thomas linked to several papers regarding mutation rates. If I am not mistaking they virtually all had numbers around 100. 128 was just a number from 1 paper. Also I used the talkorigins number because I thought that talkorigins was reliable. The paper says: "Copyright 1999-2003
[Text Last updated: May 23, 1999]
[Links edited: June 20, 2003]"Well, if the links have been updated recently (this year), why did they not change the numbers in the article? Anyway, estimates can be near this:
http://216.239.39.104/search?q=cache:FAZpZWD6CYQJlantsciences.montana.edu/Bergey/Biol301/Biol-301(2003)/Genetic%2520Roulette.pdf+mutations+per+individual+humans&hl=en&ie=UTF -8(If this site doesn't link correctly go to google, type in mutations per individual human, and see the results. I think that this is the genetic roulette paper by Crow.)Or higher:Estimate of the mutation rate per nucleotide in humans - PubMedInterestingly enough, the above paper that agrees with a higher mutation rate also agree that U=3, which may have some very strong implications for evolutionary theory (as you seem to disagree with this number)."It appears to me you are less interested in performing a defensible calculation than you are in pushing an agenda. Otherwise you would not use outdated or flat out false numbers to push your case. You can't plead ignorance, because I know you were given references at NAIG. I don't even know why you want to persist with the lysozyme example. You got waxed on that one at NAIG. Perhaps another example might be better?"So now you can discern my intentions? Look, I am a pretty nice fellow, but I do not like it when I am accused of something that there is no substantiation for. In fact, if I was just looking to push a bad model, then I would have no reason to change Spetner's original model. But I did. As far as getting "waxed" on NAiG-I have participated in my fair share of debates. I can assure you that I hardly ever get completely waxed-just ask Asmodean, Butch, Prof Weird, Roland (rjw), skepticboy, etc.. In fact, I wanted to discuss the issue more but Thomas decided he did not want to. I am NOT saying that he ran away-I am merely saying that I did not get a chance to completely corroborate to develop my model. If you want, we can again set up the calculation:100 mutations per individual (Crow's estimate)
1/500 selection coefficient
10000 members average in a population of langurs
15,000,000 yrs. of evolution
4 yrs. / generationThis yields a total of 1,000,000 mutations per generation (10K x 100) x 3750000 generations (15 million yrs. / 4 yrs. per generation) = 3750000000000. This could overturn a genome of 3 billion nucloetides 1250 times. This /3 (correct nucleotide) = 416. 416/500^9 = 0.19, or 19%. However even this favorable calculations has several flaws. First of all, just because an animal is able to reproduce at 4yrs. old doesn't mean that it is going to. A 14 yr. old human can reproduce, but the average generation time is around 20 years. So the number could be higher than 4 yrs. Secondly we do not know that any of the other 2 mutations at each site couldn't have been beneficial. Using Haldane's number, if 1 mutation can be fixed every 300 generations, this is 1 mutation per 1200 years. Over the course of the langur evolution a maximum of 12500 beneficial mutations could have been fixed. We know that the vast majority of mutations are neutral. Let's say only 3% of the mutations are in the coded region. This is 112500000000 mutations. Let's say that beneficial mutations occur in a ratio to harmful mutations of 50 to 1 (I do not know the actual number-however I assume that evolution would like the most beneficial mutations possible). So this is 2250000000 competing for fixation, and only 12500 at maximum can be fixed. (It is important that we use the maximum number for fixation because the more mutations that can be fixed, the less mutations have to compete, meaning a better chance of fixation.) We know that 9 nucleotides out of this 12500 were fixed, so the 9 nucleotides were competing against 2249987509 (2250000000-124991). For 1 specific nucleotide this is 2239987509/9 = 249998612. So the probability of getting all 9 nucleotides is 1/249998612^9.
fFinally once we calculate the probability for other convergences it becomes extremely improbable. For example, if rhodopsins of the eye converged in a similar manner (I don't have the actual figures), then the probability would be 0.19x0.19= 0.036, or about 3%. When other convergences are considered, the numbers drop.I think that the best criticism of my work was by the fellow that wrote that the events in evolution are not isolated events.

Thank you all for the replies. I would like to address some of them."To deal with the part replying to my post (buried very deeply) the calculation of 1/22^9 assumes that there are 9 attempts, each of which has a 1/22 probability of success, each of which must succeed.
This has the following problems:Firstly we do not know that the probability is 1/22. As I have stated it is not the case that all the beneficial mutatione available will be equally likely, and those that are observed will tend to be those of a higher probability (just as when rolling two dice, we see a total of "7" more often than "12")"This is true. I took an around average value suggested by evolutionist G. G. Simpson, which was 0.1. He also suggested that a value of 0.01 could work in selection."Secondly we do not know that it is the case that only one of these mutations is available at any one time. If two were available the probability at that step is 2/22. Having only one available at each time assumes that there s a single order that must be followed."Not necessarily. If there is 3 mutations, a, b, and c, the order can be cba, abc, bca, acb, etc.. The order is not really important, as long as they appear. My second calculation took care of a mutation appearing multiple times. Besides, my calculation means that the correct mutation occurred at a frequency of 1 per every 22 beneficial mutations. Likely the ratio in reality would not be favorable for evolution, since there is so many sites to mutate. This calculation implies that on average 22 beneficial (point) mutations are required to keep evolution moving."Most seriously we do not know that there are only 9 steps available. Indeed as I point out given your numbers we would expect there to be 750 steps in the available time."The question is not how many steps occurred overall, but how many steps it took to converge on the nine nucleotides. Even if you didn't like my first calculation, what is wrong with my second or third? Besides, this number really doesn't deal with steps. For example, all 9 nucleotides could have been fixed in possibly less than 500 yrs. In fact, according to my calculation it wouldn't matter if all 9 were fixed in a day. It just means that evolution will have 22 different possibilities (mutations) to chose from here in order to keep evolution going. If on average there are 22 different possibilities to choose from, then the probability would be 1/22^9.--------------------------------------------------------------------------------
"Dillan: I do not assume that 2 out of there point mutations at a specific site are beneficial, just like I don't assume that 1/3 mutations at a specific site are beneficial (as someone may have inferred from my calculations). I just said that there is no way of knowing that the other two couldn't have been beneficial.
