Do you really understand the mathematics of evolution?

And you in the fish evolve into mammals clique think I have trouble with the english language. 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. I tried putting this sentence into Google Translate, it still comes out nonsense. 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

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.

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.

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.

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! 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.

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.

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. 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".

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.

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

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.

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

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.

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? 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!

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.