What have we accomplished?

And your kind does? Where are the fish evolves to mammals kind scientific explanations of the Kishony and Lenski evolutionary experiments?You won't give it because your pseudo-scientific beliefs only self serve your atheism. You have chosen the wrong faith and it blinds you to the physical and mathematical facts of life.

AZPaul3 is right about one thing, the "Kishony and Lenski experiments means nothing to us fish-to-mammal aficionados". These experiments reveal your delusions. And I do want to thank you for your help in the conclusion section of my next paper. And you must think that peer-reviewers live in your imaginary, mythological aether because that is where the paper goes next. Somebody needs to teach you fish-to-mammals aficionados how to do Markov Chain processes to describe DNA evolution. You should watch this video:
https://www.youtube.com/watch?v=n1GxFKtxF-I
Then you will understand why the "Kishony and Lenski experiments means nothing to us fish-to-mammal aficionados". These experiments expose your delusions. And if your "fish-to-mammal aficionados" were really experts on evolution, they would give the correct mathematical explanation for these two experiments but they and you don't.

I'm not the one who thinks that fish evolve into mammals yet can't explain the simplest examples of evolution. It is you fish-to-mammal aficionados that have lost contact with reality and you have blindly bought into this irrationality. Next you will be telling us all the earth is flat. You need to come to your senses, the ignorance and delusions of the fish-to-mammal aficionados is harming people with drug-resistant infections and failed cancer treatments.

Don't any of you fish-to-mammal aficionados read anything beyond fossil tea-leaf reading journals and Mad magazine? Of course, you won't find any papers explaining the physics and mathematics of evolution in Nature and NEJM. That's why drug-resistant infections and failed cancer treatments continue to be a problem. If we had to depend on the fish-to-mammal aficionados to explain the physics and mathematics of evolution it would never happen. You are just too blind to see it.

So you think that the fish-to-mammal aficionados are the ones with the intellect? Where's the fish-to-mammal aficionados' mathematical explanation of the Kishony and Lenski experiments? Where are all the fish-to-mammal aficionados with any mathematical skills? Why don't you show your mathematical expertise and use the Markov chain mathematics and show that you are related to a banana?

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:
The basic science and mathematics of random mutation and natural selection
And I'm not going to explain that mathematical relationship to you here. You will have to wait until that paper is published. I've given you more than enough hints for you to figure it out yourself if you had the slightest skills in probability theory but you don't. But if you want, you can use the Jukes-Cantor model to show how closely related to bananas you are, we would be amused by that claim. None of the fish-to-mammals aficionados will be skeptical of that claim.

You've shown what your mathematical capabilities are, you have none. That's why you think you are related to bananas. I defend my mathematical claims with empirical evidence. You can start with the Kishony and Lenski evolutionary experiments. You prove your claims of the mathematics of Markov chains show you are related to bananas. That's strong empirical evidence you are presenting. Are all you fish-to-mammals aficionados so mathematically incompetent? At least Taq could figure out that it takes 3e9 replications for every possible substitution to occur on average once in every site of a genome for a mutation rate of e-9. Why stop there? You fish-to-mammals aficionados might actually learn something about DNA evolution.

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:
Jukes Cantor Model of DNA substitution
They do a step by step derivation of the Jukes-Cantor, Markov chain model. Then go down in the link and find this line: You get this plot: That is the probability of the particular mutation occurring as a function of the number of generations. 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. That probability will be close to 1 at about 1e8 replications. Otherwise, the rest of the derivation is ok. 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. 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. Study and understand this link and you will understand the Jukes-Cantor model. But this model is only valid for an evolutionary process of one mutation at a time in a sequential evolutionary process. It will not work if more than a single mutation is required to improve fitness. In other words, this model will predict the behavior of the Kishony experiment if only a single drug is used and the step increase in concentration only requires a single mutation for adaptation. And since the mutation rate is e-9 for that empirical experiment, it will take 5*(1/e-9) replications to give a fully drug-resistant variant. But, if Kishony were to use 2 drugs, or the increase in drug concentration requires 2 or more mutations to improve fitness, the Jukes-Cantor model will not work. You will have to wait to I publish my next paper if you want to know how that math is done. Of course, you won't understand that either.Edited by Kleinman, : Typo error

The only thing you have proven is that you are a direct descendant from bananas. And I suggest you submit your work for publication, in Mad magazine. 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. 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 Another blunder on your part. 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. 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. These are the two probability equations from that link:
P(A|A,,t)=1/4(1-e^{-8t})
and
P(different|A,,t)=3/4(1-e^{-8t})
That graph is a plot of the second probability curve. You are correct on this point (mark this day on your calendar). That curve approaches an asymptote of 0.75, not 1, and that is the equilibrium point for that site. Too bad that DNA evolution is not an equilibrium process. 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: So, show us how to apply the Jukes-Cantor model to the Kishony experiment. You won't. I've shown you how to use that model to predict the Kishony experiment because when the Jukes-Cantor model reaches equilibrium, all it shows you is the number of replication necessary to reach that equilibrium and that number is simply 1/(mutation rate). But feel free to use this model to demonstrate how you are descended from bananas. I'll wager I'll get a paper peer-reviewed and published on Markov chains and DNA evolution before you do. Why don't you write a paper using the Jukes-Cantor model showing that you are a direct descendent from bananas?

Go for it PaulK, show us how to use the Jukes-Cantor model and that you are a direct descendent to bananas.
quote: Even to the non-homologous portions of the genome? So that's why you think you are a direct descendent to bananas. Oh? So the Jukes-Cantor model only applies to a single individual? I'm beginning to believe that you are a direct descendant of bananas. Do you know how to solve the Jukes-Cantor model without assuming a Poisson distribution? I bet you don't. 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. So when are you going to submit your paper for publication that shows that the Jukes-Cantor model says you are directly related to bananas?

Nothing if you want to claim that you are related to bananas.

If you are dumb enough to believe that you can ignore the non-homologous portions of genomes to do DNA phylogenetics, that's the only reply you deserve. Go publish a paper showing you are a direct descendent of bananas.

Have you sobered up yet? All you have to do is cherry-pick the correct homologous gene from a banana, plug it into the Jukes-Cantor model, and voil, you have bananas in your family tree. Who knew that bananas grow on a tree?

jar will help you on you bananas-to-humans family tree. And you aren't the only one who thinks he's a banana!
https://www.youtube.com/watch?v=hmmi7QB33qk

Is jar going to teach us how fish evolve into mammals? jar, you need to lay off the juice. You are starting to suffer from the DTs.