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Author Topic:   Do you really understand the mathematics of evolution?
AZPaul3
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(2)
Message 16 of 60 (876462)
05-20-2020 12:41 PM
Reply to: Message 14 by Kleinman
05-20-2020 10:53 AM


Re: Responses nwr and AZPaul3
So why doesn't it take 10 or 100 replications for each evolutionary step?

What evolutionary step? The edge of the next gradient? Do you know how far that is? Do you know the size of the bacteria?

What makes you think resistance was not achieved in the first 10 generations in some subset of the population? What makes you think that resistance wasn't lost again in the next 10? What makes you think resistance could not have been developed and lost many times by many disparate subsets of the population in this long slog across the gradient?

You don't know how evolution works do you?

Don't you find this surprising that drug-resistant bacteria would appear in bacterial populations that were never exposed to the antibiotics and there was resistance to many different antibiotics?

If you understood how evolution worked you wouldn't find such an occurrence surprising either. Just because the natural selection side of the process isn't being tested yet doesn't mean the random mutation side doesn't still occur.

Thus is the power of accumulating genetic diversity in a large population.

You are correct, neither Kishony nor any members of the Kishony team have ever published a paper describing the mathematics of their experiment. Kishony only talks about the billion replications in his video which I linked to in Message 3.

You're citing as their scientific data the informal talk of the group's PopSci outreach video? Academic quality noted.

So, why don't you tell us how large the population must be for these drug-resistant variants to appear?

From a minimum of 1 to an indeterminate maximum. And you don't understand why that is do you.

Edited by AZPaul3, : No reason given.


Factio Republicana delenda est.

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NosyNed
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Member Rating: 3.8


(3)
Message 17 of 60 (876467)
05-20-2020 1:22 PM
Reply to: Message 14 by Kleinman
05-20-2020 10:53 AM


evolution
Don't you find this surprising that drug-resistant bacteria would appear in bacterial populations that were never exposed to the antibiotics and there was resistance to many different antibiotics?

Why would that be at all surprising? That question of yours makes it sound like you expect a mutation to appear because it is needed. But that has nothing to do with it. I'm being silly but it almost makes it seem like you have no clue about evolution.


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Kleinman
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From: United States
Joined: 10-06-2016


Message 18 of 60 (876475)
05-20-2020 5:29 PM


Responses nwr, AZPaul3, and NosyNed
Kleinman writes:

Are you familiar with the work of Haldane, Kimura, and many other population geneticists?

nwr writes:

Somewhat. The mathematics that they use is ordinary mathematical probability theory. Is that what you mean by "mathematics of evolution"?


The mathematics of evolution requires different mathematics depending on the evolutionary process that you are trying to describe. You can't use the mathematics of DNA evolution to describe competition and fixation but you can have both processes occurring simultaneously such as what is occurring with the Lenski experiment. And the mathematics of recombination is different than either DNA evolution or competition and fixation. Mendelian genetics is a simple example of a recombination model. DNA evolution is stochastic (it can be modeled as a random walk or done as a simple probability problem using the "at least one rule"). Competition and fixation, on the other hand, is deterministic (unless you are talking about fixation by drift).
Kleinman writes:

So why doesn't it take 10 or 100 replications for each evolutionary step?

nwr writes:

I puzzled as to why you would think that.
Evolution isn't a mechanical system to grind out a sequence of steps leading to a particular result. Rather, evolution is a system of keeping the population well adapted to a changing environment.


But that's exactly what the Kishony experiment is demonstrating. His lineages are grinding out replications until some lucky member gets the correct mutation that enables that variant to grow in the next higher concentration drug region. Then that new variant must grind out more replications until some lucky descendent gets the next beneficial mutation that enables that new variant to grow in an even higher drug concentration region. It's a random walk with lots of members taking random steps but only the lucky few get to grow in the next higher drug concentration regions.
Kleinman writes:

Don't you find this surprising that drug-resistant bacteria would appear in bacterial populations that were never exposed to the antibiotics and there was resistance to many different antibiotics?

nwr writes:

No, that is not at all surprising.
Evolution is a system of trial and error, in order to see what works well. If you are using trial and error methods, then you are going to try out things that turn out to not work. So the bacteria population tries mutations that turn out to not be currently helpful. That's what we should expect.

