What's wrong with Alan's Model of "rmns"?

[Bill Rogers]

Lots of people have pointed out obvious problems with Alan's model...

1. It doesn't model selection
2. It applies only to situations in which multiple, lethal selection pressures are applied suddenly to a population

but there's another problem that seemed unimportant, but perhaps is not.

Alan is convinced he's had an important insight showing what's wrong with standard Haldane or Kimura style models of population genetics. And that is that the important thing to follow is the absolute number of geneotypes rather than the relative frequency of genotypes. That's because, per Alan, what matters to the probability of getting a second beneficial mutation is the number of organisms carrying the first mutation - the number of wild type organisms is irrelevant because they are on their own trajectory at that point and don't affect what happens to the single mutants, who, likewise, are on their own, independent trajectory. On this view, relative frequency doesn't matter.

At first I thought this was just a trivial error, since relative frequency and absolute numbers are just related by the population size (even if you have to make population size a function of time). But it's not trivial; it's at the heart of what Alan doesn't understand about evolution. When you imagine independent trajectories for different genotypes you are ignoring competition. And, if you ignore competition, then, indeed, the "multiplication rule of probabilities" means that it will take a phenomenally long time to get some target set of mutations in one organism.

But competition is pretty much the rule, not the exception. Darwin's basic insight was that far more young of a given species are produced than can be supported by the environment and that competition will lead to gradual selection for the more fit - those more able to use food sources efficiently, withstand environmental stresses, avoid predation, find mates, etc. If you pretend that there are infinite resources and infinite space and infinite opportunities to reproduce, well, then, indeed every genotype will go off on a trajectory of its own, the odds of accumulating a specific collection of beneficial mutations will be infinitesimal, and nothing much will happen in the way of evolution.

I thought that Alan's insistence on absolute numbers versus relative frequencies was just a quirk, but it's actually essential for excluding competition from his model, and thus making evolution impossible except in cases where the applied selections are so strong that they make competition moot anyway.

[D Feenstra]

Op zaterdag 7 oktober 2017 14:40:02 UTC+2 schreef Bill Rogers:

> Lots of people have pointed out obvious problems with Alan's model...
>
> 1. It doesn't model selection
> 2. It applies only to situations in which multiple, lethal selection pressures are applied suddenly to a population

Hello, I am quite new to this group. Could you tell me where I can find a detailed description of this model?

[John Harshman]

http://onlinelibrary.wiley.com/doi/10.1002/sim.7070/abstract

[D Feenstra]

Op zaterdag 7 oktober 2017 15:30:02 UTC+2 schreef John Harshman:

Thank you, John. Unfortunately the paper is behind a paywall so I can't really do much other than guess unfortunately.

So if I understand this correctly, based on limited information, Alan uses a model that ends up seperating the concept of competition within a population from genotype mutation, in order to argue that it'd take a very long time for certain mutations to accumilate in a population.

However, due to competition and natural selection, specific genotypes with certain mutations will become dominant in a species if the mutation or series of mutations is beneficial compared to others.

That seems like a critical mistake by Alan, if I understood it correctly.

[Sean Dillon]

NONE of us have seen the paper, which is part of the issue. He's making empirical claims that none of us can check, based on math that none of us have seen, and claiming to have disproved "RMNS" as sufficient to account for the evolution of life on Earth, based on a couple papers that have only been academically cited by himself.

The heart of his argument is that, if a population is confronted with more than one selection pressure at once, the mutation(s) that address one selection pressure will be depressed in their ability to propagate by the other selection pressure.

IOW, if a population is confronted with dangerous temperature conditions and the introduction of a caustic chemical to the environment at the same time, the mutations that adapt for temperature won't spread, because the caustic chemical holds them down, and the mutations that adapt for the caustic chemical won't spread because the temperature holds them down. Therefore, the population cannot efficiently evolve in reaction to its environment, and will tend to be held in relative evolutionary stasis, or die out.

[jillery]

A pool is now available for how long it takes for some poster to
completely demolish your argument by asserting "LOL".

--
I disapprove of what you say, but I will defend to the death your right to say it.

Evelyn Beatrice Hall
Attributed to Voltaire

[jillery]

The good DrDr recently posted this "formula":

******************************************
> I've made this suggestion before, but if you really want people here to
> discuss your math, why don't you post a link to your actual paper that
> isn't behind a paywall. Put a .pdf file up on your personal website (or
> dropbox or whatever) and post a link to it here.
Sorry, I can't do that, it would violate the copyright agreement I
have with John C. Wiley. But I will give you the fundamental governing
binomial probability equation here:
P(X)=(1?(1-P(Beneficial)?)^(n?nG)) where;
X is the particular beneficial mutation,
P(beneficial) is the probability of all possible mutation that can
occur at the particular site that it is the beneficial mutation,
? is the mutation rate
n is the population size
nG is the number of generations that n replicates.
n*nG can be written in more general terms for a population which
varies every generation as a double summation of n for each generation
over the total number of generations.
.
Every evolutionary step by rmns on an evolutionary trajectory is of
the form above where the joint probability of the evolutionary
trajectory occurring is computed using the multiplication rule of each
individual probability equation.
*******************************************

Not sure if that helps you.

