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Author | Topic: Do you really understand the mathematics of evolution? | |||||||||||||||||||||||||||||||||||||||
mike the wiz Member Posts: 4755 From: u.k Joined: |
Kleinman writes: So, do you really understand the mathematics of evolution, in particular, DNA evolution? Can't say I do, but what type of, "evolution" do you mean. For example do you think the bacteria in these experiments have shown descent by modification in undergoing anatomical changes at the macro level proving that all of the designs of anatomy into the millions, can come about this way? I know the maths that count; bacteria + bacteria = bacteria. How about the maths of the transitional species for macro evolution? How many would have to have existed in the past? That would be an interesting study for someone like you. Do you know why? Because the disparity of animal phyla in the Cambrian precedes diversity but Darwin's tree would predict the opposite. That's because to get to the level of phyla FROM something like your bacteria as an example, would take a very long time indeed, and there would have to be a lot of evolutionary diversity before reaching the phyla level, because to evolve differences at the phyla level would take hundreds of millions of years. So mathematically since you know maths and I don't, you are my go-to man, in explaining to me what is the number of transitional species that would have had to exist across all of evolutionary time COMPARED to the ones they propose they have found? I am going to say my guess leads me to below 5%. Logically that means it would be slothful induction fallacy to infer macro evolution is true mathematically, when most of the evidence is conspicuously absent. Why below 5%? That's easy to figure out even for a non-math guy like me. Because if they PROPOSE they've found about 300 transitionals on their transitional list, then even if only 3000 transitionals existed over the full span of evolutionary history, that would only be 10%. But to say 3000 transitionals existed over the full course of the history of life on earth would be LOGICALLY PREPOSTEROUS. Ergo, there would likely have been hundreds of thousands, ergo the percentage of transitionals they have found has to be tiny ergo evolution truly is limited to turning bacteria into bacteria, according to logical reasoning I DO KNOW.
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Kleinman Member (Idle past 363 days) Posts: 2142 From: United States Joined: |
Kleinman writes:
In this discussion, we are talking about two evolutionary processes. The first evolutionary process is what Darwin calls the "struggle for existence" or what we usually call competition. And the second evolutionary process is what Darwin calls "adaptation" or what we are calling DNA evolution. The Lenski and Kishony experiments are both DNA evolution processes with the important distinction that the Lenski experiment is being carried out in a highly competitive environment. So, do you really understand the mathematics of evolution, in particular, DNA evolution?mike the wiz writes: Can't say I do, but what type of, "evolution" do you mean. For example do you think the bacteria in these experiments have shown descent by modification in undergoing anatomical changes at the macro level proving that all of the designs of anatomy into the millions, can come about this way? The only clear gross anatomical changes that is occurring in these experiments is that Lenski's bacteria are getting larger.
mike the wiz writes:
What the Lenski and Kishony experiments show is that every evolutionary transitional step takes a billion replications and that just for a single selection pressure environment. And the reason for this is the multiplication rule of probabilities. I know the maths that count; bacteria + bacteria = bacteria. How about the maths of the transitional species for macro evolution? How many would have to have existed in the past? That would be an interesting study for someone like you. Do you know why? Because the disparity of animal phyla in the Cambrian precedes diversity but Darwin's tree would predict the opposite. A common misconception is the notion that a series of microevolutionary changes can add up to a macroevolutionary change. This is mathematically incorrect. Microevolutionary changes don't add, they are linked by the multiplication rule of probabilities because each of these mutations are random events.
mike the wiz writes:
Your basic idea is correct. If I understand your argument correctly, you are saying there should be far more transitional fossils in the fossil record for the theory of evolution to be correct. To get a sense of the numbers, there have been about 50 T rex skeletons discovered and it is highly unlikely that there were billions of T rexes (pinnacle predator). So if it takes a billion replications (under the best of circumstances) for each evolutionary step, where are all these vast numbers of transitional fossils of reptiles transforming into birds and fish transforming into mammals when there are 50 fossils of a single pinnacle predator which most likely existed in very small numbers compared to those replicators lower in the food pyramid? From this link: That's because to get to the level of phyla FROM something like your bacteria as an example, would take a very long time indeed, and there would have to be a lot of evolutionary diversity before reaching the phyla level, because to evolve differences at the phyla level would take hundreds of millions of years. So mathematically since you know maths and I don't, you are my go-to man, in explaining to me what is the number of transitional species that would have had to exist across all of evolutionary time COMPARED to the ones they propose they have found? I am going to say my guess leads me to below 5%. Logically that means it would be slothful induction fallacy to infer macro evolution is true mathematically, when most of the evidence is conspicuously absent. Why below 5%? That's easy to figure out even for a non-math guy like me. Because if they PROPOSE they've found about 300 transitionals on their transitional list, then even if only 3000 transitionals existed over the full span of evolutionary history, that would only be 10%. But to say 3000 transitionals existed over the full course of the history of life on earth would be LOGICALLY PREPOSTEROUS. Ergo, there would likely have been hundreds of thousands, ergo the percentage of transitionals they have found has to be tiny ergo evolution truly is limited to turning bacteria into bacteria, according to logical reasoning I DO KNOW.How many T-Rex were there in the dino era? - Quora "The food pyramid of most ecosystems is accurately described relative species abundance as a power of ten, decreasing from, e.g., 10,000 primary producers (plants), to 1000 herbivores to 100 secondary carnivores, to 10 top predators, and finally 1 pinnacle predator."
