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Author Topic:   Do you really understand the mathematics of evolution?
Kleinman
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Posts: 386
From: United States
Joined: 10-06-2016
Member Rating: 1.1


Message 166 of 239 (878181)
06-26-2020 4:30 PM
Reply to: Message 165 by Straggler
06-26-2020 4:13 PM


Re: Does competition accelerate DNA evolution?
Straggler writes:

You are either due a Nobel prize for revolutionising the whole of biology. Or you are a crackpot.
If I had to put money on which of those two is more probable....

Well - You are the probability whiz - You tell me - Which is more likely?


I really like the Isaac Newton quote: If I have seen further than others, it is by standing upon the shoulders of giants. And there are even some biologists and geneticists in that group. God has given me a gift and I hope it benefits people and reduces suffering in this world.

This message is a reply to:
 Message 165 by Straggler, posted 06-26-2020 4:13 PM Straggler has responded

Replies to this message:
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vimesey
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Posts: 1131
From: Birmingham, England
Joined: 09-21-2011
Member Rating: 3.5


(1)
Message 167 of 239 (878182)
06-26-2020 4:36 PM
Reply to: Message 166 by Kleinman
06-26-2020 4:30 PM


Re: Does competition accelerate DNA evolution?
If I have seen further than others, it is by standing upon the shoulders of giants.

God has given me a gift

I’m curious - do you think those two statements are saying the same thing ?


Could there be any greater conceit, than for someone to believe that the universe has to be simple enough for them to be able to understand it ?

This message is a reply to:
 Message 166 by Kleinman, posted 06-26-2020 4:30 PM Kleinman has not yet responded

Replies to this message:
 Message 168 by Tangle, posted 06-26-2020 4:39 PM vimesey has responded

  
Tangle
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Posts: 7710
From: UK
Joined: 10-07-2011
Member Rating: 2.8


Message 168 of 239 (878183)
06-26-2020 4:39 PM
Reply to: Message 167 by vimesey
06-26-2020 4:36 PM


Re: Does competition accelerate DNA evolution?
Uh oh, now he thinks he's Newton.

Je suis Charlie. Je suis Ahmed. Je suis Juif. Je suis Parisien. I am Mancunian. I am Brum. I am London.I am Finland. Soy Barcelona

"Life, don't talk to me about life" - Marvin the Paranoid Android

"Science adjusts it's views based on what's observed.
Faith is the denial of observation so that Belief can be preserved."
- Tim Minchin, in his beat poem, Storm.


This message is a reply to:
 Message 167 by vimesey, posted 06-26-2020 4:36 PM vimesey has responded

Replies to this message:
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vimesey
Member
Posts: 1131
From: Birmingham, England
Joined: 09-21-2011
Member Rating: 3.5


Message 169 of 239 (878184)
06-26-2020 4:41 PM
Reply to: Message 168 by Tangle
06-26-2020 4:39 PM


Re: Does competition accelerate DNA evolution?
He must have got hit on the head or something.

Could there be any greater conceit, than for someone to believe that the universe has to be simple enough for them to be able to understand it ?

This message is a reply to:
 Message 168 by Tangle, posted 06-26-2020 4:39 PM Tangle has not yet responded

  
jar
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Posts: 32654
From: Texas!!
Joined: 04-20-2004
Member Rating: 1.8


Message 170 of 239 (878185)
06-26-2020 4:42 PM
Reply to: Message 168 by Tangle
06-26-2020 4:39 PM


Re: Does competition accelerate DNA evolution?
... of gab!

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

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Kleinman
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Posts: 386
From: United States
Joined: 10-06-2016
Member Rating: 1.1


Message 171 of 239 (878189)
06-26-2020 5:05 PM


Just the mention of God here is like turning on the light in the kitchen.

Replies to this message:
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vimesey
Member
Posts: 1131
From: Birmingham, England
Joined: 09-21-2011
Member Rating: 3.5


Message 172 of 239 (878190)
06-26-2020 5:17 PM
Reply to: Message 171 by Kleinman
06-26-2020 5:05 PM


You’re right - I’m a cook - it brings me running.

Could there be any greater conceit, than for someone to believe that the universe has to be simple enough for them to be able to understand it ?

This message is a reply to:
 Message 171 by Kleinman, posted 06-26-2020 5:05 PM Kleinman has not yet responded

  
Straggler
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Posts: 10312
From: London England
Joined: 09-30-2006
Member Rating: 3.0


Message 173 of 239 (878192)
06-26-2020 7:03 PM
Reply to: Message 166 by Kleinman
06-26-2020 4:30 PM


Re: Does competition accelerate DNA evolution?
In purely objective mathematical statistical terms which is more probable:

A) You are correct and on the verge of overthrowing one of the most established scientific theories ever conceived thus demanding that all the multiple strands of evidence and discoveries supporting that theory be revisited and alternate explanations (which you are unable to provide as - I quote - “not my job”) be found.

