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Author Topic:   Do you really understand the mathematics of evolution?
Kleinman
Member (Idle past 334 days)
Posts: 2142
From: United States
Joined: 10-06-2016


Message 91 of 239 (877231)
06-08-2020 7:46 PM
Reply to: Message 90 by Taq
06-08-2020 6:29 PM


Re: Does competition accelerate DNA evolution?
Kleinman writes:
Do the math for the simplest case, assume there are only 2 possible beneficial mutations.
Taq writes:
It would take half as many divisions.
I don't know who taught you probability theory but they failed to teach you the difference between additive and complementary events. The question is, does a beneficial mutation occur or does it not occur, those are complementary outcomes. And then, what happens for the next evolutionary step? Are there multiple possible beneficial mutations for that step as well?
Kleinman writes:
Why don't you try first?
Taq writes:
It would be nice to see some reciprocation.
I've given you the links where I show how to do the math for single beneficial mutations. I've done the math for multiple beneficial mutations. I just haven't submitted it for peer-review and publication yet. But, if you can't do the math, I'll show you how to do it here.
Kleinman writes:
You probably won't understand this but competition and fixation is a first law of thermodynamics process and DNA evolution is a second law of thermodynamics process.
Taq writes:
All of biology boils down to thermodynamics, as do all physical processes. In a simplistic model, energy flows from the Sun to photsynthesizers to herbivores to carnivores. There is about 10% energy transfer at each trophic level. The total energy is limited in our solar system, and energy can't increase in our isolated solar system. Imperfect replicators competing for limited resources is what drives evolution.
Then you should recognize the thermodynamics for the Lenski experiment. The energy source for the experiment is glucose (and citrate for some of the variants but let's ignore that for the moment). It takes energy (glucose) to replicate. 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. DNA evolution, on the other hand, is an equilibrium problem. Selection is trying to order the genome to give the most efficient replicator. That's a second law problem. Another way of looking at this is that DNA evolution is a Markov chain (random walk). You can read about that here:
Entropy rate - Wikipedia.
Make sure to read further down the page to the section titles "Entropy rates for Markov chains"
Kleinman writes:
And I don't know what you are seeing with introns and exons. You barely understand the basic principles of DNA evolution to single selection pressure.
Taq writes:
When you compare functional genes between species you will see fewer differences between exons than you will introns. I understand selective pressures just fine.
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.
Kleinman writes:
And you should understand why DNA evolution is slowed in a competitive environment.
Taq writes:
"Slower" is a relative term. What are you comparing to? Are you comparing it to a population that increases exponential towards infinity?
Compare the Kishony experiment with the Lenski experiment. 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. At 6 1/2 doublings/day, that's about 30 to 150 days of growth for every beneficial mutation.
Kleinman writes:
You have already shown that it takes 3e9 replications for a beneficial mutation to occur. So, when you have populations such as Lenski's populations where many variants are competing for a fixed amount of glucose, that will limit the number of replications for all variants.
Taq writes:
The number of replications is the same per culture because they are observed to reach the same density, and are started from the same number of bacteria.
But, until fixation occurs, there are variants that ultimately will go extinct consuming resources that the more fit variant could use to replicate. You know, thermodynamics applies to biological systems.
Kleinman writes:
Then, the most fit variant must drive to extinction the less fit variants in order to have sufficient resources for that most fit variant in that particular lineage to accumulate its 3e9 replications for the next beneficial mutation.
Taq writes:
You are assuming that the mutations have to come in a specific order. If there are multiple beneficial mutations then you can have a mix of those beneficial mutations in the population simultaneously.
No, I'm assuming there is a wide variety of variants in Lenski's populations. The first variant that gets fixed will be the most fit variant. The second variant that gets fixed will be the second most fit variant and so on. In other words, the most beneficial mutation gets fixed first and because it gives the most improvement in fitness and that variant gets fixed most rapidly. The next most beneficial mutation gets fixed next but takes slightly more time for fixation because the improvement in fitness is less than what the first beneficial mutation did. As the experiment has gone on, each evolutionary step is taking longer because the improvement in fitness from the particular beneficial mutation is decreasing at each evolutionary step.
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?

