Rebuttal To Creationists - "Since We Can't Directly Observe Evolution..."

AZPaul3:

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Taq has his fish and he's playing with it.

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Taq likes to tell fish stories.Did you hear the one about the one-armed fisherman? He was telling his friend about one of the fish he caught. He held up his arm and said, "It was that long"!

AZPaul3:

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Sounds a lot like the math you use.

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AZPaul3 will now explain the physics and mathematics of the Kishony and Lenski biological evolutionary experiments. He won't because unlike the one-armed fisherman, AZPaul3 doesn't have a leg to stand on.

Percy:

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You're claiming it, you explain it. First provide the specific equation from Haldane's paper that you're referring to, then convert it into units of Joules.

Kleinman:

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I already have but I'll do it again.

Percy:

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There was no equation in what followed. Please present the Haldane equation you're talking about, then convert it to Joules. Using math equations.

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OK, here's Haldane's frequency equation again:pnA + qna = 1Do this in the context of the Lenski experiment.Call the total amount of energy available in the glucose for survival and replication is "T". We can use units of Joules though I prefer the units of (stones*furlongs^2)/(fortnight^2). That energy is sufficient to support 495 million replications of his E. coli. Let n_p = the total number of replications of the p variant in one day's growth. Let n_q = the total number of replications of the q variant in one day's growth. Thenn_p + n_q = 495,000,000 and n_p/495,000,000 + n_q/495,000,000 = 1Now, let the amount of energy for a single replication of a p variant be er_p and the energy of replication of the q variant be er_q. Note that er_p < er_q and that energy difference is the selection parameter. Then, applying the first law,n_p*er_p + n_q*er_q = T and if you want the equation in the form of Haldane's frequency equation, divide by T which gives:(n_p*er_p)/T + (n_q*er_q)/T = 1

Kleinman:

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Now the effective population size can be slightly smaller than the actual population size under certain circumstances that I'm sure you know what they are. Remind me again what the population size you use is. Wasn't it 100,000? That gives the generations to fixation of that mutant gene of 4*100,000=400,000 generations.

Taq:

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Ne is usually drastically smaller than N.

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By comparing the likelihood of various demographic models, we estimate that the effective population size of human ancestors living before 1.2 million years ago was 18,500, and we can reject all models where the ancient effective population size was larger than 26,000.
Just a moment...

Kleinman:

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That gives the generations to fixation of that mutant gene of 4*100,000=400,000 generations. That really helps. Your lower division equation gave an estimate of 900,000 generations for the fixation of a neutral mutation. How many generations since the divergence of humans and chimps from the common ancestor?

Taq:

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I already explained this a previous post. Let's use an effective population size of 20,000 as described above. That would be 80,000 generations to fix a neutral allele, and at 25 years per generation that would be 2 million years. This means the earliest populations in the human lineage that had just split away from the chimp population would be fixing neutral mutation that occurred 2 million years before that. Every generation after that would be fixing neutral mutations that occurred 2 million years before them. Where is the problem?

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Let's do a little math. 2,000,000 years/25 years/generation = 80,000 generations. Congratulations, you've fixed 1 neutral mutation.

Kleinman:

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You still haven't figured out that different combinations of adaptive mutations give different lineages on different evolutionary trajectories.

Taq:

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You still haven't figured out that lineages combine in a sexually reproducing population. Your genome is the merger of your father's and mother's lineage. Every single birth is a mixture of lineages.

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Since you won't attempt to do the mathematics of recombination, let's talk about a simpler case, cells that do replication by mitosis, such as cancer cells. How would you compute the probability of a mutant drug-resistant cancer cell line evolving from an original progenitor cancer cell? You do know that cancer cells are diploid and they reproduce by mitosis. And how does this affect the possible success or failure of targeted cancer therapies?

Kleinman:

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Taq likes to tell fish stories.

Taq:

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Fish stories? Who is the one claiming that 98% of the human genome outside of coding regions is one monolithic sequence that is all moving towards fixation as a single unit in a way that magically excludes any new mutations that occur?

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Don't be silly. I don't think the non-coding region is one monolithic sequence. This is the region that contains the control system that turns on and off the genes in the coding region that allows differentiation of the original stem cell into a fully formed adult and controls all the biological processes in that individual to sustain life.You are squirming like a worm, you must be fishing.

Kleinman:

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OK, here's Haldane's frequency equation again:
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pnA + qna = 1

Percy:

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That's merely an identity. Since any locus can possess only one of A or a, then by definition p(A) + p(a) = 1 by definition.

