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Bill Holbert  

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Author  Topic: Explaining the proEvolution position  
Admin Director Posts: 12565 From: EvC Forum Joined: 
I think you must have set some sort of record for repeating mathematical claims while doing so little actual math. It would make Percy very happy if you could make a mathematical presentation that supports your claims. Your very general and self evident equation doesn't do this in a way apparent to anyone.
 
Kleinman Member (Idle past 700 days) Posts: 136 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 http://isites.harvard.edu/...Papers/Weinreichetal2006.pdf 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 µ – 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)µ 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)µ 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)µ)^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)µ)^n)^nGA = (1  P(BeneficialA)µ)^(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)µ)^(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)µ, complementary rule 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)µ)^(n*nGA))*(1  (1  P(BeneficialB)µ)^(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.
 
Admin Director Posts: 12565 From: EvC Forum Joined: 
You're repeating the same selfevident math you presented in Message 214, and you've provided no values. To repeat what I just said, you must substitute actual values into your equation demonstrating evolution impossible, and if you don't then I will drop this thread into summation mode.
 
Dr Adequate Member Posts: 16069 Joined: Member Rating: 4.1 
Shouldn't that read "some members"?
But your math doesn't model this amplification in any way. Unlike, for example, my simulation.
Again, where's the math? All your middleschool math deals with so far is the probability of two mutations arising in a given period of time, it says nothing about how they get amplified.
 
Admin Director Posts: 12565 From: EvC Forum Joined: 
You've cited these inaccessible papers too many times. Until they're made publicly available, each time you cite them henceforth I will suspend you for 24 hours. About doing "the first fundamental steps of the calculation," you haven't made any calculations based upon the single equation you presented. Edited by Admin, : Grammar.
 
Kleinman Member (Idle past 700 days) Posts: 136 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.
 
Kleinman Member (Idle past 700 days) Posts: 136 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.
 
Admin Director Posts: 12565 From: EvC Forum Joined: 
I know you sent RAZD copies of your papers, but it isn't fair to the other participants to carry on a discussion about information to which they are not privy, and in any case, here at EvC Forum one must present the information one is discussing in the thread, not just provide a link, and especially not one that's behind a paywall. When making a point that depends upon information in one of your papers, please present that information in this thread.
You do still seem to be committing the sharpshooter fallacy when you mention a "correct mutation," and you haven't made any substantive response. Just so no one's confused let me mention that you evidently clicked the "reply" button to Modulous's Message 373, but you were actually replying to RAZD's Message 374.
 
Admin Director Posts: 12565 From: EvC Forum Joined: 
 
Kleinman Member (Idle past 700 days) Posts: 136 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 middleschool 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.  
jar Member Posts: 30934 From: Texas!! Joined: Member Rating: 1.6 
 
ringo Member Posts: 15766 From: frozen wasteland Joined: Member Rating: 2.5 
You can multiply nonzero probabilities until the cows come home and you'll always get a nonzero result. That's mathematics, son! Edited by ringo, : "never" > "always" (sign error)  
Coyote Member (Idle past 85 days) Posts: 6117 Joined: 
Evolution has been going along just fine, in its bumbling and haphazard way, for a couple of billion yearsas shown by many different lines of evidenceso any mathematical model that claims otherwise is just wrong. Religious belief does not constitute scientific evidence, nor does it convey scientific knowledge. Belief gets in the way of learningRobert A. Heinlein In the name of diversity, college student demands to be kept in ignorance of the culture that made diversity a valueStultisTheFool It's not what we don't know that hurts, it's what we know that ain't soWill Rogers If I am entitled to something, someone else is obliged to payJerry Pournelle If a religion's teachings are true, then it should have nothing to fear from science...dwise1 "Multiculturalism" demands that the US be tolerant of everything except its own past, culture, traditions, and identity.  
Tangle Member Posts: 6391 From: UK Joined: Member Rating: 3.5 
Well this is a wasted opportunity. Kleinman came along with a patronising teacherish attitude and stupidly extravagant claims which he refused to support. Had he chosen to take a different route by properly explaining his ideas on his specific issue of combination therapy for HIV treatment he might have gained some traction and maybe even been able to move a little way towards a ToE discussion. Instead he chose to piss everyone off. He should have been choked off at his 3rd or 4th post that said simply this: quote: That approach was never going to win him any friends. Je suis Charlie. Je suis Ahmed. Je suis Juif. Je suis Parisien. Life, don't talk to me about life  Marvin the Paranoid Android "Science adjusts it's views based on what's observed.  
Dr Adequate Member Posts: 16069 Joined: Member Rating: 4.1 
Kleinman promised us that his mathematics would overturn the theory of evolution, prove in particular that birds are not descended from dinosaurs, "unravel the bloody mess that evolutionists have made", overturn the theories of Haldane and Kimura, and prove the remarkable proposition that evolution slows down, rather than speeding up, as a result of additional selection pressures. And what do we get? Over the course of his 135 posts, he has presented us with a handful of trivial equations which would meet the approval of any evolutionary biologist, or indeed any middleschooler  accompanied by ever more vehement repetition of his grandiose claims. Insofar as he has gotten around to making any particular mistakes, I feel that they have been sufficiently answered in this thread, so it would be redundant to make a list; and unless he wishes to add some fresh errors in his summation, we may as well leave it at that. 


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