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Author Topic:   Rebuttal To Creationists - "Since We Can't Directly Observe Evolution..."
Taq
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Posts: 9972
Joined: 03-06-2009
Member Rating: 5.5


Message 227 of 2926 (898430)
09-23-2022 6:20 PM
Reply to: Message 225 by Kleinman
09-23-2022 5:52 PM


Re: Apples and oranges
Populations are made up of individuals. You can't average over populations to determine what is happening with each individual.
I'm not averaging. I'm summing. Do you know the difference?
If you think your model is correct, use it to describe what is happening in the Kishony and Lenski experiments.
You can't use a sexually reproducing population to model an asexually reproducing population. Do you know why?
Explain why it takes a billion replications for each adaptive mutational step in these experiments.
The mutation rate in E. coli is about one mutation per 1,000 replications.
quote:
. The major conclusions are (i) the mutation rate of a wild-type E. coli strain is ∼1 × 10−3 per genome per generation;
The size of the E. coli genome is about 5 million bases. At 3 SNP's per base that would be 15 million possible SNP's. This would then require 15 million * 1,000 generations to produce all possible mutations if we assume all mutations are equally probable and no repeat mutations (which isn't true, but we are just estimating here). That would be 15 billion replications for E. coli. If we also assume that there is just a single beneficial mutation possible in the entire genome, then it would take that many replications to get that one beneficial mutation. If there are thousands of possible beneficial mutations then it would take far fewer replications.
The mutation rate for humans is 50,000 mutations per 1,000 births, not 1 like in E. coli. If we look at a 6 billion base diploid genome, that is 18 billion possible SNP's. At 50 mutations per offspring that would require 360 million births to get all of the possible SNP's like our model above. Moreover, these mutations would not be kept in lineages. They would spread through the population. Some would be lost because the mutation would be heterozygous to begin with and not everyone will have offspring in a steady population. However, a sizeable chunk of this variation can be kept because they are not limited to one lineage.
At a steady population of just 100,000 humans it would take 3,600 generations for all of these mutations to occur in our simplistic model. At 25 years per generation, that would be 90,000 years. There would be many different beneficial mutations possible across the ancestral genome, and those would continually move towards fixation as 5 million new mutations are created in each generation.
The reason why there are steps in both the Kishoni and Lenski experiments is because different beneficial mutations in different genes can not be combined into a single E. coli genome. That wouldn't be the case for a sexually reproducing population. In a sexually reproducing population a beneficial mutation that happens in gene A in one individual and a beneficial mutation that happens in gene B in another individual can be combined into a single genome in later generations.
Do you understand this?

This message is a reply to:
 Message 225 by Kleinman, posted 09-23-2022 5:52 PM Kleinman has replied

Replies to this message:
 Message 228 by Kleinman, posted 09-23-2022 7:51 PM Taq has replied

  
Taq
Member
Posts: 9972
Joined: 03-06-2009
Member Rating: 5.5


(1)
Message 229 of 2926 (898446)
09-24-2022 2:37 AM
Reply to: Message 228 by Kleinman
09-23-2022 7:51 PM


