Evolution and Probability

Dillan: 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.FK: Perhaps you have a reading comprehension problem, because I didn't say this is what you said. I said If you mean that there are slim odds that two species’ genomes would converge to a large degree You are going to have to clarify how much of the genome you think evolutionists believe converged. Please don’t make up numbers. Show me some hard evidence.Dillan: By the way, what is the new estimate for U?FK: The last time I spoke with Adam his estimate of U was 2.2. This was after the human genome was decoded. But you can e-mail him at a.c.eyre-walker@sussex.ac.uk and ask him yourself. The implications of this are that it would make the number of conceptions (not births as Fred writes) less than 20 instead of the 60 Fred wishes you to believe.Dillan: 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.FK: 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.Dillan: 1). If the webpage for talkorigins has been updated this year, why have they not changed their figure for mutations per individual.FK: 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.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.Dillan: 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.FK: My postulation absolutely negates your assertion. Without birth control, when sexually reproducing species reach reproductive age they start to reproduce. Female langurs become sexually active as young as 3. I can assure you that the generation time is not 7 years. Or do you think they became sexually mature and decided to postpone having offspring until they were more financially secure? In humans, the generation time is going to closely correspond to the average age at marriage.Dillan: If I wanted, I could change the calculation around to where evolution is extremely improbable.FK: Which renders it absolutely useless. Your problem is that you are trying hard to plug in numbers that give you a preconceived low probability. This was obvious from your first post, where you ignored recent estimates in favor of those you felt lowered the probability.FK

Your 1/22 value is not derived from Simpson. It came from your own estimate of the number of beneficial mutations available at each satep assuming that they are equiprobable.-----If 2 out of the possible results at a step are convergent then the probability of getting one of them at that step is 2/22. To say that this is "not necessarily" the case is to go against your own assumptions. Not that you give any reason why it should not be the case.------------Sicne you allow 15 million years for the convergence, then you have to allow 750 steps for the convergence unless you can provide a better estimate of the number of steps available. Allowing only 9 as your original calculation did is obviously not valid. If your other calculations produce different results then there is an inconsistency in your models.Others have criticised your calculation based on the number of mutations - and I note other problems such as the assumption that all the mutations involved are equally likely (false both on probability of occurrence and probability of fixation) and the assumption of a constant population of 10,000 rather than a larger stable population which splits or is reduced in size by environmental stress.Since you have not answered the probalems with your 1/22^9 calculation - notably the point that since there are far more than 9 steps available it will give a result that is far too low - why do you continue to insist that it is correct ?

I read an article a while ago that said it had been
found that each of us has as many as four genetic
differences from our parents.Everyone.Not everyone has lethal or debilitating genetic diseases
(although some do).Any non-lethal mutation that has an expression that is
accessible to the environment can be beneficial in the
right environment.The comment that mutations are detrimental has no real
evidence -- after all unless we sequence everyone and compare
them to their parents how can we be sure how many
mutations we all carry (as I say some recentish research
suggests around four).All of these features are contrary to the assumptions upon
which the calculations have been made -- isn't that enough
to scratch them and try again with a better mutation model?...and the Maxwell Demon of natural selection needs to be
incorporated somehow too.

Peter: I read an article a while ago that said it had been
found that each of us has as many as four genetic
differences from our parents.FK: To clarify, that was probably "expressed" differences, or differences in coding regions. The actual mutation rate is quite a bit higher than 4 per generation, but most mutations are in non-coding regions.A comment that I missed earlier:Dillan: Let's say only 3% of the mutations are in the coded region.FK: If only about 1% of the genome is coding, why would 3% of all mutations fall in coding regions?FK

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Apparently you don't know that tautologies are necessarily true.

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Paul, you’ve completely missed the point, and I see you are continuing your error in posts to Dillan. Let’s recap:1) You claim some mutations would have higher probabilities and they would be more likely to be found as a result.
2) Dillan replied that the mutation rate and selection value represent an average.
3) You reply that the actual values are likely ABOVE the average.
4) I reply that this is a nonsense statement without evidence to back it up.
5) You defend your claim by invoking a tautology based on #1 above. The truth of the tautology itself IS NOT THE ISSUE, the issue is that the tautology DOES NOT SUPPORT YOUR CLAIM that Dillan’s AVERAGE is too low.Just because those with higher probability (or selective value) are more likely to appear does not mean there are necessarily enough of this type to offset those with probabilities below the average that either eventually fixate or vanish so we don't see them!

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I note that you have had the wisdom to drop any further comment on probability theory.