OR

B) Your mathematical model doesn’t accurately model evolution as it actually occurs.

You are the stats whizz. You tell me objecively speaking which is more likely?


This message is a reply to:
 Message 166 by Kleinman, posted 06-26-2020 4:30 PM Kleinman has responded

Replies to this message:
 Message 174 by Kleinman, posted 06-26-2020 7:10 PM Straggler has responded

  
Kleinman
Member
Posts: 386
From: United States
Joined: 10-06-2016
Member Rating: 1.1


Message 174 of 239 (878193)
06-26-2020 7:10 PM
Reply to: Message 173 by Straggler
06-26-2020 7:03 PM


Re: Does competition accelerate DNA evolution?
Straggler writes:

You are the stats whizz. You tell me objecively speaking which is more likely?


Technically, this is a probabilities model, not a statistical model. And can't you tell a fish story when you hear one?

This message is a reply to:
 Message 173 by Straggler, posted 06-26-2020 7:03 PM Straggler has responded

Replies to this message:
 Message 175 by Straggler, posted 06-27-2020 5:48 AM Kleinman has responded

  
Straggler
Member
Posts: 10312
From: London England
Joined: 09-30-2006
Member Rating: 3.0


Message 175 of 239 (878203)
06-27-2020 5:48 AM
Reply to: Message 174 by Kleinman
06-26-2020 7:10 PM


Re: Does competition accelerate DNA evolution?
Have it your way.

Objectively speaking which is more probable?

And can't you tell a fish story when you hear one?

I know cod science when I see it...

(Ba ba boom)


This message is a reply to:
 Message 174 by Kleinman, posted 06-26-2020 7:10 PM Kleinman has responded

Replies to this message:
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driewerf
Junior Member
Posts: 12
Joined: 08-14-2010


Message 176 of 239 (878209)
06-27-2020 8:15 AM
Reply to: Message 46 by mike the wiz
05-28-2020 6:09 AM


quote:
I know the maths that count; bacteria + bacteria = bacteria.

No you don't know what counts. You obviously don't know anything about what you are discussing. But above all, 160 years after the Wilberforce-Huxley debate, creationists have still zero science to offer, and only mockery.
And so Thomas Huxley's answer still resonates:
"If the question is put to me would I rather have a miserable ape for a grandfather or a man highly endowed by nature and possessed of great means of influence and yet who employs these faculties and that influence for the mere purpose of introducing ridicule into a grave scientific discussion, I unhesitatingly affirm my preference for the ape."

This message is a reply to:
 Message 46 by mike the wiz, posted 05-28-2020 6:09 AM mike the wiz has not yet responded

  
Kleinman
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Posts: 386
From: United States
Joined: 10-06-2016
Member Rating: 1.1


(2)
Message 177 of 239 (878210)
06-27-2020 8:51 AM
Reply to: Message 175 by Straggler
06-27-2020 5:48 AM


Re: Does competition accelerate DNA evolution?
Straggler writes:

Have it your way.
Objectively speaking which is more probable?

Kleinman writes:

And can't you tell a fish story when you hear one?

Straggler writes:

I know cod science when I see it...

(Ba ba boom)


On the scale of fish humor, I could go lower than that just for the halibut. But I won't do that because I don't want you to flounder on the mathematics of DNA evolution.

This message is a reply to:
 Message 175 by Straggler, posted 06-27-2020 5:48 AM Straggler has not yet responded

  
Kleinman
Member
Posts: 386
From: United States
Joined: 10-06-2016
Member Rating: 1.1


Message 178 of 239 (878219)
06-27-2020 12:03 PM


The mathematics of DNA evolution
OK, back to the explanation of the mathematics of DNA evolution. In Message 164, I give the probability equation for some member of the founding colony in the Kishony experiment to get the first beneficial mutation A. That equation again is:

P(A)=1-P(Ac)=1-((1−P(BeneficialA)μ)^n)

It should be seen when the number of replications in that colony, n, is large enough, mutation A will occur. And for a (beneficial) mutation rate of e-9, that will be on average 1 occurrence for every e9 replications.

When that mutation occurs and that variant with mutation A migrates into the next higher drug-concentration region, it will start a new colony in which members of that colony need another beneficial mutation (call it B) in order to grow in the next higher drug-concentration region of that environment. That mutation B could occur even if it doesn't migrate into the next higher drug-concentration region but later, I will explain why this is much less probable. So, we can calculate the probability of mutation B occurring on some member of this new colony in the same manner as we computed the probability of mutation A occurring in the original founder's colony. We start with the probability of mutation B occurring in a single replication.