FK: There is also no way of knowing whether Pluto is covered with a fine layer of cheddar cheese. But I think you would agree that it would be highly unlikely. Again, I asked you to make a probability calculation so we can have some idea of the odds. You seem reluctant to do so in this case. I do wonder why (not really)"Okay. I have tried to get a grasp of how many beneficial mutations may have occurred-which is why I included Haldane's number, which can be used to set the maximum number of beneficial mutations to be fixed in a certain time frame."I snipped the hemoglobin stuff, because there is really nothing there that we can apply any calculations to. It is not stated how many nucleotides are believed to have converged. Surely you don’t believe that evolutionists think the entire molecule converged?"Your right, I do not believe that. However I am quite certain that some nucleotides have converged (likely more than 9-like the langur example)."All you have done is show that evolutionists believe that hemoglobin is descended from an ancient ancestor of hemoglobin. You are going to have to do a lot better than that if you want to make the same type of argument that you did about lysozyme."Well then let's have a look at the lysozyme example."Dillan: I do think that creationists devastate evolution at some points.FK: You will have to turn me on to some of these devastating arguments. I have been debating this for 10 years and have never seen one."My statement really did not pertain to the particular topic of this thread. However some great books to read include: Creation: Facts of Life, In the Beginning was Information, Refuting Evolution (1 + 2), Creationist Scientists Answer Their Critics, In Six Days, etc."Dillan: However when this happens convergent evolution has a number of paths to take. This means that the probability that two species will take the same path is very slim.FK: That all depends. If you mean that there are slim odds that two species’ genomes would converge to a large degree, then you are correct. No evolutionist, however, would suggest such a thing. To present this as a refutation of evolution is certainly attacking a straw man."Please do not put words in my mouth. I never said 'to a large degree'. I will attempt to show why that convergence is slim in a moment."Dillan: The reason I used 7 is because I searched for the relevant material on the internet but could not find any information on the generation time. I didn't know if Thomas had made an error or not. However, I used 5 yrs. below. If you want I can recalculate using 3 or 4.Yes, why don’t you recalculate it using 4 years per generation and 128 mutations per generation? I don’t think you will be pleased with the result."Nope, I think I will be just fine with it. You seem to only want to hear the model that goes in your favor. However I can do the same thing that you are doing, as we will see in a moment."Dillan: So now you can discern my intentions?FK: Yes, I can. When Creationists ignore certain bodies of evidence that don’t support their preconceived notions, I question their motives. If you read Fred’s article, you will see that he is guilty of the same. Did you know that Eyre-Walker has updated their estimate of U, and that there are a number of estimates out there, lower than the ones Fred uses? Did you see how Fred ignored lower estimates and only did calculations with the higher estimates? Fred ignores all of that in favor of any estimates that tend to support his position. That’s why he is an engineer, and not a scientist. A scientist engaged in such behavior would have zero credibility. (Not that Fred has credibility anyway)."First of all, I never claimed that the creationist position does not have holes. In fact, I thinkt that the weakest area is geology. But, there are other areas that are strong in my opinion. There are also weak points in an atheists position that accepts mainstream beliefs. There are several unanswered questions about the big bang (and I got this straight from a grad student studying astronomy at Cambridge-Butch. Very likeable fellow. Shot down most of my creationist arguments right out of the gate in our debate. However he did admit that there were some unanswered questions. Pleasure talking with him), many just so stories in evolution, no absolute concensus on the mechanism of evolution, plaguing problems with the origin of life, etc.By the way, what is the new estimate for U?"Dillan: As far as getting "waxed" on NAiG-I have participated in my fair share of debates. I can assure you that I hardly ever get completely waxed-just ask Asmodean, Butch, Prof Weird, Roland (rjw), skepticboy, etc.. In fact, I wanted to discuss the issue more but Thomas decided he did not want to. I am NOT saying that he ran away-I am merely saying that I did not get a chance to completely corroborate to develop my model.FK: No, you were pretty well manhandled. It looked to me like Thomas just got bored."I freely admit that many of my original calculations were worthless. However I am still trying to improve them."Dillan: If you want, we can again set up the calculation: 100 mutations per individual (Crow's estimate)FK: Or, you could use Nachman’s estimate that you linked to of 175. This completely changes the outcome. Now you are looking at about 100% probability of convergence. What you can conclude from this is that the probability of convergence in this case is somewhere between 2% and 100%. This is not exactly a damning argument against convergent evolution. Do you have a better example?"True, I could use Nachman's estimate. Then again instead of using 0.1% as a typical selective value I could use 0.01%. This does not require any leap out of logic-in fact G.G. Simpson said it could work for evolution. I quote Spetner, who refers to Simpson as saying: "He even noted that a value of 0.01% would surely be effective in natural seleciton, and even 'much weaker slection could well be effective.'" So instead of their being a 1/500 chance, there would be a 1 in 5000 chance. Even a mutation rate of 175 base pairs per individual wouldn't help you out here. Would this alter the probability? You bet. I merely took Crow's value and other values given to me to incorporate in a calculation. It is important to note that even though a percentage like 25% is possible, that doesn't make it likely. In fact, the chances are against it that it would occur. It all has to deal with the numbers that you originally incorporate into your calculation. I don't think that I have incorporated any outrageous numbers. However you have still not addressed two points I brought up. 1). If the webpage for talkorigins has been updated this year, why have they not changed their figure for mutations per individual. 2). The paper whose numbers you embrace also agrees with a higher mutation rate also agree that U=3, which may have some very strong implications for evolutionary theory (as you seem to disagree with this number). This would mean that Fred was right in his calculation of 60 births per individual."Dillan: First of all, just because an animal is able to reproduce at 4yrs. old doesn't mean that it is going to. A 14 yr. old human can reproduce, but the average generation time is around 20 years.FK: But it wasn’t always. A couple of hundred years ago the generation time was about 14 years. As soon as women came of age, they married and began to reproduce. This is still the case in 3rd world countries. But nowadays in the U.S., we don’t have too many marriages before girls turn 18. In fact, the average age at marriage is 24. That’s why the average generation time is 20 years or so. But as late as 1950, the average marrying age for a girl in India was 13 years."I was not aware of this. However, have you thought that this short generation time has anything to do with the length of their lives? Early American colonists died in their 30's and 40's. You could pick any isolated example to prove your point, as could I. The fact is that you do not have to reproduce once you attain the ability to. Some may be able to reproduce at 12. I have heard of several cases where girls around 12 have had kids. Does this negate your postulation that the generation time used to be 14? No, just as your postulation does not negate my original position."Dillan: Using Haldane's number, if 1 mutation can be fixed every 300 generations, this is 1 mutation per 1200 years.FK: I am not really seeing how Haldane is relevant here. Are you sure you understand Haldane’s argument?"I have the main idea of Haldane. He put a speed limit on evolution. You could use this information to determine how many mutations could be fixed in a certain period of time, or how fast each one was fixed. This is important, as explained earlier, because we need to know how many beneficial mutations occurred and were fixed. This could only improve my case, and at best would leave your probability calculation untouched (since you assume no other beneficial potential for mutations at the same site as the 9 that were fixed)."Dillan: For example, if rhodopsins of the eye converged in a similar manner (I don't have the actual figures), then the probability would be 0.19x0.19= 0.036, or about 3%. When other convergences are considered, the numbers drop.FK: And by slightly changing the assumptions, the probability will again go to 100%. Perhaps you need some new material. I have yet to see one of these mathematical disproofs of evolution that stood up to scrutiny.FK"Refer to my above comments on this. If I wanted, I could change the calculation around to where evolution is extremely improbable.

