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Author | Topic: Explaining the pro-Evolution position | |||||||||||||||||||||||
Kleinman Member (Idle past 362 days) Posts: 2142 From: United States Joined: |
quote:rmns is suppressed long before extinction occurs. Even if the population can survive multiple different simultaneous selection pressures, you won't get the amplification necessary for rmns to work efficiently. That's what all the real, measurable and repeatable examples of rmns show. quote:So let's say you put an itsy bitsy little bit of thermal stress on the Lenski bacteria, do you think the evolutionary process will speed up (more beneficial mutations per generation) of slow down? Do you think the evolutionary trajectories and the mutations for adaptation depend on the intensity of selection? quote:Actually, you might find a target gene, you might get a spore that can survive. quote:There's no real difference in the math. You are still dealing with nested binomial probability problems. We can get a sense what goes with a selection pressure that target many genes with the Lenski experiment. The improvement in fitness is so small with each beneficial mutation that amplification is very difficult for that slightly more fit variant due to competition with other variants. Lenski is running his experiment in 10ml tubes. If he ran the experiment in 1 liter containers, you might see amplification occur more quickly because you are allowing for larger populations than his e7-e8. On the other hand, you can see from the video of bacteria evolving resistance on the large petri dish, you don't have the environmental resource limitation, only the targeted antibiotic selection pressure so that rmns process works very quickly.
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Kleinman Member (Idle past 362 days) Posts: 2142 From: United States Joined: |
quote:E. coli long-term evolution experiment - Wikipedia quote:That's about 1 beneficial mutation per thousand generations. If you think that's fast, would you argue about Haldane's dilemma? As for the Citrate metabolizer (e coli has alway been able to metabolize Citrate because it has a Krebs cycle), appeared at about generation 31500, not at 100 generations. The problem is not in the citric acid cycle for e coli, it is in the ability to transport citrate in the presence of oxygen. If I recall, those variants were spherical forms and so it may be that a mutation causing a defective cell wall allows the citrate to enter. And yes, my equations include the possibility for this type of more rare mutation.
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Kleinman Member (Idle past 362 days) Posts: 2142 From: United States Joined: |
quote:You think starvation is a soft selection pressure? All adaption by rmns requires lineages to address nested binomial probability problems. It doesn't matter whether they are antimicrobial agents, starvation, dehydration, thermal stress, predation, diseases, you name it. And why do you keep ignoring my question whether the intensity of selection alters the evolutionary trajectory to adaptation? If the same selection pressure is applied at low intensity, does it require different mutations for adaptation than if the selection pressure occurs at high intensity?
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Kleinman Member (Idle past 362 days) Posts: 2142 From: United States Joined: |
quote:So do you think the amplification time (starvation alone=>about 1000 generations per beneficial mutation) would speed up if a small thermal stress was added to his populations or would the number of generations per beneficial mutation increase? quote:Large numbers of low intensity selection pressures do not cause rmns to work, you get drift under these conditions.
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Kleinman Member (Idle past 362 days) Posts: 2142 From: United States Joined: |
quote:Of course, that's what selection pressures do. Selection pressures drive down populations unless the populations can adapt to those pressures. quote:Taq, there is no such thing as a probability value over 1. Why don't you watch some youtube videos on probability theory, eg Khan Academy https://www.youtube.com/watch?v=uzkc-qNVoOk&list=PL06A16C...
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Kleinman Member (Idle past 362 days) Posts: 2142 From: United States Joined: |
quote:But the populations are amplifying improving the probability that the first beneficial mutation will land on some member of a population quote:I disagree with you. I think combination selection pressures are the rule in nature. Drought, starvation, thermal stress, disease, predation,... quote:How large is that population size for dinosaurs? And remember, or learn, that rmns occurs on lineages, you know, common descent. And that quadrillion population is now reduced to a new lineage of 1 with that first beneficial mutation. And until that variant amplifies, the probabilities are very low that the 2nd beneficial mutation will occur on one of its descendants. quote:Well then how did Weinreich measure so many different variants from his one targeted antibiotic selection pressure? quote:What do you think you are seeing in the video. Do you think that all the colonies are giving the same variants? quote:The non-antibiotic resistant variants amplify until the resources of the plate are exhausted. They were not able to do enough replication trials to get that beneficial mutation.