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Taq Member Posts: 10084 Joined: Member Rating: 5.1 |
Kleinman writes: The reason this is the case is that the carrying capacity in the drug-free region is not large enough to accommodate both the wild-type and the drug-resistant variants multiplication. Then make the region larger.
That answers that, you don't understand the mathematics of evolution so you snip out the part highlighted in red. If you understood the mathematics you would know that you can't ask a vague question and expect a specific mathematical answer. It's a bit like asking for the probability of a raffle without supplying the number of players, number of tickets, and so forth. The number of beneficial mutations is going to differ between genomes and between environments. You can't ask for a calculation without supplying those numbers.
What you refuse to accept is that the steps in every evolutionary trajectory are joint by the multiplication rule. I do refuse to accept statements that are false. The steps can be taken one at a time, and don't need to be taken all at once. In a fitness landscape, you don't have to go from the bottom of the hill and reach the top in one giant leap.
You can't explain mathematical behavior of the Kishony or Lenski experiments so now you start storytelling. That's like asking for the mathematical behavior for airplanes. You have to ask specific questions, such as the equations for lift on the wings of a specific plane, or the thermodynamics of a specific engine. You ask such vague questions and fail to understand that they can't lead to specific mathematical answers.
It doesn't matter which evolutionary trajectory that a lineage takes. It doesn't change the math. That's patently false. Different pathways are going to have different numbers of beneficial mutations which affects the math.
Is that so? You are obviously not aware that single-drug therapy has been the standard of care for infectious diseases for years. That's why MRSA is so common. How many people on the globe right now are taking multiple antibiotics at this very moment? How many more people are asymptomatic carriers of both MSSA and MRSA?
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Taq Member Posts: 10084 Joined: Member Rating: 5.1 |
mike the wiz writes: I know the maths that count; bacteria + bacteria = bacteria. How about the maths of the transitional species for macro evolution? Since you seem to be playing the creationist name game, we would have to ask what a transition would be. Humans evolving from an ape ancestor would be microevolution:Ape+Ape=Ape Humans evolving from a shared mammal ancestor would be microevolution:Mammal+Mammal=Mammal Humans evolving from a shared vertebrate ancestor would be microevolution:Vertebrate+Vertebrate=Vertebrate Humans evolving from a shared eukaryote ancestor would be microevolution:Eukaryote+Eukaryote=Eukaryote Because the disparity of animal phyla in the Cambrian precedes diversity but Darwin's tree would predict the opposite. The earliest branches of the tree of life are found in the earliest fossil records. That is exactly what Darwin predicted.
So mathematically since you know maths and I don't, you are my go-to man, in explaining to me what is the number of transitional species that would have had to exist across all of evolutionary time COMPARED to the ones they propose they have found? I am going to say my guess leads me to below 5%. Why don't you do the math, and back it up with facts? How many more species lived during the history of life compared to the fossils we have in our collections? What's the number and where's you math?
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Kleinman Member (Idle past 363 days) Posts: 2142 From: United States Joined: |
Kleinman writes:
If you understood the mathematics of evolution, you would understand how much larger the region needs to be for the experiment to work.
The reason this is the case is that the carrying capacity in the drug-free region is not large enough to accommodate both the wild-type and the drug-resistant variants multiplication.Taq writes: Then make the region larger.Kleinman writes:
How much simpler of an evolutionary experiment can you make than either the Kishony or Leski experiments? If you don't know the exact values for the mutation rates and population sizes, write out the mathematics with those numbers as variables. If you can't do it, I'll show you how to do the math.