Again I would like to thank everyone for the replies. This may be my last post on the topic, but then again I may see fit to reply a few more times. The replies now are getting very repetitive. I would like to address a few of the points (mainly Fredmahns-Fred pretty much sums up my position in reply to PaulK)."Yes, or we could use 0.3% or 0.7% which would also require no leap of logic. All of which will vary your probability between effectively 0% and 100%. So what must I conclude from this? Attempting to disprove evolution, when so little is known about the actual values needed to plug into the model, is a completely worthless approach. You can’t really say anything at all about whether or not convergent evolution is possible. You have waffled all over the place on the assumptions, and this renders the output meaningless. The only conclusion I can accept based on this exercise is that the probability of convergent evolution for the 9 nucleotides in lysozyme is somewhere between 0% and 100%. So we learned exactly nothing."There can be selection coefficients this high, but can this be used in the working of natural selection? Do you propose that this is typical? What sources do you have to substantiate your claim? At least I am partially justified in using my 0.01% number, relying on a quote by Simpson. Simpson said he felt a frequent value may be 0.1%, which is what I originally used, however he also noted that a selective value of 0.1% is NOT easily observed. Spetner states, "He even noted that a value of 0.01% would surely be effective in natural selection, and even 'much weaker selection could well be effective.' Applied geneticists who breed plants and animals for commercial application, by necessity deal with larger selective values, usually one percent, or even as high as 10%. ... Expertis in evolution and natural selection, however, hold that evolution must rely on smaller values." See, there is no problem in my using 0.01% as an average selective value of a beneficial mutation. However, while Simpson said the number could indeed be less than 0.1%, I did not see him say that the average could be more.If we rearrange the numbers we can create any probability we like. Using mainstream numbers, I have constructed a probability. This probability says that more likely than not the 9 nucleotides wouldn't converge. (This would even prove to be true if the probability was 49% in favor of evolution-as there would be a greater chance-51%-that it wouldn't occur.) Royal Truman, in an article found at http://www.trueorigin.org/schneider.asp said, "We shall examine the algorithm offered. One could write a computer program which 'shows' that random natural processes would drive rocks from a quarry up a steep mountain in thousands of discrete steps, for every simulation run. One only has to use an unrealistic number of earthquakes and improperly model the effects not leading to our intended programming goal. The details matter very much to determine the true net outcome, as we shall find with the program[1] I am going to discuss. Overlooked details in such flawed simulations might not be obvious. Vast number of unrealistically hard earthquakes would affect not only the movement of our rocks but the surrounding mountain would be systematically destroyed." This quote demonstrates two things: 1. We can't just simply incorporate only the numbers that are favorable to our position. I used numbers that are acceptable in the mainstream, whereas I see no substantiation for the >0.1 values (on average). 2. No model is complete-we can easily overlook details. I am guilty of this. There is probably some bit of information out there that can improve my model.If we only incorporate numbers that are beneficial to evolution, like a 0.7% selection coefficient, and a mutation rate of 175 mutations per individual, then you will get your desired result. However this follows an element of just so story telling. (I apologize to the administator, however I felt that this must be said. If you prefer, I could say that this is a 'possibly how' story). Using realistic numbers I calculated that the chances are more likely than not that the mutation won't occur." I am not associated with Talk.Origins, so maybe you should write and ask them. Maybe they are just unaware of the fact. But you have been given more up to date estimates from the literature, so you really have no excuse for using lower numbers. Genetics is a very fast moving field. Relying on old data in this field is a fool’s errand."First of all, evolutionists refer to talkorigins articles often, as I did. Talkorigins updates their webpages often, and they have very competent evolutionists monitoring the website. Second, I know that there are higher estimates. In fact, I made reference to this in one of my posts. However I also made references to a lower mutation rate. In fact, if we use 100 mutations per individual, like Crow did, then this can coincide with the talkorigins article range of 50-100 mutations per individual."Oops. There’s a paragraph you can throw in the trash. That’s one estimate from your article that is no longer valid. Of course you admitted earlier that you are aware of this, which makes me wonder why it’s still there."Are you refering to Smith's estimate? Why is it out of date? What is the most commonly accepted percentage of the coded portion of the DNA?Oh, and by the way, where did you get the information that langurs sexually mature at three to four years old? I am not saying that this is untrue, but I would like to read the material for myself.Finally I would like to apologize to FK for any misunderstandings that I have made from reading his posts. It seems that we are both getting a bit cranky judging by the tone of our posts. I will do my best to stop this in future posts.

In regard to the mutation rate, check out this website: http://home.earthlink.net/~misaak/guide/CB/CB100.htmlIt just shows that the mutation number can vary, and that my original ccalculation is not necessarily incorrect."Very large mutations are rare, but mutations are ubiquitous. There is roughly 0.1 to 1 mutation per genome replication in viruses and 1/300 mutations per genome per replication in microbes. Mutations rates for higher organisms vary quite a bit between organisms, but excluding the parts of the genome in which most mutations are neutral (the junk DNA), the mutation rates are also roughly 1/300 per effective genome per cell replication. Since sexual reproduction involves many cell replications, humans have about 1.6 mutations per generation. This is likely an underestimate, because mutations with very small effect are easy to miss in the studies. Including neutral mutations, each human zygote has about 64 new mutations. [Drake et al, 1998] Another estimate concludes 175 mutations per generation, including at least 3 deleterious mutations [Nachman & Crowell, 2000]."