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I really saw little value in replying any further to all the handwaving. Using probabilities to draw baselines or establish a criteria to determine the validity of something are frequently used by scientists, despite Mark’s equivocal attempt to dismiss them. It seems obvious you agree with me on this, or else you would have embraced Mark’s argument instead of debating further with Dillan.

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I did not make either of the assertions "most evolutionary changes are due to insertions/deletions/transpositions"

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Then what the heck are you saying? You clearly implied the above.The problem transpositions pose for evolutionists is that they have all the ear-markings of non-NeoDarwinian behavior, ie they are likely non-random events.

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But don't expect to see Fred update his argument anytime soon, as most of the newer estimates are going against him.

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They are? Which ones? Surely you would not just say this without being expected to produce evidence?My queries show three new estimates since my article: the slightly lower Keightley-revised number, and two studies that support U=3 or higher. I guess in the world of Fedmahn one is more than two.

No, Fred the fact is that I have not missed the point, the fact is that you and Dillan do not understand probability theory to even the basic level needed for these arguments.To make things clear let us apply the points to the sum of two dice.1) Some values are more probable than others and therefore appear more often. Do you disagree with that ?2) If we use Dillan's idea of the average the probability is 1/11 for EVERY possible sum.3) The probability of the actual sequence may well be HIGHER than 1/11 raised to the number of rolls. After all the probability of getting any of the values in the range 7-9 is higher than 1-11 and 2/3 of all rolls will be in that range.4) You assert that it is nonsense without evidence. In other words I cannot tell that the probability of getting 2 sevens is higher than 1/121 as Dillan says without evidence. Despite the fact that probability theory tells me that the probability is 1/36.
It follows therefore that you should throw Spetner's calculations out since you regard probability theory as worthless. Spetner needs to provide evidence instead.5) As I have shown above the tautology does support my point. When the probability varies a calculation that assuems that all results cannot be accepted as reliable. What Dillan needs is EVIDENCE to support HIS assumption of equiprobability.In the absence of evidence Dillan's assumption of equiprobability can be taken as likely false. Just as I said.And what does Mark have to do with MY points on probability theory - which you dropped the discussion of. I hope that you dropped it because your handwaving was so obvious.And no, I did not imply that "most evolutionary changes are due to
insertions/deletions/transpositions" at all. A large proportion is not necessarily a majorityAnd transpositions are not contrary to Darwinian theory at all. Darwinian theory has no problem wiith the idea that mutations are typically caused by chemical reactions - no matter how deterministic they might be under a highly detailed analysis.

I don't have time to review this thread right now, but the rate at which it is accumulating posts indicates a strong possiblity of babble, albeit with a strong technical slant. I have two requests:

1. Please skip all the "tweak the other fella's nose" type of stuff. I would like to see this thread become impersonal and focused strictly on the topic rather than the people discussing the topic.
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2. Please slow down the post rate and make a greater effort to understand what the other side is saying before replying. For example, I think I noticed some posts implying that people said things they did not say, or responding to points not made.

Here are examples of the type of comments I no longer want see in this thread, with no attribution:

• This is a just-so story. I smell a logical fallacy coming
• Translation: The mathematical evidence is devastating for my position, so I’ll pretend the assumptions are too vague to produce reliable results.
• I am so sorry that you think that mathematics is a fairytale - but I do not intend to rewrite it to meet your needs.
• LOL! You don’t need evidence? In a way I don’t blame you for taking this position. Meanwhile, I will stick to hard evidence instead of tautologies to defend my position!

My goal is to have a discussion that other people can follow, and right now this thread doesn't appear to be meeting that goal. If I have to temporarily close the thread to help make this happen I will.------------------

--	Percy
	EvC Forum Administrator

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To make things clear let us apply the points to the sum of two dice.
1) Some values are more probable than others and therefore appear more often. Do you disagree with that ?
2) If we use Dillan's idea of the average the probability is 1/11 for EVERY possible sum.
3) The probability of the actual sequence may well be HIGHER than 1/11 raised to the number of rolls. After all the probability of getting any of the values in the range 7-9 is higher than 1-11 and 2/3 of all rolls will be in that range.

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This is both a good and bad analogy, good because it illustrates the point you are trying to make, bad because it is a strawman analogy in how you are using it. By using the dice analogy you are using what is called a Gaussian distribution. The problem is that you are trying to impose this distribution on Dillan’s model and have essentially erected a strawman, particularly with #2 above. That is, you’ve essentially drawn your X-axis above an axis you arbitrarily assigned to Dillan (that is why I asked you to justify your claim that the true average was above Dillan's). More importantly, your Gaussian model doesn't apply because the individual nucleotide probabilities are a really a fractal distribution, and the Fisher/Spetner/Dillan mutation rate/selection values represent the average of that distribution.