If they could not produce occasional antibiotic resistant variants when not useful, then they also could not produce them when would be useful.


Good, so now learn how to do the mathematics of this process. Try to understand why it takes a billion replications for a lineage to accumulate each particular mutation that gives resistance to the antibiotic used in the Kishony experiment. And by the way, the same principle applies to the lineages in the Lenski experiment, however, they are not accumulating the mutations which give drug resistance (in fact, those mutations disappear from his populations), Lenski's lineages are accumulating mutations which give more efficient usage of the limited glucose available.

Kleinman writes:

So why doesn't it take 10 or 100 replications for each evolutionary step?

AZPaul3 writes:

What evolutionary step? The edge of the next gradient? Do you know how far that is? Do you know the size of the bacteria?

What makes you think resistance was not achieved in the first 10 generations in some subset of the population? What makes you think that resistance wasn't lost again in the next 10? What makes you think resistance could not have been developed and lost many times by many disparate subsets of the population in this long slog across the gradient?

You don't know how evolution works do you?


You are conflating geometry and genetics. The correct mutation which would allow a variant to grow in the next higher concentration region could occur in 10 or 100 replications, but it might take more than a billion replications as well. But try and recall what the meaning of a mutation rate is and that is a binomial probability problem (does the beneficial mutation occur or not). And if the mutation rate is 1e9, you will have on average only one occurrence of that particular mutation every billion replications. Since this is a binomial probability problem, check and see what the standard deviation and variance are for this problem and why the number of replications is much more likely to be close to a billion replications.
Kleinman writes:

Don't you find this surprising that drug-resistant bacteria would appear in bacterial populations that were never exposed to the antibiotics and there was resistance to many different antibiotics?

AZPaul3 writes:

If you understood how evolution worked you wouldn't find such an occurrence surprising either. Just because the natural selection side of the process isn't being tested yet doesn't mean the random mutation side doesn't still occur.

Thus is the power of accumulating genetic diversity in a large population.


I don't and didn't find this surprising but Lenski did. That's why he wrote a paper on this issue and he didn't explain why it happens. And if you consider the Kishony experiment when he used Ciprofloxacin, his population of a billion not only will have a high probability of having the first beneficial mutation for Ciprofloxacin resistance, he also has a high probability of a variant with a beneficial mutation for Trimethoprim (which won't help that variant in the Ciprofloxacin environment).
Kleinman writes:

You are correct, neither Kishony nor any members of the Kishony team have ever published a paper describing the mathematics of their experiment. Kishony only talks about the billion replications in his video which I linked to in Message 3.

AZPaul3 writes:

Your citing as their scientific data the informal talk of the group's PopSci outreach video? Academic quality noted.


Hey, you run with the data you have. Would you be more comfortable with the Lenski experiment data? In his experiment, he gets fixation for each beneficial mutation in a range of 200-1000 generations/mutation. He gets about 5e8 replications/day based on about 6 1/2 doublings/day (generations). So, how many replications for each beneficial mutation in the Lenski experiment?
Kleinman writes:

So, why don't you tell us how large the population must be for these drug-resistant variants to appear?

AZPaul3 writes:

From a minimum of 1 to an indeterminate maximum. And you don't understand why that is do you.


I can narrow down your estimate from 1 to infinity a little bit and you could as well if you understood how to do the mathematics of evolution.

Kleinman writes:

Don't you find this surprising that drug-resistant bacteria would appear in bacterial populations that were never exposed to the antibiotics and there was resistance to many different antibiotics?

NosyNed writes:

Why would that be at all surprising? That question of yours makes it sound like you expect a mutation to appear because it is needed. But that has nothing to do with it. I'm being silly but it almost makes it seem like you have no clue about evolution.


I've never said that. I know that mutations are random events. So, now that you understand why you don't need antibiotics for drug-resistant variants to appear, why should medical providers be discouraged from using antibiotics?