I would like to thank everyone for the replies. I will address a few here:"Dillan: 2). The paper whose numbers you embrace also agrees with a higher mutation rate also agree that U=3,FK: That estimate of U was made before the human genome was decoded. The number of genes was believed to be higher in the past, which would render estimates of U too high. Most estimates of U that I have seen over the past two years are between 1.5 and 3. Adam’s group is on the cutting edge in this field, so he probably has better numbers than you will find anywhere else. But don't expect to see Fred update his argument anytime soon, as most of the newer estimates are going against him."You said that the mutation estimate of 175 per individual was a "more recent" estimate, yet you imply the U estimate is oudated. The authors of the paper at Page not found - Biozentrum meyer/BiotransPhysiol2003.pdf
suggest that the mutation rate is around 100 per individual and give an estimate of U that is around 3. This would justify Fred's number. Also in Fred's paper under the Addendum he says, "3/22/2002 - Yet more support comes from the recent article in Genetics titled '"Positive and Negative Selection on the Human Genome" (Justin C. Fay,* Gerald J. Wyckoff* ,1 and Chung-I Wu*. Genetics 158, 1227-1234. 2001.). This article was unwittingly brought to my attention by evolutionist Dr Scott Page (see our debate on this matter). The authors of the Genetics article write:'The genomic deleterious mutation rate is likely much larger given our estimate that 80% of amino acid mutations are deleterious and given that it does not include deleterious mutations in noncoding regions, which may be quite common. [emphasis mine].'Using their estimates, the required offspring number rises to at least 60 offspring per breeding couple! (for explanation, see my opening comments in my debate with Dr Page.)"
This is fairly recent. Heck, even if U was 1.6 as suggested by Adam that is still means that 10 conceptions just to keep the genetic degradation near equilibrium! I don't think that primates conceive this much on average, but I am not for sure. (Humans can, but it is very rare when they do.)"Dillan: There can be selection coefficients this high, but can this be used in the working of natural selection?
FK: Didn’t Thomas point out to you that in the case of the peppered moth the selection coefficient had actually been measured to be slightly greater than 0.5? That’s real experimental data for you, not some ancient quote based on incomplete information. I think I would go with the recent data instead of using old quotes to lower the estimate as needed."I don't remember Thomas saying this, but he could have. It doesn't matter, because we cannot base all of evolution on just one example. Besides, even with the selection coefficient this high the variety of colors in the peppered moths stayed the same-that is that there were still black and white variations. The frequency of each color changed, but the colors involved remained constant. Therefore the variation did not take over the population. If it did take over the population, you may have a point. However it didn't. (By the way, I thought the 0.1%-0.01% values were just for beneficial mutations, not necessarily the variations between the two species. There are black and white colored humans, but did not necessarily achieved by mutation and selection. If you take just two moderately dark people you can produce much variation in the offspring as far as 'color' is concerned. This is just a result of sexual recombination.)"Dillan: Using mainstream numbers, I have constructed a probability.FK: No, you have constructed a probability using outdated numbers. You have two recent estimates of the mutation rate; 128 and 175. You used 100 to lower the probability, and that’s also why you used the 7 year generation time.'Well, I don't know about the 128 number, but I think that the 175 mutation rate was proposed in 2000. However, an even more recent estimate of this can be found at Nature - Not Found "Similar genome-wide comparison requirements are arising in other contexts. For instance, new mutations have accumulated in the human population at a rate of 1—100 mutations per generation over the past 5,000 generations"
Nature 409, 856 - 859 (2001); doi:10.1038/35057055I will go more in depth on the langur generation time in just a moment."Dillan: (This would even prove to be true if the probability was 49% in favor of evolution-as there would be a greater chance-51%-that it wouldn't occur.)FK: Do you even understand what these probabilities mean?"Yes, I believe I do."If the true probability were 10%, that would mean that 1 out of every 10 cases we look at will be successful. That means that we would see cases of this in the animal world. Your original argument would have been powerful if indeed the probabilities had been set up correctly and they were actually something like 1 in 100 billion. But if you are retreating to arguments like 49% means it probably wouldn’t occur then it’s time to give up this argument and move on to the next one."I never said that when a probability is 49% that it couldn't occur. In fact it could. I just said that in the isolated case of the langur, it probably wouldn't. You seem to want to incorporate more examples into the equation."Dillan: If we only incorporate numbers that are beneficial to evolution, like a 0.7% selection coefficient, and a mutation rate of 175 mutations per individual, then you will get your desired result. However this follows an element of just so story telling. (I apologize to the administator, however I felt that this must be said. If you prefer, I could say that this is a 'possibly how' story). Using realistic numbers I calculated that the chances are more likely than not that the mutation won't occur.FK: That’s quite misleading on your part. You don’t have to plug in both; if you plug in either you will get the desired result (assuming you don’t change your other initial assumptions). We also get the desired result by assuming more langur generations (more than 15 million years), or a 3-4 year generation time."I have already talked about the mutation rate. I will also talk about the langur generation time later. I just used estimates from Simpson about the average selective value for mutations. I think that my results can be just as valid as yours. So which is correct? I don't know. We need more information about a concensus of opinion on what these numbers should be."Dillan: First of all, evolutionists refer to talkorigins articles often, as I did. Talkorigins updates their webpages often, and they have very competent evolutionists monitoring the website. Second, I know that there are higher estimates. In fact, I made reference to this in one of my posts. However I also made references to a lower mutation rate. In fact, if we use 100 mutations per individual, like Crow did, then this can coincide with the talkorigins article range of 50-100 mutations per individual.FK: You don’t seem to get it. Crow’s estimate was also pre-HGP. Yes, Talk.Origins updates their website often, but as you can see the text in that article has not been updated since 1999. These guys are not getting paid for this, so it is possible to have information in an article that has been superceded by more recent data. By insisting on using a mutation rate from that article, when more recent estimates are available, demonstrates that you are not really interested in doing this problem with the highest possible level of accuracy."The article that I listed above includes HGP. In fact, that is the main theme of the paper is to give an update and summary of it. It uses the estimate of 100 mutations per individual (or possibly less-so when I used 75 mutations per individual I was not necessarily completely wrong)."Dillan: Oh, and by the way, where did you get the information that langurs sexually mature at three to four years old? I am not saying that this is untrue, but I would like to read the material for myself.FK: Let me get this straight. You are pushing this argument, and you don’t actually know the langur generation time? I have a better idea. Start doing better background checks before pushing an argument. It is pretty easy to find out about langurs. You should have no problem confirming this."Nope. I was just asking where you had found your information. In fact you tell me later. You say,
'Dillan: Oh, and by the way, where did you get the information that langurs sexually mature at three to four years old? I am not saying that this is untrue, but I would like to read the material for myself.
FK: Here is your last freebie. I would expect, as I am sure others would, that you research these issues in depth before developing your argument. Relying on 2nd hand or outdated sources for your information is not the way to conduct research.For the Hanuman Langur:"Sexual maturity is achieved after 3 years".ADW: Semnopithecus entellus: INFORMATIONFor the Douc Langur:"Females reach sexual maturity at about 4 years, while the males reach it at 4-5 years".Blue Planet Biomes - Red-shanked Douc LangurFK"Here are my sources: Page not found – Wisconsin National Primate Research Center – UW—Madison
Which says sexual maturity occurs at 5-6 years for males and 4-5 years for females.At Animal Info - Yunnan Snub-nosed Monkey - 16k - the article says,
"Animal Info - Yunnan Snub-nosed Monkey
(Other Names: Biet's or Black Snub-nosed Monkey, Black or Yunnan Golden Monkey, Yunnan Snub-nosed Langur)
Rhinopithecus bieti (Pygathrix bieti, P. roxellana bieti, )...
