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Author Topic:   Mutations Confirm Common Descent
sensei
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Posts: 467
Joined: 01-24-2023


Message 91 of 106 (907420)
02-23-2023 2:16 PM
Reply to: Message 89 by Taq
02-22-2023 10:40 AM


It would be easiest to consider a model with a single DNA base, I suppose. In a population of size N, with zero mutations for this base, it may to to 1 mutation at rate mu * N per generation.
When n individuals have this mutation, it will go to n + 1 with probability p, and to n - 1 with probability 1 - p. For beneficial mutations, p would be greater than 1/2.
Numerically, this is east to iterate to find the distribution after a certain number of generations, for fixed p = 1/2 for example. Or draw a random p from a probability distribution, where we use estimates of beneficial mutation, neutral mutation, bad mutation ratios. But it gets complicated fast, as we would need some continuous probability distribution for p values between 0 and 1.

This message is a reply to:
 Message 89 by Taq, posted 02-22-2023 10:40 AM Taq has replied

Replies to this message:
 Message 92 by Taq, posted 02-23-2023 3:11 PM sensei has replied

  
Taq
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Posts: 9851
Joined: 03-06-2009
Member Rating: 4.5


Message 92 of 106 (907423)
02-23-2023 3:11 PM
Reply to: Message 91 by sensei
02-23-2023 2:16 PM


sensei writes:
Numerically, this is east to iterate to find the distribution after a certain number of generations, for fixed p = 1/2 for example. Or draw a random p from a probability distribution, where we use estimates of beneficial mutation, neutral mutation, bad mutation ratios. But it gets complicated fast, as we would need some continuous probability distribution for p values between 0 and 1.
In the equation for neutral fixation the probability of a mutation reaching fixation is just the number of genomes with the mutation compared to the total population of genomes. Since humans are diploid, you would take the population size and multiple by 2 to cover 2 genomes per person. When a mutation first occurs in a population with 1 million individuals the probability of that mutation reaching fixation is 1 in 2 million (1 million people = 2 million genomes).

This message is a reply to:
 Message 91 by sensei, posted 02-23-2023 2:16 PM sensei has replied

Replies to this message:
 Message 94 by sensei, posted 02-24-2023 3:51 AM Taq has replied

  
sensei
Member
Posts: 467
Joined: 01-24-2023


Message 93 of 106 (907433)
02-24-2023 3:43 AM
Reply to: Message 90 by Phat
02-22-2023 10:47 AM


Re: Sensei seems sensible
Well, feel free to join the conversation, I suppose.

This message is a reply to:
 Message 90 by Phat, posted 02-22-2023 10:47 AM Phat has replied

Replies to this message:
 Message 95 by Phat, posted 02-24-2023 8:27 AM sensei has not replied

  
sensei
Member
Posts: 467
Joined: 01-24-2023


Message 94 of 106 (907435)
02-24-2023 3:51 AM
Reply to: Message 92 by Taq
02-23-2023 3:11 PM


That is the correct math for one dimensional random walk between two fixed boundaries. If the data would show different rates outside of the models confidence ranges, we may need to see if near extinction events could explain higher fixation for example, as fixation becomes more likely in smaller populations, with boundaries closer together.

This message is a reply to:
 Message 92 by Taq, posted 02-23-2023 3:11 PM Taq has replied

Replies to this message:
 Message 96 by Taq, posted 02-24-2023 10:46 AM sensei has replied

  
Phat
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Posts: 18149
From: Denver,Colorado USA
Joined: 12-30-2003
Member Rating: 1.1


Message 95 of 106 (907453)
02-24-2023 8:27 AM
Reply to: Message 93 by sensei
02-24-2023 3:43 AM


Re: Sensei seems sensible
I'm just a member of the peanut gallery munching on snacks and watching the discussion. We do have some questions for you at Message 275 however. I said that you were sensible, so now I and others are going to test you.

This message is a reply to:
 Message 93 by sensei, posted 02-24-2023 3:43 AM sensei has not replied

  
Taq
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Posts: 9851
Joined: 03-06-2009
Member Rating: 4.5


Message 96 of 106 (907473)
02-24-2023 10:46 AM
Reply to: Message 94 by sensei
02-24-2023 3:51 AM


sensei writes:
That is the correct math for one dimensional random walk between two fixed boundaries. If the data would show different rates outside of the models confidence ranges, we may need to see if near extinction events could explain higher fixation for example, as fixation becomes more likely in smaller populations, with boundaries closer together.
In a bottleneck situation you would get a surge in fixed mutations, if memory servers. The dynamics of population size will definitely have an effect.