P(B) = P(BeneficialB)μ

Compute the complement:

P(Bc)=1−P(BeneficialB)μ

Compute the probability that mutation be won't happen in nA replications where nA is the number of replications of that new colony formed by the A mutant (variant):

P(Bc)=(1−P(BeneficialB)μ)^nA

Take the complement of that equation to determine the probability of that at least 1 B mutation will occur in nA replications:

P(B)=1-P(Bc)=1-((1−P(BeneficialB)μ)^nA)

The plots for this equation will be identical to the plots for the P(A) equation. You can go back to Message 164 if you want to review this.

To compute the joint probability of mutation B occurring on some member that already has mutation A can be done using the multiplication rule for joint independent events for this case. That joint probability is written as follows:

P(A)P(B)=(1-((1−P(BeneficialA)μ)^n))*(1-((1−P(BeneficialB)μ)^nA))

This same recursion calculation can be done for mutation C for the next higher drug-concentration region, mutation D... and you will obtain an equation that looks like this:

P(A)P(B)P(C)P(D)...=a series of at least 1 probability equations

That's how DNA evolution works for a single selection pressure targeting a single gene where each evolutionary transition requires only a single beneficial mutation to improve fitness. That's how the Kishony experiment works. But the Kishony experiment won't work if the step increase in drug-concentration is too large. That is if two or more mutations are required to increase fitness to that next higher drug concentration. I'll go over that mathematics next week and I will also give the mathematics which explains what will happen if Kishony tries to use two or more drugs in his experiment, even at low concentration increases. After that, I will explain why the Jukes-Cantor/Felsenstein models of DNA evolution are incorrect.

Is this making sense to you dwise1?


  
PaulK
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Posts: 16316
Joined: 01-10-2003
Member Rating: 1.7


Message 179 of 239 (878257)
06-28-2020 4:46 AM


An important note regarding models of evolution
From the Wikipedia article Models of DNA Evolution

The models described on this page describe the evolution of a single site within a set of sequences. They are often used for analyzing the evolution of an entire locus by making the simplifying assumption that different sites evolve independently and are identically distributed. This assumption may be justifiable if the sites can be assumed to be evolving neutrally. If the primary effect of natural selection on the evolution of the sequences is to constrain some sites, then models of among-site rate-heterogeneity can be used.

Let us note that there will be selection constraining some sites in a Kishony experiment.


Replies to this message:
 Message 180 by Kleinman, posted 06-28-2020 10:12 PM PaulK has responded

  
Kleinman
Member
Posts: 386
From: United States
Joined: 10-06-2016
Member Rating: 1.1


Message 180 of 239 (878314)
06-28-2020 10:12 PM
Reply to: Message 179 by PaulK
06-28-2020 4:46 AM


Re: An important note regarding models of evolution
PaulK writes:

From the Wikipedia article Models of DNA Evolution

The models described on this page describe the evolution of a single site within a set of sequences. They are often used for analyzing the evolution of an entire locus by making the simplifying assumption that different sites evolve independently and are identically distributed. This assumption may be justifiable if the sites can be assumed to be evolving neutrally. If the primary effect of natural selection on the evolution of the sequences is to constrain some sites, then models of among-site rate-heterogeneity can be used.

Let us note that there will be selection constraining some sites in a Kishony experiment.


I'm glad to see that you are starting to think about this. That's part of the problem with these DNA evolution models. But by far, the biggest problem is this assumption:
Wikipedia writes:

For a stationary process, where Q does not depend on time t, this differential equation can be solved.


What that means is that as time goes on the Markov chain goes to equilibrium. That is the frequency of each base at the site considered go to 0.25 and no longer changes. Real evolutionary processes don't do anything like that.

Think about what happens in a competitive environment where fixation occurs, the frequency of the given base at that site will go to 1. Jukes-Cantor and all the derivative models are incorrect for describing real evolutionary processes because these processes don't even get near to approaching equilibrium. The Kishony experiment starts with a founder bacterium in the drug-free region. When that variant does 3e9 replications, if the initial base at that site of the founder was a T, on average 3e9 - 3 members of the population will still have a T at that site, 1 member will have an A base at that site, another member will have a C base at that site, and the third member will have a G at that site. The initial E vector at time 0 will be almost exactly the same as the E vector after 3e9 replications. DNA evolution is a non-stationary Markov process.

Tomorrow I will go over the "at least one method" of DNA evolution for two sites in the genome and I'll show you how to draw the state transition diagram for a second-order Markov chain for DNA and what happens if you make the same assumption as for the first-order Markov chain. And you can try and find a blunder in this math.


This message is a reply to:
 Message 179 by PaulK, posted 06-28-2020 4:46 AM PaulK has responded

Replies to this message:
 Message 181 by PaulK, posted 06-29-2020 12:19 AM Kleinman has responded

  
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