That answers that, you don't understand the mathematics of evolution so you snip out the part highlighted in red.Taq writes: If you understood the mathematics you would know that you can't ask a vague question and expect a specific mathematical answer. It's a bit like asking for the probability of a raffle without supplying the number of players, number of tickets, and so forth. The number of beneficial mutations is going to differ between genomes and between environments. You can't ask for a calculation without supplying those numbers.Kleinman writes:
I've never said that the all the steps have to taken all at once. Why don't you try to understand what it takes to make a single evolutionary step? The math isn't that difficult.
What you refuse to accept is that the steps in every evolutionary trajectory are joint by the multiplication rule.Taq writes: I do refuse to accept statements that are false. The steps can be taken one at a time, and don't need to be taken all at once. In a fitness landscape, you don't have to go from the bottom of the hill and reach the top in one giant leap.Kleinman writes:
If I was going to ask you about the mathematical behavior of airplanes and flight, I would start with Newton's 2nd law and ask how you would derive Bernoulli's equation. But we are not talking about flight, we are talking about DNA evolution and competition. So, derive for us the mathematics which describes a lineage accumulating a specific set of mutations allowing adaptation to a selection pressure. When you do that, you will understand the mathematics of the Kishony experiment (and the Lenski experiment as well).
You can't explain mathematical behavior of the Kishony or Lenski experiments so now you start storytelling.Taq writes: That's like asking for the mathematical behavior for airplanes. You have to ask specific questions, such as the equations for lift on the wings of a specific plane, or the thermodynamics of a specific engine. You ask such vague questions and fail to understand that they can't lead to specific mathematical answers.Kleinman writes:
You are wrong Taq. The mathematics for any step on an evolutionary trajectory is the same regardless of the selection pressure. The same equation that describes a step of DNA evolution for the Kishony experiment applies to the Lenski experiment.
It doesn't matter which evolutionary trajectory that a lineage takes. It doesn't change the math.Taq writes: That's patently false. Different pathways are going to have different numbers of beneficial mutations which affects the math.Kleinman writes:
A study was done at one of the hospitals in my area. What they did is swabbed and cultured everyone's (patients, employees, visitors) nose on entry. 50% were carriers of MRSA. This coincides with the numbers in my medical practice. About 50% of the soft tissue infections I treat are community-acquired MRSA. The question you should ask is, why are hospital-acquired MRSA infection resistant to more antibiotics than community-acquired MRSA?
Is that so? You are obviously not aware that single-drug therapy has been the standard of care for infectious diseases for years. That's why MRSA is so common.Taq writes: How many people on the globe right now are taking multiple antibiotics at this very moment? How many more people are asymptomatic carriers of both MSSA and MRSA?mike the wiz writes:
mike the wiz has already admitted that he doesn't understand the mathematics of evolution. So, I'll help him with the answer. Are you familiar with Markov chains? I don't think you are so here is a link that explains the concept. I know the maths that count; bacteria + bacteria = bacteria. How about the maths of the transitional species for macro evolution?Taq writes: Since you seem to be playing the creationist name game, we would have to ask what a transition would be.Models of DNA evolution - Wikipedia This link gives a mathematical definition for a transition, they call it a transition matrix. Read about and try to learn something about the mathematics of DNA evolution.
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Taq Member Posts: 10084 Joined: Member Rating: 5.1 |
Kleinman writes: How much simpler of an evolutionary experiment can you make than either the Kishony or Leski experiments? If you don't know the exact values for the mutation rates and population sizes, write out the mathematics with those numbers as variables. Write out the mathematics of what? Fixation of mutations through neutral drift? What exactly?
Why don't you try to understand what it takes to make a single evolutionary step? The math isn't that difficult. The math is different for different steps. That's the point.
So, derive for us the mathematics which describes a lineage accumulating a specific set of mutations allowing adaptation to a selection pressure. How many mutations? How strong is the selective pressure? Do you want me to just list the basic equations with no numbers in them?
The mathematics for any step on an evolutionary trajectory is the same regardless of the selection pressure. Bullshit. If there are 15 possible beneficial mutations for a specific beneficial phenotype it will behave differently than if there is 1 possible beneficial mutation. This can also shift as the genetic background shifts due to epistatic interactions.
A study was done at one of the hospitals in my area. What they did is swabbed and cultured everyone's (patients, employees, visitors) nose on entry. 50% were carriers of MRSA. This coincides with the numbers in my medical practice. How many of those people were on antibiotics? Is the environment different between carriers? In other words, is there person to person variation with respect to their immune systems and condition of their nasal and pharyngeal environments? Is the competing flora the same in each person? What selective pressures does each person present to their flora, including MSSA and MRSA? Wouldn't you say that MRSA exists in many varying environments, with antibiotics being present in a very small percentage of them?
