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Author Topic:   Do you really understand the mathematics of evolution?
Kleinman
Member
Posts: 528
From: United States
Joined: 10-06-2016
Member Rating: 1.1


Message 226 of 239 (878655)
07-02-2020 5:06 PM
Reply to: Message 225 by PaulK
07-02-2020 4:39 PM


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

Maybe the king can find the contact information by reading some fossil tea-leaves.

PaulK writes:

I could, but I don’t need it. She didn’t support your claim of cherry-picking and that’s all that needs to be said.


And you in the fish evolve into mammals clique think I have trouble with the english language.
Allison Zhang, Stanford University writes:

The first thing to do is align the two DNA sequences together that you’re going to compare. Make sure you’re comparing the same gene!


What do you think that "Make sure you’re comparing the same gene!" means ding-dong? I really hope you are only pretending to be a dummy.
Kleinman writes:

The king will now explain how fish evolve into mammals with frameshift mutations.

PaulK writes:

Poor Kleinman. He thinks that if we acknowledge that frameshift mutations - and indels that don’t shift the frame - we must assume that all evolutionary change is explained by frameshift mutations.


I tried putting this sentence into Google Translate, it still comes out nonsense.
Kleinman writes:

What really scares me is that I think PaulK actually was a biology teacher.

PaulK writes:

Well there’s your imagination running away with you again. I’ve never claimed any qualifications in biology and I’ve never worked as a teacher.


You have definitely proven your lack of qualifications in biology. From what you say here, it is also safe to assume that you have never been a math teacher. What I really suspect you are is an out of work comedian. You definitely have the qualifications for that.

Edited by Kleinman, : Typo


This message is a reply to:
 Message 225 by PaulK, posted 07-02-2020 4:39 PM PaulK has responded

Replies to this message:
 Message 227 by PaulK, posted 07-03-2020 12:50 AM Kleinman has responded

  
PaulK
Member
Posts: 16475
Joined: 01-10-2003
Member Rating: 1.5


Message 227 of 239 (878669)
07-03-2020 12:50 AM
Reply to: Message 226 by Kleinman
07-02-2020 5:06 PM


Re: An important note regarding models of evolution
quote:
And you in the fish evolve into mammals clique think I have trouble with the english language.

Oh, you have plenty of problems, but that’s not one on my list.

quote:
What do you think that "Make sure you’re comparing the same gene!" means ding-dong? I really hope you are only pretending to be a dummy.

Obviously you have to compare the same gene. Do you really think you can compare a gene taken from one species with a random chunk of DNA taken from another and get a decent phylogeny? You must be hoping that I am stupid enough to fall for these silly deceptions.


This message is a reply to:
 Message 226 by Kleinman, posted 07-02-2020 5:06 PM Kleinman has responded

Replies to this message:
 Message 228 by Kleinman, posted 07-03-2020 5:48 AM PaulK has responded

  
Kleinman
Member
Posts: 528
From: United States
Joined: 10-06-2016
Member Rating: 1.1


Message 228 of 239 (878680)
07-03-2020 5:48 AM
Reply to: Message 227 by PaulK
07-03-2020 12:50 AM


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

What do you think that "Make sure you’re comparing the same gene!" means ding-dong? I really hope you are only pretending to be a dummy.

PaulK writes:

Obviously you have to compare the same gene. Do you really think you can compare a gene taken from one species with a random chunk of DNA taken from another and get a decent phylogeny? You must be hoping that I am stupid enough to fall for these silly deceptions.


OK, you are not pretending. So, according to Jukes-Cantor calculation, if you compare a single gene from two different species with a single base difference between them and a mutation rate of e-8, you get 50,000,000 generations separating the two species. So, ding-dong, what if you compare a collection of 10 equivalent genes at the same time, each with only a single base difference, that means 500,000,000 generations separating the two species. Now humans and chimps have more than 20,000 coding genes and very few exactly match. So, even if they differ by a single base at each coding genetic locus, you now have 20,000*50,000,000 generations separating the two species. And that is just 1.5% of the genome that you are comparing. Now, include the regulatory portion of the genome in your analysis which is a much larger portion of the genome. How many generations separating humans and chimpanzees?

