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Author Topic:   Do you really understand the mathematics of evolution?
Taq
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Posts: 9944
Joined: 03-06-2009
Member Rating: 4.8


Message 25 of 239 (876531)
05-21-2020 5:16 PM
Reply to: Message 1 by Kleinman
05-16-2020 1:37 PM


Kleinman writes:
If you think you understand the mathematics of evolution,
Population genetics isn't one of my strong suits, but I am acquainted with it.
Is there something specific you wish to discuss? A lot of the math can be found here:
Mathematical Population Genetics: Lecture Notes
please explain the mathematics of the Kishony Mega-Plate experiment and the Lenski Long Term Evolutionary Experiment and what is the significant mathematical difference between the two experiments.
At first glance, the major differences would be population dynamics. In the Lenski experiment you had a severe population bottleneck every 10 or so generations. This large fluctuation in effective population size would certainly have effects on genetic drift.
Edited by Taq, : No reason given.
Edited by Admin, : Give link a name.

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 Message 27 by Kleinman, posted 05-21-2020 7:19 PM Taq has replied

  
Taq
Member
Posts: 9944
Joined: 03-06-2009
Member Rating: 4.8


Message 26 of 239 (876533)
05-21-2020 5:26 PM
Reply to: Message 10 by Kleinman
05-19-2020 7:59 PM


Kleinman writes:
Perhaps someone wants to try and explain why drug-resistant variants appear in Lenski's founder's population despite the fact that these bacteria were never exposed to antibiotics?
This was explained over 60 years ago. The answer is random mutations that occur in the background.
Esther and Joshua Lederberg worked out the concept of spontaneous mutations and how it results in antibiotic resistance, and you can read their 1952 paper here:
REPLICA PLATING AND INDIRECT SELECTION OF BACTERIAL MUTANTS - PMC
Luria and Delbruck worked out all of the math for the process in this paper from 1943:
https://www.genetics.org/content/28/6/491
Interestingly, the math of evolution and the math of slot machines are somewhat related:
quote:
In 1943, it had long been known that bacterial cultures rapidly develop resistance to viral infection. Some biologists argued that viruses directly induced resistance mutations, while others believed the mutations arose spontaneously before exposure to the virus. But when Luria and Delbrck first attempted to distinguish between these two hypotheses, they were frustrated by what appeared to be irritatingly inconsistent mutation rates. Then, after watching a colleague win a jackpot ($3 in dimes!) at a slot machine, Luria realized this inconsistency was telling him something: the number of mutant bacterial colonies present at the end of the experiment depended on when the mutations arose. Mutations arising in earlier generations would be present in many descendent cells (a jackpot), whereas mutations occurring in later generations would be present in only a few cells.
Salvador Luria and Max Delbrück on Random Mutation and Fluctuation Tests - PMC
Also, here's a great photo of Luria and Delbruck:
Edited by Taq, : No reason given.

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Taq
Member
Posts: 9944
Joined: 03-06-2009
Member Rating: 4.8


Message 28 of 239 (876552)
05-22-2020 11:10 AM
Reply to: Message 27 by Kleinman
05-21-2020 7:19 PM


Kleinman writes:
So, how do you apply it to the Kishony and Lenski experiments?
Properly. [/snark]
You have to focus on something specific in order for your question to make sense. Are we talking about neutral drift, and if so in what sense? Are we comparing divergence between hypermutators and non-hypermutators? Are we looking at divergence between lineages? There's a lot going on in those experiments.
What this does is it forces his populations to compete for the limited resources and the more fit variant must drive the less fit variant to extinction in order to accumulate the necessary replications for improving fitness.
Could you explain why this is the case? Why can't less fit individuals exist in small numbers?
The mathematics for DNA evolution is still the same for both, but you can see why competition slows the evolutionary process.
I would fully agree that strong selection and/or bottlenecks can reduce genetic variation. Is that what you are getting at?
I would also be interested in your comments with respect to the Lederberg's plate replica experiment and Luria and Delbruck's fluctuation assay. You seemed confused on the subject of random mutation, so I thought those experiments could shed some light on the subject.
What do you think would happen if Lenski were to run his experiment at non-optimal temperature (thermal stress) along with the starvation stress? Or if Kishony were to try to run his experiment with 2 drugs instead of 1.
If two drugs were used then it would be much more difficult for a lineage to emerge that is resistant to two drugs. If the bacteria were exposed to two drugs in sequence then the emergence of a dual resistant lineage would be much greater. However, that's not the point of the experiment. The point of the experiment is to understand the dynamics of evolution, so the experiment was designed to produce results in a time period conducive to study. Lenski, on the other hand, was a bit more ambitious.
We already know that the Kishony experiment won't work as designed unless the increase in drug concentration is limited so that a single mutation gives adaptation to the next higher drug concentration region.
Scientists do tend to focus on experiments that work, so I am failing to understand the problem here.