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And transpositions are not contrary to Darwinian theory at all. Darwinian theory has no problem wiith the idea that mutations are typically caused by chemical reactions - no matter how deterministic they might be under a highly detailed analysis.

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If they are deterministic such that they are adaptively directed, it certainly is a problem for the theory of evolution in its current paradigm.

Fred: They are? Which ones? Surely you would not just say this without being expected to produce evidence?FK: Well, let’s have a look. From your article at 404 Not Found :

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Now consider that extremely favorable assumptions for evolution were used in the Eyre-Walker & Keightley article. If more realistic assumptions are used the problem gets much worse. First, they estimate that insertions/deletions and some functional non-genic sequences would each independently add 10% to the rate. Second, and more importantly, they assume a functional genome size of only 2.25% (60K genes). When they assume a more widely accepted 3% functional genome (80K genes), they cite U = 3.1, which they admit is "remarkably high" (even this may be a favorable assumption, considering Maynard Smith estimates the genic area to be between 9 — 27%.

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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.Here’s another paragraph:

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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 Eyre-Walker and Keightley. So if we use Crow's revised rate of U=3, we get:

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B = 2e^3 = 40 births before we get one offspring that escapes a new defect!

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There’s two estimates from your article you can throw in the trash. If you read Dr. Crow’s article, he is assuming the rate is higher because he felt like 60,000 was an underestimate of the number of genes. Of course you know this, which makes me wonder why you haven’t updated the article. Crow’s estimate is no longer valid.Now, that is not to say that U might not actually be 3. It could be. But not based on the logic Dr. Crow was using.Fred: My queries show three new estimates since my article: the slightly lower Keightley-revised number, and two studies that support U=3 or higher.FK: Were you planning on sharing these queries with us? I am aware of a single study that estimated that U was 3 (or even greater). This was a pre-HGP study published 3 years ago by Nachman and Crowell. They were assuming that there were 70,000 genes in the human genome. Of course they also estimate that the total mutation rate was 175 base pairs per individual per generation. This is on the high side of most estimates, and would make their estimate of U on the high side (as would the too high estimate of the number of genes). If you have an estimate from a post-HGP study, I would certainly be interested in reading it.FK

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]."

No, it is not a bad analogy at all. Your criticism wrongly assumes - out of nothing - that I am proposing a particular distrbution. In fact all I am doing is pointing out that there IS variation in the probabilities and that Dillan's calculation fails to take this into account. I also point out that the distribution of the beneficial mutations that DO achieve fixation will be skewed towards those with a higher probability compared with the pool of available beneficial mutations - just as in my example the actual results are skewed towards 5-9 and away from 2-4 and 10-12. THIS is what justifies my claim.So the facts are that I did not suggest a gaussian model - I simply used a simple example as an illustration of the points - and that I have justified my point.So the real strawman is your claim that I proposed a Gaussian distribution for the actual data, when in fact I proposed no distribution, only rejecting the distribution implicit in Dillans mathematics. The only person to propose a distribution is Dillan who holds that a flat distribution is an adequate representation - and THAT claim remains unjustified by him or by you.As for your comment on transpositions I need only note that you have chnaged the subject. *IF* they were adaptively directed even point mutations would be a problem for the current theory of evolution. But "if"s are not evidence.[This message has been edited by PaulK, 08-30-2003]

Aside from the fact that Fred's responses are hardly adequate he has not addressed your use of 1/22^9 as the probability of achieving convergence for the langurs. (Probably because it is obviously wrong.)Do you intend to offer any justification at all for the assumption that there is only one available step for each of the mutations involved ?Or are you going to continue to rely on that assumption even though it is almost certainly false ?

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.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.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? 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.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.So, what can one conclude from this? Pretend for a moment that you are a practicing scientist, and you are presenting conclusions. Here is your major conclusion: Based on the uncertainty in mutation rate and in the selection coefficient, no conclusion can be made regarding whether convergence in the case of the langur is probable. Using the most recent estimates available, convergence appears to be likely. That’s it.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.Dillan: 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?FK: I explained why it was out of date above. Almost all of these estimates (all of them?) were made prior to the sequencing of the genome when it was believed that there were more genes and a higher coding percentage. The most recent estimates, from the Human Genome Project website at Page Not Found | ORNL are Less than 2% of the genome codes for proteins and The total number of genes is estimated at 30,000 to 35,000much lower than previous estimates of 80,000 to 140,000 that had been based on extrapolations from gene-rich areas as opposed to a composite of gene-rich and gene-poor areas.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.FK