This message is a reply to:
 Message 90 by Taq, posted 06-08-2020 6:29 PM Taq has replied

Replies to this message:
 Message 93 by Taq, posted 06-09-2020 11:35 AM Kleinman has replied

  
Kleinman
Member (Idle past 334 days)
Posts: 2142
From: United States
Joined: 10-06-2016


Message 92 of 239 (877235)
06-09-2020 9:15 AM
Reply to: Message 90 by Taq
06-08-2020 6:29 PM


A little reciprocation for Taq
Kleinman writes:
Why don't you try first?
Taq writes:
It would be nice to see some reciprocation.
OK, it appears you are not familiar with the mathematics of stochastic processes. To do the mathematics of multiple possible beneficial mutations, you need to use the "at least one rule" from probability theory. In our case, it is the probability of at least one beneficial mutation occurring among a set of multiple possible beneficial mutations occurring. Here is a short video that explains how this rule is used:
https://www.youtube.com/watch?v=KFtCj_46TzA
So, in our case, we have multiple possible beneficial mutations that occur at multiple possible sites in the genome. Then the "at least one" formula based on success at least 1 site would be:
P(of at least one success in total number sites) =
1-(1-P(of success at 1 site)^(total number of sites) where
P(of success at 1 site) = 1-(1-e-9)^N
The point here is that if N (the number of replications) is large, even one site is sufficient for that beneficial mutation to occur. With additional possible beneficial mutations will very slightly improve the probability that some beneficial mutation will occur but each of these different beneficial mutations will lead to different evolutionary trajectories for each of these variants and once these variants are on their particular evolutionary trajectories, the number of possible sites for beneficial mutations will not be large and empirical evidence shows that it is most likely just 1. Study the Weinreich results which I gave you a link to in [MSG=81].

This message is a reply to:
 Message 90 by Taq, posted 06-08-2020 6:29 PM Taq has not replied

  
Taq
Member
Posts: 9970
Joined: 03-06-2009
Member Rating: 5.6


(1)
Message 93 of 239 (877244)
06-09-2020 11:35 AM
Reply to: Message 91 by Kleinman
06-08-2020 7:46 PM


Re: Does competition accelerate DNA evolution?
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.

This message is a reply to:
 Message 91 by Kleinman, posted 06-08-2020 7:46 PM Kleinman has replied

Replies to this message:
 Message 94 by Kleinman, posted 06-09-2020 1:28 PM Taq has replied

  
Kleinman
Member (Idle past 334 days)
Posts: 2142
From: United States
Joined: 10-06-2016


Message 94 of 239 (877248)
06-09-2020 1:28 PM
Reply to: Message 93 by Taq
06-09-2020 11:35 AM