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Yes, the math and equation is quite straightforward.

Kleinman:

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Call the total amount of energy available in the glucose for survival and replication is "T". We can use units of Joules though I prefer the units of (stones*furlongs^2)/(fortnight^2). That energy is sufficient to support 495 million replications of his E. coli.

Percy:

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Where does the 495 million figure come from?

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My bad, I thought you had some familiarity with the Lenski experiment. It comes from the Lenski Michigan State website:
DM25 Liquid Medium

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The basic medium used for propagating the long-term lines is Davis minimal broth (Carlton and Brown 1981*) supplemented with glucose at a concentration of 25 mg per L, which we refer to as DM25. This medium supports a stationary-phase density of about 5 x 107 cells per ml for the founding strain of E. coli B.

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Culture volume is 10 ml, and cultures are maintained in 50-ml Erlenmeyer flasks loosely capped with small inverted beakers. Flasks are incubated at 37C and 120 rpm. Cultures are propagated daily by transferring 0.1 ml of each culture into 9.9 ml of fresh medium.

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Kleinman:

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Now, let the amount of energy for a single replication of a p variant be er_p and the energy of replication of the q variant be er_q. Note that er_p < er_q and that energy difference is the selection parameter.

Percy:

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Selection is a function of expression and adaptation, not how much energy is used in microbiological processes. And could you either learn latex or at least how to do subscripts? Are you trying to say er_p and er_q?
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And you're not deriving anything mathematically. You're simply declaring that the energy is er_p and er_q, so this is meaningless and I have no idea why you think it's useful as a conservation of energy equation. There's certainly no useful conclusions to be drawn from it:

(n_p*er_p)/T + (n_q*er_q)/T = 1

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Hey, you are the one that wanted me to put the Haldane equation in terms of energy! Do you think the p variants require more energy to replicate than the q variants? And I know, this equation is not needed, that's why I didn't do the solution for the Lenski experiment using that formulation. Haldane's version of the energy equation works just fine. Haldane's equation is normalized. This is a trivially simple conservation of energy process.And you obviously were able to understand my notation. Why should I spend my time learning another formatting protocol when you are still confused about the physics and mathematics of Darwinian evolution? Will making my notation prettier make it easier to understand? I doubt it.

Kleinman:

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OK, here's Haldane's frequency equation again:

Taq:

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You could use any frequency distribution you want. If we divided the world into those who prefer vanilla ice cream and those that prefer chocolate ice cream we could get the same comparisons. That doesn't mean preference for ice cream flavor is a conservation of energy process.

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You are confused again on this issue. Not all frequency equations are conservation of energy equations. Some frequency equations are conservation of ice cream equations (that's conservation of mass). Haldane's frequency equation pertains to the conservation of energy. What did they actually teach you about the laws of thermodynamics in your survey of physics course?

Kleinman:

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Let's do a little math. 2,000,000 years/25 years/generation = 80,000 generations. Congratulations, you've fixed 1 neutral mutation.

Taq:

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First, there are about 50 mutations that fix in every generation, not 1. Second, every generation has new neutral mutations, and some of those neutral mutations will begin to move towards fixation. The first generation in our lineage would have already had neutral mutations they inherited from their ancestors 2 million years ago.

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LOL!

Kleinman:

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Since you won't attempt to do the mathematics of recombination,

Taq:

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Why do any mathematics for someone who claims recombination doesn't even exist?

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I'm starting to wonder if Taq actually exists.

Kleinman:

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I don't think the non-coding region is one monolithic sequence.

Taq:

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Yes, you do. You claimed that all non-coding sequence is a single allele that moves towards fixation together.
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It is like an assembly line. If it takes 24 hours for Ford to make a specific car on a single assembly line, start to finish, does this mean that they only produce one car every day on that assembly line? Obviously not. As the car is finished at one station it is passed to the next, and a new car is placed at the previous station. They are all lined up behind each other moving along the assembly line. Fixation of neutral mutations work the exactly same way.

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Is Taq now an advocate for intelligent design? Living things are now made on a Ford assembly line.

Kleinman:

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I don't think the non-coding region is one monolithic sequence.

Taq:

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Yes, you do. You claimed all non-coding sequence was a single allele that moved towards fixation together.

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Now Taq is claiming that all 54.5 of the mutations in a genome don't get fixed. Taq, would you make up your mind?

Kleinman:

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LOL!

Taq:

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That's all you got?

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Actually, no. It makes me really sad that a microbiologist can't explain the evolution of antimicrobial drug resistance.

