Do you really understand the mathematics of evolution?

I'm not. I'm trying to point to the error in the assumptions and you see that error as a feature. That's why you get garbage out of the predictions you make based on these models. If you had any skill at mathematical modeling, you could modify the Jukes-Cantor model (or the Felsenstein variant) and predict the behavior of the Kishony and Lenski experiments. But, you don't have either the training or the skill. Those models don't predict anything correctly. If I put a small piece of DNA from a banana that happens to be homologous with a small piece of your DNA, into these models, they are going to say you are closely related to a banana. If you think there is some valid prediction of DNA evolution from any of these models as written, present it. You won't because there is none. All you can do is blow smoke. You don't even understand that microevolutionary transitions are random events and because of this you have to multiply the individual probabilities to compute the joint probabilities of these events happening. You don't have any capability to do these simple probability problems. You are the one who makes one blunder after another.

I don't expect adulation from the fish evolve into mammals clique. In fact, when I shed some light on this topic, this clique acts like I'm opening Dracula's coffin after sunrise. If I get adulation from anyone, it will be the people who have to deal with drug-resistant infections and failed cancer treatments. You just run in the wrong circles. There are plenty of people who can do this math, they just don't happen to be in the fish evolve into mammals clique. If you mean by descent from some common ancestor in the primordial soup, even the mathematically incompetent should see the lunacy in that. It's that human and chimp from a common ancestor which requires a little math to show the irrationality of that concept. Of course, you could send some of your DNA and chimpanzee DNA into ancestory.com and see if you get a hit. If you do get a hit, don't forget to take into account all the misses. I publish my papers and occasionally I have done conferences. But I'm a clinical physician in private practice so everything I do, I pay out of my own pocket. My work is getting more and more attention and I have enough training and skill at doing mathematical modeling that I know this is correct. But when you tell people who believe that the earth is flat that it isn't, I don't expect an easy time convincing them. It's the people with skin in the game where I expect the breakthrough to occur. What I mean by that, those people who are trying to deal with drug-resistant infections, failed cancer treatments, herbicide, and pesticide resistance. These are the people who really need to have a correct understanding of DNA evolution, not some vague understanding of the process. On the other hand, this is a major embarrassment to those in the fish evolve into mammals clique in academia who can't even explain the simplest evolutionary experiments such as the Kishony and Lenski experiments. That would be like someone in engineering claiming they can explain the motion of a building or bridge in an earthquake but can't explain the mathematics of a mass and spring or a swinging pendulum. Where I got my engineering training, they wouldn't put up with that kind of crap for a minute. So straggle back to your hole or wherever you dwell and learn something about the physics and mathematics of evolution.

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I'm not.

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Yes you did. You tried to pretend that phylogenetic analysis was derived from the figures for a single base. Either you know that’s not true or you don’t know how the models are used.

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I'm trying to point to the error in the assumptions and you see that error as a feature

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It is not an error, but since you don’t understand DNA evolution or how the models are used you can’t see that. Too bad for you.

Let's see if you have stopped thinking about the mathematics DNA evolution and how it applies to phylogenic analysis. How many bases do you have to compare and be identical in order to say these two replicators are related. And relate this to the bacteria in the Kishony experiment. And by the way, I showed you how to draw the Markov Chain transition diagram for a second-order transition and you have no idea how to write the correct transition matrix for that case. Each increase in order of the Markov chain for DNA analysis introduces another instance of the multiplication rule but you need to understand introductory probability theory to recognize this and you don't. Are all of you in the fish evolve into mammals clique this poorly trained in mathematics? It certainly seems so. When you tell us how many bases need to match and how to account for the differences over time to determine relatedness such as in the Kishony experiment then we will know who understands DNA evolution and who does not. Oh, that's right, you think these Markov equations models drift. And you think that fish drift into mammals. You cherry-pick a few minuscule portions of a couple of genomes, find a few matches and say the species are related and this is too bad for those suffering from drug-resistant infections and failed cancer treatments.

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And you think that fish drift into mammals.

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More proof that you don’t understand DNA evolution and refuse to learn.

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You cherry-pick a few minuscule portions of a couple of genomes, find a few matches and say the species are related

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Do you really think that making things up like this is useful or constructive?

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... this is too bad for those suffering from drug-resistant infections and failed cancer treatments.

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I don’t think that making a fool of yourself on an obscure Internet forum helps them much either.

Let me do the math since you are too much of a nitwit to figure it out.Here is the situation again:Weed A is exposed to pesticide A in one region and develops resistance. Weed B is exposed to pesticide B in a different region and develops resistance.We bring Weed A and Weed B into the same region. How many generations before you get resistance to pesticides A and B in a single weed?The answer is one single generation. Doesn't take much math to figure it out. There will be at least some offspring from weed A and weed B, and some of those offspring will have the mutations for both types of resistance.This is a far cry from what you claim with your "multiplicative rule". It doesn't take another 3 billion generations. It only takes 1 generation.