This message is a reply to:
 Message 94 by sensei, posted 02-24-2023 3:51 AM sensei has replied

Replies to this message:
 Message 97 by sensei, posted 03-08-2023 5:18 AM Taq has replied

  
sensei
Member
Posts: 467
Joined: 01-24-2023


Message 97 of 106 (908127)
03-08-2023 5:18 AM
Reply to: Message 96 by Taq
02-24-2023 10:46 AM


Equlibrium for different popularion sizes.
I made these graphs. The model is for a single "neutral" DNA base, that can be A or B, so two possibilities instead of the usual four.
The first graph shows equilibrium distribution for the DNA for different population sizes N, for a "mutation rate" of mu = 10^-7.
It appears that when N * mu = 1, the distribution is a flat line.
For larger populations, the distribution seems to approximate the normal distribution, as the central limit theory predicts.
For the graphs below, each individual in the initial population has base A. Population size is fixed, each step consists of picking one random individual and copying it, with mu probability of a mutation happening for the copy. At the same time, another random individual dies to keep the population size fixed.
N steps counts as 1 generation.
The gray lines are for the distribution after 1, 2, 4, 8, 16, etc generations until equilibrium has been reached.
1
2
3
4
I tried to plot the average similarity between two random individuals against time. But this requires a lot of computer memory for large populations and too long computation time on my computer.

This message is a reply to:
 Message 96 by Taq, posted 02-24-2023 10:46 AM Taq has replied

Replies to this message:
 Message 98 by Tanypteryx, posted 03-08-2023 1:06 PM sensei has replied
 Message 100 by Taq, posted 03-09-2023 12:33 PM sensei has replied

  
Tanypteryx
Member
Posts: 4267
From: Oregon, USA
Joined: 08-27-2006
Member Rating: 5.7


Message 98 of 106 (908146)
03-08-2023 1:06 PM
Reply to: Message 97 by sensei
03-08-2023 5:18 AM


Can you explain what point you are trying to demonstrate here?

Stop Tzar Vladimir the Condemned!

What if Eleanor Roosevelt had wings? -- Monty Python

One important characteristic of a theory is that is has survived repeated attempts to falsify it. Contrary to your understanding, all available evidence confirms it. --Subbie

If evolution is shown to be false, it will be at the hands of things that are true, not made up. --percy

The reason that we have the scientific method is because common sense isn't reliable. -- Taq


This message is a reply to:
 Message 97 by sensei, posted 03-08-2023 5:18 AM sensei has replied

Replies to this message:
 Message 99 by sensei, posted 03-09-2023 4:16 AM Tanypteryx has replied

  
sensei
Member
Posts: 467
Joined: 01-24-2023


Message 99 of 106 (908155)
03-09-2023 4:16 AM
Reply to: Message 98 by Tanypteryx
03-08-2023 1:06 PM


I'm showing the data from the model. We can use it for whatever.
One of the things that I see is that under this model, in very large populations, practically none of the "neutral" DNA is fixed (at 0 or 1).
The gray lines in the graphs are actually more precisely for generations 1, 3, 7, 15, 31, 63 (2^n - 1).
What possible predictions do you think we can make from here?

This message is a reply to:
 Message 98 by Tanypteryx, posted 03-08-2023 1:06 PM Tanypteryx has replied

Replies to this message:
 Message 101 by Tanypteryx, posted 03-09-2023 12:49 PM sensei has not replied

  
Taq
Member
Posts: 9851
Joined: 03-06-2009
Member Rating: 4.5


Message 100 of 106 (908203)
03-09-2023 12:33 PM
Reply to: Message 97 by sensei
03-08-2023 5:18 AM


sensei writes:
I made these graphs.
I'm not seeing any images, sorry. EvC is picky on how it displays images. For most of my posts I use html code which seems to work most of the time. If you see one of my posts with pictures in it you can hit the peek button and see how I did it.
The model is for a single "neutral" DNA base, that can be A or B, so two possibilities instead of the usual four.
What does this have to do with the topic at hand? How does it relate to the opening posts?