The question you should ask is, why are hospital-acquired MRSA infection resistant to more antibiotics than community-acquired MRSA? That's a question you should answer. Different ecologies?
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Kleinman Member (Idle past 363 days) Posts: 2142 From: United States Joined: |
Kleinman writes:
Fixation isn't occurring in the Kishony experiment. Write out the mathematics of DNA evolution for the Kishony experiment. It appears you don't understand the difference between competition and adaptation.
How much simpler of an evolutionary experiment can you make than either the Kishony or Leski experiments? If you don't know the exact values for the mutation rates and population sizes, write out the mathematics with those numbers as variables.Taq writes: Write out the mathematics of what? Fixation of mutations through neutral drift? What exactly?Write out the mathematics of what? Fixation of mutations through neutral drift? What exactly?Kleinman writes:
It isn't, but if you think it is, just do the mathematics for the first step for the Kishony experiment.
Why don't you try to understand what it takes to make a single evolutionary step? The math isn't that difficult.Taq writes: The math is different for different steps. That's the point.Kleinman writes:
I'll make it as easy as possible, just do the mathematics for the first beneficial mutation for the Kishony experiment.
So, derive for us the mathematics which describes a lineage accumulating a specific set of mutations allowing adaptation to a selection pressure.Taq writes: How many mutations? How strong is the selective pressure? Do you want me to just list the basic equations with no numbers in them?Kleinman writes:
It isn't. You just haven't learned how DNA evolution works yet. Try doing the math for the first beneficial mutation in the Kishony experiment. It's clear you need a hint to get started. Start with a single bacterium that doesn't have the correct mutation and starts replicating in the drug-free region. Then write out the probability equation of that particular mutation occurring at least once in N replications for a given mutation rate.
The mathematics for any step on an evolutionary trajectory is the same regardless of the selection pressure.Taq writes: Bullshit. If there are 15 possible beneficial mutations for a specific beneficial phenotype it will behave differently than if there is 1 possible beneficial mutation. This can also shift as the genetic background shifts due to epistatic interactions.Kleinman writes:
None of the employees or visitors were on antibiotics, and yes there is great variability in the immune status of the individuals. That should give you a big clue on why hospital-acquired MRSA is resistant to more antibiotics than community-acquired MRSA.
A study was done at one of the hospitals in my area. What they did is swabbed and cultured everyone's (patients, employees, visitors) nose on entry. 50% were carriers of MRSA. This coincides with the numbers in my medical practice.Taq writes: How many of those people were on antibiotics? Is the environment different between carriers? In other words, is there person to person variation with respect to their immune systems and condition of their nasal and pharyngeal environments? Is the competing flora the same in each person? What selective pressures does each person present to their flora, including MSSA and MRSA? Wouldn't you say that MRSA exists in many varying environments, with antibiotics being present in a very small percentage of them?Kleinman writes:
You touched on a key reason, the immune status of inpatients vs outpatients. The question you should ask is, why are hospital-acquired MRSA infection resistant to more antibiotics than community-acquired MRSA?Taq writes: That's a question you should answer. Different ecologies? And I noticed that you snipped out the portion about Markov Chains and the transition matrix. It's probably too much for you at this point. Try to understand the "at least on rule" from probability theory. That's a little easier way to understand DNA evolution.
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Taq Member Posts: 10084 Joined: Member Rating: 5.1 |
Kleinman writes: Write out the mathematics of DNA evolution for the Kishony experiment. You need to be more specific.
It isn't, but if you think it is, just do the mathematics for the first step for the Kishony experiment. You haven't supplied enough information to do the calculations, nor have you defined the question with enough specificity.
I'll make it as easy as possible, just do the mathematics for the first beneficial mutation for the Kishony experiment. What is the mutation rate? How many beneficial mutations are possible? What is the specific mutation, and what are the biases for transition and transversion mutations in the bacteria being used?
It isn't. You just haven't learned how DNA evolution works yet. The math seems pretty straightforward. If there are 15 possible beneficial mutations that can produce antibiotic resistance then resistance will emerge sooner than it would if there was 1 possible beneficial mutation.
Start with a single bacterium that doesn't have the correct mutation and starts replicating in the drug-free region. Then write out the probability equation of that particular mutation occurring at least once in N replications for a given mutation rate. How many possible beneficial mutations are there?
