|
Register | Sign In |
|
QuickSearch
EvC Forum active members: 59 (9164 total) |
| |
ChatGPT | |
Total: 916,927 Year: 4,184/9,624 Month: 1,055/974 Week: 14/368 Day: 14/11 Hour: 2/1 |
Thread ▼ Details |
|
Thread Info
|
|
|
Author | Topic: Do you really understand the mathematics of evolution? | |||||||||||||||||||||||||||||||||||||||
Taq Member Posts: 10085 Joined: Member Rating: 5.6
|
Kleinman writes: I don't know who taught you probability theory but they failed to teach you the difference between additive and complementary events. I don't see how that applies here. If there are two possible mutations that confer antibiotic resistance then it would take half as many divisions (on average) to get a antibiotic resistant colony than it would if there was only one possible mutation that confers resistance. Can you please explain why my math is wrong?
So, any glucose consumed by variants that ultimately go extinct is energy denied to the most fit variant which slows the ability of that variant to replicate. If we took away competition, what would happen to those mutations you are describing as being fit? Would they be swamped out by the less fit mutations?
Selection is trying to order the genome to give the most efficient replicator. That's a second law problem. I think that goes a bit too far. It might be better to say that both DNA evolution and thermodynamics are stochastic processes.
Do you think that the non-coding regions of genomes are not important? What if those exons do modulation of the introns? You don't understand how to do the mathematics of selection. You have only demonstrated a vague understanding of selection so far. It would be helpful if you refrained from insulting peoples' knowledge on the subject and actually addressed what they are saying. Just some advice. I was talking about specific non-coding regions called introns, not non-coding DNA in general. There is non-coding DNA that does have function, but the vast majority of intron sequence shows no evidence of having function. Exons in functioning genes do have function. So what do we see when we compare functioning genes shared by eukaryotic species? We see that sequence conservation in exons is much higher than it is in introns. How do you explain this?
The Kishony experiment variants accumulate 5 beneficial mutations in about 10 days (about 1 beneficial mutation every 2 days). The Lenski variants take between 200 to 1000 generations to accumulate each beneficial mutation. How much of that is due to the strength of the selective pressures?
Why don't you tell us the total number of replications necessary for an evolutionary step in the Lenski experiment if fixation takes 200 generations? That would be dependent on the strength of the selective pressure.
|
|||||||||||||||||||||||||||||||||||||||
Taq Member Posts: 10085 Joined: Member Rating: 5.6 |
Kleinman writes: What's wrong with your math (just not quite correct) is that you are trying to do the mathematics with the averages (the mean) rather than doing the probability calculation correctly as I showed you how to do in the previous post. It's the same simplified model we used for calculating 1 mutation.
And no, the population won't be swamped out by the less fit variants because the more fit variants (without drug-resistance) are also happily replicating. If there is no competition then the less fit variants outnumber the fit variant by billions to one when the mutation occurs. That ratio won't change because there is nothing limiting the growth of the population when there is no competition.
The first law of thermodynamics is deterministic (conservation of energy). The second law of thermodynamics is stochastic. Correct. How heat moves through a system is very distantly related to DNA evolution to the point that false analogies start to emerge.
Don't be so thin-skinned. Don't be an asshole.
My explanation for this is that introns are much more important to the phenotype of a replicator than the exons. For example, two species each can have a beta-keratin gene but the expression of that gene (which is determined by the non-coding regions of the genome) determines the phenotype. Perhaps you are unfamiliar with how exons and introns work. The introns are the pieces of the gene that span the regions between the exons. Introns are clipped out during RNA maturation while the exons are stitched together to produce the mature mRNA. It is the mature mRNA that is translated into protein.
The non-coding DNA responsible for regulating gene trascription is found upstream of the first exon in the vast majority of cases. The DNA responsible for post-translational regulation through micro-RNA is found after the last exon. The introns are only very rarely used for gene regulation.