[Sean Dillon]

On Saturday, October 7, 2017 at 7:40:02 AM UTC-5, Bill Rogers wrote:
> Lots of people have pointed out obvious problems with Alan's model...
>
> 1. It doesn't model selection
> 2. It applies only to situations in which multiple, lethal selection pressures are applied suddenly to a population

I would add: highly TARGETTED selection pressures for which the range of genetic responses is in fact very limited.

"I don't have to run faster than then bear, I just have to run faster than you."

[Ernest Major]

His model also seems to assume no standing variation at the loci under
selection.

--
alias Ernest Major

[Bill Rogers]

Yes. If he actually had a model that included "ns" he could set the mutation rate to zero and let "ns" act on the previously existing variants. It seems like he has absorbed the "but where did the information come from?" meme from his sources, so he's fixated on mutations and indifferent to selection.

>
> --
> alias Ernest Major

[Andre G. Isaak]

In article <ee61c288-5e5b-483e...@googlegroups.com>,

Alan's problem (or rather among Alan's many problems) is that he is
interested exclusively in preventing the evolution of antibiotic
resistance through the application of multidrug therapy. So he describes
situations where multidrug resistance is extremely unlikely to evolve
(which is, of course, the entire point of multidrug therapy) and then
concludes from those situations that evolution can't happen.

He's been asked to discuss examples that don't involve multidrug
resistance (where the whole point is to minimize the chances of
adaptation). He came up with multipesticide resistance.

Andre

--
To email remove 'invalid' & replace 'gm' with well known Google mail service.

[Bob Casanova]

On Sat, 07 Oct 2017 10:47:01 -0400, the following appeared
in talk.origins, posted by jillery <69jp...@gmail.com>:

Put me down for 100 quatloos on "damn near immediately".
--

Bob C.

"The most exciting phrase to hear in science,
the one that heralds new discoveries, is not
'Eureka!' but 'That's funny...'"

- Isaac Asimov

[jillery]

On Sat, 07 Oct 2017 10:56:35 -0700, Bob Casanova <nos...@buzz.off>
wrote:

Due to the continuing clvil war on Triskelion, quatloos are worthless.
In God We Trust, all others pay in gold-pressed latinum.

[D Feenstra]

Op zaterdag 7 oktober 2017 16:50:02 UTC+2 schreef Sean Dillon:

> The heart of his argument is that, if a population is confronted with more than one selection pressure at once, the mutation(s) that address one selection pressure will be depressed in their ability to propagate by the other selection pressure.
>
> IOW, if a population is confronted with dangerous temperature conditions and the introduction of a caustic chemical to the environment at the same time, the mutations that adapt for temperature won't spread, because the caustic chemical holds them down, and the mutations that adapt for the caustic chemical won't spread because the temperature holds them down. Therefore, the population cannot efficiently evolve in reaction to its environment, and will tend to be held in relative evolutionary stasis, or die out.

Thanks. Huh. That's interesting. It seems a bit weird that he doesn't account for all the potential variables here, which we would find in nature.

I might be understanding this completely wrong, but one could easily conceive of a scenario like that of Alan in which populations would migrate away from one of the selection pressures, gaining mutations along the way,
or they simply gain both beneficial mutations, in seperate members of the entire populations, where over time it is inevitable for a member with mutation A to meet another member with mutation B, producing offspring with both mutations. Sure, a population might be reduced in size, but that would be the nature of Alan's proposed situation.



Op zaterdag 7 oktober 2017 16:50:02 UTC+2 schreef jillery:

Thank you very much. I'll try to understand it a bit more in the coming days lol.

[Bob Casanova]

On Sat, 07 Oct 2017 17:14:49 -0400, the following appeared

....or germanium, if we can just get New York off the
ground...

IMT
Made the sky
Fall

And as an aside, and FWIW, I have the entire final stanza
from that poem (the only one actually printed in the novel)
in memory, as I also have in memory the final "The History"
in Star Bridge by Williamson and Gunn. And "The Charge of
the Light Brigade". A cluttered heap of trivia is my mind,
and it only seems to get worse as I age.

[jillery]

On Sun, 08 Oct 2017 11:53:21 -0700, Bob Casanova <nos...@buzz.off>

That's nothing. I recall the theme song to Gilligan's Island [1]


[1] Another joke. Thank you in advance for not pooping on it.

