Rebuttal To Creationists - "Since We Can't Directly Observe Evolution..."

The mutation rate in the equation is the number of mutations per person per generation.

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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)

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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, .

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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)
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Taq:

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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.

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You should watch this video, the derivation of your calculation begins at about the 6:00 minute mark.
https://www.youtube.com/watch?v=l2Y8oC6G1us&ab_channel=Kr...
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.

Edited by Kleinman, : Correct math

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.

Kleinman:

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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.

Taq:

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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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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. What is the initial frequency for your calculation? It certainly isn't 1/2N. 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. 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? You should watch the entire video. It gives a very sensible explanation of the equation you are trying to use. 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.
Mutation rate - Wikipedia

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There are several natural units of time for each of these rates, with rates being characterized either as mutations per base pair per cell division, per gene per generation, or per genome per generation.

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I put the boldfacing on the correct definition for mutation rate to be used for this calculation. 90,000 generations/fixation, Haldane's estimate of only 300 generations/fixation but that's with selection. So, when are you going to learn how to do the mathematics of adaptive DNA evolution and give a correct description of the Kishony and Lenski experiments? Don't you think a microbiologist should know how to do that math?

1/2N is the fraction of the population that has the mutation when the mutation first occurs. That's what that means. The equation applies equally to every neutral mutation in the genome. 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. 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. 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.

Kleinman:

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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.

Taq:

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1/2N is the fraction of the population that has the mutation when the mutation first occurs. That's what that means.

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Why are you doing this to yourself? 1/2N is the frequency of the mutant allele. For a diploid population, there are 2N copies of the allele at the particular genetic locus. One of those 2N copies is the first mutant allele. Only 1 member of that population has that mutant allele. The fraction of the population with a mutant allele initially is 1/N.

Kleinman:

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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.

Taq:

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The equation applies equally to every neutral mutation in the genome.

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It applies to any mutant allele but only for a single genetic locus.

Kleinman:

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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?

Taq:

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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.

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You don't understand this equation. You have even confused the number of copies of alleles with population size. There are 2N copies of an allele in a diploid population size N. And if you somehow want to extrapolate this model to the entire genome means that the entire genome is being fixed. ringo, if you are reading this post, this is GIGO.

Kleinman:

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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.

Taq:

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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?
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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.

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If you want to do the math for a mutation not in a coding portion of the genome, then the number of bases in that sequence is one and the mutation rate you need to use is 1.1x10-8. That's about 9,000,000 generations to fixation. Post a link to a paper or biology lecture where they do a neutral mutation fixation calculation the way you want to do it. You are just blowing smoke. Nobody does the calculation the way you want because it is nonsense.

Kleinman:

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90,000 generations/fixation, Haldane's estimate of only 300 generations/fixation but that's with selection.

Taq:

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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.

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Fixations aren't adaptation you should understand this by now from the results of the Lenski experiment. Large numbers of replications are what is required for DNA adaptive evolution. Certainly, small populations can have mutations fix more rapidly than large populations. You get all the mutations your parents have plus a few new ones for your own. Populations do exhaustive searches of all possible mutations in order to get just one member with an adaptive mutation. That's why it takes a billion replications for each adaptive mutation in the Kishony and Lenski experiments for a mutation rate of 1e-9. The reason is that "at least one" calculation applies to every site in the genome. The reason why humans have much larger populations than chimps is that humans can do farming on an industrial scale. It is clear that humans had this capability 10,000 years ago. They understood how to irrigate and use animals for labor. You have a population of about 1 billion population with 2 billion chromosome sets replications and use your mutation rate of 1.1x10-8. That doesn't give you many genome replications to work with for adaptive evolution to operate, even if you want to include recombination.

Taq:

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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.

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Taq, the math gets orders of magnitude worse if it takes 2 or more mutations to give an improvement in fitness. It introduces another instance of the multiplication rule for each selection condition the population must adapt to. That's really bad for your belief in universal common descent but really good for the fields of medicine and agriculture. It gives a successful treatment of HIV and inhibition of the evolution of herbicide-resistant weeds and pesticide-resistant insects. I don't know if you are ready for that math yet but if you or any other readers of this thread are interested, you can find that paper here:
The mathematics of random mutation and natural selection for multiple simultaneous selection pressures and the evolution of antimicrobial drug resistance
Don't worry Percy, I'll post equations and quotes in my next few posts if Taq is finished with his neutral fixation model.