Re: Does competition accelerate DNA evolution?
Kleinman writes:
I don't know who taught you probability theory but they failed to teach you the difference between additive and complementary events.
Taq writes:
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 an 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?
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. If you want to have a better understanding of this math, study the binomial distribution because you are using the mean of that distribution for your math. But that distribution has a variance and standard deviation. So when you claim that for the 2 beneficial mutation case that the number of replications will be reduced by half (ie 1.5e9) will fall within the range of the variance of the binomial distribution.
Kleinman writes:
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.
Taq writes:
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?
We see what happens to the less fit variants in the Kishony experiment. As long as there are sufficient resources in the drug-free region, they happily replicate. 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. Remember, of the 3e9 replications that occur for the drug-resistant variant to appear, only about 14e6 will be mutants, the vast majority of that population will be exact clones of the founder wild-type.
Kleinman writes:
Selection is trying to order the genome to give the most efficient replicator. That's a second law problem.
Taq writes:
I think that goes a bit too far. It might be better to say that both DNA evolution and thermodynamics are stochastic processes.
The first law of thermodynamics is deterministic (conservation of energy). The second law of thermodynamics is stochastic. One means of modeling the mathematics to describe DNA evolution is the Markov Chain process:
Models of DNA evolution - Wikipedia
and Markov Chains have an entropy rate associated with that process.
Entropy rate - Wikipedia
In particular, read the section "Entropy rates for Markov chains"
The problem with the Markov Chain models given in the Wikipedia link above is that they are assuming the transition matrix is stationary and that the evolutionary process goes to equilibrium (that is the distribution of bases goes to equilibrium). What this means is the frequency of A, C, G, and T's go to 0.25. That certainly isn't happening in either the Kishony or Lenski experiments. My next paper will explain how to correct these models so that they predict DNA evolution.
Kleinman writes:
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.
Taq writes:
It would be helpful if you refrained from insulting peoples' knowledge on the subject and actually addressed what they are saying. Just some advice.
Don't be so thin-skinned.
Taq writes:
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?
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.
Kleinman writes:
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.
Taq writes:
How much of that is due to the strength of the selective pressures?
Both experiments only require single beneficial mutations for improvement in fitness. You should now have some idea what would happen if it takes 2 mutations to improve fitness. The reason why the Kishony experiment evolves so much more rapidly is the much larger carrying capacity. The more fit variants in the Kishony experiment have a new niche to grow in without competition which allows exponential growth. It doesn't take long to accumulate the 3e9 replications necessary for the next beneficial mutation, about 30 doublings of that variant will do it.
Kleinman writes:
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?
Taq writes:
That would be dependent on the strength of the selective pressure.
You have got it backward. You should be able to compute the strength of the selection pressure based on a fixation rate of 200 generations for the Lenski experiment. You know Lenski starts each day with a population of 5e6. At the end of the day, he has a population of 5e8 of which he bottlenecks that population to 1% of the previous day's population. You should be able to compute the intensity of selection from those numbers.

This message is a reply to:
 Message 93 by Taq, posted 06-09-2020 11:35 AM Taq has replied

Replies to this message:
 Message 96 by Taq, posted 06-09-2020 4:03 PM Kleinman has replied

  
vimesey
Member
Posts: 1398
From: Birmingham, England
Joined: 09-21-2011


Message 95 of 239 (877264)
06-09-2020 3:42 PM
Reply to: Message 89 by Kleinman
06-08-2020 2:57 PM


Re: Does competition accelerate DNA evolution?
Researchgate - a social networking site ?
Anything peer reviewed in a scientific journal bucko ?

Could there be any greater conceit, than for someone to believe that the universe has to be simple enough for them to be able to understand it ?

This message is a reply to:
 Message 89 by Kleinman, posted 06-08-2020 2:57 PM Kleinman has not replied

  
Taq
Member
Posts: 9970
Joined: 03-06-2009
Member Rating: 5.6


Message 96 of 239 (877265)
06-09-2020 4:03 PM
Reply to: Message 94 by Kleinman
06-09-2020 1:28 PM


Re: Does competition accelerate DNA evolution?
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.

This message is a reply to:
 Message 94 by Kleinman, posted 06-09-2020 1:28 PM Kleinman has replied

Replies to this message:
 Message 97 by Kleinman, posted 06-09-2020 5:09 PM Taq has replied

  
Kleinman
Member (Idle past 334 days)
Posts: 2142
From: United States
Joined: 10-06-2016


Message 97 of 239 (877266)
06-09-2020 5:09 PM
Reply to: Message 96 by Taq
06-09-2020 4:03 PM