Re: Apples and oranges
Kleinman writes:
Summing what? You start with the assumption that you have a population of 100,000. Is it 100,000 humans, 100,000 chimpanzees, 100,000 common ancestors, or some combination of all 3? If you don't consider each individual and what happens with each replication, you have mush.
I'm summing the number of mutations that happen in the population in that generation. We can also sum the mutations that happen over generations. I don't understand why this is so hard to understand.
They would be 100,000 individuals. In the last ~1.5 million years they would be humans. In the last 200,000 years they would be anatomically modern humans, i.e. H. sapiens. Prior to ~1.5 million years they would be human ancestors. They would never be chimps.
So you think that adaptive alleles are formed differently for asexual reproducers and sexual reproducers?
No, I don't. The difference is how the mutations are passed on to offspring. Do you understand the difference between diploid and haploid genomes? Do you understand how you got half of your genome from your father and half from your mother? Do you understand how this is different from bacteria who only have one parent that they are a clone of?
I use a mutation rate value of 1e-9 or approximately 1 mutation for every billion replication, a slightly higher mutation rate.
If you use that number for the human mutation rate then you are way off.
It is that lucky member with the base substitution at the particular site that gives some resistance to the drug being used but there is only one member at this time with that first adaptive mutation.
How many possible mutations result in antibiotic resistance? That's the first question you need to answer.
This process works the same way for asexual or clonal replicators as well as sexual replicators. The 1/(mutation rate) replications are occurring at every site in the genome, the population is doing an exhaustive search of the entire sample space, and all mutations are being sampled, beneficial, neutral, and detrimental. The probability of beneficial mutation B occurring on some member with beneficial mutation A depends on the number of replications the A variant can do. This is how adaptive alleles are formed no matter whether the replicator is asexual or sexual. Replication of a site in a genome is the random trial and the possible outcomes at that site are a mutation occurs or a mutation does not occur.
The difference is the mutation segregation seen in the Kishony and Lenski experiments. That doesn't happen in sexually reproducing populations except in cases where the mutations are close to one another on the same chromosome.

This message is a reply to:
 Message 228 by Kleinman, posted 09-23-2022 7:51 PM Kleinman has replied

Replies to this message:
 Message 230 by Kleinman, posted 09-24-2022 9:35 AM Taq has replied

  
Taq
Member
Posts: 9972
Joined: 03-06-2009
Member Rating: 5.5


(3)
Message 235 of 2926 (898553)
09-26-2022 10:56 AM
Reply to: Message 230 by Kleinman
09-24-2022 9:35 AM


Re: Apples and oranges
Kleinman writes:
Is the population of 100,000 exact clones of each other or are there different variants in the population with different sets of mutations?
They would have variation just like your average sampling of mammal species.
Are all 100,000 individuals on the exact same evolutionary trajectory and do all their descendants over generations remain on that same evolutionary trajectory where each individual gets the same set of mutations as every other individual or do the different individuals get different sets of mutations and the population is genetically diverging?
Again, mutations spread through a sexually reproducing population.
There will already be mutant variants at the target site. On the other hand, with meiosis, you have parents each passing half the genome. If I understand your argument correctly, you are claiming that one parent passes beneficial alleles from their set of chromosomes and the other parent passes their beneficial alleles from their set of chromosomes. If I understand your argument correctly, then your population must be diverse and not clones.
It means that mutations from different lineages are combined. You keep asking how these beneficial mutations are put in the same lineage. This is how.
How many beneficial alleles are in your population? What is the frequency of the different beneficial alleles in your population? Which members have the beneficial alleles? Are these beneficial alleles homozygous or heterozygous in each of the members? And how do you compute the probability that a descendant will get these beneficial alleles from any two parents in your population of 100,000?
This is going to differ based on a myriad of conditions. There is no single answer for any of those questions. Even in the Lederberg experiment there was a 1,000 fold difference in the beneficial mutation rate for two different phenotypes. The very fact that you pretend there is a beneficial mutation rate only highlights your misunderstandings of how evolution works.
Let's say you have "m" possible beneficial mutations. What is the probability of at least one of those "m" possible beneficial mutations occurring in "n" replications? It doesn't change the number of replications much from only a single beneficial mutation.
Really? Even with a very small population of 100,000 individuals it only took 90,000 years to get all possible SNP's with 360 million births. If there are 20 million possible beneficial mutations this would be 20 million out of 18 billion possible SNP's. This gives us a 1 in 900 chance of getting a beneficial mutation. This means we only need 18 births to get a beneficial mutation. 18 is a lot different than 360 million.
What????
Its from the Lenski paper you keep citing. It's the first sentence in the abstract.
quote:
When large asexual populations adapt, competition between simultaneously segregating mutations slows the rate of adaptation and restricts the set of mutations that eventually fix.
Distribution of fixed beneficial mutations and the rate of adaptation in asexual populations

Are you telling me you don't understand the paper you keep citing?