The reason why the Kishony experiment evolves so much more rapidly is the much larger carrying capacity. If a mutation only confers a tiny increase in fitness it would seem that this allele would increase in number slower than a mutation that is 100% required in order to grow in a specific environment.
|
|||||||||||||||||||||||||||||||||||||||
Taq Member Posts: 10085 Joined: Member Rating: 5.6 |
Kleinman writes: That's right, and I'm showing you how to do the calculation more accurately so that you will have a better understanding of what is happening physically. Just so we are on the same page, if we use the same simple model that we used before we would need half as many divisions if there are 2 possible mutations for antibiotic resistance as compared to 1 possible mutation for resistance.
If the carrying capacity of the environment is large enough, all the variants will still replicate and the population will increase in diversity. When the population reaches the carrying capacity of the environment, the competition between variants will occur. It is that competition which increases the relative numbers of beneficial mutations. If there is no competition then all mutations are passed on at the same rate.
The Kimura model of diffusion is a competition/fixation model, not a DNA evolution model. Correct. Thermodynamics is the movement of heat through a system, not the diffusion of alleles.
When considering fitness, with respect to competition and fixation, it is relative fitness, that is the ability of one variant of a population to replicate in comparison to a different variant. When considering fitness, with respect to DNA evolution, it is the absolute fitness to reproduce, that is the ability of a given variant to replicate sufficiently to have a reasonable probability of the next beneficial mutation occurring. The time it takes to reach sufficient numbers for an additional beneficial mutation to occur in the same lineage is a product of relative fitness. Let's also not forget about sexual reproduction which can combine the beneficial mutations from two lineages.
|
|||||||||||||||||||||||||||||||||||||||
Taq Member Posts: 10085 Joined: Member Rating: 5.6 |
Kleinman writes: As an average, the simple model you are using is ok, but I'm trying to get you to a higher level of understanding of the math and physics. Any way you slice it, increasing the number of possible beneficial mutations reduces the number of generations needed to get a beneficial mutation. It changes the math as I said earlier.
If the carrying capacity of the environment is large enough to allow a population to grow without competition occurring, the absolute number of all variants will increase but the most fit variants will have more offspring than the less fit variants in the same time interval. If there is no competition then there are no individuals who are fitter.
DNA evolution in no way is a diffusion process, competition can be modeled as a diffusion process and the reason this can be done is that competition and fixation is an example of conservation of energy. Here's a paper where they show this mathematically: https://www.ncbi.nlm.nih.gov/...33847/pdf/pnas00072-0402.pdf That doesn't mean that DNA evolution is thermodynamics.
Somehow you are stuck on this idea that DNA evolution is a function of relative fitness. It isn't. It is the absolute fitness (the number of replications) which determines the probability of a beneficial mutation to occur. That would be the reproduction rate, not absolute fitness.
Do you really think you are ready to start doing the mathematics of recombination? And once again we get insults and condescension. Do you have a point you want to get to, or just insult people while demanding that they do math problems?
|
|||||||||||||||||||||||||||||||||||||||
Taq Member Posts: 10085 Joined: Member Rating: 5.6 |
Kleinman writes: Now, if the population has to evolve to 2 or more simultaneous selection pressures simultaneously, that changes the math a lot. Once again, that depends heavily on the number of possible beneficial mutations. If you only need 2 simultaneous mutations out of 2 million possible beneficial sites, then you don't need that many replications, relatively speaking.
Kishony's population in the drug-free region when they achieve their 3e9 replications will have on average, every possible point mutation. Some of those point mutations will be detrimental, even to the point that it causes the death of that variant. You can't have detrimental mutations when there is a lack of competition. In a model without competition there are no possible lethal mutations or detrimental mutations. You would also have equal fecundity across all lineages. It is only with competition that you get changes in allele frequencies.
But it is! DNA evolution is a random walk process. That's not thermodynamics. Thermodynamics is the distribution of energy and work in a system. That it happens to share patterns with other processes does not mean the two processes are the same thing. The air pressure from an explosion dissipates by the inverse square law. Photon density decreases from the source by the inverse square law. This doesn't mean that sound waves are photons.