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Kleinman Member (Idle past 362 days) Posts: 2142 From: United States Joined: |
quote:Fast enough for what? This is an experiment with only a single selection pressure. Somehow you have gotten in your mind that adding selection pressures will speed up this process. rmns is nothing more than nested binomial probability problems, that's the mathematical fact of life. And adding more selection pressures simply adds more binomial probability problems for the lineage to solve.
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Kleinman Member (Idle past 362 days) Posts: 2142 From: United States Joined: |
quote:Do you think the intensity of selection in the Lenski experiment is hard or soft? quote:Again? That would make Percy unhappy. quote:Now I would like to see some empirical evidence of that, you obviously have that. If that were true, why would sequencing HIV be of any value to identify drug-resistant variants? quote:Why might that happen?
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Kleinman Member (Idle past 362 days) Posts: 2142 From: United States Joined: |
quote:That's not your fixation calculation again? Stop being sneaky.
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Kleinman Member (Idle past 362 days) Posts: 2142 From: United States Joined: |
quote:Interesting paper. So do you agree with them when they said, "We conclude that the rarity of the LTEE mutant was an artifact of the experimental conditions and not a unique evolutionary event. No new genetic information (novel gene function) evolved." quote:The basic science and mathematics of random mutation and natural selection - PubMed The mathematics of random mutation and natural selection for multiple simultaneous selection pressures and the evolution of antimicrobial drug resistance - PubMed Random recombination and evolution of drug resistance - PubMed I did the first fundamental steps of the calculation earlier in the thread but you can see the full mathematics in the publications. And this mathematics is not based on near extinction. These calculations simply describe what populations have to do to accumulate beneficial mutations in order to adapt to selection pressures.
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Kleinman Member (Idle past 362 days) Posts: 2142 From: United States Joined: |
This message is a response to post 365, 366, 367
quote:You think that drought, starvation, thermal stress, disease, predation,... are conservative selection pressures? NOT quote:Yes, one of the many things you do not know. I thought the theory of evolution was settled science? Well, at least you know that fixation and amplification aren't the same thing now. quote:It is your fixation calculation again. quote:Are you sure about that, it has been a while since I read his papers but I think he uses 10%. So if you think he increases his intensity of selection the evolutionary process will go faster or slower? quote:Actually elementary. So I left off in the mathematics after computing the probability of mutation A occurring in the population. I was just about to compute the probability of mutation B occurring on a member with mutation A. I think I'll start this mathematics tomorrow. quote:Reducing selection pressure only increases the diversity of populations. No directional selection there. quote:Adaptive evolution, meet nested binomial probability problems and the multiplication rule of probabilities.
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Kleinman Member (Idle past 362 days) Posts: 2142 From: United States Joined: |
quote:A review: We are presenting the mathematics of the simplest case of rmns, that is a single selection pressure targeting a single gene. The derivation of the equations is done in the context of an empirical example of rmns, that of a bacteria evolving resistance to an antibiotic. This empirical example can be found at icommons.harvard.edu In the Weinreich paper he measured the mutations which evolved resistance to a particular antibiotic. There were a wide variety of variants which evolved resistance but all had in common in that it took 5 mutations to evolve high resistance to the antibiotic. The first beneficial mutation determined the evolutionary trajectory for that variant and the next 4 beneficial mutations required for that evolutionary trajectory. The derivation for the mathematics of rmns for this problem will be done in general terms. That is that a sequence of mutations A,B,C,D and E occur where each ensuing beneficial mutation gives increasing resistance (and therefore improved fitness to reproduce) to the antibiotic selection pressure. The first step in doing the mathematics of this stochastic process is to recognize that there are two random trials occurring in rmns. The two random trials are the replication (where the two possible outcomes are that a mutation occurs or does not occur at the particular site) and the mutation itself is a random trial (where