None of the employees or visitors were on antibiotics, and yes there is great variability in the immune status of the individuals. There is also a lot of variability in the flora of each individual, the genetic makeup of the flora competing with S. aureus, and there is still variability between strains of MRSA. It isn't like the simple lab experiments you are describing where there are far fewer variables.
And I noticed that you snipped out the portion about Markov Chains and the transition matrix. It's probably too much for you at this point. It isn't. You don't seem to understand how to ask specific questions. There's no reason to move on to the more complex stuff if you can't figure out the simple stuff. Edited by Taq, : No reason given.
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Kleinman Member (Idle past 363 days) Posts: 2142 From: United States Joined: |
Kleinman writes:
Sorry, I thought you were familiar with the concept of molecular evolution. Read this paragraph: Write out the mathematics of DNA evolution for the Kishony experiment.Taq writes: You need to be more specific.Molecular evolution - Wikipedia Kleinman writes:
I've given you enough specificity, you just don't understand molecular evolution well enough to formulate the probability equation that relates the mutation rate and number of replications of a particular variant to determine that probability. Read the above paragraph I linked to and think about it for a while.
It isn't, but if you think it is, just do the mathematics for the first step for the Kishony experiment.Taq writes: You haven't supplied enough information to do the calculations, nor have you defined the question with enough specificity.Kleinman writes:
The mutation rate is a variable, call it "mu". And for simplicity, assume the mutation rate is the same for transitions and transversion. And initially assume there is only a single beneficial mutation. Once you understand the simple case, I'll show you how to do the math for multiple beneficial mutations.
I'll make it as easy as possible, just do the mathematics for the first beneficial mutation for the Kishony experiment.Taq writes: What is the mutation rate? How many beneficial mutations are possible? What is the specific mutation, and what are the biases for transition and transversion mutations in the bacteria being used?Kleinman writes:
More than a single possible beneficial mutation changes the math only slightly. First do the math for the simpler case.
It isn't. You just haven't learned how DNA evolution works yet.Taq writes: The math seems pretty straightforward. If there are 15 possible beneficial mutations that can produce antibiotic resistance then resistance will emerge sooner than it would if there was 1 possible beneficial mutation.Kleinman writes:
Start with one. Once you do that math, then you can try to do the math when there are multiple possible beneficial mutations.
Start with a single bacterium that doesn't have the correct mutation and starts replicating in the drug-free region. Then write out the probability equation of that particular mutation occurring at least once in N replications for a given mutation rate.Taq writes: How many possible beneficial mutations are there?Kleinman writes:
Try doing the math for the simple lab experiments first. And in any mathematical model, you want to include only those variables that have a significant effect on the predictability of that model. If we were studying Newton's laws, I wouldn't expect you to predict the motion of a bridge or building in an earthquake. You need to start your study with the motion of a pendulum or a mass and spring. Once you master the simple cases, you can go on to the more complex cases.
None of the employees or visitors were on antibiotics, and yes there is great variability in the immune status of the individuals.
Taq writes: There is also a lot of variability in the flora of each individual, the genetic makeup of the flora competing with S. aureus, and there is still variability between strains of MRSA. It isn't like the simple lab experiments you are describing where there are far fewer variables.Kleinman writes:
You've got a point there. So do the mathematics for a single beneficial mutation with a constant mutation rate as a function of the number of replications of a particular variant. Hint: Use the "at least one rule" from probability theory.
And I noticed that you snipped out the portion about Markov Chains and the transition matrix. It's probably too much for you at this point.Taq writes: It isn't. You don't seem to understand how to ask specific questions. There's no reason to move on to the more complex stuff if you can't figure out the simple stuff.
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Taq Member Posts: 10084 Joined: Member Rating: 5.1 |
Kleinman writes: Sorry, I thought you were familiar with the concept of molecular evolution. I am familiar with the concept. What you don't seem to be familiar with is the mathematics of molecular evolution. Otherwise, you would understand the specifics needed in a question. As an example, I have a big bag full of tiles. I reach in and draw out a tile with the number 33523 on it. What is the probability that I would draw out a tile with that number on it? Can you answer that question?
The mutation rate is a variable, call it "mu". And for simplicity, assume the mutation rate is the same for transitions and transversion. And initially assume there is only a single beneficial mutation. Thank you. That is the type of specifics needed. Vaguely asking for the math of evolution just won't do. We will also assume a 4.6 million base pair genome as is seen in the E. coli model organism. If mu is mutations per base per replication then we would multiply mu by the number of bases in the genome which is 4.6E6*mu, this represents the number of mutations per replication. If we are requiring a specific substitution, then we would need 3 substitutions at each base to produce all possible mutations, or 1.38E7 mutations. The final equation is 1.38E7/(4.6E6*mu) as the number of replications needed. Is that what you are looking for?