"In the genus <../../gloss.htm> Rhinopithecus, males reach sexual maturity at 7 years, females at 4 - 5 years (Nowak 1999 <../../refn.htm>)."
At Animal Info - Douc Monkey
"Age to Maturity:
Females: 4 years; males: 4 - 5 years"
So which numbers should we use? 4, 5, or 7? I think that the average would be around 5. After all, the females can't mate until males mature sexually. However the number 7 was included in one of the papers above, so I wasn't deliberately avoiding the hard facts.
Using 5 yrs/generation, 100 mutations per inidividual, we still only get a probability of a 2% chance (0.026), or about 1/50. Not impossible, but still not very likely. I do believe these numbers are reasonable. I have yet to see a reason why they are not.I am sorry that I haven't had the time to reply to more of you. However I will do my best to do so in the future.-dillan

In the book, Creation Facts of Life, by Gary Parker, he has a section on mutations and probability. He states, "Problem number one is the mathematical. I won't dwell on this one, because it's written up in many books and widely acknowledged by evolutionists themselves as a serious problem for their theory.Fortunately, mutations are rare. They occur on an average of perhaps once in every ten million duplications of a DNA molecule (10^7, a one followed by seven zeroes). On the other hand, it's not that rare. Our bodies contain nearly 100 trillion cells (10^14). So the odds are quite good that we have a couple of cells with a mutated form of almost any gene. A test tube can hold millions of bacteria, so, again, the odds are quite good that there will be mutatant forms among them.The mathematicaal problem for evolution comes when you want a series of related mutations. Teh odds of getting two mutations that are related to one another is the product of the separate probabilities: one in 10^7 x 10^7, or 10^14....Any two mutations might produce no more than a fly with a wavy edge on a bent wing....So what are the odds of getting three mutations in a row? That's one in a billion trillion (10^21)....It was at this level (just four related mutations) that microbiologists gave up on the idea that mutations could explain why some bacteria are resistant to four different antibiotics at the same time....So even by the wildest 'guesstimates', the universe isn't old enough or big enough to reach odds like the 1 in 10^3,000,000 that Huxley, an evolutionist, estimated as the odds against the evolution of the horse."I know that within several generations, nearly the entire genome would be overturned by the many mutations involved. However, related mutations need not be preserved. Mutations that have a selective advantage could be preserved, but this doesn't mean that it is related. For example, let's say that the environment changes and four related mutations are needed in a certain area in the genome in order to survive. However many other beneficial mutations could be present. The odds against these mutations appearing in enough time and being preserved are not very good.Also, as we see with the peppered moths, the environment can change in a short period of time. That means that old mutations that were once beneficial have the potential to be harmful later on. That means that it may be very hard for a mutation to completely take over a population before environmental changes render it harmful or neutral, thus making it unlikely to be preserved.

Thank you for the reply PaulK and FK. In it, FK said,"Dillan: You said that the mutation estimate of 175 per individual was a "more recent" estimate, yet you imply the U estimate is oudated.
FK: It is clear that you don’t really understand how these estimates work. An estimate of the overall mutation rate will not necessarily be affected by a lowered estimate of the total amount of coding DNA. However, the value of U depends directly on the amount of coding DNA, so post-HGP estimates will be lower. In other words, the 175 estimate could be just fine, but the estimate of U is outdated because it is based on the assumption that there are 70,000 genes."Okay, I am just fine with this. However I still have a few problems. For instance, there would be around 10 conceptions just to maintain genetic equilibrium. However, evoluiton is not looking to maintain genetic equilibrium. It is trying to maintain forward progression. So would then the number of conceptions be much higher? Perhaps 20 on average?"Dillan: The authors of the paper at Page not found - Biozentrum
suggest that the mutation rate is around 100 per individual and give an estimate of U that is around 3. This would justify Fred's number.FK: Because someone on the Internet says U=3 does not justify Fred’s number. You need to go to the primary literature; that is where you will find the most recent research. Your link gives no reference for this estimate. Most likely they got this from one of the outdated estimates. This is from a teaching lecture in Switzerland, and there is no indication (and it is highly unlikely) that they measured the value themselves. There is also no indication when they last updated the slides. If you really want to make a case with these slides, you need to write and find out their source for the estimate. I am afraid you will be disappointed. On the other hand, the mutation rates that you have been given (128 and 175) are the most recent estimates, based on actual measurements."I thank you for pointing this out to me, and I will try to go to the primary literature from now on. I have emailed Adam Eyre-Walker about the matter. I asked him for the most recent estimate of U was, as well as the number of mutations per nucleotide per individual."Dillan: 'The genomic deleterious mutation rate is likely much larger given our estimate that 80% of amino acid mutations are deleterious and given that it does not include deleterious mutations in noncoding regions, which may be quite common. [emphasis mine].'Using their estimates, the required offspring number rises to at least 60 offspring per breeding couple! (for explanation, see my opening comments in my debate with Dr Page.)'This is fairly recent. Heck, even if U was 1.6 as suggested by Adam that is still means that 10 conceptions just to keep the genetic degradation near equilibrium! I don't think that primates conceive this much on average, but I am not for sure. (Humans can, but it is very rare when they do.)FK: I really think you should try to focus on one argument at a time. If you want to discuss Fred’s misconceptions and erroneous conclusions, maybe you should start a new thread. If you really think that 10 conceptions for a primate is too much, I suggest you do a little more background work. How many conceptions do you think occur today in 3rd world countries among humans? Do you have any idea as to how high the spontaneous abortion rate is?"Okay, in the future I will perhaps discuss Fred's 'misconceptions'. However if Fred represented the authors of the Wu paper correctly, then this could have severe consequences for evolutionary theory-namely that there must be 60 births per individual just to maintain genetic equilibrium!At any rate, the 10 conceptions were just to maintain equilibrium. Evolution, however, is a forward process. So how many conceptions would it take to keep evolution moving? 