[Alan Kleinman MD PhD]

On Saturday, October 7, 2017 at 5:40:02 AM UTC-7, Bill Rogers wrote:
> Lots of people have pointed out obvious problems with Alan's model...
>
> 1. It doesn't model selection

It's pretty sad when you adopt John's argument that my model doesn't model selection. After all, John's awareness of probability theory is limited to the addition theorm and he regularly applies that theorem incorrectly. Absolute fitness to reproduced is measured by the number of replications and I assure you, that variable is in my equations. Your problem is that you only can see selection in terms of relative fitness to reproduce when it is the absolute fitness to reproduce which determines the probability of a beneficial mutation occurring.

> 2. It applies only to situations in which multiple, lethal selection pressures are applied suddenly to a population

That explains why you didn't see emergence of resistance in your Malaria study and why combination therapy drives HIV to extinction. You are a very smart cookie Bill to use multiple, lethal selection pressures and apply them suddenly for your treatment of Malaria, you don't see emergence of resistance. On the other hand, perhaps you don't quite see that when Malaria populations can achieve absolute numbers of e12 and that there is a reasonable probability of a double beneficial mutation occurring.

>
> but there's another problem that seemed unimportant, but perhaps is not.
>
> Alan is convinced he's had an important insight showing what's wrong with standard Haldane or Kimura style models of population genetics.

I don't say that Haldane's and Kimura's model are necessarily wrong, it is that they are inaccurate and incomplete in describing the physics of rmns. What Haldane and Kimura are attempting to describe is half of the cycle which constitute the rmns phenomenon. The half of the cycle they are attempting to describe is the amplification phase of rmns. Haldane's concept of the substitution of a more beneficial allele for a less beneficial allele in a population is neither necessary nor sufficient for amplification to occur. This is well demonstrated in the Kishony experiment where multiple different colonies are evolving resistance to the antibiotic without the other variants disappearing. Kimura uses the same conceptual approach as Haldane but instead of modeling fixation as a substitution process, he models it as a diffusion process. On the other hand, you might try to apply the Haldane and Kimura models to the Lenski experiment because in this case you have different variants competing for a fixed amount of resources. In this case, the more fit variants will drive the less fit variants to extinction potentially causing “fixation”. But it doesn't matter, even if the particular variant now has a relative frequency of 1, this variant must still have sufficient absolute fitness (do enough replications) to have a reasonable probability of another beneficial mutation occurring on this particular variant (thus creating a new variant). Neither Haldane nor Kimura correctly take into account the multiplication rule of probabilities for rmns in their models.

> And that is that the important thing to follow is the absolute number of geneotypes rather than the relative frequency of genotypes. That's because, per Alan, what matters to the probability of getting a second beneficial mutation is the number of organisms carrying the first mutation - the number of wild type organisms is irrelevant because they are on their own trajectory at that point and don't affect what happens to the single mutants, who, likewise, are on their own, independent trajectory. On this view, relative frequency doesn't matter.

You are restating my argument correctly. Another way of saying this is that a mutation which might be beneficial for one variant may very well be detrimental to a different variant on a different evolutionary trajectory.

>
> At first I thought this was just a trivial error, since relative frequency and absolute numbers are just related by the population size (even if you have to make population size a function of time). But it's not trivial; it's at the heart of what Alan doesn't understand about evolution. When you imagine independent trajectories for different genotypes you are ignoring competition. And, if you ignore competition, then, indeed, the "multiplication rule of probabilities" means that it will take a phenomenally long time to get some target set of mutations in one organism.

I don't ignore competition at all. In fact, all that competition for resources in an environment does is slow down the rmns process. The empirical evidence clearly demonstrates this. The population attempting to adapt to a set of selection pressures which also must compete against different variants in the same environment for the same resources will not be able to reproduce as efficiently as if they didn't have this competition. This is why the Lenski experiment takes so many generations for each beneficial mutation. And what do you think would happen in the Kishony experiment if he grew not only e coli but also staphlococcus on the same plate? The competition between the two bacterial populations would limit the growth of either colonies reducing the absolute fitness of both reducing the ability of either population to adapt to the antibiotic selection pressure.

>
> But competition is pretty much the rule, not the exception. Darwin's basic insight was that far more young of a given species are produced than can be supported by the environment and that competition will lead to gradual selection for the more fit - those more able to use food sources efficiently, withstand environmental stresses, avoid predation, find mates, etc. If you pretend that there are infinite resources and infinite space and infinite opportunities to reproduce, well, then, indeed every genotype will go off on a trajectory of its own, the odds of accumulating a specific collection of beneficial mutations will be infinitesimal, and nothing much will happen in the way of evolution.

