Summations Only

Ah, I get it. You don't understand what it means for a mutation to be random.In Message 15 you wrote: So really, it isn't. Mutations aren't necessarily purely random like Brownian Motion.And the link you provided confirms that:"Darwinian Evolution Can Follow Only Very Few Mutational Paths to Fitter Proteins"The randomness of mutations is with respect to fitness, not randomness like Brownian Motion.There can be predictable causes of mutations, its just that you can't predict them from the perspective of the phenotype. But down at the genotypic level, you very well may be able to.So this game you're trying to play is to get to: "See, the probability is so low that those mutations couldn't have been random, so therefore the Theory of Evolution is wrong because it requires mutations to be random."The fact that we'd all see through that baloney is why you have to take this convoluted route of asking questions that you already know the answers to and trying to "help" us figure out what you're getting at.

I don't believe you. Natural selection (NS) does not change the probabilities. (well, I mean it can, but that's irrelevant to this)With respect to fitness (i.e. where NS operates), the mutations are random.With respect to the genome, the mutations may not be truly random like Brownian Motion is.

I think that they are not rare events.I think that they are random with respect to fitness.I think they may or may not be truly random like Brownian Motion, depending on the mutation. Me personally? No.Scientists? Maybe. Which mutation and which site? No, that's complete nonsense. Natural selection doesn't do stuff. I bet if I subjected my balls to some particular radiation that we could cause particular mutations that I could pass on to my offspring, but that's the kind of stuff that I'm calling irrelevant. No, not necessarily. And it depends what you mean by "random".Like, there is a series of events that causes a particular mutation to happen. It may be that once that process is kicked off, that it is inevitable that the particular mutation will occur. That would not be random. That would be repeatable and testable.And like the paper that you linked to said, for some mutations there are particular pathways that are more probable to occur than others.

quote:

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Darwinian Evolution Can Follow Only Very Few Mutational Paths to Fitter Proteins.

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"This implies that the protein tape of life may be largely reproducible and even predictable."

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Does that sound random to you?

And at that level is what I'm talking about when I say that you are wrong to look at these as purely random events on which you should be making probability calculations.Having a particular mutation at a particular site may or may not be random. Wrong. Natural Selection does not do stuff, it is an effect. But coin tosses are completely independent. What if the odds of a particular mutation occurring are dependent on previous states? Huh? That's like me asking you the frequency of rolling a 7 on a die, for any die with any number of sides for either a fair or unfair die... No, it isn't. It is a measurement of how many mutations of a particular type one would expect to see over a given amount of time. No, the environment changes the population sizes. Natural selection is the differential successes that the populations have because of the effect that the environment has on them.And if NS did change the probabilities of mutations occurring, then how could you treat those mutations as random? If I know what kind of radiation causes which mutations, and I do it on purpose, then those mutations would not be random. Have you tried doing a Google Scholar search for "non random mutations"?I'll tell you what; when you start providing evidence for your claims, I'll come back and start looking for sources to provide you. Right, and if whether or not a mutation occurs can be affected by previous states, unlike a coin toss, then those mutations do not occur by chance alone, i.e. they are not truly random.I'm pretty sure that I hit the nail on the head in my first reply to you: You're misunderstanding what the Theory of Evolution means by calling a mutation random.It does not mean that all mutations happen purely by chance, like you are using it.Natural Selection occurs at the phenotype, and from that perspective, mutations do appear to occur purely from chance (and even in this case there are exceptions). The ToE talks about mutations being random with respect to fitness.That "with respect to fitness" is the important part you are missing, which is allowing you to make the mistake of treating mutations as a result of pure independent chance that you can then do coin-toss-like probability calculations on at the genetic level.You can't treat all mutations as independent events and then provide a probability calculation to say that the odds of these particular mutations happening in series is impossible.

There's no reason to believe that at all.

There's no reason to believe that your probability equations are the general solution for rmns, and there is no reason to believe that your probability equations apply to all replicators.You have probability equations for particular replicators in particular situations. You've provided no evidence or argument for them applying as a general case or for all replicators.The closest you've come to it is: "show me one that doesn't", and that is neither evidence nor argument.