Evolution and Probability

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.

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"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."

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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.)

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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 ?

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"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)."

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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.

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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.

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"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)"

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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.

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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.

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"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."

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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?

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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.

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.
Your attempt to dispute my example using coin toses is clearly irrelevant. It employs the same technique of artificially partitioning the attempts as Spetner does - and naturally produces similar effects of producing an erroneously low probability. Your objection even misses the point that Spetner does not distinguish between the variosu possible beneficial mutations - in this case and therefore there is no sequence to consider.In short it is your obejction that is bogus - and quite obviously so.I will add that calling observations "just-so stories" is - well pretty absurd. Insertions, deletions and transpositions contitute a large proportion of the mutations in vertebrates. http://www.amazon.com...
"...most organisms tolerate only relatively low levels of point mutation in a generation [1]. Instead, they have evolved mechanisms that generate multiple sequence changes in a single step...""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, 08-27-2003]

So if I apply Spetner's techniques to a simpler situation and show that they produce a result that is obviously wrong is is an "irrelevant analogy".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 ?And of course I am not looking at different changes - neither was Spetner for the purposes of the calculation being discussed at this point. Therefore it is your objection that is irrelevant.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).While such errors persist your calculations reflect only on your ability to apply probability theory.

Let's take a slightly different look at the langur example using your figures.Accordign to Spetner a species tends to last about a million years. So given 15 million years there should be 15 speciations. This figure seems to work for the horse evolution, and you implicitly assume that langurs are evolving at the same rate.According to your figures each speciation involves 50 steps so there are 15*50 = 750 steps within the relevant time period.Making the conservative assumption that only one of the convergent mutations is available at each step and assuming that all the beneficial mutations available are equiprobable (both assumptions work agaisnt evolution) we need on average 9 * 22 = 198 steps to get all 9 convergent mutations. Since 198 is significantly less than 750, based on your own figures and assumptions it is very likely that the convergence would occur within the time available - indeed more likely than not.

Apparently you don't know that tautologies are necessarily true. In that respect appealing to a tautology is BETTER than evidence - evidence can never provide absolute logical certainty. I will stick to my position of accepting necessary truths rather than join you in denying them.I note that you have had the wisdom to drop any further comment on probability theory.And no, I am not redefining my position in any way. I did not make either of the assertions "most evolutionary changes are due to insertions/deletions/transpositions" or "that the mechanism that produces these multiple sequence changes has evolved".So let us not shift the goal posts as you attempt to do. Spetner assumes that evolution relies almost entirely on point mutations for some reason. Authorities working in the field say that other mutations producing larger changes at the molecular level play a significant role in evolution.To quote from the extract a t Amazon again:
'As emphasized by Jim Shapiro (this volume), " the conventionalexplanations, that randomly-generated... changes accumulate one locus at a time, are unconvincing on both functional and probabilistic grounds...."' (ellipses in original)"Ed Trifonov observes, "evolution is translocation and transposition, rather than point mutation". Nina Fedoroff (this volume) and Jim Shapiro (this volume) emphasize that transposable elements and other genetic repeats "modularize" the genome, by creating segments that are likely to rearrange, and thus play active roles in genome reorganization and evolution. "

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")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.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.Since you have explicitly denied that your model makes the assumptions required to support your calculation the question remains - why insist that the calculation is correct when it misrepresents your model ? And if you don't understand the meaning of the calculation why are you attempting a probabilistic argument at all ?

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 ?

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.

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 ?

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.

The example I gave is closer than the idea of many people buying a ticket. I thought that I had made it quite clear that according to your there are a good many more steps available in the langur example than the nine your calculation assumes.Evolution does not depend on strict sequences of mutations - typically different traits are evolving at the same time. So many different sequences will give the same result. And evolution does not even have a fixed goal so the number of paths that produce significant evolution is even greater.Your objection is redundant - beneficial mutations will deal with the enviromental needs by definition. The pleiotropic effects of some mutations also come out in the wash - if they are beneficial overall. As for your assertion that evolution "almost always relies on related mutations" perhaps you would like to explain it. Related in what way ? And how much if it is - again - a question of which changes are beneficial ?The first step in improving either calculation is to get an estimate of the number of attempts available. Assuming only a single attempt for each success is obviously wrong.
And for Parker's calculations we also need to consider that the probability of getting two related mutations is the sum of the probability of ALL possible related pairs - not the probability of getting a specific pair.

Evolution does not always preserve species so we don't need a certain success. Predator-prey relations are more typically an "arms race" than one species obtaining an overwhelming advantage - likely because every advantage is in fact a trade-off and there are diminishing returns in pushing past the optimal point.Just off the top of my head, your hypothetical bees might survive by improving speed, manoueverability or by changes to the venom in their sting. And the changes only have to keep the losses to predators down to an acceptable level. So even in your example - which certainly does not seem typical - the situation is not as bad as you suggest.The situation you describe is most likely to happen when a new predator is introduced to an environment. And to the best of my knowledge extinction IS the most likely result (how many island species are driven to extinction or endangered by the introduction of rats ?) . So I don't see why evolution should be expected to deal with it at all. It sounds more like a problem for Spetner's non-random mutations which SHOULD be more effective in dealing with that sort of situation.

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) ?