Certainly the limitation of resources constitutes selection pressures but what is the resource limitation in your malaria study? Not much because this parasite can achieve populations of e12 in a single sufferer. And with populations this size, two drug therapy does not necessarily constitute sudden, lethal selection pressures as your study demonstrated. Competition between variants for resources of the environment only slows the rmns process against any other selection conditions the environment is offering.

>
> I thought that Alan's insistence on absolute numbers versus relative frequencies was just a quirk, but it's actually essential for excluding competition from his model, and thus making evolution impossible except in cases where the applied selections are so strong that they make competition moot anyway.

If you think about this a little more carefully Bill, you may come to the correct conclusion that my model works correctly whether there is competition between variants or no competition between variants. Competition between variants only slows the ability of the particular variants to achieve the number of replications necessary give a reasonable probability of a beneficial mutation occurring. rmns works much more efficiently when variants do not have to compete with each other. But the number of replications required to give a reasonable probability of a beneficial mutation occurring on a particular variant remains the same whether there is competition from other variants or not. Competition between variants reduces the absolute reproductive fitness of all variants in the environment.

[Bill Rogers]

On Monday, October 9, 2017 at 4:30:03 AM UTC-4, Alan Kleinman MD PhD wrote:
> On Saturday, October 7, 2017 at 5:40:02 AM UTC-7, Bill Rogers wrote:
> > Lots of people have pointed out obvious problems with Alan's model...
> >
> > 1. It doesn't model selection
> It's pretty sad when you adopt John's argument that my model doesn't model selection. After all, John's awareness of probability theory is limited to the addition theorm and he regularly applies that theorem incorrectly. Absolute fitness to reproduced is measured by the number of replications and I assure you, that variable is in my equations. Your problem is that you only can see selection in terms of relative fitness to reproduce when it is the absolute fitness to reproduce which determines the probability of a beneficial mutation occurring.

But you don't model selection. There is no parameter in your model for the fitness of the wild type or the mutants. You simply say "amplification occurs". That's not a model of selection. As I've said before, you could prove that your model incorporated selection simply by setting the mutation rate to zero. Start with a mix of genotypes with different fitness and model the change in their populations over time.

>
> > 2. It applies only to situations in which multiple, lethal selection pressures are applied suddenly to a population
> That explains why you didn't see emergence of resistance in your Malaria study and why combination therapy drives HIV to extinction. You are a very smart cookie Bill to use multiple, lethal selection pressures and apply them suddenly for your treatment of Malaria, you don't see emergence of resistance. On the other hand, perhaps you don't quite see that when Malaria populations can achieve absolute numbers of e12 and that there is a reasonable probability of a double beneficial mutation occurring.

The selection pressures you are imagining are indeed lethal. You simply calculate that in a large enough population there would be a reasonable probability for the occurrence of double mutants resistant to both lethal selections. The failures, according to your model, are not due to non-lethality of the selections, only to the size of the starting population and the chance that it will contain a double mutant. So, in spite of your gripes, you are still modelling lethal selections.

>
> >
> > but there's another problem that seemed unimportant, but perhaps is not.
> >
> > Alan is convinced he's had an important insight showing what's wrong with standard Haldane or Kimura style models of population genetics.
> I don't say that Haldane's and Kimura's model are necessarily wrong, it is that they are inaccurate and incomplete in describing the physics of rmns. What Haldane and Kimura are attempting to describe is half of the cycle which constitute the rmns phenomenon. The half of the cycle they are attempting to describe is the amplification phase of rmns.

Yeah, the "amplification phase of rmns" that's what other people here call selection.

>Haldane's concept of the substitution of a more beneficial allele for a less beneficial allele in a population is neither necessary nor sufficient for amplification to occur. This is well demonstrated in the Kishony experiment where multiple different colonies are evolving resistance to the antibiotic without the other variants disappearing. Kimura uses the same conceptual approach as Haldane but instead of modeling fixation as a substitution process, he models it as a diffusion process. On the other hand, you might try to apply the Haldane and Kimura models to the Lenski experiment because in this case you have different variants competing for a fixed amount of resources. In this case, the more fit variants will drive the less fit variants to extinction potentially causing “fixation”. But it doesn't matter, even if the particular variant now has a relative frequency of 1, this variant must still have sufficient absolute fitness (do enough replications) to have a reasonable probability of another beneficial mutation occurring on this particular variant (thus creating a new variant). Neither Haldane nor Kimura correctly take into account the multiplication rule of probabilities for rmns in their models.

When you say "the variant most still have sufficient absolute fitness," all you mean is that the variant must be able to reproduce to fill the carrying capacity of the environment. That's no problem in most real settings; it is a problem if you are treating an infection with two lethal drugs and the variant you are talking about has resistance to only one of the drugs.