Kleinman:

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Is Taq now an advocate for intelligent design? Living things are now made on a Ford assembly line.

Taq:

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Given your lack of response, are you tacitly agreeing that we should see fixation of neutral mutations in each generation?
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Or are you still so confused that you think only 1 mutation can move towards fixation at a time, and that all other neutral mutations can not begin to move towards fixation until that 1 neutral mutation is fixed?

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Watch out, there's a stampede of neutral mutation coming down a Ford assembly line. Obviously, they need better quality control.

Kleinman:

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Now Taq is claiming that all 54.5 of the mutations in a genome don't get fixed.

Taq:

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That's what I have claimed all along.

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How many neutral mutations are lost?

Kleinman:

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It makes me really sad that a microbiologist can't explain the evolution of antimicrobial drug resistance.

Taq:

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In the case of beta-lactam resistance, one pathway is mutations produce an enzyme capable of breaking down the antibiotic.

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Pathway? What pathway? How do mutations take a pathway?

Taq:

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What does this have to do with human evolution?

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Don't both humans and bacteria have DNA? Do human mutations have a pathway?

Kleinman:

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Watch out, there's a stampede of neutral mutation coming down a Ford assembly line.

Taq:

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Then I will assume you accept the claim that around 50 neutral mutations reach fixation in each generation.

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On what do you base that assumption?

Kleinman:

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How many neutral mutations are lost?

Taq:

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(N*u)-u

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where N is the population size and u is the number of mutations per individual per generation.

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You better use Latex or you will get Percy angry. So for human evolution using your equation you get:
(100,000*54.5)-54.5
Is that new math?

Kleinman:

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Pathway? What pathway? How do mutations take a pathway?

Taq:

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Here you go:
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click here

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Percy says you shouldn't just post links. You need to post a quote from the link.

Kleinman:

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Don't both humans and bacteria have DNA?

Taq:

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That doesn't answer my question.
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What does the evolution of antibiotic resistance in bacteria have to do with human evolution?

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Are implying that bacteria and humans both don't have DNA?

Kleinman:

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On what do you base that assumption?

Taq:

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Your inability to address what I wrote.

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Did you write something about how mutations take a pathway? All I saw was a link. I can post a link to a paper that shows how bacteria take a mutational pathway and it correctly predicts the behavior of the Kishony and Lenski biological evolutionary experiments. Here the link:
The basic science and mathematics of random mutation and natural selection
Here's a quote from the paper.

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The mutation and natural selection phenomenon can and often does cause the failure of antimicrobial, herbicidal, pesticide and cancer treatments selection pressures. This phenomenon operates in a mathematically predictable behavior, which when understood leads to approaches to reduce and prevent the failure of the use of these selection pressures. The mathematical behavior of mutation and selection is derived using the principles given by probability theory. The derivation of the equations describing the mutation and selection phenomenon is carried out in the context of an empirical example. Copyright © 2014 John Wiley & Sons, Ltd.

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Kleinman:

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So for human evolution using your equation you get:
(100,000*54.5)-54.5
Is that new math?

Taq:

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Yes, of the ~5 million neutral mutations that occur in that generation all but ~50 will be lost at some point after that generation. Of course, this depends on the mutation remaining neutral and not being influenced by linkage disequilibrium. At the end of the day, the equation for neutral fixation is an idealized genome and population, something akin to the ideal gas laws.

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So, every member of your population gets the same 54.5 mutations every generation. Does every human on earth have the same neutral mutations as every other human?

Taq:

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Google "evolutionary pathway". Start reading.

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I don't need to, I already know how to do the mathematics of evolutionary pathways. You should learn how to do that math as well, you being a microbiologist and all.

Kleinman:

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Are implying that bacteria and humans both don't have DNA?

Taq:

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What does the evolution of antibiotic resistance in bacteria have to do with human evolution?

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You need to learn that the mathematics of the evolution of adaptive alleles is the same for all replicators, neither ploidy nor recombination changes that fact. You just won't accept that fact because it refutes the notion of universal common descent.

Kleinman:

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Did you write something about how mutations take a pathway?

Taq:

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I wrote this:
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I already explained this a previous post. Let's use an effective population size of 20,000 as described above. That would be 80,000 generations to fix a neutral allele, and at 25 years per generation that would be 2 million years. This means the earliest populations in the human lineage that had just split away from the chimp population would be fixing neutral mutation that occurred 2 million years before that. Every generation after that would be fixing neutral mutations that occurred 2 million years before them. Where is the problem?
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And this:
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Given your lack of response, are you tacitly agreeing that we should see fixation of neutral mutations in each generation?
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Or are you still so confused that you think only 1 mutation can move towards fixation at a time, and that all other neutral mutations can not begin to move towards fixation until that 1 neutral mutation is fixed?