Edited by Taq, .


This message is a reply to:
 Message 230 by Kleinman, posted 09-24-2022 9:35 AM Kleinman has replied

Replies to this message:
 Message 237 by AZPaul3, posted 09-26-2022 11:04 AM Taq has not replied
 Message 240 by Kleinman, posted 09-26-2022 12:51 PM Taq has replied

  
Taq
Member
Posts: 9972
Joined: 03-06-2009
Member Rating: 5.5


(1)
Message 236 of 2926 (898554)
09-26-2022 11:03 AM
Reply to: Message 231 by Kleinman
09-24-2022 11:13 AM


Re: Video not available
Kleinman writes:
I already pointed out previously that Haldane's frequency equation was a conservation of energy process based on the principle that it takes energy to replicate. However, Flake and Grant demonstrate this mathematically in the following paper:
An Analysis of the Cost-of-Selection Concept
You will notice that their model applies to species with haploid genomes, not diploid genomes like that seen in primates.
quote:
It is shown for a continuous haploid model that the common standard assumptions usedin calculating the cost of gene substitution, namely, large constant population size and small constant selective value, are unnecessary.
This is done because it is the number of replications of the more fit variant that determines the probability of the next adaptive mutation occurring in this subset of the population.
Which doesn't apply in sexually reproducing species.

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 Message 231 by Kleinman, posted 09-24-2022 11:13 AM Kleinman has not replied

  
Taq
Member
Posts: 9972
Joined: 03-06-2009
Member Rating: 5.5


(1)
Message 239 of 2926 (898561)
09-26-2022 12:20 PM
Reply to: Message 233 by Kleinman
09-25-2022 4:37 PM


Re: Apples and oranges
Kleinman writes:
The correct analogy for your raindrop concept would be, what is the probability of two particular raindrops ending up in the same body of water?
A raindrop falls and runs downhill to a small stream. Small streams flow into a larger river. Larger river dumps into ocean. Same body of water.
Sexual reproduction is analogous. Lineages flow into each other and form the larger body of variation that is the population.
If you understood how sexual reproduction works you would be able to figure these things out.
And you must model DNA evolution and the accumulation of adaptive mutations in a lineage using the multiplication rule.
Not for sexually reproducing populations.

This message is a reply to:
 Message 233 by Kleinman, posted 09-25-2022 4:37 PM Kleinman has replied

Replies to this message:
 Message 241 by Kleinman, posted 09-26-2022 1:02 PM Taq has replied

  
Taq
Member
Posts: 9972
Joined: 03-06-2009
Member Rating: 5.5


Message 242 of 2926 (898572)
09-26-2022 1:28 PM
Reply to: Message 240 by Kleinman
09-26-2022 12:51 PM


Re: Apples and oranges
Kleinman writes:
Are some of the variants more fit than other variants and are they engaged in biological evolutionary competition?
Beneficial mutations on separate genes would not be in competition with each other because they could merge into the same lineage.
You aren't answering my question about whether all 100,000 individuals are on the same evolutionary trajectory.
Yes I am. Because genes move through the population this puts the population on the same trajectory. The only way this could not be the case is if there is an interruption in gene flow between subpopulations.
What is the probability of beneficial alleles in a diverse population recombining in the same descendant?
Your father is homozygous for a beneficial mutation in gene A. Your mother is homozygous for a beneficial mutation in gene B. You have a 25% chance of getting both beneficial mutations. Do you understand this or not?
Added in edit: The probability would actually be 100% if both parents were homozygous. The 25% chance is if both parents were heterozygous for their respective beneficial allele.
How do 20 million possible beneficial mutations end up in the lineages of all humans?
Natural selection drives beneficial genes to fixation, and sexual recombination drives the merger of beneficial alleles into the same genome.
Try reading beyond the abstract:
That is for asexual populations. Primates reproduce sexually.
OK, Haldane's frequency equation for a sex-linked diploid is:
pn^2AA + 2pnqnAa + qn^2aa = 1
Which of the variants fix in the population, AA, Aa, or aa?
That's for a single allele. What about different genes?
It's the number of replications of a particular allele that determines the probability of an adaptive mutation occurring at some site in that allele.
In the Lederberg experiment the mutation rate was the same for all bacteria. Spectinomycin resistance occurred once in every 10 billion divisions and phage resistance occurred once in every 10 million divisions. How do you explain this?