You are the one who brought up the subject of recombination while we were still discussing DNA evolution. I know how to do the mathematics of random recombination, I've already published the mathematics. I've told you how to set up the problem, read Message 101. I'll even give you another hint. Let the total population size be "n" and the number of members with beneficial allele A is nA, the number of members with beneficial allele B is nB and the remainder of the population which has neither beneficial allele A nor beneficial allele B is nC. Figure out this math and you will understand why recombination has very little effect on DNA evolution. Again, why don't you do the math and discuss it? If that is your point then prove it. Let's say there are two dominant beneficial alleles A and B. In the diploid sexually reproducing population you also have the wild type a and b, and the alleles are on separate chromosomes. How many replications does it take to get an individual with AB in the sexually and asexually reproducing populations? Edited by Taq, : No reason given.
|
|||||||||||||||||||||||||||||||||||||||
Taq Member Posts: 10085 Joined: Member Rating: 5.6 |
Kleinman writes: If it takes 2 (and they don't need to be simultaneous) mutations to improve fitness, the number of replications goes into the trillions for there to be a reasonable probability of that happening. Let's see your math.
There is no such thing as a detrimental (fatal) mutation unless there is competition? Correct. It seems you are starting to catch on.
What happens if there is a mutation that causes the failure of some vital metabolic pathway? That would only happen in a model where there is competition. In a model free from competition there would be no lethal mutations.
The first law of thermodynamics pertains to energy. DNA evolution is a second law of thermodynamics process. The second law of thermodynamics also pertains to energy. It doesn't pertain to DNA evolution. Just because they use some of the same concepts does not make them the same thing.
Obviously you are ignoring the links I've given you to Markov chain DNA evolution models and Markov chain entropy. You seem to be under the impression that Markov chain entropy is the same as thermodynamic entropy. It isn't.
I have done the math and it has been peer-reviewed and published and is also in the National Library of Medicine. Great, then discuss it here. GET TO THE POINT!!
|
|||||||||||||||||||||||||||||||||||||||
Taq Member Posts: 10085 Joined: Member Rating: 5.6 |
Kleinman writes: I'll say it again and as many times as necessary for you to get it. DNA evolution is a Markov Chain process. I already knew that. Is that your grand point? This has been common knowledge for a while. Here is an excerpt from TalkOrigins:
quote: Why don't you tell us all what that difference is. Thermodynamics deals with energy. A Markov chain model of DNA evolution does not.
How many times do you want me to post the links to the papers? I want you to discuss them. What point are you trying to make, and how do those papers relate to that point? Edited by Taq, : No reason given.
|
|||||||||||||||||||||||||||||||||||||||
Taq Member Posts: 10085 Joined: Member Rating: 5.6 |
Kleinman writes: Try to apply their mathematics to the Kishony or Lenski experiment (or for that matter, any other real empirical example of DNA evolution). Could you show us how to properly use mathematics to model human evolution using actual sequences?
Your understanding of thermodynamics doesn't go any further than the first law. Thermo = temperaturedynamics = movement All the laws of thermodynamics involve energy. It's right there in the name.
And the point I'm trying to make is that your link to 29+ Evidences for Macroevolution is based on an incorrect application of the mathematics. Ok. They use an incorrect model. Now what?
|
|||||||||||||||||||||||||||||||||||||||
Taq Member Posts: 10085 Joined: Member Rating: 5.6 |
Kleinman writes: But note, only about 1e11 people have live in our entire history. That doesn't give many beneficial mutations to work with when it takes 3e9 replications for each of those mutations. Let's do some back of the envelope calculations. The human mutation rate is about 50 point mutations per person per generation. Let's be conservative and use a 25 year generation time, a constant 100,000 person population, and 5 million years since diverging from chimps. That would be 5 million mutations per generation spread across the entire population. In 5 million years we would have 200,000 generations. 5 million mutations per generation over 200,000 generations is 1E12 mutations that have happened over the history of human evolution. So how many point mutations separate humans and chimps? 35 million. Let's say half of those mutations occurred in each lineage, so 17.5 million mutations in the human lineage. This means that we needed to keep just 0.00175% of the total mutations that did happen. Does that math seem right to you?