Whatever problems I have in English pale to your problems in biology and mathematics.


This message is a reply to:
 Message 227 by PaulK, posted 07-03-2020 12:50 AM PaulK has responded

Replies to this message:
 Message 229 by PaulK, posted 07-03-2020 9:01 AM Kleinman has responded

  
PaulK
Member
Posts: 16475
Joined: 01-10-2003
Member Rating: 1.5


Message 229 of 239 (878685)
07-03-2020 9:01 AM
Reply to: Message 228 by Kleinman
07-03-2020 5:48 AM


Re: An important note regarding models of evolution
quote:
So, according to Jukes-Cantor calculation, if you compare a single gene from two different species with a single base difference between them and a mutation rate of e-8, you get 50,000,000 generations separating the two species.

No. According to the Jukes-Cantor calculation 3/4 of the bases should have changed in 50,000,000 generations. That’s going to be more than one. A lot more.

quote:
So, ding-dong, what if you compare a collection of 10 equivalent genes at the same time, each with only a single base difference, that means 500,000,000 generations separating the two species

Assuming that the genes were of roughly equal length it would mean that they agreed on the divergence time. Which would be well under. 50,000,000 generations.

If you can handle the math, or even read the pages you cite you should know that much.


This message is a reply to:
 Message 228 by Kleinman, posted 07-03-2020 5:48 AM Kleinman has responded

Replies to this message:
 Message 230 by Kleinman, posted 07-03-2020 9:34 AM PaulK has responded

  
Kleinman
Member
Posts: 528
From: United States
Joined: 10-06-2016
Member Rating: 1.1


Message 230 of 239 (878686)
07-03-2020 9:34 AM
Reply to: Message 229 by PaulK
07-03-2020 9:01 AM


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

So, according to Jukes-Cantor calculation, if you compare a single gene from two different species with a single base difference between them and a mutation rate of e-8, you get 50,000,000 generations separating the two species.

PaulK writes:

No. According to the Jukes-Cantor calculation 3/4 of the bases should have changed in 50,000,000 generations. That’s going to be more than one. A lot more.


So, when you said "I’ve never claimed any qualifications in biology", you are now claiming some qualifications? So, which 3/4ths of bases have changed and show us how you use that information for constructing a DNA phylogenetic tree.

You know PaulK, I'm actually learning something here!

Kleinman writes:

So, ding-dong, what if you compare a collection of 10 equivalent genes at the same time, each with only a single base difference, that means 500,000,000 generations separating the two species

PaulK writes:

Assuming that the genes were of roughly equal length it would mean that they agreed on the divergence time. Which would be well under. 50,000,000 generations.


So, as the number of genes being analyzed increases and the number of genetic differences increases, the divergence time goes down. I'm impressed, you have just proven that your parents are bananas.

This message is a reply to:
 Message 229 by PaulK, posted 07-03-2020 9:01 AM PaulK has responded

Replies to this message:
 Message 231 by PaulK, posted 07-03-2020 9:47 AM Kleinman has responded

  
PaulK
Member
Posts: 16475
Joined: 01-10-2003
Member Rating: 1.5


Message 231 of 239 (878687)
07-03-2020 9:47 AM
Reply to: Message 230 by Kleinman
07-03-2020 9:34 AM


Re: An important note regarding models of evolution
quote:
So, when you said "I’ve never claimed any qualifications in biology", you are now claiming some qualifications? So, which 3/4ths of bases have changed and show us how you use that information for constructing a DNA phylogenetic tree.

I don’t claim any biology qualifications. But this is mathematics. And no, Jukes-Cantor won’t tell you which bases change as you ought to know.

quote:
So, as the number of genes being analyzed increases and the number of genetic differences increases, the divergence time goes down.