Edited by Taq, .


This message is a reply to:
 Message 240 by Kleinman, posted 09-26-2022 12:51 PM Kleinman has replied

Replies to this message:
 Message 244 by Kleinman, posted 09-26-2022 2:35 PM Taq has replied

  
Taq
Member
Posts: 9972
Joined: 03-06-2009
Member Rating: 5.5


Message 243 of 2926 (898573)
09-26-2022 1:33 PM
Reply to: Message 241 by Kleinman
09-26-2022 1:02 PM


Re: Apples and oranges
Tell us how you think adaptive alleles are evolved in sexually reproducing populations.
Let's use antibiotic resistance as our model.
We have two populations of the same bacterial species. We put one population on a plate that has antibiotic A and another population on a plate with antibiotic B. We get resistant colonies on both plates. We then mix the two populations together in media that has no antibiotic. How many of those bacterial descendants of this mixed population are going to have both mutations for resistance to both drugs? None, if the bacteria are reproducing asexually.
Do the same for a diploid sexually reproducing population. What are the results? Could you find bacterial descendants of the mixed population that has both resistance markers if they are found on different genes? YES!!

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 Message 241 by Kleinman, posted 09-26-2022 1:02 PM Kleinman has not replied

  
Taq
Member
Posts: 9972
Joined: 03-06-2009
Member Rating: 5.5


Message 245 of 2926 (898582)
09-26-2022 3:40 PM
Reply to: Message 244 by Kleinman
09-26-2022 2:35 PM


Re: Apples and oranges
Kleinman writes:
So, in your model of human evolution, the fixation of beneficial alleles does not occur?
Fixation of beneficial mutations does occur in my model. Why you think otherwise is beyond me.
In your model, does every human lineage have equal reproductive fitness? Do any human lineages go extinct?
There would be variation of fitness across individuals just like in any mammalian population.
Do any human lineages go extinct?
The only lineages that actually exist are the y-chromosome and mitochondrial lineages because those are haploid, and those can go extinct.
I don't think you are doing your math correctly on that one. But WRT your model, do all the fathers in your model have beneficial allele A and all the mothers have beneficial alleles B?
The math was wrong. It should be 100% if the father and mother are homozygous.
If a father is homozygous for a beneficial mutation in gene A and a mother is homozygous for a beneficial mutation in gene B, 100% of offspring will have one copy of each beneficial mutation. Do you agree or not?
How do you compute the probability that all these beneficial mutations end up in a single lineage in your model?
If they are all being driven to fixation because of selection then that would be population wide for all of the beneficial mutations. If you are asking for the specific equations, those are found in population genetics:
Population Genetics
How do you compute the rapid fixation of 20 million beneficial mutations in your model?
Fixation wouldn't need to be rapid.
You have yet to show how you do a fixation calculation for your model for a single genetic loci let alone 20 million genetic loci.
quote:
Natural Selection results in change of allele frequency (q) [read as "delta q"]
in consequence of differences in the relative fitness (W)
of the phenotypes to which the alleles contribute.
Fitness is a phenotype of individual organisms.
Fitness is determined genetically (at least in part).
Fitness is related to success at survival AND reproduction.
Fitness can be measured & quantified (see below).
i.e., the relative fitness of genotypes can be assigned numerical values.
The consequences of natural selection depend on the dominance of fitness:
e.g., whether the "fit" phenotype is due to a dominant or recessive allele.
Then, allele frequency change is predicted by the General Selection Equation:
delta q = [pq] [(q)(W2 - W1) + (p)(W1 - W0)] / Wbar
where W0, W1, & W2 are the fitness phenotypes
of the AA, AB, & BB genotypes, respectively
Theory of Natural Selection
The equations are all over the internet. It's not like it's a secret.
Where did the resistance allele come from that the phage transmits? What if the phage transmitted some other allele besides a resistance allele?
Phage resistance doesn't come from the phage genome. It is due to mutations in the gene tonB. I will ask again.
In the Lederberg experiment the mutation rate was the same for all bacteria. Spectinomycin resistance occurred once in every 10 billion divisions and phage resistance occurred once in every 10 million divisions. How do you explain this?
And to your comment here, you have assumed that the two subsets of your sexually reproducing population each have fixed their respective resistance alleles so they exist at frequencies of 1 in their respective populations.
If they didn't have the resistance marker then they wouldn't have grown on the antibiotic plate. 100% of the bacteria on each plate carry the mutation for each antibiotic.
If we assume both subsets have equal population sizes when you combine the frequencies of the resistance alleles for each drug will be 0.5.
Exactly. The two lineages have merged. Half the population has both mutations. If they are now challenged by both antibiotics half of the population will survive, and 100% will have both mutations in the same lineage, and it wouldn't have required iterative mutations.
quote:
And BTW, combination therapy works for the treatment of malaria which can do sexual reproduction.
What would happen if one village used one drug and a village close by used a different drug? Could you have resistance to each drug develop in each village, and then find both resistance markers in the offspring between those two resistant populations? The answer is yes. The same mutations wouldn't have to repeat themselves in each population.

