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Author Topic:   Do you really understand the mathematics of evolution?
PaulK
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Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 127 of 239 (877705)
06-20-2020 1:19 PM
Reply to: Message 126 by vimesey
06-20-2020 6:34 AM


And quite enlightening it is, although hardly surprising, especially in light of the previous thread.

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 Message 126 by vimesey, posted 06-20-2020 6:34 AM vimesey has not replied

  
PaulK
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Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


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 replied

  
PaulK
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Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 181 of 239 (878323)
06-29-2020 12:19 AM
Reply to: Message 180 by Kleinman
06-28-2020 10:12 PM


Re: An important note regarding models of evolution
quote:
I'm glad to see that you are starting to think about this.
I don’t think that is going to last.
quote:
That's part of the problem with these DNA evolution models.
No, it really isn’t a problem. These are models of neutral evolution. They are used to estimate divergence times between species. Since neutral evolution dominates and since it is not practical to identify which loci were selected in the distant past - except by divergence from these models - that’s obviously a sensible thing.
quote:
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.
I think you will find that neutral evolution would. The fact that the models don’t describe selection is not an error at all. It’s an intentional feature.
Edited by PaulK, : Fixed tag

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 Message 180 by Kleinman, posted 06-28-2020 10:12 PM Kleinman has replied

Replies to this message:
 Message 182 by Kleinman, posted 06-29-2020 6:08 AM PaulK has replied

  
PaulK
Member
Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 183 of 239 (878339)
06-29-2020 6:49 AM
Reply to: Message 182 by Kleinman
06-29-2020 6:08 AM


Re: An important note regarding models of evolution
quote:
So you are going to stop thinking? Why? Are you afraid you might actually learn how DNA evolution works?
No, I think you’ll be unhappy because I am thinking and because I do have a good idea of how DNA evolution works.
quote:
Perhaps you think that making assumptions that have no connection with reality will give you any kind of accurate estimate of divergence times between species, but that would just be another example that you don't understand introductory probability theory.
Many bases will be varying neutrally. So a model of neutral evolution will give a reasonable estimate.
quote:
You are on a roll, one error after another. Do you think that fish evolve into mammals and reptiles evolve into birds by neutral evolution?
No, of course not. But do you think the majority of bases are under selective constraint in the Kishony experiment? It’s only a few that are under selection for antibiotic resistance. Others will be under stabilising selection, but hardly the entire genome.
quote:
So, why do you think you can use a model of neutral evolution to estimate divergence times between species?
Because many bases will be evolving neutrally. Really it’s not so hard. Of course, looking for bases that change more slowly also helps - neutral change can be too fast.
quote:
In fact, in your world, not even fixation can occur whether due to drift or selection.
And there is another bizarre assertion. The equilibrium would be roughly equal proportions of each base in a single genome.

This message is a reply to:
 Message 182 by Kleinman, posted 06-29-2020 6:08 AM Kleinman has replied

Replies to this message:
 Message 184 by Kleinman, posted 06-29-2020 11:26 AM PaulK has replied

  
PaulK
Member
Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 185 of 239 (878351)
06-29-2020 11:39 AM
Reply to: Message 184 by Kleinman
06-29-2020 11:26 AM


Re: An important note regarding models of evolution
quote:
Do you think taking a small portion of homologous genome from two different species, ignoring all the other differences in the genomes will give a reasonable estimate of the time separating the two?
A small portion, certainly not, you’d want a number of genes to get a robust result,
quote:
Sure, every base in the genome is subject to selection. That's why if a detrimental mutation occurs somewhere in the genome, at a minimum, its relative fitness is reduced with respect to the rest of the population
Oh dear, oh dear, oh dear. This is not at all a rational argument. In fact it is a complete non-sequitur. There are bases which can freely change without deleterious or beneficial effect.
quote:
PaulK, you are really confused here. The Jukes-Cantor/Felsenstein Markov models are only considering a single site in the genome. How did you get so confused on this subject?
The distribution of the bases in an interbreeding population wouldn’t be random. So how could you apply the probabilities across individuals?
Anyway, until you recognise that DNA evolution is driven by neutral drift, you do not understand the mathematics of DNA evolution.

This message is a reply to:
 Message 184 by Kleinman, posted 06-29-2020 11:26 AM Kleinman has replied

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 Message 186 by Kleinman, posted 06-29-2020 12:18 PM PaulK has replied

  
PaulK
Member
Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 187 of 239 (878362)
06-29-2020 1:05 PM
Reply to: Message 186 by Kleinman
06-29-2020 12:18 PM


Re: An important note regarding models of evolution
quote:
But that's exactly the incorrect approach they are doing with these Markov models. The Jukes-Cantor and derivative models only consider a single site in the genome.
Applying the model to multiple sites is hardly a difficult idea to grasp. Indeed it’s implicit in the part I quoted for you earlier,
quote:
I know, and they show how closely related to a banana you are.
You’re only showing that you’re bananas.
quote:
Oh my, Oh my, now you are going down the Taq trail. Before you toss in recombination, you had better learn how DNA evolution works first.
Apparently I know how DNA evolution works better than you. You do realise that the DNA sequences found in the population are not independent?