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Why don't you try to model a real experiment such as the Kishony or Lenski experiment? Describe how the evolutionary pathway works in either of those experiments and see if any of your models fit these experiments. That's what a scientist would do.

Kleinman:

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So, every member of your population gets the same 54.5 mutations every generation.

Taq:

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That's what fixation means.

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So every generation every new member of the population gets 54.5 new unique mutations to their genome while 54.5 of the neutral mutations they inherited from their parents are fixed and these same 54.5 neutral mutations are identical to every new member of the population. And the next generation, their offspring will get 54.5 new neutral mutations that are unique to each individual while 54.5 of their inherited neutral mutations will be fixed in every member of the population. And that happens generation after generation for tens of thousands of generations. You have quite an imagination.

Kleinman:

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Does every human on earth have the same neutral mutations as every other human?

Taq:

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No, they don't. As already described, neutral mutations occur at different points in the past so they are all at different points in their journey towards either being lost or becoming fixed.

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How many neutral mutations fixed in the Lenski experiment after 70,000 generations?

Kleinman:

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You need to learn that the mathematics of the evolution of adaptive alleles is the same for all replicators, neither ploidy nor recombination changes that fact.

Taq:

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Then you don't know how the mathematics or biology of adaptive alleles works.

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Then why has the math that I"ve presented been able to predict that each step in the Kishony experiment would take a billion replications? This paper was published years before Kishony performed his experiment. And this same math explains why his two drug experiment doesn't work and what it would take for that experiment to work. This math and physics is way over the head of someone trained in microbiology. That's why microbiologists can't explain the physics and mathematics of the evolution of drug resistance.

Taq:

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In asexual organisms you can't combine mutations that happen in independent lineages. In sexually reproducing species you can combine mutations that are in contemporaneous genomes. That makes a massive difference in how adaptive alleles evolve.

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Taq now thinks that recombination can recombine mutations at the same genetic loci of both parents. How did you get so confused on this subject?

Kleinman:

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Why don't you try to model a real experiment such as the Kishony or Lenski experiment? Describe how the evolutionary pathway works in either of those experiments and see if any of your models fit these experiments. That's what a scientist would do.

Taq:

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So you aren't going to address what I said?

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I'm not interested in some fantasy model that you dredge up in your confused imagination. If you think your ridiculous model fits reality in any way, apply it to a real-world, measured, and repeatable experimental example. You won't because you know you are blowing smoke.

Kleinman:

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So every generation every new member of the population gets 54.5 new unique mutations to their genome while 54.5 of the neutral mutations they inherited from their parents are fixed and these same 54.5 neutral mutations are identical to every new member of the population.

Taq:

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The 54.5 neutral mutations that fix in each generation would have entered into the gene pool hundreds of thousands or millions of years before they became fixed. Those mutations would have been found in nearly everyone just prior to reaching fixation. Are we agreed?

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Do microbiologists know how to computer program? Take your model, and start with a population that has almost identical genomes except for each member in that population has unique random mutations scattered at different sites in the genome. Randomly choose two parents out of that population. Choose a mutation rate. Randomly select portions of each genome and recombine those portions to create a new genome while adding new unique random mutations to that genome based on your chosen mutation rate. Do that to the entire population until you create a new generation of descendants. Repeat that cycle and measure how many neutral mutations are fixed in the population as a function of the number of generations.

Kleinman:

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How many neutral mutations fixed in the Lenski experiment after 70,000 generations?

Taq:

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An asexual species with a very different mutation rate can not accurately model a sexually reproducing species with a different mutation rate.

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You are right about that. Mutations in an asexually reproducing population can only be lost by selection. On the other hand, mutations can be lost in a sexually reproducing population if the wrong allele is passed in the recombination process. So do a computer simulation of your model and see if you can verify your claims.

Kleinman:

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Then why has the math that I"ve presented been able to predict that each step in the Kishony experiment would take a billion replications?

Taq:

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The mistake you keep making is in forgetting that sexually reproducing species merge lineages. You keep claiming that beneficial mutations have to happen sequentially in an isolated lineage. This isn't the case in sexually reproducing populations. You also make the mistake of thinking every single adaptation will have the same rate as antibiotic resistance. There is no reason to think this is true as shown by a thousand fold difference for the rate of antibiotic and phage resistance in E. coli.