This message is a reply to:
 Message 97 by sensei, posted 03-08-2023 5:18 AM sensei has replied

Replies to this message:
 Message 102 by sensei, posted 03-09-2023 1:34 PM Taq has replied

  
Tanypteryx
Member
Posts: 4267
From: Oregon, USA
Joined: 08-27-2006
Member Rating: 5.7


Message 101 of 106 (908214)
03-09-2023 12:49 PM
Reply to: Message 99 by sensei
03-09-2023 4:16 AM


sensei writes:
I'm showing the data from the model. We can use it for whatever.
OK, good.
sensei writes:
What possible predictions do you think we can make from here?
Well, it's your model, why don't you tell us?

Stop Tzar Vladimir the Condemned!

What if Eleanor Roosevelt had wings? -- Monty Python

One important characteristic of a theory is that is has survived repeated attempts to falsify it. Contrary to your understanding, all available evidence confirms it. --Subbie

If evolution is shown to be false, it will be at the hands of things that are true, not made up. --percy

The reason that we have the scientific method is because common sense isn't reliable. -- Taq


This message is a reply to:
 Message 99 by sensei, posted 03-09-2023 4:16 AM sensei has not replied

  
sensei
Member
Posts: 467
Joined: 01-24-2023


Message 102 of 106 (908231)
03-09-2023 1:34 PM
Reply to: Message 100 by Taq
03-09-2023 12:33 PM


Do you see images or links to images now?
I described the model simplifications that I used.
Starting from a fixed DNA base, it takes millions of generations to reach equilibrium.
Depending on how much of DNA is junk or neutral, comparing DNA of two individuals and finding 99.9% similarity, seems very high, compared to my model for such large population.
Is it because we are still far from equilibrium?

This message is a reply to:
 Message 100 by Taq, posted 03-09-2023 12:33 PM Taq has replied

Replies to this message:
 Message 103 by Taq, posted 03-09-2023 1:46 PM sensei has replied

  
Taq
Member
Posts: 9851
Joined: 03-06-2009
Member Rating: 4.5


Message 103 of 106 (908232)
03-09-2023 1:46 PM
Reply to: Message 102 by sensei
03-09-2023 1:34 PM


sensei writes:
Do you see images or links to images now?
Yes, I see them.
Starting from a fixed DNA base, it takes millions of generations to reach equilibrium.

Depending on how much of DNA is junk or neutral, comparing DNA of two individuals and finding 99.9% similarity, seems very high, compared to my model for such large population.
Is it because we are still far from equilibrium?
I'm still not seeing the relationship between this model and what is presented in the opening posts. What does this have to do with the ratio of transition to transversion mutations?

This message is a reply to:
 Message 102 by sensei, posted 03-09-2023 1:34 PM sensei has replied

Replies to this message:
 Message 104 by sensei, posted 03-09-2023 2:58 PM Taq has replied

  
sensei
Member
Posts: 467
Joined: 01-24-2023


Message 104 of 106 (908236)
03-09-2023 2:58 PM
Reply to: Message 103 by Taq
03-09-2023 1:46 PM


You are comparing DNA of primates and found that it fits predictions of a common ancestor. So I'm trying to see if other predictions fit as well. Because we don't want to be cherry picking only data that fits our hypothesis now, I suppose.
Or do you think it's better to start a new topic?

This message is a reply to:
 Message 103 by Taq, posted 03-09-2023 1:46 PM Taq has replied

Replies to this message:
 Message 105 by Taq, posted 03-09-2023 3:41 PM sensei has replied

  
Taq
Member
Posts: 9851
Joined: 03-06-2009
Member Rating: 4.5


Message 105 of 106 (908249)
03-09-2023 3:41 PM
Reply to: Message 104 by sensei
03-09-2023 2:58 PM


sensei writes:
You are comparing DNA of primates and found that it fits predictions of a common ancestor.
Yes, and that prediction is the ratio of transition to transversion mutations, along with CpG transitions.
So I'm trying to see if other predictions fit as well.
If you want to discuss a different prediction then feel free to start a new thread.
Because we don't want to be cherry picking only data that fits our hypothesis now, I suppose.
We also don't want a Gish Gallop.
Or do you think it's better to start a new topic?
I do think that.

This message is a reply to:
 Message 104 by sensei, posted 03-09-2023 2:58 PM sensei has replied

Replies to this message:
 Message 106 by sensei, posted 03-16-2023 4:27 AM Taq has not replied

  
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