This message is a reply to:
 Message 186 by Kleinman, posted 06-29-2020 12:18 PM Kleinman has replied

Replies to this message:
 Message 190 by Kleinman, posted 06-29-2020 2:08 PM PaulK has replied

  
PaulK
Member
Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 192 of 239 (878375)
06-29-2020 3:02 PM
Reply to: Message 190 by Kleinman
06-29-2020 2:08 PM


Re: An important note regarding models of evolution
quote:
And if you assume a stationary transition matrix, you will be making your same blunder twice. You know, there's an old saying, there's no education in the second kick of a mule. Are you going to show that you are twice as close to a banana?
And you still have no idea. Look, if you can’t understand how these models are used, just admit it rather than inventing silly straw we.
quote:
It's your mathematics which you claim is correct that shows you are related to a banana! If you do the Markov chain mathematics correctly, you can predict the behavior of the Kishony experiment. That may not be as much fun as your math showing you are related bananas but it is the correct math.
It’s the correct math when selection is tightly constraining the viable outcomes at that site, but that’s hardly the normal case for DNA evolution.
quote:
But mutations are random and that's why DNA evolution works the way I'm showing you
Well you’re wrong because it mostly doesn’t.
quote:
I'm showing you. And you are not related to bananas. You aren't even related to chimpanzees. You would understand this if you knew how to do the Markov mathematics of DNA evolution correctly. Keep thinking about it, it might come to you.
Since you don’t know how DNA evolution works, your arguments are worthless.

This message is a reply to:
 Message 190 by Kleinman, posted 06-29-2020 2:08 PM Kleinman has replied

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 Message 193 by Kleinman, posted 06-29-2020 4:54 PM PaulK has replied

  
PaulK
Member
Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 194 of 239 (878408)
06-29-2020 5:40 PM
Reply to: Message 193 by Kleinman
06-29-2020 4:54 PM


Re: An important note regarding models of evolution
quote:
I know exactly how fish evolve into mammals clique use these models.
Then why are you misrepresenting it?
quote:
I know exactly where they make their error in their assumptions and I know exactly how to correct the error so that the model works correctly to predict the behavior of experiments such as the Kishony and Lenski experiments
The models aren’t meant to predict the results of those experiments.
So the mistake is all yours.

This message is a reply to:
 Message 193 by Kleinman, posted 06-29-2020 4:54 PM Kleinman has replied

Replies to this message:
 Message 196 by Kleinman, posted 06-29-2020 6:22 PM PaulK has replied

  
PaulK
Member
Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 198 of 239 (878421)
06-30-2020 12:16 AM
Reply to: Message 196 by Kleinman
06-29-2020 6:22 PM


Re: An important note regarding models of evolution
quote:
I'm not.
Yes you did. You tried to pretend that phylogenetic analysis was derived from the figures for a single base. Either you know that’s not true or you don’t know how the models are used.
quote:
I'm trying to point to the error in the assumptions and you see that error as a feature
It is not an error, but since you don’t understand DNA evolution or how the models are used you can’t see that. Too bad for you.

This message is a reply to:
 Message 196 by Kleinman, posted 06-29-2020 6:22 PM Kleinman has replied

Replies to this message:
 Message 199 by Kleinman, posted 06-30-2020 4:26 AM PaulK has replied

  
PaulK
Member
Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 200 of 239 (878456)
06-30-2020 1:02 PM
Reply to: Message 199 by Kleinman
06-30-2020 4:26 AM


Re: An important note regarding models of evolution
quote:
And you think that fish drift into mammals.
More proof that you don’t understand DNA evolution and refuse to learn.
quote:
You cherry-pick a few minuscule portions of a couple of genomes, find a few matches and say the species are related
Do you really think that making things up like this is useful or constructive?
quote:
... this is too bad for those suffering from drug-resistant infections and failed cancer treatments.
I don’t think that making a fool of yourself on an obscure Internet forum helps them much either.

This message is a reply to:
 Message 199 by Kleinman, posted 06-30-2020 4:26 AM Kleinman has replied

Replies to this message:
 Message 203 by Kleinman, posted 06-30-2020 2:47 PM PaulK has replied

  
PaulK
Member
Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 204 of 239 (878471)
06-30-2020 3:15 PM
Reply to: Message 203 by Kleinman
06-30-2020 2:47 PM


Re: An important note regarding models of evolution
quote:
We keep waiting for you to show us how it works.
As I keep telling you that DNA evolution is predominantly neutral.
Until you grasp that point you will continue to blunder.
You cannot make an accurate model until you understand what you are modelling.