You just don't get it poor Taq. You haven't done any math you ding-a-ling. You think the world is filled with only A variant weeds and B variant weeds. And suppose you also think that both variants are homozygous at both loci for each variant. So no matter which variants mate, you will get an AB offspring. Well you would be wrong because you are a mathematically incompetent dumb-cluck because even in that circumstance the multiplication rule applies.Let's see if I can explain it simply enough so that even a dumbbell math drop-out can understand how the multiplication rule still applies. Assume both fields have equal populations for simplicity so the frequency of A variants will be 0.5 and the frequency of B variants will be 0.5. Then, the probability of an A-B recombination event in a single recombination will be 0.5, not 1.0 because you can also have an A-A (probability 0.25) recombination event and a B-B (probability 0.25) recombination event. So your next argument is going to be, there are millions of recombination events going on here and surely, an A-B recombination event will occur in at least one of those recombination events. And you would be right. A fish evolves into mammals clique member can set up a scenario where he can breed herbicide-resistant weeds.That's why you should never give advice to farmers how to use herbicides. And this is why you are such a slow learner about the Kishony experiment. Imagine you haven't used any herbicides on your two fields but they have their 1.5e9 (assume they are diploid) genome replication descending from some herbicide sensitive founders. In that population, you are going to have 1 A variant resistant to one herbicide and 1 B variant that is resistant to the other herbicide. The probability of the A-B recombination event is not 0.5 as in your contrived scenario, it is 2*(1/1.5e9)*(1/1.5e9) in a single recombination event. But you argue, there are millions of recombination events, at least 1 will be an A-B recombination event. Why don't you try and do that math? Recombination has very little effect on DNA evolution and if you understood the math, you would understand why. Farmers are a lot smarter than you, they don't use two different herbicides on adjacent fields, select for the herbicide-resistant variants to each herbicide, allow those herbicide-resistant variants to repopulate their fields and allow them to recombine to give multi-herbicide resistant variants.On the other hand, maybe they would if they have the same understanding of evolutionary biology that you have. You really need to learn about the multiplication rule and how it affects not only DNA evolution but also random recombination.

We keep waiting for you to show us how it works. But all you present to us is one blunder after another. Why don't you present us with an example where this isn't being done? So, when you said the following in Message 183 about the single site Markov Chain model you think you are a mathematical genius? PaulK, I would recommend that you watch either the Harvard or MIT lectures on Markov Chain mathematics on YouTube (both are very good) except I don't think you will understand either lecture. So why don't you do a search on YouTube and find some lectures geared toward high school students? You might understand those lectures (if you work really hard at it). You in the fish evolve into mammals clique really aren't very good at this math thing. Of course, that explains why you don't understand DNA evolution. But you sure know how to blow smoke. The problem is that it is really stinky smoke.

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We keep waiting for you to show us how it works.

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As I keep telling you that DNA evolution is predominantly neutral.Until you grasp that point you will continue to blunder.You cannot make an accurate model until you understand what you are modelling.

Does fixation ever occur with neutral evolution? Because the existing Markov models (Jukes-Cantor and the derivatives models) don't go to fixation, they go to equilibrium with a distribution of bases at that site. For example, the Jukes-Cantor and Kimura models go to frequencies of A, C, G, and T = 0.25. If there is fixation, shouldn't the frequency of one of the bases go to 1 and the others to 0? Let's see if we can get you to start thinking again.

So you just ignore the scenario. I can see why since it disproves your entire thesis.I never assumed they would be homozygous. Heterozygotes for A and B would have 25% of the offspring with AB. Have you never heard of a Punnett square? Read what I wrote:Weed A is exposed to pesticide A in one region and develops resistance. Weed B is exposed to pesticide B in a different region and develops resistance.We bring Weed A and Weed B into the same region. How many generations before you get resistance to pesticides A and B in a single weed?The answer is one single generation. Doesn't take much math to figure it out. There will be at least some offspring from weed A and weed B, and some of those offspring will have the mutations for both types of resistance.I never said 100% of the population. I said one weed, or some of the offspring. Please read what I write. Imagine that I have. We are discussing my scenario, not yours. If your views of DNA evolution only work in very narrow scenarios then you have a serious problem.

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Does fixation ever occur with neutral evolution?

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Fixation of alleles does. But that can include a degree of polymorphismWith regard to individual bases however I think it will come down to the numbers. How long does it take to reach equilibrium? The mere fact that it would eventually is insufficient. The values seen within a population are not independent. The distant descendants of an individual may be divided between two or more populations - indeed that is exactly the case that phylogenetic analysis is looking for.Further, for more distant relatives sites that freely vary are not useful because they change too quickly. So it appears that the models are accurate on that score.

Is that what they are modeling with these Markov chain models? Ok, so you are saying that that distant relative has some base at a site, and over time that base mutates to the 3 other bases when it reaches equilibrium? That kind of sounds like fixation in reverse. With fixation, you have all possible bases at the given site initially and with fixation, all but one of the bases disappear from the population. So which happens in the real world, equilibrium, or fixation? With regards to equilibrium, what variable in these models affects the rate of reaching equilibrium? Could you give us an empirical example that demonstrates this?

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Is that what they are modeling with these Markov chain models?

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Obviously not. But if you are concerned with phenotypic change the distinction is important.

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Ok, so you are saying that that distant relative has some base at a site, and over time that base mutates to the 3 other bases when it reaches equilibrium?

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I am saying that it is possible for the site to be in equilibrium - with all four bases roughly equally represented - among the distant descendants. But at the same time the site is fixed in some or all of the populations existing at that time.

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So which happens in the real world, equilibrium, or fixation?

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Both. At the same time. As explained above. Fixed in some populations but not in equilibrium over all the descendants.

I thought you said they were modeling neutral evolution. That is drift, isn't it? And doesn't fixation occur with drift? So, what exactly are they modeling with these Markov chain models? Now you really have me confused. These models as time proceeds go to a condition when "all four bases roughly equally represented". So, are you saying that the genomes in the distant relative were already at equilibrium? And, how can the site be fixed and have "all four bases roughly equally represented" at the same time? How do they tell when the genetic sequence they put into the model is fixed or at equilibrium? And if a base is fixed in a population, does it over time go to equilibrium and if a site is at equilibrium in a population does it go to fixation?