This message is a reply to:
 Message 244 by Kleinman, posted 09-26-2022 2:35 PM Kleinman has replied

Replies to this message:
 Message 246 by Kleinman, posted 09-26-2022 5:23 PM Taq has replied

  
Taq
Member
Posts: 9972
Joined: 03-06-2009
Member Rating: 5.5


Message 247 of 2926 (898595)
09-26-2022 6:05 PM
Reply to: Message 246 by Kleinman
09-26-2022 5:23 PM


Re: Apples and oranges
Kleinman writes:
The math is way beyond you. 20 million beneficial mutations * 300 generations/fixation = 6 billion generations
The neutral fixation rate in diploid organisms is essentially the mutation rate, which is 50 mutations per generation. Beneficial mutations would fix at a higher rate than neutral mutations.
How much variation? And how many different lineages in your population?
Every time you ask for lineages in a sexually reproducing population you demonstrate you don't know what you are talking about.
So you are claiming that no human lineages have ever gone extinct? What happens to the less fit human lineages when the most fit are fixed in the population?
I am saying that asking for lineages in a sexually reproducing population makes no sense because of the intermingling of alleles and mutations.
What happens to the less fit human lineages when the most fit are fixed in the population?
If the most fit are fixed in the population then there is no less fit. They are all equally fit.
That's still not quite right.
It is. Father is AAbb, mother is aaBB. All offspring will be AaBb. 100% of offspring will have the beneficial mutation for both gene A and gene B.
Fixation isn't rapid and Haldane's mathematical estimate of 300 generations/fixation has been verified experimentally.
The difference is that in sexually reproducing species you can have more than one mutation moving towards fixation at a time. They are moving towards fixation in parallel.
Plug in a selection coefficient and tell us how many generations to fixation.
You don't even understand how sexual reproduction works. Why don't you start there.
So the resistance allele has to evolve in the bacteria and the phage acquires the gene and transmits it to drug-sensitive bacteria.
No. I am simply acting as if bacteria were suddenly diploid and sexually reproducing. Phage is not moving any genes around. In one population you get antibiotic resistance through mutation. In another you get phage resistance through mutation (not through any transport of DNA from phage). When you bring the two bacterial diploid sexually reproducing populations you get offspring with both antibiotic and phage resistance.
Do you know any microbiologists that know how drug resistance evolves?
This microbiologist does understand it just fine.
The probability of that happening depends on the frequency of the different resistance alleles in the population.
That's not what happens in the Lenski and Kishony experiments, is it?