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Well, that is some progress. At least you are admitting that my model of adaptive evolution is correct for asexually replicating organisms. You should also agree that this model is correct for replicators that replicate by mitosis such as cancer cells. Of course, adaptive mutations have to occur sequentially. Don't you believe that a series of microevolutionary changes add up to a macroevolutionary change? That's almost correct. Once you understand that microevolutionary changes are random events, the joint probabilities of these events don't add, you have to use the multiplication rule. And the probability of an adaptive mutation occurring somewhere in an allele depends on the number of replications of that allele. It doesn't matter whether that allele is in an asexual replicator or a sexual replicator. That allele has to replicate and somehow be passed to the offspring. Understand rubberband?

Kleinman:

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Taq now thinks that recombination can recombine mutations at the same genetic loci of both parents. How did you get so confused on this subject?

Taq:

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Where did I ever say that?????
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You are aware that there is more than one gene in the human genome, right?
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You are aware that beneficial mutations can happen in different genes, right?

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We are talking about the formation of adaptive alleles. Aren't you saying that recombination can take half of one allele with one beneficial mutation from one parent to recombine with the other half of that allele with another beneficial mutation from the other parent to give an allele with two beneficial mutations? Is that what you mean when you say that beneficial mutations don't have to happen sequentially?

Kleinman:

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I'm not interested in some fantasy model that you dredge up in your confused imagination. If you think your ridiculous model fits reality in any way, apply it to a real-world, measured, and repeatable experimental example. You won't because you know you are blowing smoke.

Taq:

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Then all you have is denial.

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That and a model of adaptive evolution that fits the experimental data, a published model of random recombination, and an understanding of the physics and mathematics of biological evolution. You should try and learn it, you might understand the subject of microbiology better.

Kleinman:

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Do microbiologists know how to computer program? Take your model, and start with a population that has almost identical genomes except for each member in that population has unique random mutations scattered at different sites in the genome. Randomly choose two parents out of that population. Choose a mutation rate. Randomly select portions of each genome and recombine those portions to create a new genome while adding new unique random mutations to that genome based on your chosen mutation rate. Do that to the entire population until you create a new generation of descendants. Repeat that cycle and measure how many neutral mutations are fixed in the population as a function of the number of generations.

Taq:

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I already showed you the model. It's the equations for fixation of neutral mutations.

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Kimura compared his mathematical model of fixation with a computer simulation. Why don't you? Don't worry Taq, I know you won't do this, you are just blowing smoke. So what do you want to do next, learn the mathematics of random recombination or the mathematics of adaptive evolution to multiple simultaneous selection pressures?

Kleinman:

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At least you are admitting that my model of adaptive evolution is correct for asexually replicating organisms.

Taq:

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I've agreed all along that your model for asexual organisms based on the Kishony and Lenski experiments is accurate for asexual organisms. What I keep telling you is that it isn't an accurate model for sexual species like humans.

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You are getting this wrong Taq. Recombination does not create new alleles, it only shuffles existing alleles. And any time a particular allele is replicated and passed on to the offspring, there is a chance for a beneficial mutation occurring on that allele. Instead of thinking in terms of the replication of the entire genome as the random trial, think in terms of the allele being replicated as the random trial. Then in the "at least one" probability calculation, "n" becomes the number of replications of the (potential) resistance allele instead of the number of replications of the subpopulation with that resistance allele. Once different resistance alleles at different genetic loci have evolved, then you have the possibility of a resistance allele for one selection condition at a particular genetic locus in one parent recombining with a different resistance allele for a different selection condition at a different particular genetic locus from the other parent appearing in the offspring. That probability depends on the frequency of the different alleles in the population. Bottom line, the mathematics of the formation of the resistance alleles in asexual replicators is the same for sexually reproducing replicators. Recombination has no significant effect on this process, that's why combination therapy works for the treatment of HIV, combination herbicides, and combination pesticides work despite they are being used on replicators that do recombination. The probability of a recombination event defeating combination herbicides and pesticides occurs only under very specific conditions.

Kleinman:

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Of course, adaptive mutations have to occur sequentially.

Taq:

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No, they don't have to. You can have multiple adaptive mutations that are all moving towards fixation at the same time. Even as those beneficial mutations move towards fixation, new beneficial mutations can occur and begin to move towards fixation.

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Different adaptive alleles can increase in frequency in a population if each of the alleles give increased reproductive fitness for each of the variants. But that doesn't happen because the selection pressure for the variant that doesn't have the resistance allele for that pressure is inhibiting its reproduction, and visa versa for the other variant with the other resistance allele. That's why combination therapy works for the treatment of HIV. Variants with resistance alleles to one drug or another don't get any significant improvement in reproductive fitness so they don't reproduce any better than variants without resistance alleles.