This message is a reply to:
 Message 203 by Kleinman, posted 06-30-2020 2:47 PM Kleinman has replied

Replies to this message:
 Message 205 by Kleinman, posted 06-30-2020 3:38 PM PaulK has replied

  
PaulK
Member
Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 207 of 239 (878486)
06-30-2020 4:48 PM
Reply to: Message 205 by Kleinman
06-30-2020 3:38 PM


Re: An important note regarding models of evolution
quote:
Does fixation ever occur with neutral evolution?
Fixation of alleles does. But that can include a degree of polymorphism
With regard to individual bases however I think it will come down to the numbers. How long does it take to reach equilibrium? The mere fact that it would eventually is insufficient. The values seen within a population are not independent. The distant descendants of an individual may be divided between two or more populations - indeed that is exactly the case that phylogenetic analysis is looking for.
Further, for more distant relatives sites that freely vary are not useful because they change too quickly. So it appears that the models are accurate on that score.

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 Message 205 by Kleinman, posted 06-30-2020 3:38 PM Kleinman has replied

Replies to this message:
 Message 208 by Kleinman, posted 06-30-2020 5:22 PM PaulK has replied

  
PaulK
Member
Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 209 of 239 (878495)
06-30-2020 5:32 PM
Reply to: Message 208 by Kleinman
06-30-2020 5:22 PM


Re: An important note regarding models of evolution
quote:
Is that what they are modeling with these Markov chain models?
Obviously not. But if you are concerned with phenotypic change the distinction is important.
quote:
Ok, so you are saying that that distant relative has some base at a site, and over time that base mutates to the 3 other bases when it reaches equilibrium?
I am saying that it is possible for the site to be in equilibrium - with all four bases roughly equally represented - among the distant descendants. But at the same time the site is fixed in some or all of the populations existing at that time.
quote:
So which happens in the real world, equilibrium, or fixation?
Both. At the same time. As explained above. Fixed in some populations but not in equilibrium over all the descendants.

This message is a reply to:
 Message 208 by Kleinman, posted 06-30-2020 5:22 PM Kleinman has replied

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 Message 210 by Kleinman, posted 06-30-2020 6:12 PM PaulK has replied

  
PaulK
Member
Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 211 of 239 (878530)
07-01-2020 7:47 AM
Reply to: Message 210 by Kleinman
06-30-2020 6:12 PM


Re: An important note regarding models of evolution
quote:
I thought you said they were modeling neutral evolution. That is drift, isn't it? And doesn't fixation occur with drift
Fixation occurs within a population and populations are outside the scope of the model. It’s a model of DNA evolution, not population genetics.
quote:
Now you really have me confused. These models as time proceeds go to a condition when "all four bases roughly equally represented". So, are you saying that the genomes in the distant relative were already at equilibrium? And, how can the site be fixed and have "all four bases roughly equally represented" at the same time?
No, you’ve done that to yourself. I really don’t know how you make up this stuff. The equilibrium state is reached in the distant descendants who are divided amongst a number of populations. The base may be fixed in some populations but it is not fixed over all the populations combined.
quote:
How do they tell when the genetic sequence they put into the model is fixed or at equilibrium?
Why would they need to? That isn’t what these models are about.
quote:
And if a base is fixed in a population, does it over time go to equilibrium and if a site is at equilibrium in a population does it go to fixation?
For the purposes of this discussion that doesn’t matter at all. The models don’t deal with populations and don’t need to.

This message is a reply to:
 Message 210 by Kleinman, posted 06-30-2020 6:12 PM Kleinman has replied

Replies to this message:
 Message 212 by Kleinman, posted 07-01-2020 9:41 AM PaulK has replied

  
PaulK
Member
Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 213 of 239 (878554)
07-01-2020 1:21 PM
Reply to: Message 212 by Kleinman
07-01-2020 9:41 AM


Re: An important note regarding models of evolution
quote:
Competition, drift, DNA evolution, recombination,... are all part of population genetics. You are very confused about this subject.
If you think you can get population level information out of a model which doesn’t deal with the concept of populations at all, you are the one that is confused. Population genetics deals with the dynamics of evolution within populations, so that is obviously more appropriate,
quote:
I'm not confused about the subject of population genetics, I'm confused about your explanation of the subject. First, you claim that these Markov models are models of neutral evolution and now you are claiming something different
Oh dear, you are deeply confused. I‘m not claiming anything different at all. I’m just trying to interpret the probabilities produced by the models in terms of the genes we might find, taking into account simple facts like the fact that genes are inherited and that individual bases have a low mutation rate so that closely related individuals will tend to have very similar genes (especially in your favourite haploid populations)
quote:
And now you are saying that in neutral evolution "The equilibrium state is reached in the distant descendants who are divided amongst a number of populations". And now you are saying "The base may be fixed in some populations but it is not fixed over all the populations combined." So, if you are going to try to apply any of these models to real genetic sequences, how do you know when the sequence you are using is from a fixed population or a population that has reached equilibrium?
It don’t believe that it matters, not for the actual applications of the models. Why should it ? If you want to interpret the probabilities as frequencies among descendants, go ahead. But the model won’t give you the distribution. Even you should be able to see that.
I guess I should leave the task of educating you to better teachers, with great patience (which you will no doubt sorely try).

This message is a reply to:
 Message 212 by Kleinman, posted 07-01-2020 9:41 AM Kleinman has replied

Replies to this message:
 Message 214 by Kleinman, posted 07-01-2020 2:01 PM PaulK has replied

  
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