More than a single possible beneficial mutation changes the math only slightly. But it does change it.
If we were studying Newton's laws, I wouldn't expect you to predict the motion of a bridge or building in an earthquake. You need to start your study with the motion of a pendulum or a mass and spring. Once you master the simple cases, you can go on to the more complex cases. The problem is that you are asking for the math of a bridge without being specific as to what properties of the bridge you are interested it. Are you interested in the tensile strength of the cables? Are you interested in the aerodynamic profile of the bridge in the wind? Do you see the problem? Edited by Taq, : No reason given.
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Kleinman Member (Idle past 363 days) Posts: 2142 From: United States Joined: |
Kleinman writes:
Then explain to us the following quote from this link (and show your math): Sorry, I thought you were familiar with the concept of molecular evolution.Taq writes: I am familiar with the concept. What you don't seem to be familiar with is the mathematics of molecular evolution. Otherwise, you would understand the specifics needed in a question.Molecular evolution - Wikipedia Wikipedia writes:
Because mutations are extremely rare, they accumulate very slowly across generations. While the number of mutations which appears in any single generation may vary, over very long time periods they will appear to accumulate at a regular pace.Taq writes:
Yes, I can answer this question. If the draw of the tiles is random and the probability of drawing any particular tile is equal (same size, same shape, etc.), then that probability is 1/N, where N is the total number of tiles in the bag. See Taq, that's how you use variables in a probability calculation.
As an example, I have a big bag full of tiles. I reach in and draw out a tile with the number 33523 on it. What is the probability that I would draw out a tile with that number on it? Can you answer that question?Kleinman writes:
OK
The mutation rate is a variable, call it "mu". And for simplicity, assume the mutation rate is the same for transitions and transversion. And initially assume there is only a single beneficial mutation.Taq writes: Thank you. That is the type of specifics needed. Vaguely asking for the math of evolution just won't do. We will also assume a 4.6 million base pair genome as is seen in the E. coli model organism.Taq writes:
That's a little different way of looking at the math but that is essentially correct. And if mu=1e-9, 1.38E7/4.6E6*mu)=3.00E+09. The reason why your estimate is 3x larger than my estimate, I'm assuming the mu is the "beneficial" mutation rate and you are assuming the "total" mutation rate where there are 3 possible incorrect mutations at the particular site. If mu is mutations per base per replication then we would multiply mu by the number of bases in the genome which is 4.6E6*mu, this represents the number of mutations per replication. If we are requiring a specific substitution, then we would need 3 substitutions at each base to produce all possible mutations, or 1.38E7 mutations. The final equation is 1.38E7/(4.6E6*mu) as the number of replications needed. Is that what you are looking for? Now, what happens to that 1 variant member of the 3e9 population with the beneficial mutation in the Kishony experiment?
Kleinman writes:
Not significantly. When we finish with the simpler model, we can discuss how multiple beneficial mutations affect the math.
More than a single possible beneficial mutation changes the math only slightly.Taq writes: But it does change it.Kleinman writes:
That's a problem for you, not for me. The purpose of mathematical modeling is to do an analysis of a physical system. For example, if you want to do the analysis of a bridge, the geometry of the bridge is a variable, the physical properties are a variable, the loading forces are variables. So if you change the material used for making the cables which have a different tensile strength, you can just change that one variable and see how that affects the stresses in the structure. The math you did above is ok but it is not as flexible as writing the full governing equations of the evolutionary process. For example, what happens if the bacteria used has a different genome length? Do you think that will change the number of replications for the beneficial mutation to occur?
If we were studying Newton's laws, I wouldn't expect you to predict the motion of a bridge or building in an earthquake. You need to start your study with the motion of a pendulum or a mass and spring. Once you master the simple cases, you can go on to the more complex cases.Taq writes: The problem is that you are asking for the math of a bridge without being specific as to what properties of the bridge you are interested it. Are you interested in the tensile strength of the cables? Are you interested in the aerodynamic profile of the bridge in the wind? Do you see the problem?
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Taq Member Posts: 10084 Joined: Member Rating: 5.1
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Kleinman writes: Then explain to us the following quote from this link (and show your math): Not until you explain how "show us the mathematics of evolution" is specific enough to approach any equation or question.
If the draw of the tiles is random and the probability of drawing any particular tile is equal (same size, same shape, etc.), then that probability is 1/N, where N is the total number of tiles in the bag. See Taq, that's how you use variables in a probability calculation. You got it wrong. You are assuming that all the tiles have different numbers. They could all have the same number, for all you know.