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Taq
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Posts: 9944
Joined: 03-06-2009
Member Rating: 4.8


Message 34 of 239 (876722)
05-26-2020 5:35 PM
Reply to: Message 31 by Kleinman
05-26-2020 9:31 AM


Re: Trying to give nwr more than a vague understanding of DNA evolution
Kleinman writes:
It is you who is wrong nwr. DNA evolution is a binomial probability problem. The random trial is a replication and the two possible outcomes are, does a beneficial mutation occur or does a beneficial mutation does not occur. That is analogous to a coin toss problem where the random trial is the toss of the coin and the two possible outcomes does a head occur or does a head not occur.
No analogy is perfect, but I don't think a coin toss is a good one. First, the benefice of a mutation can be small or great, not simply heads or tails. Second, the same mutation can be neutral or detrimental in one genetic background and beneficial in another. A lottery might be a better comparison where someone can win 5 bucks or hundreds of millions, and the winning ticket from one drawing won't necessarily be a winner in the next.
It doesn't matter whether the environment is static or not.
Umm, yes it does. Read up on fitness landscapes and niche specialization. As you near an optimum the number of beneficial changes is greatly reduced. A changing environment results in optimized species being less optimize which increases the number of potential beneficial changes.
If they were to change their environments at any time during the performance of the experiment, that would mean they would be changing the evolutionary trajectories for increasing fitness making those evolutionary trajectories more complex.
Why would it be more complex? If you changed temperature or salt concentrations at the same time I don't see how it would be more complex, as long as those conditions weren't immediately lethal.

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 Message 31 by Kleinman, posted 05-26-2020 9:31 AM Kleinman has replied

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Taq
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Posts: 9944
Joined: 03-06-2009
Member Rating: 4.8


(1)
Message 39 of 239 (876749)
05-27-2020 11:47 AM
Reply to: Message 38 by Kleinman
05-27-2020 9:28 AM


Re: Responsed to nwr and jar
Kleinman writes:
That's why when Kishony runs his experiment with ciprofloxacin, any variant with a mutation that might be beneficial for trimethoprim (or any other class of antibiotics for that matter) cannot successfully evolve on his plate.
I don't see why this would be the case. If resistance to cipro is gained by a single substitution mutation then it wouldn't matter if the founding population also has a single substitution for trimethoprim resistance. It is just a matter of having enough divisions to get that cipro mutation. If you took a cipro resistant colony and grew it up in large numbers on trimethoprim plates you would have the same chances of getting that mutant as you would with a cipro sensitive clone.

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Taq
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Posts: 9944
Joined: 03-06-2009
Member Rating: 4.8


(2)
Message 40 of 239 (876750)
05-27-2020 11:59 AM
Reply to: Message 35 by Kleinman
05-26-2020 7:15 PM


Re: Trying to give nwr more than a vague understanding of DNA evolution
Kleinman writes:
That's correct that a mutation can be neutral or detrimental in one environment (what you call a genetic background) and beneficial in another.
Genetic background and environment are two different things. What I am talking about is epistasis:
"Epistasis is a phenomenon in genetics in which the effect of a gene mutation is dependent on the presence or absence of mutations in one or more other genes, respectively termed modifier genes."
Epistasis - Wikipedia
What changes could you make to the Kishony experiment to make his populations evolve more quickly?
You could change growth temperature, salt concentration, protein sources, carbon sources, and so on. Growing bacteria in the same environment for long periods of time moves them towards a peak in the fitness landscape where very few if any mutations improving fitness.
Fitness landscape - Wikipedia
Let's say that Kishony uses two drugs instead of one in his experiment. Let's say one drug requires mutations A1, A2, A3 for adaptation, and the other drug requires mutations B1, B2, B3.
For a single drug it would be A1, A2, and A3. It would be the same pathway, and it wouldn't be more complex. The pathways for resistance to each drug are the same no matter how many drugs are present.
Why would you think that adaptation to salt concentrations would give the require the same mutations as thermal stress?
I never said they would. If the bacteria are adapting to multiple new challenges at the same time then this will select for many new beneficial mutations in many genes. If we are measuring evolution as the fixation of beneficial mutations, then a big change in environment will result in a higher rate of evolution.
Also, there could be overlap in salt and temperature adaptations, such as chaperone proteins that could stabilize proteins in both high temps and different salt concentrations (i.e. heat shock proteins).