Re: Does competition accelerate DNA evolution?
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.
Taq writes:
It's the same simplified model we used for calculating 1 mutation.
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.
Kleinman writes:
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.
Taq writes:
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.
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. This is why it is so important to discuss the Kishony and Lenski experiments together. You can see the distinct difference between the evolutionary processes when you have DNA evolution without intense competition as in the Kishony experiment and DNA evolution with intense competition as seen in the Lenski experiment. The Kishony experiment is more comparable to how drug-resistance occurs in the clinical medical situation as you so rightly pointed out that the carrying capacity of our gut is quite large, large enough for drug-resistant variants to be preexisting without antibiotics ever being used on that subject.
Kleinman writes:
The first law of thermodynamics is deterministic (conservation of energy). The second law of thermodynamics is stochastic.
Taq writes:
Correct. How heat moves through a system is very distantly related to DNA evolution to the point that false analogies start to emerge.
Incorrect. The Kimura model of diffusion is a competition/fixation model, not a DNA evolution model. Kimura wrote a different model for DNA evolution. Not only are you having difficulty with the math, but you are also having difficulty with the physics. Here's Kimura's diffusion model of fixation"
https://www.ncbi.nlm.nih.gov/...icles/PMC1210364/pdf/713.pdf
I already gave you the Wikipedia link on the Markov Chain which gives reference to Kimura's DNA evolution model. I happen to prefer Haldane's model of fixation (substitution). Haldane was right about his 300 generations/fixation estimate that he obtained from his analysis. Lenski's experiment demonstrates his claim. What Haldane was incorrect about was his claim "The principle unit process in evolution is the substitution of one gene for another at the same locus". The Kishony experiment shows that this is wrong.
Kleinman writes:
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.
Taq writes:
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.
I have a general idea of how this works and it wouldn't surprise me if you know a lot more about this particular aspect of biochemistry. My work focuses more on the fundamental basic science of how genetic transformations occur. I'm going to suggest that the same mathematical principles that I'm putting forth here describing the formation of new alleles applies to the non-coding portions of the genome which control and modulate the coding portions of the genome. Lenski's studies might reveal some empirical evidence since he is measuring his mutations everywhere in the genome. You might get some clues on the function of the non-coding regions of the E coli by the mutations getting fixed at those locations.
Kleinman writes:
The reason why the Kishony experiment evolves so much more rapidly is the much larger carrying capacity.
Taq writes:
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.
You are conflating 2 concepts here. 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. For example, consider the Kishony experiment, a member of the population get a beneficial mutation for the drug environment. That variant may very well have a lower relative fitness compared to the wild-type in the drug-free environment but in the drug region, that variant has the fecundity sufficient to get the next beneficial mutation.

This message is a reply to:
 Message 96 by Taq, posted 06-09-2020 4:03 PM Taq has replied

Replies to this message:
 Message 98 by Taq, posted 06-09-2020 6:45 PM Kleinman has replied

  
Taq
Member
Posts: 9970
Joined: 03-06-2009
Member Rating: 5.6


Message 98 of 239 (877267)
06-09-2020 6:45 PM
Reply to: Message 97 by Kleinman
06-09-2020 5:09 PM


Re: Does competition accelerate DNA evolution?
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.

This message is a reply to:
 Message 97 by Kleinman, posted 06-09-2020 5:09 PM Kleinman has replied

Replies to this message:
 Message 99 by Kleinman, posted 06-09-2020 8:26 PM Taq has replied

  
Kleinman
Member (Idle past 334 days)
Posts: 2142
From: United States
Joined: 10-06-2016


Message 99 of 239 (877268)
06-09-2020 8:26 PM
Reply to: Message 98 by Taq
06-09-2020 6:45 PM


Re: Does competition accelerate DNA evolution?
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.
Taq writes:
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.
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.
Kleinman writes:
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.
Taq writes:
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.
What competition does is remove the less fit variants from a population. The relative frequency of the less fit variant(s) decreases and the relative frequency of the more fit variant increases. 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. So, the relative frequencies of the different variants can be changing during this process. But remember, if you sum up the relative frequencies of all variants, it will equal 1.
Kleinman writes:
The Kimura model of diffusion is a competition/fixation model, not a DNA evolution model.
Taq writes:
Correct. Thermodynamics is the movement of heat through a system, not the diffusion of alleles.
You said, "How heat moves through a system is very distantly related to DNA evolution to the point that false analogies start to emerge.". 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
And the Kimura paper on fixation is using a standard heat transfer model which not only has a diffusion term in it, it also has a convection and energy storage term.
Kleinman writes:
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.
Taq writes:
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.
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. And the accumulation of those replications are slowed if the variant must compete with other variants for a limited amount of resources in the environment.
Taq writes:
Let's also not forget about sexual reproduction which can combine the beneficial mutations from two lineages.
Do you really think you are ready to start doing the mathematics of recombination? This mathematics is a little more complicated than Mendelian genetics. I've written a paper on this subject, but sorry that paper is behind a paywall. If you want to read that paper, here's a link to it:
Random recombination and evolution of drug resistance - PubMed
If you don't have access to the journal, I'll show you how to set up the mathematics and see if you can derive the equations yourself. But recombination has very little effect on DNA evolution.