20 on average? I don't know. Oh, and by the way I said that I knew that humans could concieve that much, but I didn't know if it was the average. Also I still don't know if our hominid ancestors on average conceived 10 times."Dillan: I don't remember Thomas saying this, but he could have. It doesn't matter, because we cannot base all of evolution on just one example. Besides, even with the selection coefficient this high the variety of colors in the peppered moths stayed the same-that is that there were still black and white variations. The frequency of each color changed, but the colors involved remained constant. Therefore the variation did not take over the population. If it did take over the population, you may have a point. However it didn't. (By the way, I thought the 0.1%-0.01% values were just for beneficial mutations, not necessarily the variations between the two species. There are black and white colored humans, but did not necessarily achieved by mutation and selection. If you take just two moderately dark people you can produce much variation in the offspring as far as 'color' is concerned. This is just a result of sexual recombination.)FK: Frankly, I can’t make any sense out of this. You seem content to run with a very old estimate, based on zero experimental data over an actual experimental finding. What is your evidence that the proper estimate in the lysozyme case is 0.1, or 0.01? None, you are just relying on outdated quotes. This is no way to develop a model. On the other hand, the one actual measured value of a selection coefficient that has been provided was 0.53. IF you want to challenge that, you need to come up with a measurement, not a quote dating to before the discovery of DNA."Well, if I am to challenge something I need the original source to refer to. What source said the selection coefficient was .53? And where in your source does it say that 0.53 is the average selection coefficient? Anyway, the peppered moths really do not show what you would wish them to. In langurs, the entire population has the nucleotides that converged on lysozyme. However, even during the period where black moths survived better, there were still white moths (although they were at a lower frequency). The population of moths never gained ubiquitous traits, whereas the langur did. This poses another problem for the evolution of the langur. As we have seen with the peppered moths, the environment can change in a short period of time. That means that old mutations that were once beneficial have the potential to be harmful later on. That means that it may be very hard for a mutation to completely take over a population before environmental changes render it harmful or neutral, thus making it unlikely to be preserved. So again we see that it may be hard (but not impossible) to preserve the 9 beneficial nucleotides."Dillan: I never said that when a probability is 49% that it couldn't occur. In fact it could. I just said that in the isolated case of the langur, it probably wouldn't. You seem to want to incorporate more examples into the equation.FK: Along the same lines, in the isolated case of a single person buying a lottery ticket, the odds of winning are slim. But we can find cases where someone won, can’t we? That’s one point. You really don’t seem to understand what this probability means. If 49% was the exact number (which it’s not) then we could say for every 2 cases we consider with these same assumptions, we will find one case of convergence. However, as I have amply demonstrated, you don’t have enough certainty in several of your model parameters to make any conclusion. The key point you need to consider is: What is your margin of error? Based on what I have seen, it is huge."You are correct in saying that my calculations have a HUGE margin for error. Right now we really do not know the correct mutation rate, the correct selection coefficient, the number of years involved (I got the estimate of 15 million yrs. from Thomas), etc. However if convergence is so likely, as you suggest, why do we not see more cases of it? I am only aware of a few examples of genetic convergence."Dillan: The article that I listed above includes HGP. In fact, that is the main theme of the paper is to give an update and summary of it. It uses the estimate of 100 mutations per individual (or possibly less-so when I used 75 mutations per individual I was not necessarily completely wrong).FK: I suggest you reread the article. The 100 estimate is from the 1999 paper by Eyre-Walker. It is not a post-HGP estimate."What you have failed to mention here is that the paper that contains the 175 estimate is also pre-HGP. Which estimate is correct then? I would say it is likely that the Eyre-Walker estimate is closer to being correct since the authors of the paper that was written post-HGP used it. If it had been incorrect, or if somehow the HGP suggested that the number was wrong, then I do not know why they would use it. And if the 175 estimate is closer, why didn't they use that estimate?I have noticed that you say the most recent estimates are 128 or 175. That is a huge difference. The difference is greater between 175 and 128 than 128 and 100. In fact you said that the mutation rate was between 100-175. I do not see a problem with me using the 100 estimate."Dillan: So which numbers should we use? 4, 5, or 7? I think that the average would be around 5. After all, the females can't mate until males mature sexually. However the number 7 was included in one of the papers above, so I wasn't deliberately avoiding the hard facts.FK: Your main problem is that you are demanding precision where precision is not available. There is no magic number here for the number of generations. It may range from 3 to 6, which means your answer is going to have a large error associated with it. By the way, the number 7 was for a specific case of the maturity of males in one species. The maturity of males is going to have little to do with the length of a generation; the sexual maturity of females is the key."True, there would be a large margin for error in my calculations. That is why I chose 5 in my original calculations (and also 7)."Dillan: Using 5 yrs/generation, 100 mutations per inidividual, we still only get a probability of a 2% chance (0.026), or about 1/50. Not impossible, but still not very likely. I do believe these numbers are reasonable. I have yet to see a reason why they are not.FK: They are not reasonable because you are still ignoring the most recent estimates we have of the mutation rate in favor of older estimates that support your argument. This is just moon dust revisited. In addition, you have provided no justification at all that 15 million years is all that would be available. You have not come close to making a case. But even if your numbers were accurate and the probability was 2%, that says that 1 in 50 cases we examine with these parameters would result in convergence. So, 15 million later when we find a case of convergence, how can you argue that this was not the 1 in 50? Your entire argument is going nowhere."Hopefully I will get the most recent estimate of a mutation rate if Adam emails me. However if it was 1 chance in 50, why do we not see more examples of genetic convergence then? It seems like that you are saying, "Someone will have to win the genetic lottery." If there was 1 in every 50 cases, and there are around 1,000,000 species on the planet (which there's not), then that would mean 20,000 genetic convergences. You said that genetic convergences were actually very rare. This would seem to me to be too many."Actually, this is just plain wrong. False inputs lead to faulty conclusions. The mutation rate is wrong, and I don't even know what 'The odds of getting two mutations that are related to one another' is supposed to mean.FK"I thought that the mutation rate was around 1 copying error every 10 million replications. However Nachman (whose estimate you like) estimated "The average mutation rate was estimated to be approximately 2.5 x 10(-8) mutations per nucleotide site or 175 mutations per diploid genome per generation."Should I use 2.5 x 10(-8)? That would seem to make the probability worse. Also what I mean by related mutations is mutations combined related to a certain and perhaps need function. For example, lets say that in order for a certain human to gain resistance to a posion from an animal, it will need 4 mutations (minimum) at a certain site in the DNA. The probability that these mutations will appear and be related is 2.5 x 10(-8) x 2.5 x 10(-8) x 2.5 x 10(-8) x 2.5 x 10(-8). Another thing to factor in is that the same mutation at a certain site may have different affects, depending on what the mutations around it are. For example, if a certain mutation caused the function of a protein to change, then a mutation in that protein may cause a different affect than the same mutation in an old protein. This case is especially grim when there is a major change in the environment, and the related mutations are needed desperately for the survival of the species."Gary Parker is making the same error as you did in calculatign the probability of convergence as 1/22^9. The underlying assumption is that the probability of getting a certain number of successes is constant regardless of the number of attempts.