The reason why your estimate is 3x larger than my estimate, I'm assuming the mu is the "beneficial" mutation rate and you are assuming the "total" mutation rate where there are 3 possible incorrect mutations at the particular site. mu is mu. In a 4.6 million base genome there are 13.8 million possible substitution mutations, so if you are calculating the number of replications needed to produce all possible mutations, one of which is the one of interest, then you need to use the 13.8 million number.
Now, what happens to that 1 variant member of the 3e9 population with the beneficial mutation in the Kishony experiment? It is able to expand into the region with antibiotics.
That's a problem for you, not for me. When someone asks a vague question and expects a specific answer the problem lies with the person asking the vague question.
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Kleinman Member (Idle past 363 days) Posts: 2142 From: United States Joined: |
Kleinman writes:
Let's put the quote back up which I ask you to explain: Then explain to us the following quote from this link (and show your math):Taq writes: Not until you explain how "show us the mathematics of evolution" is specific enough to approach any equation or question.Molecular evolution - Wikipedia Wikipedia writes:
Taq, you have actually started to explain why mutation accumulates very slowly across generations in your previous post when your math shows that it takes 3e9 replications for the first beneficial mutation in the Kishony experiment. So, how many replications of that new variant for the next beneficial mutation to occur on that variant? Hint: Just apply your math again. And note, that is the regular pace for a single selection pressure.
Because mutations are extremely rare, they accumulate very slowly across generations. While the number of mutations which appears in any single generation may vary, over very long time periods they will appear to accumulate at a regular pace.Kleinman writes:
You got me on that one. You have got to watch your assumptions.
If the draw of the tiles is random and the probability of drawing any particular tile is equal (same size, same shape, etc.), then that probability is 1/N, where N is the total number of tiles in the bag. See Taq, that's how you use variables in a probability calculation.Taq writes: You got it wrong. You are assuming that all the tiles have different numbers. They could all have the same number, for all you know.Kleinman writes:
13.8 million are the total number of possible variants (if we consider substitutions only) from the initial founder wild-type bacterium in the Kishony experiment. How many replications necessary for the variant with the first beneficial mutation expected to occur?
The reason why your estimate is 3x larger than my estimate, I'm assuming the mu is the "beneficial" mutation rate and you are assuming the "total" mutation rate where there are 3 possible incorrect mutations at the particular site.Taq writes: mu is mu. In a 4.6 million base genome there are 13.8 million possible substitution mutations, so if you are calculating the number of replications needed to produce all possible mutations, one of which is the one of interest, then you need to use the 13.8 million number.Kleinman writes:
And how many replications of that variant necessary for the next beneficial mutation to occur?
Now, what happens to that 1 variant member of the 3e9 population with the beneficial mutation in the Kishony experiment?Taq writes: It is able to expand into the region with antibiotics.Kleinman writes:
I understand this discussion is difficult for you. It doesn't bother me if I don't get all the information necessary to give an exact answer. If fact, in the world that I work in, that is the usual case. When you asked your tile question, I gave an answer and made an implicit assumption that the tiles had different numbers and you showed my implicit assumption could be wrong. So, here's a specific question. How many replications necessary for the 13.8 million variants to occur in an evolutionary step in the Kishony experiment?
That's a problem for you, not for me.Taq writes: When someone asks a vague question and expects a specific answer the problem lies with the person asking the vague question.
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Taq Member Posts: 10084 Joined: Member Rating: 5.1
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Kleinman writes: Let's put the quote back up which I ask you to explain:Molecular evolution - Wikipedia Look at the rest of the subtopics on that Wiki page.
quote: When you ask for the mathematics of molecular evolution you are asking about all of those things. In order to supply you with the math of evolution we would have to post VOLUMES of equations. Do you understand how ludicrous that is?
Taq, you have actually started to explain why mutation accumulates very slowly across generations in your previous post when your math shows that it takes 3e9 replications for the first beneficial mutation in the Kishony experiment. Slowly? It happens in a matter of days, doesn't it?
You got me on that one. You have got to watch your assumptions. Exactly. When you lack specifics you have to make assumptions, and that can make calculations worthless. That's why I'm asking for specifics. On top of that, you are asking for the mathematics for an entire field, not a specific situation.
How many replications necessary for the variant with the first beneficial mutation expected to occur? That's a bit like asking how many lotteries are necessary to get a winner, or how many tickets you need to buy in order to win the lottery. It varies. It possible, however improbable, that you could have 10 or 100 times more replications than the number I calculated and not get the mutation. There could be other times where you get the mutation in the first few replications. From my reading, the best way to model this is a Poisson distribution which Luria and Delbruck worked up in their papers.