Kleinman:

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Once you understand that microevolutionary changes are random events, the joint probabilities of these events don't add, you have to use the multiplication rule.

Taq:

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You also have to figure in the number of possible beneficial mutations at any point in the history of a lineage. How many times have I pointed this out?
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The mistake you keep making is that you pretend as if only 1 beneficial mutation can move towards fixation at a time. That's wrong. Do you understand why that is wrong?

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Have you read this paper?
The basic science and mathematics of random mutation and natural selection
In this paper, I modeled the results Weinreich obtained and published in Darwinian Evolution Can Follow Only Very Few Mutational Paths to Fitter Proteins.

From The_Basic_Science:

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What this empirical example demonstrates is that the sequence of mutations must occur in an order of ever increasing fitness in order for the evolutionary process to have a reasonable chance of occurring. In addition, this example demonstrates that there is more than a single sequential order, which can occur. In other words, not every member of the population must have the same sequence of mutations in order to evolve resistance to the antibiotic selection pressure. The population of bacteria has subdivided into subpopulations, each taking their own trajectory to achieve resistance to this particular selection pressure.

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If we label one subpopulation ‘1’, that subpopulation must get mutation A1 followed by mutation B1, in turn followed by mutation C1, then D1 and finally E1 in order to evolve resistance to the antibiotic selection pressure. If we label another subpopulation ‘2’, that subpopulation must get a different set of mutations, which we can label A2 followed by mutation B2, in turn followed by mutation C2, then D2 and finally E2 in order to evolve resistance to the antibiotic selection pressure. Each of the subpopulations that Weinreich and his co-authors describe has their own set of mutations, which lead to the evolution of a high-resistance ????-lactamase allele. Each of the subpopulations are evolving independently of the other subpopulations. Once a particular subpopulation starts on an evolutionary trajectory, the replication of members from that subpopulation do not contribute to trials for the next beneficial mutation in a different subpopulation on a different evolutionary trajectory.

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Replications of variants in subpopulation 1 do not change the probability of an adaptive mutation occurring in subpopulation 2. Each lineage is on its own particular evolutionary trajectory. That's why the different lineages in the Lenski experiment do not have identical genetic sequences. The population in one vial is taking a different evolutionary trajectory to improved fitness from populations in other vials. What these lineages do have in common is the number of generations to fixation and adaptation for each evolutionary step.

Kleinman:

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Aren't you saying that recombination can take half of one allele with one beneficial mutation from one parent to recombine with the other half of that allele with another beneficial mutation from the other parent to give an allele with two beneficial mutations?

Taq:

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Can you just for a moment realize that there is more than one gene in a genome? Please?

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Of course, I know that. What you are doing is conflating the DNA adaptive evolutionary process and recombination. They are two different physical process with two different mathematical behaviors. Can you just for a moment realize that recombination does not create new alleles? Please?

Taq:

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Imagine that there is a new beneficial mutation in gene A and a new beneficial mutation in gene B in the same generation. They are on different chromosomes. Both beneficial mutations start moving towards fixation at the same time. Let's say that both mutations reach 5% of the population. This means there is a 0.05*0.05 = 0.025 chance that out of two parents each will have one of the beneficial mutations. Let's say they are both heterozygous for their individual mutations. This means that 25% of their offspring WILL HAVE BOTH MUTATIONS. Do you see how this works?
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While these two mutations are moving towards fixation and increasingly found in the same genomes, there will be new beneficial mutations that are appearing, and they too will go through the same process and be combined with the beneficial mutations already in the population.

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Finally, you are starting to think about the mathematics of recombination. Your calculation is off by a factor of 2.

Kleinman:

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That and a model of adaptive evolution that fits the experimental data, a published model of random recombination, and an understanding of the physics and mathematics of biological evolution. You should try and learn it, you might understand the subject of microbiology better.

Taq:

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I understand it just fine. The fact you don't understand the difference between asexual and sexual reproduction means you are the one who needs to catch up.

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When will you learn that recombination does not create new alleles?

Kleinman:

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Kimura compared his mathematical model of fixation with a computer simulation. Why don't you? Don't worry Taq, I know you won't do this, you are just blowing smoke. So what do you want to do next, learn the mathematics of random recombination or the mathematics of adaptive evolution to multiple simultaneous selection pressures?