For example the probability of getting 10 heads when tossing a coin 10 times is 1/2^10 = 1/1024. But if you toss the coin 11 times or 20 times or a 100 the probability goes up, Surely you see that the odds are very much in favour of getting 10 heads out of one hundred attempts - certainly not worse than 1000:1.If you just toss the coin 11 times then, out of the 2048 possible sequences there are 12 that include 10 heads (the sequence can be 11 heads or one of 11 sequences with 10 heads and one tail - one for each possible position of the tail in the sequence). The probability then is 12/2048 = 6/1024.Please recognise that you have no business trying to make probabilistic answers without a firm grasp of probability theory."Let me see if I can sum up what you are saying in an analogy. You are saying that I am calculating the odds of just one ticket winning the lottery, where as there could be many people playing the lottery. Therefore the odds that someone may win the lottery may be very great.The only problem that I have with this is that evolution depends in nearly every evoluitonary sequence of some kind of pattern of mutations. For one thing nearly all of them must be beneficial. Secondly they must relate to the environmental needs of the organism in whatever sitution they are in. Another factor that complicates the equation is that in the real world genes often affect more than one trait (pleiotropy), or more than one gene affects a given trait (polygeny). For example, ReMine states, "...in flies there is a gene affecting eye color that also afects the reproductive organs." So the probability is even lower that you will get a series of related mutations that do not affect other functions in a harmful manner. Since evolution almost relies on related mutations, it is the rule rather than the exception. Since there are nearly limitless ways in which mutations can rearrange an organisms genome, it seems unlikely that a certain series of related copying errors will appear and take over, not just once, but in every case of evolutionary progression. If you disagree with this, would you please set up an equation that is more accurate? If I am wrong I hope that we can work through this equation together to find the correct answer.

PaulK, if you are saying that evolution may take many different paths with many different mutations, that is correct. However, in environmental extreme conditions an almost specific series of related mutations must occur so that a species could survive. For example, let's say that there is a population of extremely fast predator birds that feast on bees. There may be many potential mutations in the bee population that could serve for further evolution. The key factor is that these potential mutations may not be related to their needs at the moment. If the bee is to survive it would need mutations related to how fast it could fly. It may need bigger wings, a more aerodynamic structure, etc.. Similarly if these predator birds all but depleted the bee population, then they may need specific mutations that would allow them to adapt to a new diet. A mutation in the bee for a longer antenna may not help it in the situation that I mentioned above, however it may help it in another environmental condition. Since the selective values of the mutations are very context dependent, there may be only a small number of related mutations that could serve for the purpose of ongoing evolution at any one time.

Thank you for the replies PaulK and FK. Right now, it looks as if FK may have been correct in his criticism of my original calcualtions. I know that I have drug out this debate for a very long time, but I wanted to make sure your logic was consistent. I am not a creationist to hold to dead arguments. In fact, at one time I was opposed to the use of information theory as an adequate argument for design. Just ask Fred Williams or Paul Willis (if Paul remembers). I have since changed my opinion about the matter after reading some material on it. Right now, mine is not a powerful argument at all, and has taken a completely different direction than what I had intended it to go. I intended to email Spetner about the matter but was unable to find an email address. Does anyone here know how I can get in touch with him?As for Parker's number, it may be a powerful argument yet, but I need to develop it some more. As for now, I will say that both of you have indeed given some very powerful criticisms to my model and both of you are worthy opponents. The question now is, where do we go from here? I am going to try to gather some evidence for Parker's calculation. If you would, help me use Parker's number to set up a correct calculation. It is clear that his calculations have no contraints involved.Again, I would like to thank you for the correspondence. I will more than likely post again on the matter, perhaps even in a day or two. I may post on this thread or I may start a new one.

Thank you all for the replies.PK: As I read Parker's model he is talking about the probability of a point mutation at a specific location in one birth (it's about the right order of magnitude). So Parker is assuming that there are two specific births and in each one a specific mutation must occur. In reality there will probably be multiple generations available for each and many possible mutations (Parker even implicitly assumes that each mutation can only have ONE related mutation). As it stands Parker's calculation is worthless - the assumptions that need to be made for it to apply are far divorced from reality.
To get probability theory to work you have to be VERY specific about what you are working out. Parker is working out the probability of a specific sequence of events of probability 10^-7 occurring with only one attempt for each. That's the wrong thing to calculate - if evolution really did work in a way where that calculation would apply Darwinian evolution would be out by now, without Parker needing to do a thing.Personally I don't think the argument can be saved. The basic concept might stand a chance, but to do it right would be a lot of work even if the numbers are available.Start with this question. To what extent are related mutations needed ? Could the observations that idea is based on be better explained by selection bias (we notice related clusters) and natural selection (if a particular mutation improves fitness related mutations will be more likely to improve fitness) ?Dillan: Are you suggesting that you have read Parker's model before? I found it in his book, Creation: Facts of Life. I do agree that the probabilities need some constraints. In addition to your questions, some more may inclued: How many mutations can one specific mutation be related to? Are related mutations necessary? How much time is available and how many mutations have occurred?I will seek to answer these questions, but I doubt that the information is out there. I think that Parker got his information from the book Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution (at least I think that this is the title). If anyone here has read the book, or if anyone knows how I can get ahold of it, I would appreciate it if you would tell me. Just because a book is old doesn't make its' contents any less truthful.Percy:"dillan writes:
In fact, at one time I was opposed to the use of information theory as an adequate argument for design.While information theory has been mentioned in passing several times in this thread, it did not seem to me that you were using an argument based on information theory but rather on probability. If you think you're using an information theory argument then I'm somehow just not seeing it. Maybe the thread title led me astray."You misunderstand. This thread had nothing to do with information theory-I was just saying that I try not to hold to dead creationist arguments. However I feel that information theory is a very strong argument for design."The Creationist information theory argument, as I understand it, goes something like this:Rather than using the mathematical definition of information introduced by Claude Shannon and upon which modern information theory is based, introduce a different definition of information that purports to somehow measure semantic meaning or knowledge."Right now there is no formula to measure semantic meaning or quality. A book may contain many pages, but the actual information content may be very low. However another book may contain few pages, but the information content may be very high. What Gitt is trying to do is set up a pattern for detecting design. This is not a different definition of information, but rather an extention of Shannon's. However, Shannon's definition constitutes the lowest level of information."Assume that the equations of modern information theory still apply to this alternative definition of information."Shannon's definition may be used for transmission and storage. In fact I think that Gitt used it to determine that cells have the highest compact information storing density around. However his equations are useless when determining the quantity of, or detecting the prescence of, semantic information (or pragmatic or apobetic)."Present as an axiom that this type of "information" can only be created by intelligent beings such as ourselves."Nope-information comes from information. For example, when cells divide, there is no intelligence involved. The only factor is that one information system gave rise to another. The ultimate origin, however, is always linked to intelligence and volition."Conclude that since mutations are the result of a random process rather than of intelligent beings that mutations cannot create new information.