This message is a reply to:
 Message 246 by Kleinman, posted 09-26-2022 5:23 PM Kleinman has replied

Replies to this message:
 Message 248 by Kleinman, posted 09-26-2022 7:32 PM Taq has replied

  
Taq
Member
Posts: 9972
Joined: 03-06-2009
Member Rating: 5.5


Message 250 of 2926 (898619)
09-27-2022 10:40 AM
Reply to: Message 248 by Kleinman
09-26-2022 7:32 PM


Re: Apples and oranges
Kleinman writes:
That is hilarious.
You think this is hilarious?
quote:
For a diploid population of size N and neutral mutation rate u , the initial frequency of a novel mutation is simply 1/(2N), and the number of new mutations per generation is 2Nu. Since the fixation rate is the rate of novel neutral mutation multiplied by their probability of fixation, the overall fixation rate is (2Nu)x(1/2N) = u. Thus, the rate of fixation for a mutation not subject to selection is simply the rate of introduction of such mutations.
Fixation - Wikipedia(population_genetics)
All that intermingling of alleles and mutations and still they fix at a rate of greater than 50/generation.
Generation 1 there are 5 beneficial mutations that occur in the population and they fix at generation 51. In generation 2 there are another 5 beneficial mutations, and they fix at generation 52. In generation 3 there are another 5 beneficial mutations and they fix at generation 53. See a pattern here?
That's fitting, the less fit aren't fit for life anymore.
I see you are just blabbering now.
How did all the fathers end up AAbb and all the mothers aaBB?
Why would all the fathers need to be AAbb in order for at least one father to be AAbb? Same for mothers.
Do you think that Haldane was wrong when he wrote this:
Generation 1 there are 5 beneficial mutations, and in generation 301 they are fixed. In generation 2 there are 5 beneficial mutations, and in generation 302 they are fixed. See a pattern?
Why should it surprise you when a scientist puts an agent into a population that transfers a resistance allele?
Phage do not transfer phage resistance in the Lederberg experiment. The phage in the experiment binds to the gene product of tonB. Mutations in the tonB gene prevent phage from binding to the bacteria.
I will ask again. Why does spectinomycin resistance occur once every 10 billion replications in E. coli and phage resistance occurs once every 10 million replications? Why is there a 1,000 fold difference?
Tell us how the Kishony experiment works.
Read the Kishony experiment. What you fail to understand is that the Kishony experiment is largely irrelevant to how humans evolved.
You still haven't figured out the difference between DNA evolution, biological evolutionary competition, and recombination.
I'm not the one who hasn't figured it out.

This message is a reply to:
 Message 248 by Kleinman, posted 09-26-2022 7:32 PM Kleinman has replied

Replies to this message:
 Message 251 by Kleinman, posted 09-27-2022 11:38 AM Taq has replied

  
Taq
Member
Posts: 9972
Joined: 03-06-2009
Member Rating: 5.5


Message 252 of 2926 (898628)
09-27-2022 11:48 AM
Reply to: Message 251 by Kleinman
09-27-2022 11:38 AM