Wrong again. The divergence time is lower than your estimate because your estimate is hopelessly wrong. And since the divergence is based on the proportion of changed bases, it won’t change unless that proportion is changed.


This message is a reply to:
 Message 230 by Kleinman, posted 07-03-2020 9:34 AM Kleinman has responded

Replies to this message:
 Message 232 by Kleinman, posted 07-03-2020 10:03 AM PaulK has responded

  
Kleinman
Member
Posts: 528
From: United States
Joined: 10-06-2016
Member Rating: 1.1


Message 232 of 239 (878689)
07-03-2020 10:03 AM
Reply to: Message 231 by PaulK
07-03-2020 9:47 AM


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

So, when you said "I’ve never claimed any qualifications in biology", you are now claiming some qualifications? So, which 3/4ths of bases have changed and show us how you use that information for constructing a DNA phylogenetic tree.

PaulK writes:

I don’t claim any biology qualifications. But this is mathematics. And no, Jukes-Cantor won’t tell you which bases change as you ought to know.


Are you now claiming some qualifications in mathematics? If so, show us the mathematics used to compute the divergence time if two sites are considered.
Kleinman writes:

So, as the number of genes being analyzed increases and the number of genetic differences increases, the divergence time goes down.

PaulK writes:

Wrong again. The divergence time is lower than your estimate because your estimate is hopelessly wrong. And since the divergence is based on the proportion of changed bases, it won’t change unless that proportion is changed.


You just said, "Assuming that the genes were of roughly equal length it would mean that they agreed on the divergence time. Which would be well under. 50,000,000 generations." and now you are claiming qualifications in mathematics, show us the mathematics that it would be "well under. 50,000,000 generations".

This message is a reply to:
 Message 231 by PaulK, posted 07-03-2020 9:47 AM PaulK has responded

Replies to this message:
 Message 233 by PaulK, posted 07-03-2020 10:18 AM Kleinman has responded

  
PaulK
Member
Posts: 16475
Joined: 01-10-2003
Member Rating: 1.5


Message 233 of 239 (878690)
07-03-2020 10:18 AM
Reply to: Message 232 by Kleinman
07-03-2020 10:03 AM


Re: An important note regarding models of evolution
quote:
Are you now claiming some qualifications in mathematics? If so, show us the mathematics used to compute the divergence time if two sites are considered.

No sensible person would use only two sites. You couldn’t get a usable estimate that way.

quote:
You just said, "Assuming that the genes were of roughly equal length it would mean that they agreed on the divergence time. Which would be well under. 50,000,000 generations." and now you are claiming qualifications in mathematics, show us the mathematics that it would be "well under. 50,000,000 generations".

I said that they would agree on the divergence time. I.e. each considered individually would give about the same divergence time.

I also said that the divergence time would be well under 50,000,000 generations because only a small proportion of the bases has changed. In 50,000,000 generations 0.75 of the bases would be changed according to Jukes-Cantor with the given parameters.


This message is a reply to:
 Message 232 by Kleinman, posted 07-03-2020 10:03 AM Kleinman has responded

Replies to this message:
 Message 234 by Kleinman, posted 07-03-2020 10:38 AM PaulK has responded

  
Kleinman
Member
Posts: 528
From: United States
Joined: 10-06-2016
Member Rating: 1.1


Message 234 of 239 (878700)
07-03-2020 10:38 AM
Reply to: Message 233 by PaulK
07-03-2020 10:18 AM


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

Are you now claiming some qualifications in mathematics? If so, show us the mathematics used to compute the divergence time if two sites are considered.

PaulK writes:

No sensible person would use only two sites. You couldn’t get a usable estimate that way.


Do the math for any number of sites you think is sensible. And please show your math.
Kleinman writes:

You just said, "Assuming that the genes were of roughly equal length it would mean that they agreed on the divergence time. Which would be well under. 50,000,000 generations." and now you are claiming qualifications in mathematics, show us the mathematics that it would be "well under. 50,000,000 generations".

PaulK writes:

I said that they would agree on the divergence time. I.e. each considered individually would give about the same divergence time.