Yes. That is true for every mutation throughout the genome, not just in genes. It applies to all bases in the genome. Please learn what chromosomes are, what cross-overs are, and how meiosis works. The entire genome is not passed on as a unit. Recombination happens within a chromosome. The copies of different chromosomes are passed on independently of each other. Just as mutations in genes are evolving independently, so too are the mutations outside of genes.In a population of 100,000 and a mutation rate of 50 mutations per genome per generation you will get 5 million mutations. The equation for neutral fixation states that 50 of those mutations will reach fixation if all 5 million mutations are neutral. Coding portions of the genome make up just 1-2%. Sorry, but there is more than one base outside of coding regions. In fact, there are billions.You also never put any units on your 1.1E10-8 figure. Why is that? Is it because it is the per base mutation rate across the entire genome? When they measured the mutation rate in humans do you think they only looked at coding regions? Mutations don't fix one at a time. They fix in parallel. 1 billion births with 1.1E-8 mutations per nucleotide per birth in a 6 billion base diploid genome is 1E9*1.1E-8*6E9 = 66 billion mutations. In a 6 billion base genome there are 18 billion possible SNP's. 1 billion births is more than enough to get every possible non-lethal mutation kicking around on the globe somewhere if all mutations are equally probable. Mutations fix in parallel, not sequentially. Again, where are the units on your mutation rate? For such a claim you would first need to calculate all of the possible combinations of 2 mutations that would be beneficial. If there are billions and billions of possible beneficial combinations then they wouldn't be hard to find.

Kind of funny when cranks and trolls think they a smarter than everyone else. You gave him the rope, he hung himself but he is still going. When I am shown I have no idea what I am talking about I shut up and slink away. Not this guy.

Kleinman:

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1/2N is the frequency of the mutant allele.

Taq:

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Yes. That is true for every mutation throughout the genome, not just in genes.

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You are having trouble doing undergraduate lower division work so I don't know whether I should give you this paper but why not?
THE AVERAGE NUMBER OF GENERATIONS UNTIL FIXATION OF A MUTANT GENE IN A FINITE POPULATION
Kimura carries out the computation of the fixation of a mutant gene. His calculation doesn't depend on the mutation rate.

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This shows that an originally rare mutant gene in a population of effective size Ne, takes about 4Ne generations until it spreads to the whole population if we disregard the cases in which such a gene is eventually lost from the population

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Now the effective population size can be slightly smaller than the actual population size under certain circumstances that I'm sure you know what they are. Remind me again what the population size you use is. Wasn't it 100,000? That gives the generations to fixation of that mutant gene of 4*100,000=400,000 generations. That really helps. Your lower division equation gave an estimate of 900,000 generations for the fixation of a neutral mutation. How many generations since the divergence of humans and chimps from the common ancestor?

Kleinman:

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Taq, the math gets orders of magnitude worse if it takes 2 or more mutations to give an improvement in fitness. It introduces another instance of the multiplication rule for each selection condition the population must adapt to.

Taq:

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For such a claim you would first need to calculate all of the possible combinations of 2 mutations that would be beneficial. If there are billions and billions of possible beneficial combinations then they wouldn't be hard to find.

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You still haven't figured out that different combinations of adaptive mutations give different lineages on different evolutionary trajectories. That math is way over your head. You should stick to trying to figure out an undergraduate lower division equation of neutral fixation.

Taq has his fish and he's playing with it.

AZPaul3:

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Taq has his fish and he's playing with it.

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Taq likes to tell fish stories.Did you hear the one about the one-armed fisherman? He was telling his friend about one of the fish he caught. He held up his arm and said, "It was that long"!

Sounds a lot like the math you use.

AZPaul3:

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Sounds a lot like the math you use.

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AZPaul3 will now explain the physics and mathematics of the Kishony and Lenski biological evolutionary experiments. He won't because unlike the one-armed fisherman, AZPaul3 doesn't have a leg to stand on.

There was no equation in what followed. Please present the Haldane equation you're talking about, then convert it to Joules. Using math equations.--Percy

It might help if you ceased placing a higher priority on being obnoxious than on constructive discussion.--Percy