only a particular mutation gives benefit). The possible outcomes for a mutation are written as follows: P(-∞ < X < +∞) = P(Ad) + P(Cy) + P(Gu) + P(Th) + P(iAd) + P(iCy) + P(iGu) + P(iTh) + P(del) + = 1 Where Ad, Cy, Gu and Th represent substitutions of the particular bases, if the base is preceded by an "i", it means the insertion of that base, "del" means deletion of the base and the "..." term represents all other mutations possible. Included in that "..." term would be the mutation that caused the Citrate metabolizer in the Lenski experiment. We now define a term P(BeneficialA) where the value of P(BeneficialA) is determined by the particular mutation which gives benefit. If the beneficial mutation is a substitution of Ad, P(BeneficialA)=P(Ad), if the beneficial mutation is an insertion of Th, P(BeneficialA)=P(iTh) and so on. We then define — the probability (frequency) that an error in replication will occur at a particular site in a single member in one replication. Then the probability that mutation A occurs in a single member in a single generation is: P(A) = P(BeneficialA) We then use the complementary rule of probabilities to compute the probability that mutation A will not occur in a single member in a single replication. P(Ac) = 1 - P(A) = 1 - P(beneficialA) where P(Ac) is the probability that mutation A will not occur. We can then define "n", the population size and using the multiplication rule of probabilities, compute the probability that mutation A will not occur in "n" replications. P(Ac) = (1 - P(BeneficialA))^n We can then define "nGA" the number of generations the population "n" replicates for the probability of mutation A to occur. And again using the multiplication rule gives: P(Ac) = ((1 - P(BeneficialA))^n)^nGA = (1 - P(BeneficialA))^(n*nGA) And to obtain the probability of mutation A occurring in a population size "n" in "nGA replications we again use the complementary rule which gives: P(A) = 1 - (1 - P(BeneficialA))^(n*nGA) Note that n*nGA is simply the total number of replication trials for the mutation A to occur. With sufficient numbers of trials, we finally get a reasonable probability for mutation A to occur on some member of the population. That member with mutation A is the progenitor for a new lineage who are candidates for mutation B, that is a new branch on a phylogenetic tree. However, there is only one member to start with. This member must replicate for many generations so that there are a large number of members with mutation A, then there will be a reasonable probability that one of the members with mutation A on replication will get mutation B. The mathematics is done in an analogous manner as computing the probability of mutation A occurring in a population size "n" in "nGA" generations but in this case n->nA the number of members with mutation A, nGA->nGB, the number of generations the members with mutation A replicate. The calculation goes as follows: P(B) = P(BeneficialB), complementary ruleP(Bc) = 1 - P(beneficialB), multiplication rule P(Bc) = (1 - P(BeneficialB))^nA, again multiplication rule P(Bc) = ((1 - P(BeneficialB))^nA)^nGB = (1 - P(BeneficialB))^(nA*nGB), and finally complementary rule P(B) = 1 - (1 - P(BeneficialB))^(nA*nGB) And to compute the joint probability of some member of the population getting both mutation A and B, we use the multiplication rule: P(A)P(B)= (1 - (1 - P(BeneficialA))^(n*nGA))*(1 - (1 - P(BeneficialB))^(nA*nGB)) The calculation for the mutations C,D and E occurring is done in the exact same manner. What is seen that in order for this evolutionary process to occur, we have a cycle of beneficial mutation followed by amplification of that mutation in order to improve the probability of the next beneficial mutation. That rate of amplification is strongly dependent on environmental conditions, that is the other selection pressures that are acting on the population at that time. The simplest example of how this cycle of beneficial mutation followed by amplification of the mutation can be disrupted is by applying a second selection pressure simultaneous with the first selection pressure. Not only does this make the evolutionary trajectory more complex, the amplification process for any beneficial mutation for one selection pressure is interfered with by selection pressures targeting other genetic loci. One can easily substitute values into the above equations using a spreadsheet program using different values for the mutation rates and populations sizes and determine the probabilities. An interesting extension of this mathematics is determining the probabilities when more than a single selection pressure are acting at the same time where it requires 2 (or more simultaneous) beneficial mutations in order to improve fitness. Anyone here besides me want to try to do that computation? Perhaps you can find a way to rescue your theory of evolution from the multiplication rule of probabilities. And feel free to substitute 1 for any of the P(Beneficial) terms.