If you are going to relate this to DNA evolution, it takes energy to replicate, replication is the random trial for a beneficial mutation, only those lineages which replicate sufficiently have a reasonable probability of increasing their information to the environmental selection conditions. The energy needed to replicate DNA is a function of its length, not its sequence. Edited by Taq, : No reason given.
|
|||||||||||||||||||||||||||||||||||||||
Taq Member Posts: 10085 Joined: Member Rating: 5.6 |
Kleinman writes: That math works ok if all you want to do is compute mutational divergence. But that has virtually nothing to do with DNA evolution. You are changing your tune. This is what you said before:
But note, only about 1e11 people have live in our entire history. That doesn't give many beneficial mutations to work with when it takes 3e9 replications for each of those mutations. That's wrong. As shown above, there were about 1E12 mutations that happened in the human lineage after it split from the chimp lineage. The human haploid genome is only 3E9 bases long. That's enough mutations to change each base 300 times over. Your numbers are way off. Let's look at it a different way. There are 3E9 bases in the human haploid genome, so we would need 9E9 point mutations to get all possible substitutions. At 50 mutations per person, that would be 180 million births to get all mutations. Right now, there are 130 million births each year. It would take less than two years for the current population to get all of those mutations, assuming the chances of all mutations is equal.
Try doing the same math for the Lenski experiment. I am starting to get the feeling that the only things that exist in your universe is the Lenski and Kishony experiments.
That is a minuscule amount of the energy needed to replicate. The energy difference between two DNA sequences is even less. So why do you keep trying to relate DNA sequence to thermodynamics? Edited by Taq, : No reason given.
|
|||||||||||||||||||||||||||||||||||||||
Taq Member Posts: 10085 Joined: Member Rating: 5.6 |
Kleinman writes: If adaptation requires the lineage to accumulate mutations A and B, it's going to take 3e9 replications for a variant to get mutation A and that variant with mutation A will need to do 3e9 replications to get mutation B regardless of how long the genome is. As I feared, E. coli and the two oft mentioned experiments are all that exists in your universe. You appear to be using the mutation rate from E. coli in human genetics. That is obviously wrong. In E. coli there is just one mutation in every few hundred replications. In humans, there are about 50 mutations in a single replication. You need to account for this. You also need to account for diploid genomes and sexual reproduction. If mutation A happens in one individual and mutation B happens in another individual then their descendants can mate and have offspring with both mutations.
All you are describing here is genetic diversification. Or perhaps you think every one is getting identical mutations. Do you agree that it takes less than two years for every possible point mutation to occur in at least one individual within the modern human population? Yes or no?
It's the information in the DNA sequence that is related to thermodynamics, specifically the second law. They are only related in the sense that they use some of the same equations.
|
|||||||||||||||||||||||||||||||||||||||
Taq Member Posts: 10085 Joined: Member Rating: 5.6 |
Kleinman writes: If you think that DNA evolution works differently in bacteria than any other replicator, produce your mathematical and empirical evidence to prove this. You seriously have to ask how asexual and sexual reproduction differs mathematically?
If you understood DNA evolution, you would understand that the mutation rate doesn't dominate the process. It is the multiplication rule of probabilities which dominates the DNA evolution process. This is why the Kishony experiment, as designed, will not work with 2 or more drugs. Just make his mega-plate vastly larger then you can achieve the population sizes need for this DNA evolutionary process to work. You once again fail to understand the impact of sexual reproduction.
So what? All you have shown is diversification, not DNA evolution. It's a yes or no question. Do you agree that it takes less than two years for every possible point mutation to occur in at least one individual within the modern human population? Yes or no?
All it takes, for a mutation rate of 1e9, for there to be 3e9 replications for you to get on average some member of the population with one of every possible point mutation. That number is 0.18E9 for humans. I did the math. Did you look at it?