So the divergence of two sites would give "about the same divergence time"? You just said, "No sensible person would use only two sites. You couldn’t get a usable estimate that way." Why can you get divergence times for one site or many sites but two sites is not sensible?
PaulK writes:

I also said that the divergence time would be well under 50,000,000 generations because only a small proportion of the bases has changed. In 50,000,000 generations 0.75 of the bases would be changed according to Jukes-Cantor with the given parameters.


Then which sites do you use to determine DNA phylogenics? And how do you do the math since you now claim that you are qualified in that subject?

This message is a reply to:
 Message 233 by PaulK, posted 07-03-2020 10:18 AM PaulK has responded

Replies to this message:
 Message 235 by PaulK, posted 07-03-2020 10:54 AM Kleinman has responded

  
PaulK
Member
Posts: 16475
Joined: 01-10-2003
Member Rating: 1.5


Message 235 of 239 (878703)
07-03-2020 10:54 AM
Reply to: Message 234 by Kleinman
07-03-2020 10:38 AM


Re: An important note regarding models of evolution
quote:
Do the math for any number of sites you think is sensible. And please show your math.

Let’s start with some simpler math. When the Jukes-Cantor model reaches equilibrium, 3 quarters of the bases should have changed.

If at that point only one base in the gene has changed, how many bases would you expect to be in the gene?

And for a bonus biology question: could a gene be that length?

quote:
So the divergence of two sites would give "about the same divergence time"?

Well let’s try some more simple mathematics. If one base in a gene 10,000 bases long has changed what proportion of bases has changed ?

If you have two genes, each 10,000 bases long and one base in each has changed, what proportion of bases has changed?

Are the two proportions different ?

quote:
You just said, "No sensible person would use only two sites. You couldn’t get a usable estimate that way." Why can you get divergence times for one site or many sites but two sites is not sensible?

Because you aren’t just counting the sites that have changed, you’re also counting all the sites that haven’t. Which comes to a lot more than just two.


This message is a reply to:
 Message 234 by Kleinman, posted 07-03-2020 10:38 AM Kleinman has responded

Replies to this message:
 Message 236 by Kleinman, posted 07-03-2020 11:59 AM PaulK has responded

  
Kleinman
Member
Posts: 528
From: United States
Joined: 10-06-2016
Member Rating: 1.1


Message 236 of 239 (878705)
07-03-2020 11:59 AM
Reply to: Message 235 by PaulK
07-03-2020 10:54 AM


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

Do the math for any number of sites you think is sensible. And please show your math.

PaulK writes:

Let’s start with some simpler math. When the Jukes-Cantor model reaches equilibrium, 3 quarters of the bases should have changed.


Why couldn't all the bases have changed? After all, it is 50,000,000 generations. Can't some member of that population over 50,000,000 generations get a mutation at any site in the genome?
PaulK writes:

If at that point only one base in the gene has changed, how many bases would you expect to be in the gene?

And for a bonus biology question: could a gene be that length?


All I know from what you are explaining that only 3/4 of the sites in a gene have a mutation over 50,000,000 generations and 1/4 of the genome don't have a mutation. Why can't 1/4 of the gene not get a mutation?
Kleinman writes:

So the divergence of two sites would give "about the same divergence time"?

PaulK writes:

Well let’s try some more simple mathematics. If one base in a gene 10,000 bases long has changed what proportion of bases has changed ?


One would think the answer to that question depends on the mutation rate and the number of replications of that gene. But now you are telling us that 1/4 of that gene cannot have a mutation. Why is that?
PaulK writes:

If you have two genes, each 10,000 bases long and one base in each has changed, what proportion of bases has changed?

Are the two proportions different ?


I thought you said that 3/4 of the bases have changed and 1/4 of the bases haven't changed. And now you are saying that 1 base has changed and 9,999 bases haven't changed. Is this what you mean by equilibrium?
Kleinman writes:

You just said, "No sensible person would use only two sites. You couldn’t get a usable estimate that way." Why can you get divergence times for one site or many sites but two sites is not sensible?