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 Message 35 by Kleinman, posted 05-26-2020 7:15 PM Kleinman has replied

Replies to this message:
 Message 41 by Kleinman, posted 05-27-2020 1:15 PM Taq has replied

  
Taq
Member
Posts: 9944
Joined: 03-06-2009
Member Rating: 4.8


Message 42 of 239 (876753)
05-27-2020 1:34 PM
Reply to: Message 41 by Kleinman
05-27-2020 1:15 PM


Re: Trying to give nwr more than a vague understanding of DNA evolution
Kleinman writes:
You are conflating two concepts, the creation of new alleles (DNA evolution) and the expression of any one allele (epistasis).
I never confused those. Epistasis is a description of how mutations and alleles interact with one another to give rise to a phenotype.
But even if they did, why would you think that it would take fewer than a billion replications for each evolutionary step to evolve and adapt to the antibiotic selection pressure?
That's not the point. What we are saying is that big changes in environment can lead to more evolution. This is due to fitness landscapes.
The key point that you are missing here is that all these beneficial mutation somehow have to end up in some common lineage for this lineage to be adapted to all these selection pressures.
However, they don't have to be acquired all at the same time. In fact, different lineages can take different pathways, such as one lineage adapting to temperature first, followed by salt concentration. A different lineage could adapt to salt concentration first, then temperature. There could also be multiple different mutational pathways for each environmental challenge, such as bats and birds having different adaptations for flight.
But when Kishony runs his experiment with two drugs, only when some member of the population has a beneficial mutation for both ciprofloxacin and for trimethoprim will that member be able to grow in the next higher drug concentration region.
If the experiment were set up with different regions of the plate having different antibiotics then you could have lineages adapting to one drug and then the other.
And fixation is not required for DNA evolution to occur.
Then why did you say the following in a previous post?
"What this does is it forces his populations to compete for the limited resources and the more fit variant must drive the less fit variant to extinction in order to accumulate the necessary replications for improving fitness."
You are speculating.
You are also speculating when you say that adaptations to temperature and salt concentrations must be different mutations.

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 Message 41 by Kleinman, posted 05-27-2020 1:15 PM Kleinman has replied

Replies to this message:
 Message 43 by Kleinman, posted 05-27-2020 3:40 PM Taq has replied

  
Taq
Member
Posts: 9944
Joined: 03-06-2009
Member Rating: 4.8


Message 44 of 239 (876768)
05-27-2020 6:42 PM
Reply to: Message 43 by Kleinman
05-27-2020 3:40 PM


Re: Trying to give nwr more than a vague understanding of DNA evolution
Then, explain to us how epistasis affects the mathematics of either the Kishony or Lenski experiments.
The genetic background of the population will determine the probability of arriving at a beneficial mutation.
And the more complex the fitness landscape, the more complex any evolutionary trajectory.
A complex landscape can afford multiple evolutionary pathways towards increased fitness, but each pathway is as simple as it would be in a simple landscape. If you want to define complexity as the number of possible evolutionary pathways then I would agree.
Big environmental changes are far more difficult for populations to adapt to.
That depends on a lot of factors. When the first limbed fish started pushing themselves onto land they had very little competition from other land animals. However, a poorly adapted fish will have a very tough time moving onto land now since there are a lot of well adapted tetrapods filling those niches. The K/T meteor impact produced a massive change in environment, and what resulted was the radiation of mammals and birds, one of the biggest surges in evolutionary change in the fossil record.
DNA evolution works most efficiently when only a single mutation gives improved fitness in the given environment. The reason for this is the multiplication rule which requires exponentially more replications for that evolutionary process to have a reasonable probability of occurring.
What you seem to be ignoring is that there is often more than one mutation that is beneficial, and evolution can search for those solutions in parallel. It's not as if it has to be one mutation at a time. Epistasis also demonstrates that neutral mutations can become beneficial at a future time point as they interact with new mutations and new environments.
Let's use your slot-machine analogy. Let's say there are two possible jackpots, a super jackpot, and a big jackpot. And let the probability of winning the super jackpot is one in ten million and the probability of winning the big jackpot is one in a million with each pull of the arm. Do you understand how to compute the probability of winning both of those jackpots as a function of the number of pulls on the arm?
Given the right population dynamics and environments, it is pretty simple. With an initial increase of 20 million you are almost guaranteed to get the first mutation. The winner of that jackpot starts dividing until it has 2 million offspring which nearly guarantees a winner for the next jackpot.
You don't need to do that. Simply take the bacteria that has already adapted to ciprofloxacin and use those as the starter population for the trimethoprim experiment. All you are demonstrating is that DNA evolution works most efficiently a single selection pressure at a time. That's how MRSA was created except in the clinical environment.
Those types of scenarios rarely exist outside of labs. Outside of labs, species exist in a diverse ecology and rarely do they live in a tightly controlled environment that only differs by one variable.
Not so. Lenski has run experiments using thermal stress for his selection condition.
That's one lineage of one species of bacteria. It can't be generalized to all bacteria or all life.
Edited by Taq, : No reason given.