>
>
> > And that is that the important thing to follow is the absolute number of geneotypes rather than the relative frequency of genotypes. That's because, per Alan, what matters to the probability of getting a second beneficial mutation is the number of organisms carrying the first mutation - the number of wild type organisms is irrelevant because they are on their own trajectory at that point and don't affect what happens to the single mutants, who, likewise, are on their own, independent trajectory. On this view, relative frequency doesn't matter.
> You are restating my argument correctly. Another way of saying this is that a mutation which might be beneficial for one variant may very well be detrimental to a different variant on a different evolutionary trajectory.
>
> >
> > At first I thought this was just a trivial error, since relative frequency and absolute numbers are just related by the population size (even if you have to make population size a function of time). But it's not trivial; it's at the heart of what Alan doesn't understand about evolution. When you imagine independent trajectories for different genotypes you are ignoring competition. And, if you ignore competition, then, indeed, the "multiplication rule of probabilities" means that it will take a phenomenally long time to get some target set of mutations in one organism.
> I don't ignore competition at all. In fact, all that competition for resources in an environment does is slow down the rmns process.

Competition in the environment speeds up evolution; it does not slow it down. If there were infinite resources, infinite space, and infinite opportunities to reproduce, evolution barely proceed at all.

>The empirical evidence clearly demonstrates this.

No; the empirical evidence demonstrates no such thing.

>The population attempting to adapt to a set of selection pressures which also must compete against different variants in the same environment for the same resources will not be able to reproduce as efficiently as if they didn't have this competition.

The one that wins the competition will be the one the reproduces more efficiently than the others.

>This is why the Lenski experiment takes so many generations for each beneficial mutation. And what do you think would happen in the Kishony experiment if he grew not only e coli but also staphlococcus on the same plate? The competition between the two bacterial populations would limit the growth of either colonies reducing the absolute fitness of both reducing the ability of either population to adapt to the antibiotic selection pressure.

No. Whichever species grew faster on his medium would take over the experiment in short order and would develop antibacterial resistance.

> >
> > But competition is pretty much the rule, not the exception. Darwin's basic insight was that far more young of a given species are produced than can be supported by the environment and that competition will lead to gradual selection for the more fit - those more able to use food sources efficiently, withstand environmental stresses, avoid predation, find mates, etc. If you pretend that there are infinite resources and infinite space and infinite opportunities to reproduce, well, then, indeed every genotype will go off on a trajectory of its own, the odds of accumulating a specific collection of beneficial mutations will be infinitesimal, and nothing much will happen in the way of evolution.
> Certainly the limitation of resources constitutes selection pressures but what is the resource limitation in your malaria study? Not much because this parasite can achieve populations of e12 in a single sufferer. And with populations this size, two drug therapy does not necessarily constitute sudden, lethal selection pressures as your study demonstrated. Competition between variants for resources of the environment only slows the rmns process against any other selection conditions the environment is offering.
> >
> > I thought that Alan's insistence on absolute numbers versus relative frequencies was just a quirk, but it's actually essential for excluding competition from his model, and thus making evolution impossible except in cases where the applied selections are so strong that they make competition moot anyway.
> If you think about this a little more carefully Bill, you may come to the correct conclusion that my model works correctly whether there is competition between variants or no competition between variants. Competition between variants only slows the ability of the particular variants to achieve the number of replications necessary give a reasonable probability of a beneficial mutation occurring. rmns works much more efficiently when variants do not have to compete with each other. But the number of replications required to give a reasonable probability of a beneficial mutation occurring on a particular variant remains the same whether there is competition from other variants or not. Competition between variants reduces the absolute reproductive fitness of all variants in the environment.

Someone needs to think a bit more carefully, that's for sure. Consider a population which, like most wild populations of anything, is limited by the carrying capacity of the environment. The population size is approximately constant from generation to generation. That means that in each generation, there is an equal chance of a beneficial mutation occurring. When one such mutation occurs, it takes relatively few generations for that mutation to go to fixation (you'd know this if your model actually modeled selection). Once that happens, every new beneficial mutation that occurs will be occurring on a genetic background that already contains the first beneficial mutation.

So, here's a crude calculation (it's crude, but it won't differ by your full model by more than an order of magnitude or two, and as you'll see, that sort of difference won't change the conclusion).

Imagine a population of 10^5 organisms. Imagine that they each produce around 10 offspring of which, on average, only one survives to reproduce in the next generation. Imagine that by "beneficial mutation" we mean one that increases the chance that an organism bearing that mutation will be one of the approximately 1 in 10 lucky offspring that gets to survive to reproduce. And imagine that beneficial mutations happen at a rate of 10^-8 per replication.