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Kleinman Member (Idle past 362 days) Posts: 2142 From: United States Joined: |
quote:RAZD, which do you think will be larger, the mutation rate or the beneficial mutation rate? We know with mathematic certainty that the P(Beneficial) term can only have a value between 0 and 1. If you let P(Beneficial) = 1, you bracket the solution with the upper limit of the probability. Knowing or not knowing the exact value of P(Beneficial) does not have any mathematical significance on the physics of rmns. quote:Certainly, environmental conditions have a significant impact in determining whether a mutation is beneficial or not. But it doesn't change the physics of rmns and that physics consists of nested binomial probability problems linked by the multiplication rule of probabilities. quote:That's fine, but you need to understand that in order for a lineage to accumulate a set of beneficial mutations, it must do so by overcoming a set of binomial probability problems linked by the multiplication rule. If you have an interest in solving medical problems such as less than durable cancer treatments, you need to understand the physics you are dealing with. This will become even more important as the use of targeted cancer therapies are developed. Targeted selection pressures give the easiest binomial probability problems for a replicator to solve by rmns. If you are going to gamble with replicators, you had better learn the rules of the game if you want to shift the odds in your favor. quote:True as well. That's why any injury to cell in the embryonic state are transmitted to all the descendent cell. But even the normal cells in our body can develop minds of their own and become cancers because of the huge numbers of replication from zygote to adulthood. And these cells, if they are not driven to extinction by targeted therapy will still come back and kill the person. We see that with the use of estrogen blocking agents in the treatment of breast cancer. The cells are suppressed until a variant appears that's no longer estrogen sensitive. A second drug targeting these cells would slow if not stop this process. quote:If you have no experience in the mathematics or probability theory, these papers will definitely confuse you. That's why when I looked for a journal to publish these papers, I wanted editors and peer reviewers who had experience with this type of mathematics. If you want to understand this mathematics, it's not that difficult but it requires a little training and some practice. If you want me to point you to sources, youtube has some good lectures on the subject. Master the mathematics of coin tossing and dice rolling and these calculations will become much clearer to you. If you have interest in improving cancer treatments and preventing antimicrobial drug resistance, learn this math. quote:And these publications I sent you explains how natural selection does this. Mutations occur all the time on replication but in order to improve fitness to reproduce, it has to be the correct mutation occurring on the correct individual to accomplish that task. quote:But in order to improve fitness requires specific patterns of mutations. Natural selection tries to select these pattern by a cycle of beneficial mutation followed by amplification of the beneficial mutation to improve fitness to reproduce. quote:Again I ask you, which is larger, the mutation rate or the beneficial mutation rate? And before you say my model is wrong, you need to understand where it is wrong and right now you are confused. When my last paper was peer reviewed, I was asked to point out why Haldane's and Kimura's models were not correct. I studied and understood their models and calculations. In fact, I even wrote an exact solution to Haldane's model to check if his approximate solution was accurate. Haldane and Kimura don't have a problem in their mathematics, they have a problem in their physics. I explain the problem in the paper on rmns with multiple simultaneous selection pressures.
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Kleinman Member (Idle past 362 days) Posts: 2142 From: United States Joined: |
quote:I've posted the equations including the fundamental steps and the derivation of the equations in post 377. This is the physics and mathematics which governs rmns, it consists of nested binomial probability problems linked by the multiplication rule of probabilities. You don't need to go to the links to learn this mathematics, I've given it to you here. Now let's hear the repetitive arguments of evolutionists that it doesn't work this way despite the fact that all real, measurable and repeatable examples of rmns obeys this mathematics.
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Kleinman Member (Idle past 362 days) Posts: 2142 From: United States Joined: |
quote:If the subpopulation with mutation A is large enough, you may get more than one member getting mutation B. But the real amplification process starts with that progenitor(s) with mutations A and B start replicating. A single member with mutation A and B in 30 generations of doubling will e9 members in the ideal case. quote:Amplification occurs when the number of replications increases for a particular variant, that doesn't necessarily happen when the relative frequency of variants in populations change. You can get fixation without any amplification just by killing off all variants except one. You need to recognize that in the stochastic process of rmns, the replication is the principle trial for this phenomenon. quote:Now Doc, I take offense to you calling this middle-school math. This is elementary school math and don't forget it. You are correct, these are not rate equations. These equations only predict how many replications are required for a particular mutation to occur on a particular individual in the population. The rate at which these probabilities change are strongly dependent on the selection conditions. The video of bacteria evolving resistance to an antibiotic shows a rapid rmns process for a single selection pressure targeting a single gene. The Lenski experiment on the other hand takes decades to evolve because of the single selection pressure targeting multiple genetic loci. Computing rates of change of relative frequencies of variants is not going to give you the correct time relationship.
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