Replies to this message:
 Message 19 by jar, posted 05-20-2020 5:33 PM Kleinman has responded
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 Message 22 by AZPaul3, posted 05-20-2020 7:45 PM Kleinman has not yet responded

  
jar
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Posts: 32512
From: Texas!!
Joined: 04-20-2004
Member Rating: 1.9


(1)
Message 19 of 60 (876476)
05-20-2020 5:33 PM
Reply to: Message 18 by Kleinman
05-20-2020 5:29 PM


Time to close this farce down
Kleinman writes:

I know that mutations are random events. So, now that you understand why you don't need antibiotics for drug-resistant variants to appear, why should medical providers be discouraged from using antibiotics?

That alone should be more than enough to simply close this thread down and adjourn for a pint.

Id10T


My Sister's Website: Rose Hill Studios     My Website: My Website

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nwr
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Posts: 5610
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 4.5


Message 20 of 60 (876478)
05-20-2020 6:24 PM
Reply to: Message 18 by Kleinman
05-20-2020 5:29 PM


Re: Responses nwr, AZPaul3, and NosyNed
His lineages are grinding out replications until some lucky member gets the correct mutation that enables that variant to grow in the next higher concentration drug region.

That's a typical creationist misunderstanding of evolution.

No, I'm not saying that you are a creationist. I am saying that your misunderstanding of evolution is similar to the misunderstanding that we commonly see among creationists.

The correct mutation which would allow a variant to grow in the next higher concentration region could occur in 10 or 100 replications, but it might take more than a billion replications as well.

Your use of "correct" further betrays your misunderstanding of evolution.

So, now that you understand why you don't need antibiotics for drug-resistant variants to appear, why should medical providers be discouraged from using antibiotics?

And for that I give you a grade of A. That's a perfect score. You have convincingly demonstrated that you are completely clueless about evolution.

Fundamentalism - the anti-American, anti-Christian branch of American Christianity

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Kleinman
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Posts: 160
From: United States
Joined: 10-06-2016


Message 21 of 60 (876479)
05-20-2020 6:34 PM
Reply to: Message 19 by jar
05-20-2020 5:33 PM


Time for jar to sober up
Kleinman writes:

I know that mutations are random events. So, now that you understand why you don't need antibiotics for drug-resistant variants to appear, why should medical providers be discouraged from using antibiotics?

jar writes:

That alone should be more than enough to simply close this thread down and adjourn for a pint.

Id10T


When you sober up, why don't you tell us what is the most common medical reason for hospital admission? Since you still probably won't see straight after you sober up, here's the data:
Most Common Diagnoses in Hospital Inpatient Stays - HCUP Fast Stats

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AZPaul3
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Posts: 4982
From: Phoenix
Joined: 11-06-2006
Member Rating: 4.0


Message 22 of 60 (876480)
05-20-2020 7:45 PM
Reply to: Message 18 by Kleinman
05-20-2020 5:29 PM


Re: Responses nwr, AZPaul3, and NosyNed
His lineages are grinding out replications until ...

No "until". The genetic grind never stops and it certainly wasn't aimed at the next "step".

What the experiment showed was that when the environment changed a part of the population was able to adapt to the new conditions.

Your "intelligent design" thinking is trying to read too much into the results.

And if the mutation rate is 1e9, you will have on average only one occurrence of that particular mutation every billion replications.

You got that mutation rate from the informal talk of the group's PopSci outreach video. It isn't real.

And it doesn't matter. When the edge of a gradient had been reached and the environment facing the population changed what happened? The blind undirected processes of evolution allowed the population to adapted to the changing environment.

That's the whole point here. Your mathinations are bogus. Unlike Haldane and others, your math does not accurately model the system you are trying to describe. You are trying to force your desired results into the model.

I can narrow down your estimate from 1 to infinity a little bit and you could as well if you understood how to do the mathematics of evolution.

Why? It doesn't matter. Despite your bogus math averages and probabilities the point stands that when the environment changed the population adapted in pretty short order. And we understand how and why.

So, now that you understand why you don't need antibiotics for drug-resistant variants to appear, why should medical providers be discouraged from using antibiotics?