So you have 10^6 replications per generation. You therefore expect one beneficial mutation in 100 generations. By the multiplication rule of probabilities you expect that double beneficial mutations will happen at a rate of 10^-16 per replication. So, roughly, you expect that it should take 10^10 generations for you to get a double beneficial mutant. This is based on using your model, without considering competition or selection, just the plain "physics of the rmns phenomenon" as you describe it. I can't really quantify how your model would incorporate "amplification" in such a system, because you never say. In any case, for a population of 10^5 organisms, you're looking at 10^10 generations for a time frame to get to two beneficial mutations in the same organism.

But realistically, what happens when there is selection and competition? You expect that within 100 generations there will appear a beneficial mutant. It takes a relatively marginal fitness difference between the mutant and the wild type for the mutant to become fixed within a few hundred generations, but let's say 1000 generations. Then you have a population that consists entirely of those with the first beneficial mutation. Now we expect another 100 generations to get a second beneficial mutation. So within 1200 generations, rather than 10^10 generations you have a double mutant.

The difference between 1200 and 10^10 is why people have told you many times in the past that once you really consider selection in your model, the probability of a double mutant no longer is correctly described by the multiplication rule of probabilities. Before you cluck and tell me I need to take a basic probability course along with Harshman, just go ahead and show what you model predicts for the situation I described here. Don't just wag your head and say "the physics of rmns is governed by a nested series of binomial distributions"; go ahead and show how your model would describe the relatively commonplace scenario described here.

[Alan Kleinman MD PhD]

On Monday, October 9, 2017 at 4:00:03 AM UTC-7, Bill Rogers wrote:
> On Monday, October 9, 2017 at 4:30:03 AM UTC-4, Alan Kleinman MD PhD wrote:
> > On Saturday, October 7, 2017 at 5:40:02 AM UTC-7, Bill Rogers wrote:
> > > Lots of people have pointed out obvious problems with Alan's model...
> > >
> > > 1. It doesn't model selection
> > It's pretty sad when you adopt John's argument that my model doesn't model selection. After all, John's awareness of probability theory is limited to the addition theorm and he regularly applies that theorem incorrectly. Absolute fitness to reproduced is measured by the number of replications and I assure you, that variable is in my equations. Your problem is that you only can see selection in terms of relative fitness to reproduce when it is the absolute fitness to reproduce which determines the probability of a beneficial mutation occurring.
>
> But you don't model selection. There is no parameter in your model for the fitness of the wild type or the mutants. You simply say "amplification occurs". That's not a model of selection. As I've said before, you could prove that your model incorporated selection simply by setting the mutation rate to zero. Start with a mix of genotypes with different fitness and model the change in their populations over time.

Like I say, you are fixated on the notion of relative fitness to reproduce when rmns is dependent on the absolute fitness to reproduce. Multiple different variants in your mix of genotypes can evolve to a particular selection pressure on their own particular evolutionary trajectory as long as they have sufficient absolute fitness to reproduce. It is the number of replications of a particular variant which determines the probability of a beneficial mutation occurring.

>
> >
> > > 2. It applies only to situations in which multiple, lethal selection pressures are applied suddenly to a population
> > That explains why you didn't see emergence of resistance in your Malaria study and why combination therapy drives HIV to extinction. You are a very smart cookie Bill to use multiple, lethal selection pressures and apply them suddenly for your treatment of Malaria, you don't see emergence of resistance. On the other hand, perhaps you don't quite see that when Malaria populations can achieve absolute numbers of e12 and that there is a reasonable probability of a double beneficial mutation occurring.
>
> The selection pressures you are imagining are indeed lethal. You simply calculate that in a large enough population there would be a reasonable probability for the occurrence of double mutants resistant to both lethal selections. The failures, according to your model, are not due to non-lethality of the selections, only to the size of the starting population and the chance that it will contain a double mutant. So, in spite of your gripes, you are still modelling lethal selections.

Your use of language is nothing short of bizarre. If you use two "lethal" selection pressures are you killing them twice? It should be obvious to you that if a selection pressure is 100% lethal, your population should go extinction (and isn't that your goal when treating malaria?), therefore your selection pressures are not 100% lethal when you see the emergence of resistance.

>
> >
> > >
> > > but there's another problem that seemed unimportant, but perhaps is not.
> > >
> > > Alan is convinced he's had an important insight showing what's wrong with standard Haldane or Kimura style models of population genetics.
> > I don't say that Haldane's and Kimura's model are necessarily wrong, it is that they are inaccurate and incomplete in describing the physics of rmns. What Haldane and Kimura are attempting to describe is half of the cycle which constitute the rmns phenomenon. The half of the cycle they are attempting to describe is the amplification phase of rmns.
>
> Yeah, the "amplification phase of rmns" that's what other people here call selection.

But fixation is not necessarily amplification. That's why Haldane's and Kimura's models are not correct physically to describe rmns.