Re: Apples and oranges
Kleinman writes:
And that rate estimated for humans is:
quote:
Using data available from whole genome sequencing, the human genome mutation rate is similarly estimated to be ~1.1×10−8 per site per generation.
The mutation rate is not the ridiculous claim of 50 mutations per generation that you made in your post. You need to put more effort into understanding the equations you use and how you define the variables in these equations. Now put the correct values in your equation and tell us how many generations to fixation for each mutation and then understand why 20,000,000 adaptive mutations are not going to fix in your model.
1.1x10-8 per site per generation. Let's see how that works out. That is a mutation every 110 million bases. There are 6 billion bases in the human diploid genome. (6E9)/(1.1E8) = 54.5 mutations per person per generation. On top of that, we have directly sequenced the genomes of parents and offspring to directly measure the number of mutations per person, and that is where the figure you cite comes from. The directly measured human mutation rate is around 50 mutations per person.
Do you also agree that the neutral fixation rate is approximately the mutation rate, meaning that for a mutation rate of around 50 mutations per person per generation that we will see 50 neutral mutations fixed per generation?
Added in edit:
Figure 2 from this paper which directly measured mutations between parents and offspring. The Y axis is the number of mutations per birth, and the x axis is the father's age at conception. As you can see, many of the mutations come from the father due to continual division of germ line cells (i.e. sperm).

Edited by Taq, .


This message is a reply to:
 Message 251 by Kleinman, posted 09-27-2022 11:38 AM Kleinman has replied

Replies to this message:
 Message 253 by Kleinman, posted 09-27-2022 12:46 PM Taq has replied

  
Taq
Member
Posts: 9972
Joined: 03-06-2009
Member Rating: 5.5


Message 254 of 2926 (898645)
09-27-2022 1:10 PM
Reply to: Message 253 by Kleinman
09-27-2022 12:46 PM


Re: Apples and oranges
Kleinman writes:
The correct value to use in your equation is 1.1x10-8, not 50.
1.1x10-8 per nucleotide per generation is the same as 54.5 mutations per person per generation for a 6 billion base diploid genome.
Moreover, we can count the mutations by comparing the genomes of parents and their offspring. That number is about 50, on average. Check out this paper:
Rate of de novo mutations, father’s age, and disease risk - PMC

Edited by Taq, .

Edited by Taq, .

Edited by Taq, .


This message is a reply to:
 Message 253 by Kleinman, posted 09-27-2022 12:46 PM Kleinman has replied

Replies to this message:
 Message 255 by Kleinman, posted 09-27-2022 1:27 PM Taq has replied

  
Taq
Member
Posts: 9972
Joined: 03-06-2009
Member Rating: 5.5


(1)
Message 256 of 2926 (898648)
09-27-2022 1:36 PM
Reply to: Message 255 by Kleinman
09-27-2022 1:27 PM


Re: Apples and oranges
And 54.5 is not the correct value to use in your equation. Just because the number of mutations that occur in a replication is 54.5 doesn't mean that all 54.5 are fixed.
The mutation rate in the equation is the number of mutations per person per generation.
quote:
For a diploid population of size N and neutral mutation rate u , the initial frequency of a novel mutation is simply 1/(2N), and the number of new mutations per generation is 2Nu. Since the fixation rate is the rate of novel neutral mutation multiplied by their probability of fixation, the overall fixation rate is (2Nu) * (1/2N) = u. Thus, the rate of fixation for a mutation not subject to selection is simply the rate of introduction of such mutations.
bolding mine
Fixation - Wikipedia(population_genetics)
If the number of new mutations in the population is 2 times the population size then the mutation rate has to be number of mutations per person. Also, the last sentence explicitly states that the rate of fixation is simply the rate of the introduction of such mutations. Across a whole genome that would be 50 mutations.
Added in edit:
We can also calculate the per nucleotide fixation rate if you want. That would end up being the per nucleotide mutation rate which is 1.1E-8 per nucleotide. At a fixation rate of 1.1E-8 per nucleotide how many fixed mutations would that be across the entire human diploid genome?

Edited by Taq, .


