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 In other words, the 175 estimate could be just fine, but the estimate of U is outdated because it is based on the assumption that there are 70,000 genes."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 - Biozentrumsuggest 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 Most likely they got this from one of the outdated estimates.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.
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