All these points are invalid. The first point is invalid because you can't redefine information to include semantic meaning or knowledge and still call it information theory. As Shannon points out in his paper right on page one:"Frequently the messages have meaning; that is they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem."
The second point is invalid because you can't take the equations of actual information theory and apply them to an alternative definition of information that includes semantic meaning. It would make as much sense as applying the rules of football or cricket to a game of chess.The third point is invalid because it must be demonstrated that only an intelligent being can create semantic information. It can't just be an axiom.The fourth point is of course valid only if the first three points are valid, but they're not, so this point also fails."I really do not want to address this topic in this post. However, I have had a discussion with Fred Williams on the matter. Look at his guestbook at The Evolution Fairytale .
Briefly, some quotes form biology and information scientists:Karl Steinbach, "The classical theory of information can be compared to the statement that one kilogram of gold has the same value as one kilogram of sand."Ernst von Weizacker, "The reason for the 'uselessness' of Shannon's theory in the different sciences is frankly that no science can limit itself to its syntactic level."G. Oshe, "While matter and energy are the concerns of physics, the description of biological phenomena are typically involves information in a functional capacity. In cybernetics the general information concept quantitatively expresses the information content of a given set of symbols by employing the probability distribution of all possible permutations of the symbols. But the information content in biological systems (genetic information) is concerned with its 'value' and its 'functional meaning', and thus with the semantic aspect of information, with its quality."Shannon's definition constitutes part, but not all, of the definition for meaningful understandable information. I suggest reading Gitt's book before making claims like yours. He devotes an entire section of his appendix to discussing Shannon's theory. I have read the article by Baldwin, but after doing some research on my own I do not think that his arguments truly stand up to scrutiny. The fact is that there has never been an example of the type of code Gitt talks about forming by chance or physical processes. For a code to truly form this way, you must show co-variance between two phenomena that exhibit statistics, syntax, semantics, pragmatics, and apobetics. It must be specified and complex. Also it must have some sort of representational function. In addition, it cannot be due to the inherent physical properties of the system. Sound waves have no inherent property to make them align in such a way that it seems as if a person of the same language is talking to you, when in actuality it is just natural forces at work. Random bits of metal do not construct computer programs, because it is not inherent to the properties of the material carrier. Likewise life's chemicals have no inherent property to make them align in such a way to maintain functional organization. As Yockey warns: "Attempts to relate the idea of order . . . with biological organization or specificity must be regarded as a play on words which cannot stand careful scrutiny. Informational macromolecules can code genetic messages and therefore can carry information because the sequence of bases or residues is affected very little, if at all, by [self-organizing] physico-chemical factors." As chemist Michael Polanyi has said: "Suppose that the actual structure of a DNA molecule were due to the fact that the bindings of its bases were much stronger than the bindings would be for any other distribution of bases, then such a DNA molecule would have no information content. Its code-like character would be effaced by an overwhelming redundancy. . . .Whatever may be the origin of a DNA configuration, it can function as a code only if its order is not due to the forces of potential energy. It must be as physically indeterminate as the sequence of words is on a printed page." Books do not write themselves. Rather, it takes an intelligence to do this. The very existence of a SETI program is, in my opinion, enough to justify the notion that more than likely life originated from an intelligent origin.Gitt says that functional information is invariably associated with five levels of information, which is in turn associated with an intelligence. I cannot demonstrate that an intelligence is always needed, because I would then have to prove a non-existence. I am just going on the data I have. Likewise you cannot prove that energy is conserved-you only rely on observational data.As I have said, I really don't want to discuss information theory in this thread. Perhaps in another I will.FK, "Dillan: As for Parker's number, it may be a powerful argument yet, but I need to develop it some more. As for now, I will say that both of you have indeed given some very powerful criticisms to my model and both of you are worthy opponents. The question now is, where do we go from here? I am going to try to gather some evidence for Parker's calculation. If you would, help me use Parker's number to set up a correct calculation. It is clear that his calculations have no contraints involved.
FK: I am not really sure why you think Parker’s argument is meaningful. First, based on the excerpt you provided, he knows very little about genetics. 2nd, I looked up his book and it was published in 1980. If he is using mutation estimates that are that old, they are frankly worthless. 3rd, he is obviously a Creationist with an agenda. I don’t trust those types of sources."1). Parker is a PhD in biology. He has had his fair share of genetics and discusses this area a bit in his book. 2). Creation: Facts of Life was published in 1994. While this is not recent, it is not as old as you would suggest. (And I am absolutely positive about this date because I own his book). 3). He is a creationist, but also a former evolutionist. In fact, he says in his book that all the evidence does not support creation. He thinks that you must weigh the evidence."There could be a simple solution to all of this Dillan. The reason that these Creationists arguments fall apart under the microscope is because evolution really happened. Don’t you think there are mathematically competent scientists working in the field? Do you know what a coup it would be to disprove evolution? It would have enormous implications. I would love to publish a paper along those lines; it would make me rich and famous. But the fact is that you only see Creationists doing so, because Creationists have an agenda to protect.I would recommend that you go to the primary literature and develop your own argument. Even though his argument has been superceded by more recent data, I think that’s what Fred Williams did with his work on U and the number of required births. But you are never going to get anywhere with the approach you are taking, especially if you try to develop an argument now based on Parker’s number. You are once again starting off with an incorrect premise.Good luck. I sincerely mean it when I say I think it would be cool if one of these mathematical arguments ever held up to close scrutiny, but I don’t see it happening. There is just too much evidence from too many fields that indicate that evolution is true.FK"I cannot base my belief in creation on just one case where evolution is shown to be within the realm of possibility. For one thing, I think that there is more evidence out there than this. For another thing, my belief has nothing to do with the science involved. I would believe in God and creation even if it seemed very nonsensical. Is that an a priori assumption? Yes, but others make the same a priori assumptions.

Thank you everyone for the replies. To PK, you are correct. Parker's numbers do need some readjusting. I will try to correct them, but I doubt that I will be able to. What were your points with Gitt information?To Percy-I may reply to you in the information thread.To FK-Parker's book was written in 1994. Take a look at this:
http://www.amazon.com...
{Shortened display form of URL, to restore page width to normal - Adminnemooseus}You were correct about Parker's degree. I don't think that we should automatically discard everything he says because of this though.Regards,dillan[This message has been edited by Adminnemooseus, 10-30-2003]