So besides being ignorant of evolution you don't know how antibiotic resistance became such an issue either.

Do you know how antibiotics work? Do you know why antibiotics are so effective in the human body? Why it's important to complete the full series? Do you understand the interconnections between the antibiotic, the immune system and the rise of resistance? Do you understand that in treatment it is not the antibiotic that finally ends the infection?


Factio Republicana delenda est.

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ringo
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Posts: 18112
From: frozen wasteland
Joined: 03-23-2005
Member Rating: 2.4


(2)
Message 23 of 60 (876494)
05-21-2020 11:50 AM
Reply to: Message 14 by Kleinman
05-20-2020 10:53 AM


Re: Responses nwr and AZPaul3
Kleinman writes:

Don't you find this surprising that drug-resistant bacteria would appear in bacterial populations that were never exposed to the antibiotics and there was resistance to many different antibiotics?


I only claim to have the first inkling of a clue about evolution but I don't find that surprising. Drug-resistant bacteria evolve, whether there are drugs in the neighbourhood or not. Hint: mutations. When drugs do mosey by, the drug-resistant bacteria survive. No mystery.

"I'm Fallen and I can't get up!"

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Diomedes
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From: Central Florida, USA
Joined: 09-13-2013
Member Rating: 5.5


(3)
Message 24 of 60 (876514)
05-21-2020 2:34 PM
Reply to: Message 23 by ringo
05-21-2020 11:50 AM


Re: Responses nwr and AZPaul3
ringo writes:

Kleinman writes:

Don't you find this surprising that drug-resistant bacteria would appear in bacterial populations that were never exposed to the antibiotics and there was resistance to many different antibiotics?


I only claim to have the first inkling of a clue about evolution but I don't find that surprising. Drug-resistant bacteria evolve, whether there are drugs in the neighbourhood or not. Hint: mutations. When drugs do mosey by, the drug-resistant bacteria survive. No mystery.

That is my understanding as well. I think some of the confusion arises from Creationists assuming that environmental pressures cause evolution to occur. That is not correct. Environmental pressures allow previous mutations that are advantageous to manifest. The mutations and their effect occurs regardless. If the mutation then results in a selective advantage for the organism, it survives and thrives.


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Taq
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Posts: 8300
Joined: 03-06-2009
Member Rating: 3.9


Message 25 of 60 (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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Replies to this message:
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Taq
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Posts: 8300
Joined: 03-06-2009
Member Rating: 3.9


Message 26 of 60 (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

Luria and Delbruck worked out all of the math for the process in this paper from 1943:

MUTATIONS OF BACTERIA FROM VIRUS SENSITIVITY TO VIRUS RESISTANCE

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 Delbrück 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

Also, here's a great photo of Luria and Delbruck:

Edited by Taq, : No reason given.


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Kleinman
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Posts: 160
From: United States
Joined: 10-06-2016


Message 27 of 60 (876538)
05-21-2020 7:19 PM
Reply to: Message 25 by Taq
05-21-2020 5:16 PM


Something has come up and I'll busy for the next few days but I wanted to respond to Taq's message. I'll try to get to the others next week.

Kleinman writes:

If you think you understand the mathematics of evolution,

Taq writes:

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:

300 Multiple Choices


Yes there is a lot of math. So, how do you apply it to the Kishony and Lenski experiments?
Kleinman writes:

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.

Taq writes:

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.


The bottleneck in the Lenski experiment is about every 6 1/2 generations. What that does is introduce a discontinuity in the mathematics which makes it very difficult to model this with a closed-form solution. You can see how I handled the discontinuity using a numerical solution here:
(PDF) Fixation and Adaptation in the Lenski E. coli Long Term Evolution Experiment

But there is another major difference between the Kishony and Lenski experiments. The Kishony experiment has a much larger carrying capacity than the Lenski experiment. 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. This slows the DNA evolution when compared with the rate of evolution in the Kishony experiment. And note, the less fit variants in the Kishony experiment are still living on in the lower drug concentration regions, no fixation required for adaptation. The mathematics for DNA evolution is still the same for both, but you can see why competition slows the evolutionary process. The less fit variants are consuming resources that the more fit variant could use to replicate and will continue to do so until these variants are driven to extinction. By the way, I show in the link above how to predict what would happen if Lenski used 1ml or 100ml of the solution instead of the 10ml.

