What have we accomplished?

The papers written by Alan Kleinman have none of the lunacy posted by Kleinman.You won’t find stuff like: ( Message 228 )Nor will you find anything supporting this assertion: ( Message 94 )Since it’s based on a failure to understand DNA evolution or how the models are used (and it isn’t to predict DNA evolution).Edited by PaulK, : Fix tag

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Your problem PaulK is that you have neither the mathematical training not the skills to recognize the mathematical relationship between the Markov chain models of DNA evolution and the "at least one" solution which was published here

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Think what you like about my mathematical ability. My understanding is quite sufficient to see that both the claims I quoted are obviously false and will not be published in a peer reviewed paper. If you are even writing such a paper.Whether you refuse to defend those claims because you know that they are false or you fear exposing your own lack of ability doesn’t matter either.

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I defend my mathematical claims with empirical evidence

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Well let’s see the empirical evidence that supports this nonsense, shall we? ( Message 228 )Explain how Jukes-Cantor leads to the conclusion that 1 base difference in a gene requires 50,000,000 generations and how you extrapolate that to 500,000,000 generations to get 1 base difference in each of 10 genes.Or don’t bother because the mathematics is quite enough to show that it is nonsense. And if you have the competence you claim you know that.

For the benefit of anyone actually interested in understanding the model. I’ll answer. But thanks for proving your incompetence.

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I've posted the links multiple times which explain the Jukes-Cantor model. Here's the one which explains how you derive the Jukes-Cantor model and that for a mutation rate of e-8, it takes 50,000,000 generations for just a single base in a single gene

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Wrong. It takes 50,000,000 generations to get to the equilibrium state, which is not a single mutations. To quote from the article:

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That is the probability of the particular mutation occurring as a function of the number of generations.

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Wrong. That is the probability of a base being different from the original state, accounting for the fact that it could mutate back. And it applies to all bases, not just one.

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Actually, if you understood this math, you would understand that is wrong. It is not the number of generations that should be plotted but the number of replications.

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No, it isn’t wrong in that either. If you understood the model you would know that,

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That probability will be close to 1 at about 1e8 replication

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No, the probability never rises above 0.75, as can be clearly seen if you look at the graph. See the quote from the article above.

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Since you don't understand the mathematics of Markov chains and joint probabilities of random events, you will not understand that each base difference will require another 1/(mutation rate) replications.

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In the model all bases are mutating independently at the same time, so after 50,000,000 generations each base is at equilibrium and has a 0.75 probability of being different from the original state. The idea that all but one base will remain the same is vanishingly unlikely. Feel free to do the calculation if you really feel like it.

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That's why it take 10*50,000,000 replications (for a mutation rate of e-8) to do the accounting for 10 base differences between 2 replicators.

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That’s why it clearly takes much less time than that. Though it will depend on the genome size.

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Study and understand this link and you will understand the Jukes-Cantor model.

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Indeed - don’t be like Kleinman who didn’t study it and got it all wrong

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But this model is only valid for an evolutionary process of one mutation at a time in a sequential evolutionary process

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By which you mean that your assertions are only valid in such a case. But that is obviously not what Jukes-Cantor is modelling.Failing to understand what the Jukes-Cantor model is actually modelling is bad enough. But the mathematical errors are also severe and fatal. Too bad you don’t understand the mathematics of Markov chains.Edited by PaulK, : No reason given.

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What a surprise, a fish-to-mammals aficionado thinks that DNA evolution is an equilibrium process. Just one more reason that shows you are a mathematically incompetent bungler.

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We are discussing the implications of the model which does reach an equilibrium. If you have to deviate from the model to make your point then you’re wrong.And that would be true even if your objection had merit.

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Are you sure you want to do this PaulK. I mean you are making one mathematical blunder after another. The Juke-Cantor describes DNA evolution at just a single site, not to all bases.
Models of DNA evolution - Wikipedia

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Only if a blunder is being right when Kleinman is stupidly wrong. The mathematical model describes how a single site evolves - and it is applied to all sites. The idea that only one site can mutate while all the others cannot change is not part of the model and has no basis in biology.

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Oh my, do you think the generation is the random trial for DNA evolution and not the replication? In your limited understanding of population genetics, do you think there are no instances where there are more than single offspring in a given generation? Another blunder on your part.