PaulK writes:

Because you aren’t just counting the sites that have changed, you’re also counting all the sites that haven’t. Which comes to a lot more than just two.


So, how many sites are changing, is it 1 or is it 7,500?

This message is a reply to:
 Message 235 by PaulK, posted 07-03-2020 10:54 AM PaulK has responded

Replies to this message:
 Message 237 by PaulK, posted 07-03-2020 12:22 PM Kleinman has responded

  
PaulK
Member
Posts: 16475
Joined: 01-10-2003
Member Rating: 1.5


Message 237 of 239 (878706)
07-03-2020 12:22 PM
Reply to: Message 236 by Kleinman
07-03-2020 11:59 AM


Re: An important note regarding models of evolution
quote:
Why couldn't all the bases have changed? After all, it is 50,000,000 generations. Can't some member of that population over 50,000,000 generations get a mutation at any site in the genome?

Feel free to calculate the probability of that happening. 0.75^n where n is the number of bases.

quote:
Why couldn't all the bases have changed? After all, it is 50,000,000 generations. Can't some member of that population over 50,000,000 generations get a mutation at any site in the genome?

I’m sure you know that you claimed that only one base would change in a gene in 50,000,000 generations. So the expected length of the gene would be 1/0.75 bases. Let’s generously round up and say two. Not exactly plausible is it?

And of course, if you really understood the mathematics you would know that already.

So obviously you are either a fraud or a troll. And either way you need help.


This message is a reply to:
 Message 236 by Kleinman, posted 07-03-2020 11:59 AM Kleinman has responded

Replies to this message:
 Message 238 by Kleinman, posted 07-03-2020 12:45 PM PaulK has not yet responded

  
Kleinman
Member
Posts: 528
From: United States
Joined: 10-06-2016
Member Rating: 1.1


Message 238 of 239 (878709)
07-03-2020 12:45 PM
Reply to: Message 237 by PaulK
07-03-2020 12:22 PM


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

Why couldn't all the bases have changed? After all, it is 50,000,000 generations. Can't some member of that population over 50,000,000 generations get a mutation at any site in the genome?

PaulK writes:

Feel free to calculate the probability of that happening. 0.75^n where n is the number of bases.


So when n is very large, the probability of any base having a mutation goes to 0? Or are you saying that when n is large and after 50,000,000 generations, only 3/4ths of the bases can have a mutation?
Kleinman writes:

Why couldn't all the bases have changed? After all, it is 50,000,000 generations. Can't some member of that population over 50,000,000 generations get a mutation at any site in the genome?

PaulK writes:

I’m sure you know that you claimed that only one base would change in a gene in 50,000,000 generations. So the expected length of the gene would be 1/0.75 bases. Let’s generously round up and say two. Not exactly plausible is it?

And of course, if you really understood the mathematics you would know that already.

So obviously you are either a fraud or a troll. And either way you need help.


Did I say that? Could you please post the message number and quote where I said that?

And if I understand your math, you are claiming that the length of a gene is 1.5 times the number of bases in that gene which you generously round up to 2. This kind of math will not change your employment status as a comedian.

And you have no idea how much you helped me!


This message is a reply to:
 Message 237 by PaulK, posted 07-03-2020 12:22 PM PaulK has not yet responded

  
Kleinman
Member
Posts: 528
From: United States
Joined: 10-06-2016
Member Rating: 1.1


Message 239 of 239 (878779)
07-04-2020 11:51 AM


Jukes-Cantor vs Taq's calculation
Since PaulK seems to be having a bit of trouble understanding the Jukes-Cantor model, here's a simple explanation of what this model is all about. It is nothing more than a variation of the same calculation Taq did at the beginning of this thread. When the Jukes-Cantor model reaches equilibrium is essentially the same as when 3e9 replications have occurred (for a mutation rate of e-9) so that on average, one of every possible substitution has occurred.

  
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