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 Message 43 by Kleinman, posted 05-27-2020 3:40 PM Kleinman has replied

Replies to this message:
 Message 45 by Kleinman, posted 05-27-2020 10:18 PM Taq has replied

  
Taq
Member
Posts: 9944
Joined: 03-06-2009
Member Rating: 4.8


Message 48 of 239 (876790)
05-28-2020 11:33 AM
Reply to: Message 45 by Kleinman
05-27-2020 10:18 PM


Re: Trying to give nwr more than a vague understanding of DNA evolution
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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 Message 45 by Kleinman, posted 05-27-2020 10:18 PM Kleinman has replied

Replies to this message:
 Message 50 by Kleinman, posted 05-28-2020 2:12 PM Taq has replied

  
Taq
Member
Posts: 9944
Joined: 03-06-2009
Member Rating: 4.8


Message 49 of 239 (876791)
05-28-2020 11:39 AM
Reply to: Message 46 by mike the wiz
05-28-2020 6:09 AM


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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Taq
Member
Posts: 9944
Joined: 03-06-2009
Member Rating: 4.8


Message 51 of 239 (876806)
05-28-2020 2:34 PM
Reply to: Message 50 by Kleinman
05-28-2020 2:12 PM


Re: Trying to give nwr more than a vague understanding of DNA evolution
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?

This message is a reply to:
 Message 50 by Kleinman, posted 05-28-2020 2:12 PM Kleinman has replied

Replies to this message:
 Message 52 by Kleinman, posted 05-28-2020 3:25 PM Taq has replied

  
Taq
Member
Posts: 9944
Joined: 03-06-2009
Member Rating: 4.8


Message 53 of 239 (876811)
05-28-2020 5:55 PM
Reply to: Message 52 by Kleinman
05-28-2020 3:25 PM


Re: Trying to give nwr more than a vague understanding of DNA evolution
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.

This message is a reply to:
 Message 52 by Kleinman, posted 05-28-2020 3:25 PM Kleinman has replied

Replies to this message:
 Message 54 by Kleinman, posted 05-28-2020 6:50 PM Taq has replied

  
Taq
Member
Posts: 9944
Joined: 03-06-2009
Member Rating: 4.8


Message 55 of 239 (876833)
05-29-2020 10:49 AM
Reply to: Message 54 by Kleinman
05-28-2020 6:50 PM


Re: Trying to give nwr more than a vague understanding of DNA evolution
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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 Message 54 by Kleinman, posted 05-28-2020 6:50 PM Kleinman has replied

Replies to this message:
 Message 56 by Kleinman, posted 05-29-2020 11:58 AM Taq has replied

  
Taq
Member
Posts: 9944
Joined: 03-06-2009
Member Rating: 4.8


(2)
Message 57 of 239 (876843)
05-29-2020 12:23 PM
Reply to: Message 56 by Kleinman
05-29-2020 11:58 AM


Re: Trying to give nwr more than a vague understanding of DNA evolution
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.

This message is a reply to:
 Message 56 by Kleinman, posted 05-29-2020 11:58 AM Kleinman has replied

Replies to this message:
 Message 58 by Kleinman, posted 05-29-2020 1:20 PM Taq has replied

  
Taq
Member
Posts: 9944
Joined: 03-06-2009
Member Rating: 4.8


(2)
Message 59 of 239 (876869)
05-29-2020 5:22 PM
Reply to: Message 58 by Kleinman
05-29-2020 1:20 PM


Re: Trying to give nwr more than a vague understanding of DNA evolution
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:
2 Forces in molecular evolution
2.1 Mutation
2.2 Recombination
2.2.1 Gene conversion
2.3 Genetic drift
2.4 Selection
2.5 Intragenomic conflict
3 Genome architecture
3.1 Genome size
3.2 Repetitive elements
3.3 Chromosome number and organization
3.4 Gene content and distribution
3.5 Organelles
4 Origins of new genes
5 In vitro molecular evolution experiments
6 Molecular phylogenetics
7 The driving forces of evolution
8 Protein evolution
8.1 Relation to nucleic acid evolution
9 Discordance with morphological evolution
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?

This message is a reply to:
 Message 58 by Kleinman, posted 05-29-2020 1:20 PM Kleinman has replied

Replies to this message:
 Message 60 by Kleinman, posted 05-29-2020 6:48 PM Taq has replied

  
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