You did that math! And it doesn't matter what the length of the genome is. Want to try that one again? Let's use your figure of one mutation per 1E9 bases. E. coli have a 4 million base genome. This means 1 mutation per 250 replications, or 0.004 mutations per replication. Humans have a 6 billion base diploid genome. This means 6 mutations per replication. This also doesn't factor in the fact that the per base mutation rate is higher in humans.
quote: So the human mutation rate is 10 fold higher than in E. coli, which is in keeping with the 50 or so mutations per replication in humans that I keep telling you about. Genome size does affect how many mutations there will be per replication, as does mutation rate.
Same physics, same math. Category error. Edited by Taq, : No reason given. Edited by Taq, : No reason given.
|
|||||||||||||||||||||||||||||||||||||||
Taq Member Posts: 10085 Joined: Member Rating: 5.6 |
Kleinman writes: If you think that DNA evolution works differently in bacteria than any other replicator, produce your mathematical and empirical evidence to prove this. Would you agree that you mutation A and mutation B can occur in different individuals and then be combined in a single descendant? If so, that differs greatly from E. coli, does it not?
The only correction you need to do to your previous math is that humans are diploid so it only takes 1.5e9 member replications to get the 3e9 genome replications. That 3e9 number is for E. coli, not humans. You keep making this mistake. For humans, you only need 0.18e9 replications.
It's the second and ensuing beneficial mutations in that lineage that have a low probability of occurring. You are ignoring sexual reproduction. The first mutation can happen in one individual and then spread through the population. The second mutation can happen at the same time as the first mutation and spread through the population. Descendants of both lineages can mate and produce offspring with both mutations. With sexual reproduction you can have selection for each mutation in parallel instead of in series.
|
|||||||||||||||||||||||||||||||||||||||
Taq Member Posts: 10085 Joined: Member Rating: 5.6 |
Kleinman writes: Yes, mutations A and B can occur in two different individuals and that by some form of lateral transfer they then can be combined in a single descendant. Lateral genetic transfer occurs between species, not within species. The word you are looking for is "sexual reproduction".
But there are some variants of e coli that can do bacterial conjugation, so no, it doesn't differ greatly. I know all about this. I have used this process in the lab to shuttle plasmids between different species of bacteria. What differs greatly is the rate at which this occurs, and it also depends heavily on the strain of E. coli. Many lab strains of E. coli are missing the genes necessary for conjugation. I would suspect that this is the case with the strains used in the the only two experiments that exist in your universe.
I posted a link to a paper where they reported that DNA evolution for eukaryotes works the same as for bacteria. Then discuss it.
But you still need to learn that the mutation rate is not the dominant factor in DNA evolution, its the multiplication rule which dominates DNA evolution. Once again, you ignore sexual reproduction.
I am not ignoring sexual recombination. You make these vague claims about mutation spreading through the population and then members from both lineages mate and produce offspring with both mutations. Why doesn't this happen with hiv causing combination therapy to fail? Because HIV is not a diploid eukaryote. That should be obvious to anyone with a tiny inkling of how genetics works.
Write out the distribution function for this situation for the probability of an nA member recombining with an nB member to give an AB descendant. You do it. I don't see any reason to do more math problems for someone who doesn't understand why HIV is not diploid.
|
|||||||||||||||||||||||||||||||||||||||
Taq Member Posts: 10085 Joined: Member Rating: 5.6 |
Kleinman writes: In fact, I'm trying to explain to you why recombination has virtually no effect on DNA evolution. I've even gone so far to set up the mathematical problem. Great. Let's see it.
So, now you are claiming that hiv doesn't do recombination because it isn't a diploid eukaryote? I am claiming that HIV is not a diploid organism that reproduces through sexual reproduction. Rare recombination events are nowhere close to mixing two haploid genomes together every generation, as well as about one recombination event per chromosome per generation. It is a question of scale.
Why do combination herbicides inhibit the evolution of herbicide-resistant weeds? Because that would require evolution against both herbicides at once. How does this apply to human evolution? Which human adaptations required the same strict selection regime?
Don't be silly, I know what kind of virus hiv is and it does recombination. What is the rate of recombination in HIV?
|
|
|
Do Nothing Button
Copyright 2001-2023 by EvC Forum, All Rights Reserved
Version 4.2
Innovative software from Qwixotic © 2024