This message is a reply to:
 Message 255 by Kleinman, posted 09-27-2022 1:27 PM Kleinman has replied

Replies to this message:
 Message 257 by Kleinman, posted 09-27-2022 3:50 PM Taq has replied

  
Taq
Member
Posts: 9972
Joined: 03-06-2009
Member Rating: 5.5


Message 258 of 2926 (898667)
09-27-2022 4:44 PM
Reply to: Message 257 by Kleinman
09-27-2022 3:50 PM


Re: Apples and oranges
Kleinman writes:
You are using a definition of mutation rate based on the entire size of the genome. 2N is the total number of alleles at a given locus and 1/2N is the initial frequency of the first mutation in that allele. The neutral mutation rate being used is just for that genetic locus. If that locus has only a single base, then the neutral mutation rate will be 1.1x10-8. If that genetic locus has 1000 bases, the neutral mutation rate will be about 1.1x10-5 (actually lower if you compute the probability of a mutation occurring at least one site when multiple possible sites are considered). The number of generations to fixation for a single neutral mutation case is about 90,000 generations.
Great, let's find the per nucleotide fixation rate. Since 2N cancels out in the equation for fixation we are left with the per nucleotide mutation rate. If the fixation rate is 1.1E-8 fixed mutations per nucleotide per generation then the number of fixed mutations in a full human genome is (6E9)*(1.1E-8) which is 66 fixed mutations per generation.

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 Message 257 by Kleinman, posted 09-27-2022 3:50 PM Kleinman has replied

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Taq
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Message 260 of 2926 (898673)
09-27-2022 6:30 PM
Reply to: Message 259 by Kleinman
09-27-2022 5:30 PM


Re: Apples and oranges
Kleinman writes:
You are making another mathematical blunder here. 1/2N is the initial frequency of the mutant allele. Only a tiny fraction of the genome has mutations.
1/2N is the fraction of the population that has the mutation when the mutation first occurs. That's what that means.
This model only makes sense when considering a single genetic locus because the entire length of the genome and the total number of genetic loci in that genome does not affect the calculation.
The equation applies equally to every neutral mutation in the genome.
Not all the mutations in an entire genome are fixed. In fact, some mutations are lost over generations. Perhaps you think that the entire genome is fixed?
I know all of this. If you think I am saying all mutations are fixed then you don't understand what the equation is saying. In a steady population of 100,000 and a mutation rate of 50 mutations per individual you will have 5 million mutations per generation, 50 of which will reach fixation if all 5 million mutations are neutral.
You cannot use the entire genome length to compute the mutation rate and do this calculation correctly. It must be done based on the mutations/locus.
Neutral mutations don't have to be in genes in order to reach fixation. That's just silly. Do you really think all of the sequence outside of genes never mutates?
The rate of fixation can be calculated for the whole genome, and there is no reason why it can't be. You seem to be hung up on the idea that alleles are only single chunks of sequence within genes. That simply isn't true. An allele can be any base that differs between two organisms within a population, and that's inside or outside of coding regions or genes.
90,000 generations/fixation, Haldane's estimate of only 300 generations/fixation but that's with selection.
The size of the effective population numbers I have seen for populations in the human lineage usually don't go above 10,000 which would require 40,000 generations for a neutral mutation to fix. At 25 years per generation, that would be 1 million years. This means the mutations reaching fixation first entered the genome 1 million years before they fix. This would also mean that the initial population that first split off from the chimp branch would be fixing neutral mutations that first appeared 1 million years before the split. Still, in each generation you will still be fixing a number of neutral mutations that is close to the per genome mutation rate.
For beneficial mutations, this only puts a 300 generation delay on fixation. If there are 5 beneficial mutations in generation 1 then they reach fixation at generation 301. Beneficial mutations that happen in generation 2 reach fixation in generation 302. Beneficial mutations that happen in generation 3 reach fixation in generation 303. See a pattern? It's not as if all mutations stop until the first mutation reaches fixation. Every generation has mutations which start their march towards extinction or fixation starting at that generation.

This message is a reply to:
 Message 259 by Kleinman, posted 09-27-2022 5:30 PM Kleinman has replied

Replies to this message:
 Message 261 by Kleinman, posted 09-27-2022 7:58 PM Taq has replied

  
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