What mutations are needed for a particular trait (e.g. wings) to arise?

I don't know how to count the mutations required. It is significant that feathers and the lung structure seem to have been inherited by birds from their dinosaurian ancestors - which certainly increases the time available.

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The natural selection part seems to make sense but random mutation does not. Every SINGLE example of a beneficial random mutation e.g. resistance to black plague in Europeans seems too improbable to have occurred purely by chance.

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On a more general point, this is a very bad argument. Probability is not something that is easy to grasp when large numbers are involved, Simply guessing is not going to produce an answer that is worth anything.Moreover, it is not enough to point out that specific beneficial mutations appear to be unlikely. If there are many possible beneficial mutations then the chance of getting A beneficial mutation will be much higher than the chance of getting any specific beneficial mutation. TO make an analogy the chance of winning the lottery is very low. The chance that someone will win the lottery is a lot higher. If you looked at the history of a large lottery and considered the probability of each of the actual winners winning you would come up with a very large number. But nobody would insist that there must be an "unexplained" force guiding the results.i

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How is this a bad argument?

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For the reasons I gave. Instead of producing any attempt to make a valid estimate you just guess - without taking into account things like the fact that there may be many mutatiosn that give adequate protection, and that there are millions of people who might acquire one or more of these mutations. The fact is that jsut saying that something seems very unlikely to you is a bad argument when you have absolutely no idea of how unliukely it really is.

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Besides I am not saying that the chances of one beneficial mutation is impossible just an entire series of them to give rise to this trait.

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And this has the same problems - and worse, if some other trait appeared instead you would make the same argument about that. So you really need to argue about the probability of ANY trait evolving.

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Thus your analogy to the lottery is incorrect. The analogy is more like the same person winning the lottery 1000 or more times..

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You don't provide any argument that would justify the "thus". Not surprisingly because you are completely wrong. There is nothing equivalent to the SAME person winning the lottery multiple times. All you are doing is picking out a pattern in hindsight - which would be quite easy to do with any random data. All that is required is that SOME traits evolve which involve multiple mutations - which will be interspersed among mutations contributing to other traits. Really you are making the same mistake again. What actually happened is "very unlikely" - but like lottery winners it is very likely that you will find SOME sequences that, in hindsight are "very unlikely" - just as it is unlikely that a particular person will win the lottery - but very likely that someone will win the lottery.Edited by PaulK, : Text trunvated on postinge

I would disagree a little. In the coin-tossing contest the rules guarantee a winner, and an opponent could argue that that invalidates the comparison (IMHO it only weakens it). In the case of the lottery it is pure statistics that is at work and that objection simply cannot apply.

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Now the chances of the first trait happening (whatever that was) is equivalent to winning the lottery...

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This is over-literal, in that you are taking an illustrative example as providing figures that are directly relevant which is incorrect. In fact it is more likely that there are several beneficial mutations which could start the development of wings, and it should be added that there are a huge number of individuals where the first mutation could have occurred. So the probability might be much higher than the chance of winning the lottery with a single ticket.

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Mutations happen at a certain rate (I guess this is quite high) for each creature. Most of the mutations are neutral and do not affect the population or creature substantially. Many of them are detrimental and the creature dies from disease.

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While detrimental mutations are more frequent than beneficial mutations it is not the case that all or even most cause the recipient to "die from disease". By definition any mutation that makes the recipient less likely to successfully produce offspring is detrimental - how this occurs is not part of the definition.

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So far the odds are not like the same person winning the lottery the same time (as I previously stated) because of the numerous failures (diseases, harmful, neutral mutations etc) over many,many generations, and also numerous sub-branches which were semi-successful at least.

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This at least is mostly right although it should be added that there are even other beneficial mutations involved. If we only looked at beneficial mutations we would see that those related to wing development are only part of the story.r

What I mean is that there were likely several other mutations that COULD have happened that would have started the development of wings. When discussing probabilities you have to consider not only the outcome that did happen but also those that did not happen but would have been as good.

I'd like to know how it is possible to tell that a bird's wing requires more "genetic information" than a feathered arm (including hand).The information "argument" is almost always a dishonest dodge. There is no valid measure of information involved. There's no argument to explain why evolution needs this (usually undefined) sort of "information" or any argument to explain why it cannot increase. That isn't always true but the alternatives I've seen are easily shot down.