Taq:

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Can you be even more of a douchebag? You can't even understand how chromosomes work, and you want to critique me for not creating a whole program? Give me a break.

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I forgive you for this because you don't know what you are doing. I've had years of training and years of experience doing mathematical modeling of physical systems and have been paid a lot of money for doing this. One of the tasks when developing a mathematical model is to test its validity by comparing it against other mathematical models and see if they give consistent results. You then test the model against experimental data and see if it gives consistent results with the data produced by the model. You make a claim and put out results that don't agree with the simple neutral fixation equation and Kimura's result when those two models give results in the same order of magnitude. At least now in your post, you are making an attempt to do the mathematics of recombination. Your attempt is off by a factor of two. Try doing a systematic analysis to figure out why. I'll help you by formulating the physical problem:Consider the following: Assume that we have a population of sexual replicators doing random recombination. Assume that the population size is size ‘n’. In this population, assume that some members of the population have a beneficial allele for one selection condition, call this allele ‘A’. Other members of the population have a beneficial allele for a second selection condition, call this allele ‘B’. The remaining members of the population have neither allele A nor allele B, call these non-A and non-B alleles ‘C’. If a member of the population with beneficial allele A at one genetic locus meets another member of the population with beneficial allele B at a different genetic locus, we assume that these members will recombine giving an offspring with both alleles A and B and thus, a more fit member of the population. The probability that a member of the population with allele A meets and recombines randomly with a member with allele B can then be computed using the principles of probability theory.The probability distribution for this empirical example is identical to the probability distribution given for random card drawing when there are only three different cards in the deck, A, B, and C. Let:n – is the total population size.
nA – is the number of members in the population with beneficial allele A.
nB – is the number of members in the population with beneficial allele B.
nC – is the number of members in the population that have neither beneficial allele A nor beneficial allele B.What is the probability distribution for this problem and compute the (correct) probability of an A member recombing with a B member to give an AB offspring.

Kleinman:

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Once different resistance alleles at different genetic loci have evolved, then you have the possibility of a resistance allele for one selection condition at a particular genetic locus in one parent recombining with a different resistance allele for a different selection condition at a different particular genetic locus from the other parent appearing in the offspring.

Taq:

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Except that we are not talking about antibiotic resistance in humans. We are talking about adapting to an open savanna. There are going to a lot of different pathways that evolution can take. It isn't anything like antibiotic resistance which is very constrained as to where beneficial mutations can occur. The two selection regimes are very, very different.

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There are not many selection conditions on a savanna, but a few, are starvation, dehydration, thermal stress (both excessively high and excessively low temperatures), disease (bacterial, fungal, parasitic, viral), toxins, and predation, to list a few. It would be sad for some member of the population to get an adaptive mutation that would give a step toward standing upright and end up dying of tetanus or starvation or any of the myriad of other selection conditions that member would face. There wouldn't be much of an improvement in fitness from that first mutation. And the selection condition doesn't change the math, it only changes the target gene(s) as demonstrated by the different selection conditions use in the Kishony and Lenski experiments. It is the number of selection conditions acting on the population that forces the probability down that a lineage can get all the mutations to improve fitness against all the selection conditions. Each additional selection condition introduces another instance of the multiplication rule into the math.

Taq:

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You are also ignoring diploidy. You don't even need recombination to get two different beneficial alleles. You just need both mutations from separate parents.

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If both parents are homozygous for the resistance allele, then you are doing 2 random trials for the next adaptive mutation in that replication. The haploid replicator gets only one trial with its replication. And you know that doubling the number of replications does not double the probability of an adaptive mutation occurring on one of those alleles. That particular adaptive allele will have to be replicated about 1/(mutation rate) times to give a reasonable probability that one of those replications give the next adaptive mutation. If the parents are heterozygous, then you don't even get the mathematical benefit of diploidy.

Kleinman:

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Bottom line, the mathematics of the formation of the resistance alleles in asexual replicators is the same for sexually reproducing replicators. Recombination has no significant effect on this process, that's why combination therapy works for the treatment of HIV, combination herbicides, and combination pesticides work despite they are being used on replicators that do recombination.

Taq:

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Multidrug strategies work because there is very strong selection. If you don't have resistance to all drugs at a moments notice then you don't reproduce. That was not the case for human evolution. Our ancestors could survive just fine without the adaptations we have now. The adaptations they did receive allowed them to slowly move out to an open savanna.
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This is another feature you are ignoring.