This message is a reply to:
 Message 98 by Taq, posted 06-09-2020 6:45 PM Taq has replied

Replies to this message:
 Message 102 by Taq, posted 06-16-2020 3:57 PM Kleinman has replied

  
Kleinman
Member (Idle past 334 days)
Posts: 2142
From: United States
Joined: 10-06-2016


Message 100 of 239 (877305)
06-11-2020 11:44 AM


Why does Taq bring up sexual reproduction when talking about DNA evolution?
Taq writes:
Let's also not forget about sexual reproduction which can combine the beneficial mutations from two lineages.
Why does Taq bring up sexual reproduction (that is recombination) when we are discussing DNA evolution? Is Taq aware of something about DNA evolution? And how do you do the mathematics of DNA evolution with a sexually reproducing population and how does this change the math?

  
Kleinman
Member (Idle past 334 days)
Posts: 2142
From: United States
Joined: 10-06-2016


Message 101 of 239 (877338)
06-13-2020 9:24 AM


A little help for Taq on how recombination affects DNA evolution
The way to understand how a population which does recombination on replication affects the DNA evolution of allele(s) involved in adaptation when compared to a clonal haploid population, is still to consider the replications of the particular allele(s). It is easily seen that clonal replication of a haploid is simply the replication of that member. However, with recombination, the particular allele(s) could be laterally transferred (or not transferred) on replication. So, as with the haploid case, the replications of the variant with the particular allele(s) are counted, so are the replications counted of the variant with the particular allele(s) in the recombination case. An experiment analogous to the Lenski experiment has been started which is demonstrating this.
Eukaryotic Adaptation to Years-Long Starvation Resembles that of Bacteria - PubMed
They are in the early stages of this experiment and have not yet measured the effects of recombination but the mathematical argument comes down to this. You have a population of many different types of recombing variants. Let's say you have some members of the population which have a beneficial allele (call it "A") at one genetic locus and other members of the population which have a beneficial allele (call it "B") at a different genetic locus. The remainder of the population has neither beneficial allele A nor beneficial allele B, call those variants "C". For a population size N, what is the probability of an A variant randomly recombining with a B variant to give an offspring with both A and B alleles?

  
Taq
Member
Posts: 9970
Joined: 03-06-2009
Member Rating: 5.6


Message 102 of 239 (877464)
06-16-2020 3:57 PM
Reply to: Message 99 by Kleinman
06-09-2020 8:26 PM


Re: Does competition accelerate DNA evolution?
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?

This message is a reply to:
 Message 99 by Kleinman, posted 06-09-2020 8:26 PM Kleinman has replied

Replies to this message:
 Message 103 by Kleinman, posted 06-16-2020 5:30 PM Taq has replied

  
Kleinman
Member (Idle past 334 days)
Posts: 2142
From: United States
Joined: 10-06-2016


Message 103 of 239 (877480)
06-16-2020 5:30 PM
Reply to: Message 102 by Taq
06-16-2020 3:57 PM