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. 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. What would it take to make that experiment work?

Have a good weekend, see y'all next week.


This message is a reply to:
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Taq
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Posts: 8300
Joined: 03-06-2009
Member Rating: 3.9


Message 28 of 60 (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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Kleinman
Member
Posts: 160
From: United States
Joined: 10-06-2016


Message 29 of 60 (876662)
05-25-2020 10:41 AM


Responses to Taq and several other members
AZPaul3's edited version of what Kleinman writes:

His lineages are grinding out replications until ...

AZPaul3 writes:

No "until". The genetic grind never stops and it certainly wasn't aimed at the next "step".


Try quoting my entire statement then perhaps you may understand what I'm saying. Here's my full quote.
Kleinman writes:

His lineages are grinding out replications until some lucky member gets the correct mutation that enables that variant to grow in the next higher concentration drug region.


And sure the grind continues (unless extinction occurs which is the most common outcome for most lineages). Too bad you don't how to do the mathematics of this grind, then you could explain the mathematics of the evolution of drug resistance.
Kleinman writes:

Don't you find this surprising that drug-resistant bacteria would appear in bacterial populations that were never exposed to the antibiotics and there was resistance to many different antibiotics?

Ringo writes:

I only claim to have the first inkling of a clue about evolution but I don't find that surprising. Drug-resistant bacteria evolve, whether there are drugs in the neighbourhood or not. Hint: mutations. When drugs do mosey by, the drug-resistant bacteria survive. No mystery.


It is not a mystery to me as well. So why should physicians be discouraged from using antibiotics when you don't need the antibiotics for resistant variants to appear? This is an especially important question when septicemia and pneumonia are the #1 and #4 causes for hospital admission which could be prevented with timely usage of oral antibiotics in the outpatient environment before these infections become severe.
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?

Taq writes:

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

Luria and Delbruck worked out all of the math for the process in this paper from 1943:

MUTATIONS OF BACTERIA FROM VIRUS SENSITIVITY TO VIRUS RESISTANCE


OK, now use this math to explain the behavior of the Kishony and Lenski experiments. And then, using those equations, predict the behavior of the Lenski experiment if he uses 1ml or 100ml of solution instead of 10ml and predict the behavior the Kishony experiment if he were to try to use two drugs instead of one.
Taq writes:

Interestingly, the math of evolution and the math of slot machines are somewhat related:


Actually, the mathematics of evolution is more like the math of coin tossing. The mathematics of evolution consists of nested binomial probability problems where each binomial probability problem is joined to the other by the multiplication rule of probabilities.

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nwr
Member
Posts: 5610
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 4.5


(2)
Message 30 of 60 (876693)
05-25-2020 9:58 PM
Reply to: Message 29 by Kleinman
05-25-2020 10:41 AM


Re: Responses to Taq and several other members
Try quoting my entire statement then perhaps you may understand what I'm saying. Here's my full quote.
Kleinman writes:

His lineages are grinding out replications until some lucky member gets the correct mutation that enables that variant to grow in the next higher concentration drug region.


And sure the grind continues (unless extinction occurs which is the most common outcome for most lineages).

I guess it is hopeless. You are continuing to make the same mistake that we often see being made by creationists. And you are damned sure that you are right, even though you are wrong.

Actually, the mathematics of evolution is more like the math of coin tossing. The mathematics of evolution consists of nested binomial probability problems where each binomial probability problem is joined to the other by the multiplication rule of probabilities.

No, that's wrong.

That's about what you would get if the environment were completely static. But the environment is changing all the time. So the probabilities are changing all the time.

The problem of drug resistant bacteria isn't that they show up. The problem is too much use of antibiotics will change the environment so that antibiotic resistant bacteria become more highly favored. And then we will see many more of them and they become a problem.


Fundamentalism - the anti-American, anti-Christian branch of American Christianity

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