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Strong selection actually accelerates adaptive evolution, it removes all the drug-sensitive variants from the population and fixing the drug-resistant variants in a very small number of generations. The only reason that single-drug therapy for treating infectious diseases has worked well at all is that most people are immune-competent. Any drug-resistant variants that remain are removed by the patient's own immune system. The reason why drug resistance is so bad in the hospital environment is that they are dealing with sicker patients, many of who are immune compromised. Drug-resistant bacteria appear as a matter of course simply by neutral evolution. All that is needed is for the population size to be large enough that mutations occur at every possible site in the genome (1/(mutation rate) replications) of that variant. The probability of getting variants with resistance alleles at multiple different loci requires an exponentially larger population if done by neutral evolution alone. But evolve a variant resistant to one drug and allow that variant to recover population size, then you will start getting variants with resistance alleles at two genetic loci. Then when that drug fails, go to a third drug... Finally, you will end up with bacteria such as MRSA.

Kleinman:

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Different adaptive alleles can increase in frequency in a population if each of the alleles give increased reproductive fitness for each of the variants. But that doesn't happen because the selection pressure for the variant that doesn't have the resistance allele for that pressure is inhibiting its reproduction, and visa versa for the other variant with the other resistance allele.

Taq:

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NO, THAT ISN'T WHAT HAPPENS IN EUKARYOTES. You still don't understand how sexual reproduction works. What you are describing is what happens in asexual species, not sexual ones.

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Sometimes I think we are talking about different things. Doesn't relative fitness differences of different variants determine which variants increase in frequency and which decrease? The more fit variants increase in frequency and the less fit variants decrease in frequency. And how is this different between asexual replicators and sexually reproducing replicators?

Kleinman:

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In this paper, I modeled the results Weinreich obtained and published in Darwinian Evolution Can Follow Only Very Few Mutational Paths to Fitter Proteins.

Taq:

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Again, you can't use asexual organisms to model sexual organisms. Please learn how sexual selection works. Also, remember that there is more than one gene in a genome.

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You are wrong Taq. The only difference in the math is that for a clonal replicator, each genome replication is one adaptive allele replication. With a diploid sexual replicator, you have two possible adaptive allele replications for each offspring. And that's only true if both parents are homozygous for the resistance allele. If they aren't homozygous, it is a Mendelian genetics calculation if an adaptive allele replication will be added to the probability calculation.

Kleinman:

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Replications of variants in subpopulation 1 do not change the probability of an adaptive mutation occurring in subpopulation 2. Each lineage is on its own particular evolutionary trajectory.

Taq:

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Please learn how sexual reproduction works.

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Please learn how to count.

Kleinman:

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What you are doing is conflating the DNA adaptive evolutionary process and recombination. They are two different physical process with two different mathematical behaviors. Can you just for a moment realize that recombination does not create new alleles? Please?

Taq:

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Can you realize for just a moment that beneficial mutations can happen in more than one gene at a time?

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You aren't ready to do that math yet. First figure out how to do the mathematics of random recombination.

Kleinman:

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I've had years of training and years of experience doing mathematical modeling of physical systems and have been paid a lot of money for doing this.

Taq:

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Where have you ever done a model for two beneficial mutations on separate chromosomes, each of which is moving towards fixation? What would that look like?

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This is the paper that explains how to compute the probability of adaptive mutations occurring at two or more genetic loci.
The mathematics of random mutation and natural selection for multiple simultaneous selection pressures and the evolution of antimicrobial drug resistance
You start the calculation by considering the Venn Diagram for a population with a beneficial allele A1 at some locus in the genome and a benficial allele A2 at a different locus in the genome. The rest of the population has neither allele. The intersection of the two subsets are variants with both the A1 and A2 alleles.And you still don't get it, competition and fixation slow adaptation. This calculation is all about determining the probability of getting an A1A2 variant as a function of the entire population size. You do this by finding the intersection of the A1 and A2 subsets. This is where another instance of the multiplication rule comes in.Apparently, you would rather do this calculation rather than the math of random recombination.

Taq:

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As shown in the paper, all beneficial alleles increased in number with each other. One did not outcompete another, nor do they have to. Why? Sexual reproduction.

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Nope, it is due to the fitness values they use in Table 1. You can get whatever change in frequency you want by manipulating fitness values.

quote:

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Selection was implemented through differences in fecundities phi_F and phi_M between the four gametes, calculated using a base fecundity value of 1,000 propagules multiplied by the relative fitness values of Table 1 in Slatkin (1975). We considered two scenarios of selection strength (selection coefficient s = 0.02 and 0.05) and three scenarios of dispersal (standard deviation of dispersal distance σdisp = 0.5, 1 and 2).

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