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Author  Topic: Evolution and Probability  
dillan Inactive Member 
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/(1e^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 rate10^7 Steps in Speciation50 Number of individuals per step: (*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 (neodarwinian theory) of evolution. They assume that small changes add up to big changes. So Spetner assumed the smallest change possiblea 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 http://www.talkorigins.org/faqs/mutations.html, "The average human being has about 50100 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 humansabout 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 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.


PaulK Member Posts: 16338 Joined: Member Rating: 1.7 
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. 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). 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) The mathematical errors don't seem to affect your model as seriously as Spetner's (because you use smaller numbers) up to the point where you try to calculate the probability of getting a specific set of beneficial mutations by raising 1/(number of beneficial mutations) to the nineth power. 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.


MarkAustin Member (Idle past 2371 days) Posts: 122 From: London., UK Joined: 
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. 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. Neither holds for evolution. Evolutionary events are not isolated  one event influences the possible sequence of future events, therefore statistical analysis is impossible. The number of possible events is unknowable  therefore the probabilities cannot be calculated after the event. Performing such calculations as are common on creationists sittes is a sure sign of mathematical illiteracy. The only statistical figure that can be derived for life is that the probability of life on Earth is 1.


dillan Inactive Member 
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. 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 500which was Stebbins' estimate of the number of steps in speciation. I know that this number is offthat 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.


dillan Inactive Member 
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. 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 be22. 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.


PaulK Member Posts: 16338 Joined: Member Rating: 1.7 
quote: I don't understand your reasoning. Why would the fact that the axctual values are likely to be ABOVE the average make you choose the average ? quote: I think you have missed the point here. If convergence on the molecular level is rare than it can be a low probability event. Spetner relies on convergence being common  confuising the usual morphological convergence with molecular convergence which to the best of my knowledge is less common. quote: No, Spetner made a major error there. It is simply invalid mathematically  and has no biological basis. quote: The point you post is in regard to your use of (1/22)^9 to calculate the probability of getting the convergent mutations. I am glad to hear that your model agrees that the assumptions implicit in that calculation are false. However that does not change the fact that the calculation is based on unreasonable assumptions and is this invalid.


derwood Member (Idle past 432 days) Posts: 1457 Joined: 
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 nonstarters. I can ask Thomas if he archived any of his rebuttals. As for me, I don't think much of anything regarding Spetner's pap. Most don't.  

derwood Member (Idle past 432 days) Posts: 1457 Joined: 
quote: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 

MarkAustin Member (Idle past 2371 days) Posts: 122 From: London., UK Joined: 
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.


Fred Williams Member (Idle past 3412 days) Posts: 310 From: Broomfield Joined: 
quote: Paul, do you have *any* evidence whatsoever to back up this claim? Not only is Dillan’s average reasonable, it is incredibly conservative. The actual values are very likely far BELOW the average, the opposite of what you claim. Why? For one, there is little or no evidence that beneficial mutations where the mutated type is more viable than the wildtype in normal environments even occur. Yet we are graciously assuming a significant generous rate of this kind. Second, just because there are “hotspots” does not necessarily increase the odds for a beneficial mutation, unless you can demonstrate that copymistakes in “hotspot” regions are more likely to be selective than those outside “hotspot” regions. Third, the model completely ignores the impact of the deleterious mutation rate. Three generous assumptions (two of them incredibly generous) yet the numbers still look horrible for evolution producing even a paltry 50 steps. Not even a toenail in 10 million years. Time to give up the fairytale! quote: This is an invalid analogy, Spetner is doing nothing of the kind. Assume a change that results in 5 new fixed nucleotides consisting of specific nucleotides a, b, c, d, and e. Spetner calculated the odds that all 5 nucleotides become fixed (except in his example he calculated a 500nucleotide change). They can become fixed in *any* order. Perhaps b, then a, then c, etc. Your analogy is bogus. It is a bit similar to an analogy Thomas tried to pull at NaiG, but unfortunately I was too busy at the time to respond (Though I was itching to do so!) quote: I tend to recall evolutionists admitting both morphological and molecular convergence are common in nature. I’ll have to do some more digging… quote: This is a justso story. I smell a logical fallacy coming… [INSERT CIRCULARREASONING REPLY HERE]


Fred Williams Member (Idle past 3412 days) Posts: 310 From: Broomfield Joined: 
quote: Translation: The mathematical evidence is devastating for my position, so I’ll pretend the assumptions are too vague to produce reliable results. Welcome to the world of evolution “science”! Dance and evade… PS. Mark, would it be presumptuous of me to predict that you also believe information science does not apply to biology?


crashfrog Member (Idle past 23 days) Posts: 19762 From: Silver Spring, MD Joined: 
Since biological systems don't contain information in the sense referred to by "information science", why would it? How come when Creationists do these probability exercises, they never try to figure out the odds of an infinitelypowerful god existing? Those odds seem much, much lower to my mind than evolution.


PaulK Member Posts: 16338 Joined: Member Rating: 1.7 
I don't need evidence to back up the claim that those with higher probability are more likely to appear. By definition they will appear proporitonately more frequently. Asserting that the actual values are far below average is  well on the face of it it is absurd, so it is your claim that is in need of support.
I am so sorry that you think that mathematics is a fairytale  but I do not intend to rewrite it to meet your needs. In short it is your obejction that is bogus  and quite obviously so. I will add that calling observations "justso stories" is  well pretty absurd. Insertions, deletions and transpositions contitute a large proportion of the mutations in vertebrates. http://www.amazon.com... "1 3 raised to the power of 4.7 million(10 2.5 million), single base changes are available to a genome with 4.7 x 106 nucleotides (E. coli); see also Arber, this volume " No circular reasoning involved. Ironically I was referred to the work quoted here by a supporter of Spetner's assertions. {Shortened display form of URL, to restore page width to normal  Adminnemooseus} [This message has been edited by Adminnemooseus, 08272003]


dillan Inactive Member 
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. 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 step22), 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 giveslike the lysozyme in langurs. They converged on at least 9 nucleotides, but could have converged on more. "Dillan, 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. 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. 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.


Fedmahn Kassad Inactive Member 
Fred: Your analogy is bogus. It is a bit similar to an analogy Thomas tried to pull at NaiG, but unfortunately I was too busy at the time to respond (Though I was itching to do so!)
FK: Yes, I am sure that’s it. You had an answer but just didn’t have time to post it. But I am sure Thomas also had an answer to your answer, but he couldn’t answer since you never posted. 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. 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. Dillan: From what we are able to calculate though, evolution is improbable. FK: How so? Dillan: 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? FK: Totally refuted it? No, because it does contain a few factual statements. On the other hand, it is riddled with errors, outdated arguments, and unwarranted conclusions. Fred has been promising to update it for quite some time, though. Some of what he cites has already been nullified by the sequencing of the human genome. For example, Crow’s estimates of U were based on an assumption that there would be more than 60,000 genes. So when Fred writes “Widely recognized geneticist James Crow in an article in the same Nature issue agrees that the deleterious rate is more likely twice the rate cited by EyreWalker and Keightley”, then this is just flat wrong since the number of genes is estimated to be 30,000 or so. There are several other examples like that in the article. I might comment when he updates it, but as it is it is not worth my time. 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



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