I understand this discussion is difficult for you. You need to understand psychological projection.
It doesn't bother me if I don't get all the information necessary to give an exact answer. It should.
How many replications necessary for the 13.8 million variants to occur in an evolutionary step in the Kishony experiment? It would take some more effort to dig through Luria and Delbruck's work and few other papers to get the probability spreads. Is this something you are really curious about, and is it worth my effort? Is the lottery analogy enough to let you know I understand the problem?
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Kleinman Member (Idle past 363 days) Posts: 2142 From: United States Joined: |
Kleinman writes:
I'm not asking you to write VOLUMES. I'm just asking you something very specific. How many replications for each evolutionary step in the Kishony experiment? And how do you compute that number of replications?
Let's put the quote back up which I ask you to explain:Molecular evolution - Wikipedia Taq writes: Look at the rest of the subtopics on that Wiki page. Look at the rest of the subtopics on that Wiki page.
quote: When you ask for the mathematics of molecular evolution you are asking about all of those things. In order to supply you with the math of evolution we would have to post VOLUMES of equations. Do you understand how ludicrous that is? Kleinman writes:
It only happens in a matter of days because the generation (doubling) time for bacteria is usually minutes. But if it is happening so quickly, why won't you tell us the number of replications that occur in those matter of days?
Taq, you have actually started to explain why mutation accumulates very slowly across generations in your previous post when your math shows that it takes 3e9 replications for the first beneficial mutation in the Kishony experiment.Taq writes: Slowly? It happens in a matter of days, doesn't it?Kleinman writes:
No, I'm not asking for the mathematics for an entire field, I'm asking for the mathematics for the number of replications for the Kishony experiment. How much more specific do you want me do get? How about just giving us the mathematics for the number of replications for a single evolutionary step in the Kishony experiment?
You got me on that one. You have got to watch your assumptions.Taq writes: Exactly. When you lack specifics you have to make assumptions, and that can make calculations worthless. That's why I'm asking for specifics. On top of that, you are asking for the mathematics for an entire field, not a specific situation.Kleinman writes:
The Poisson distribution is ok. Are you aware that the Poisson distribution is the limiting case of the binomial distribution as the mutation rate approaches 0 and the number of replications goes to infinity? How many replications necessary for the variant with the first beneficial mutation expected to occur?Taq writes: That's a bit like asking how many lotteries are necessary to get a winner, or how many tickets you need to buy in order to win the lottery. It varies. It possible, however improbable, that you could have 10 or 100 times more replications than the number I calculated and not get the mutation. There could be other times where you get the mutation in the first few replications. From my reading, the best way to model this is a Poisson distribution which Luria and Delbruck worked up in their papers.https://www.youtube.com/watch?v=ceOwlHnVCqo So use either distribution and tell us how many replications for a single evolutionary step in the Kishony experiment. Kleinman writes:
You are the one having difficulty answering a specific question. Why won't you tell us how man replications it takes for a beneficial mutation to occur for a single step in the Kishony experiment? You can even use the Poisson distribution for your answer even though the binomial distribution is the correct distribution. I can show you how to do that math if you continue to have difficulty.
I understand this discussion is difficult for you.Taq writes: You need to understand psychological projection.Kleinman writes:
Why? It's a very rare thing in life when you understand something exactly. Sometimes, all you can do is give a ballpark estimate. So far, you refuse to even call Uber to get a ride to the stadium. When are you going to give us the mathematics which estimates the number of replications necessary for a single evolutionary step in the Kishony experiment? You can even use the Poisson distribution to make your estimate.
It doesn't bother me if I don't get all the information necessary to give an exact answer.Taq writes: It should.Kleinman writes:
Just use the mean value for the Poisson distribution and you can easily compute the variance (and therefore the standard deviation) of that value to see what the spread of values are. Here is a short video that explains how to do it. How many replications necessary for the 13.8 million variants to occur in an evolutionary step in the Kishony experiment?Taq writes: It would take some more effort to dig through Luria and Delbruck's work and few other papers to get the probability spreads. Is this something you are really curious about, and is it worth my effort? Is the lottery analogy enough to let you know I understand the problem?https://www.youtube.com/watch?v=vrQ9JsAPTUc If you have difficulty applying this math to the Kishony experiment, I'll show you how to do it. So tell us how many replications required for a single evolutionary step in the Kishony experiment using the Poisson distribution.
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