>
> >Haldane's concept of the substitution of a more beneficial allele for a less beneficial allele in a population is neither necessary nor sufficient for amplification to occur. This is well demonstrated in the Kishony experiment where multiple different colonies are evolving resistance to the antibiotic without the other variants disappearing. Kimura uses the same conceptual approach as Haldane but instead of modeling fixation as a substitution process, he models it as a diffusion process. On the other hand, you might try to apply the Haldane and Kimura models to the Lenski experiment because in this case you have different variants competing for a fixed amount of resources. In this case, the more fit variants will drive the less fit variants to extinction potentially causing “fixation”. But it doesn't matter, even if the particular variant now has a relative frequency of 1, this variant must still have sufficient absolute fitness (do enough replications) to have a reasonable probability of another beneficial mutation occurring on this particular variant (thus creating a new variant). Neither Haldane nor Kimura correctly take into account the multiplication rule of probabilities for rmns in their models.
>
>
> When you say "the variant most still have sufficient absolute fitness," all you mean is that the variant must be able to reproduce to fill the carrying capacity of the environment. That's no problem in most real settings; it is a problem if you are treating an infection with two lethal drugs and the variant you are talking about has resistance to only one of the drugs.

Would you do me a favor and stop putting phrases in quotes which I have not made and then attributing them to me? Perhaps you were trying to quote this phrase that I did make "this variant must still have sufficient absolute fitness (do enough replications) to have a reasonable probability of another beneficial mutation occurring on this particular variant (thus creating a new variant)". It is not necessarily true that the variant must fill the environment to its carrying capacity in order to amplify a particular mutation. The Kishony experiment plainly demonstrates this fact. Now if you want to get the Kishony experiment to work with two drugs, you are going to need a much larger petri dish which will support much larger colonies to improve the probability of double beneficial mutations occurring.

>
> >
> >
> > > And that is that the important thing to follow is the absolute number of geneotypes rather than the relative frequency of genotypes. That's because, per Alan, what matters to the probability of getting a second beneficial mutation is the number of organisms carrying the first mutation - the number of wild type organisms is irrelevant because they are on their own trajectory at that point and don't affect what happens to the single mutants, who, likewise, are on their own, independent trajectory. On this view, relative frequency doesn't matter.
> > You are restating my argument correctly. Another way of saying this is that a mutation which might be beneficial for one variant may very well be detrimental to a different variant on a different evolutionary trajectory.
> >
> > >
> > > At first I thought this was just a trivial error, since relative frequency and absolute numbers are just related by the population size (even if you have to make population size a function of time). But it's not trivial; it's at the heart of what Alan doesn't understand about evolution. When you imagine independent trajectories for different genotypes you are ignoring competition. And, if you ignore competition, then, indeed, the "multiplication rule of probabilities" means that it will take a phenomenally long time to get some target set of mutations in one organism.
> > I don't ignore competition at all. In fact, all that competition for resources in an environment does is slow down the rmns process.
>
> Competition in the environment speeds up evolution; it does not slow it down. If there were infinite resources, infinite space, and infinite opportunities to reproduce, evolution barely proceed at all.

Perhaps this happens in your dreams after you ate a really spicy pizza but in reality, your own empirical examples which you recommended to us shows that you are wrong. Recommend to Lenski to run his experiment with both e coli and staph together instead of e coli alone or for Kishony to use both e coli and staph together in this experiment instead of e coli alone. The competition for the resources in the environment alone is enough selection pressure to drive one or the other bacterial populations to extinction. I do hope you enjoyed that spicy pizza.

>
>
> >The empirical evidence clearly demonstrates this.
>
> No; the empirical evidence demonstrates no such thing.

Really? Do you believe that competition from different variants for resources in the environment helps the absolute reproductive fitness of each of the variants? Where is your empirical evidence?

>
> >The population attempting to adapt to a set of selection pressures which also must compete against different variants in the same environment for the same resources will not be able to reproduce as efficiently as if they didn't have this competition.
>
> The one that wins the competition will be the one the reproduces more efficiently than the others.

Until the winner of the competition drives the other variants to extinction, the less fit variants will be depriving the more fit variant resources necessary to reproduce. This is a simple conservation of energy and conservation of mass problem. Why are you having trouble seeing this?

>
> >This is why the Lenski experiment takes so many generations for each beneficial mutation. And what do you think would happen in the Kishony experiment if he grew not only e coli but also staphlococcus on the same plate? The competition between the two bacterial populations would limit the growth of either colonies reducing the absolute fitness of both reducing the ability of either population to adapt to the antibiotic selection pressure.
>
> No. Whichever species grew faster on his medium would take over the experiment in short order and would develop antibacterial resistance.