Re: Does competition accelerate DNA evolution?
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.
Taq writes:
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.
It doesn't change the math much. You showed that if there were two possible beneficial mutations, it is still going to take 1.5e9 replications for at least one of those beneficial mutations to occur. What if there are 10 possible beneficial mutations? Now, if the population has to evolve to 2 or more simultaneous selection pressures simultaneously, that changes the math a lot. In fact, the number of replications for each DNA evolutionary step increases by multiple orders of magnitude. That's why Kishony's experiment will not work with two drugs or with one drug if the increase in concentration of that drug is too large requiring two or more mutations for the required increase in fitness for that region. Kishony will need a vastly larger petri dish than his mega-plate.
Kleinman writes:
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.
Taq writes:
If there is no competition then there are no individuals who are fitter.
That's not correct. Let me illustrate with the extreme case. 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. Wouldn't you say that that particular variant has lower reproductive fitness than any of the variants that are still able to replicate?
Kleinman writes:
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
Taq writes:
That doesn't mean that DNA evolution is thermodynamics.
But it is! DNA evolution is a random walk process. In particular, it is mathematically a Markov Chain process. And Markov chains are an entropy process. I gave you a link which explains this:
Entropy rate - Wikipedia
Read the paragraph titled "Entropy rates for Markov chains". And Shannon information is related to entropy:
Entropy (information theory) - Wikipedia
That's how DNA evolution is related to information.
Kleinman writes:
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.
Taq writes:
That would be the reproduction rate, not absolute fitness.
Fitness (biology) - Wikipedia
If you sum that term over time (generations), that gives you the total number of replications.
Kleinman writes:
Do you really think you are ready to start doing the mathematics of recombination?
Taq writes:
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?
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 [MSG=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.

This message is a reply to:
 Message 102 by Taq, posted 06-16-2020 3:57 PM Taq has replied

Replies to this message:
 Message 104 by Taq, posted 06-16-2020 5:51 PM Kleinman has replied

  
Taq
Member
Posts: 9970
Joined: 03-06-2009
Member Rating: 5.6


Message 104 of 239 (877482)
06-16-2020 5:51 PM
Reply to: Message 103 by Kleinman
06-16-2020 5:30 PM


Re: Does competition accelerate DNA evolution?
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.

This message is a reply to:
 Message 103 by Kleinman, posted 06-16-2020 5:30 PM Kleinman has replied

Replies to this message:
 Message 105 by Kleinman, posted 06-16-2020 6:18 PM Taq has replied

  
Kleinman
Member (Idle past 334 days)
Posts: 2142
From: United States
Joined: 10-06-2016


Message 105 of 239 (877486)
06-16-2020 6:18 PM
Reply to: Message 104 by Taq
06-16-2020 5:51 PM


Re: Does competition accelerate DNA evolution?
Kleinman writes:
Now, if the population has to evolve to 2 or more simultaneous selection pressures simultaneously, that changes the math a lot.
Taq writes:
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.
Do the math and/or present the empirical evidence! 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. Why does the Kishony experiment not work if the difference in drug concentration is too large requiring more than a single beneficial mutation? And that's when the colony has achieved 3e9 replications.
Kleinman writes:
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.
Taq writes:
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.
Or really? There is no such thing as a detrimental (fatal) mutation unless there is competition? What happens if there is a mutation that causes the failure of some vital metabolic pathway? That variant can still replicate if there is no competition. We are talking in the real world.
Kleinman writes:
But it is! DNA evolution is a random walk process.
Taq writes:
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.
The first law of thermodynamics pertains to energy. DNA evolution is a second law of thermodynamics process. Obviously you are ignoring the links I've given you to Markov chain DNA evolution models and Markov chain entropy. You can say that DNA evolution is not a thermodynamic process but you would be wrong. Read those links I gave you and find out why you are wrong.
Kleinman writes:
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.
Taq writes:
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?
I have done the math and it has been peer-reviewed and published and is also in the National Library of Medicine. I'm trying to get you to figure this out. I'll even give you another hint, the math is exactly the same as a random card drawing problem. If you say that you don't know how to do the math, I'll show you how to do it.

This message is a reply to:
 Message 104 by Taq, posted 06-16-2020 5:51 PM Taq has replied

Replies to this message:
 Message 106 by Taq, posted 06-16-2020 6:49 PM Kleinman has replied

  
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