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Of course I realise that there can be multiple offspring, but that really doesn’t affect the point. For instance the number of siblings your father had makes no difference to your DNA.

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That's because at equilibrium the probability that the base at that site will be different than the base was originally will be 0.75 and the probability the base will be the original base is 0.25.

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I’m glad I managed to set you right on this.

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What that equilibrium point represents is the point where each possible substitution has occurred at least once at that site. Go back and read this paragraph from the link

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What that equilibrium point represents is the point where the initial state has no influence on the final state, and that is rather important for understanding why 50,000,000 generations is the longest time the model could show. There is no way it could give a time of 500,000,000 generations as you claimed. Indeed, without other evidence you couldn’t conclude any relationship at all if the genomes had diverged so far.

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So, show us how to apply the Jukes-Cantor model to the Kishony experiment. You won't

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There would be ways to apply it, but certainly it should not be applied to the particular mutations that grant resistance because the model is not about selection at all. It could, however be applied to other changes in the DNA - which will occur (yes, even in the Kishony experiment there will be other mutations).Your failure to understand what the model represents is your error, not a fault in the model.

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Only if a blunder is being right when Kleinman is stupidly wrong. The mathematical model describes how a single site evolves - and it is applied to all sites. The idea that only one site can mutate while all the others cannot change is not part of the model and has no basis in biology.

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Even to the non-homologous portions of the genome?

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The non-homologous parts - if there are any - are as free to mutateAs any other parts. What that has to do with the discussion I can’t say,

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Oh? So the Jukes-Cantor model only applies to a single individual?

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The Jukes-Cantor method is used to compare the genomes of individuals, as well as to consensus genomes constructed from multiple individuals. Molecular Phylogentics

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This is really pathetic. Each state of a Markov chain process only depend on the previous state of the system, all other states have no effect.

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You can’t even get the maths right. Before the equilibrium state the probability that the base has not changed from the original is > 0.25. That is a bias in favour of the original state.The rest of the consequences are also correct. You cannot derive any number of generations > 50,000,000 from the method, with the chosen parameter. And certainly not 500,000,000 however many changes there are in the genome.That you claim otherwise is just your ignorance.

So no substantive reply. What a surprise. Not.

And still no substantive answer.

And still no substantive answer.

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But I do thank you for helping me write my conclusion to my next paper.

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If you were had read and understood Models of DNA EvolutionAnd Jukes Cantor Model of DNA Substitutionyou wouldn’t have needed my help.Odd that someone would presume to call a model wrong without understanding it or what it models.

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And you don't know where the Jukes-Cantor and derivative models are wrong. I've given you all kinds of hints to where the problem is and why it doesn't predict the behavior of the Kishony experiment correctly.

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And still you persist in your misunderstanding. Too bad for you.

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You've been so helpful in my misunderstand until now.

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I’m sorry that I’m not a better teacher then.But until you understand that Jukes-Cantor models neutral evolution - because that is the dominant form of DNA evolution - you will remain hopelessly wrong on the subject.

The models we have were produced by people far better informed than I. You could actually try to understand them instead of dismissing them because you don’t understand them.

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Of course, you won't give us the explanation of how to include selection in the Jukes-Cantor model. You first have to understand how the Jukes-Cantor model works as written. And you don't

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Oh, I think I know, but it wouldn’t be very sensible for reasons that should be obvious. But you won’t see them.

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And you don't. If you want to know how to rewrite the Jukes-Cantor model to include selection, you will have to read my next paper which you so kindly helped lift the writer's block I was having in writing the conclusion to that paper.

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If there is a paper I very much doubt that it will include any such thing. And if it is presented as a correction to the model it will doubtless be laughed at.

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You fish to mammals aficionados really have wild imaginations.

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So you can’t see the obvious problems.

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you think you understand the Jukes-Cantor model, show us how to solve for the equilibrium time without assuming a Poisson distribution. You won't because you don't understand this math. I know how to do that and the math is easy.

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It’s funny then that you’re the one who keeps failing to understand. Or demonstrate any real mathematical ability.

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You have a sickness PaulK

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I think not.

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If you think that giving the correct explanation for the evolution of drug-resistance and the failure of cancer treatment should be laughed at, there is something wrong with your mind.

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I certainly don’t think that. That idea is a product of your vivid - and sick - imagination.Get help. You need it.