Let me see if I get your argument correct. Are you really saying that a bacterial lineage will evolve more quickly against an antimicrobial agent if the particular lineage must also compete against other lineages at the same time for resources of the environment than if the lineage only had to evolve against the antimicrobial agent alone? If that's your argument, I think you had a little too much beer with your pizza.

>
> > >
> > > But competition is pretty much the rule, not the exception. Darwin's basic insight was that far more young of a given species are produced than can be supported by the environment and that competition will lead to gradual selection for the more fit - those more able to use food sources efficiently, withstand environmental stresses, avoid predation, find mates, etc. If you pretend that there are infinite resources and infinite space and infinite opportunities to reproduce, well, then, indeed every genotype will go off on a trajectory of its own, the odds of accumulating a specific collection of beneficial mutations will be infinitesimal, and nothing much will happen in the way of evolution.
> > Certainly the limitation of resources constitutes selection pressures but what is the resource limitation in your malaria study? Not much because this parasite can achieve populations of e12 in a single sufferer. And with populations this size, two drug therapy does not necessarily constitute sudden, lethal selection pressures as your study demonstrated. Competition between variants for resources of the environment only slows the rmns process against any other selection conditions the environment is offering.
> > >
> > > I thought that Alan's insistence on absolute numbers versus relative frequencies was just a quirk, but it's actually essential for excluding competition from his model, and thus making evolution impossible except in cases where the applied selections are so strong that they make competition moot anyway.
> > If you think about this a little more carefully Bill, you may come to the correct conclusion that my model works correctly whether there is competition between variants or no competition between variants. Competition between variants only slows the ability of the particular variants to achieve the number of replications necessary give a reasonable probability of a beneficial mutation occurring. rmns works much more efficiently when variants do not have to compete with each other. But the number of replications required to give a reasonable probability of a beneficial mutation occurring on a particular variant remains the same whether there is competition from other variants or not. Competition between variants reduces the absolute reproductive fitness of all variants in the environment.
>
> Someone needs to think a bit more carefully, that's for sure. Consider a population which, like most wild populations of anything, is limited by the carrying capacity of the environment. The population size is approximately constant from generation to generation. That means that in each generation, there is an equal chance of a beneficial mutation occurring. When one such mutation occurs, it takes relatively few generations for that mutation to go to fixation (you'd know this if your model actually modeled selection). Once that happens, every new beneficial mutation that occurs will be occurring on a genetic background that already contains the first beneficial mutation.
>

You are not doing your math correctly. Each generation a fixed sized population reproduces improves the probability of a beneficial mutation occurring. Each time any member of a variant reproduces improves the probability of a beneficial mutation occurring. A simple analogy is the more times you roll a die, the higher the probability that you will roll a one.

> So, here's a crude calculation (it's crude, but it won't differ by your full model by more than an order of magnitude or two, and as you'll see, that sort of difference won't change the conclusion).
>
> Imagine a population of 10^5 organisms. Imagine that they each produce around 10 offspring of which, on average, only one survives to reproduce in the next generation. Imagine that by "beneficial mutation" we mean one that increases the chance that an organism bearing that mutation will be one of the approximately 1 in 10 lucky offspring that gets to survive to reproduce. And imagine that beneficial mutations happen at a rate of 10^-8 per replication.
>
> So you have 10^6 replications per generation. You therefore expect one beneficial mutation in 100 generations. By the multiplication rule of probabilities you expect that double beneficial mutations will happen at a rate of 10^-16 per replication. So, roughly, you expect that it should take 10^10 generations for you to get a double beneficial mutant. This is based on using your model, without considering competition or selection, just the plain "physics of the rmns phenomenon" as you describe it. I can't really quantify how your model would incorporate "amplification" in such a system, because you never say. In any case, for a population of 10^5 organisms, you're looking at 10^10 generations for a time frame to get to two beneficial mutations in the same organism.
>
> But realistically, what happens when there is selection and competition? You expect that within 100 generations there will appear a beneficial mutant. It takes a relatively marginal fitness difference between the mutant and the wild type for the mutant to become fixed within a few hundred generations, but let's say 1000 generations.

Here is where you go off track. That mutant is the progenitor of a new subpopulation which must now amplify in order to improve the probability of the next beneficial mutation. If that new variant must compete for the resources of the environment with other variants as well as continue to evolve against the selection pressure, the other variants will deprive the slightly more fit variant of the resources necessary to reproduce, slowing the evolutionary process. As the more fit variant drives the less fit variant to extinction, the more fit variant will have more resources necessary to reproduce.

> Then you have a population that consists entirely of those with the first beneficial mutation. Now we expect another 100 generations to get a second beneficial mutation. So within 1200 generations, rather than 10^10 generations you have a double mutant.
>
> The difference between 1200 and 10^10 is why people have told you many times in the past that once you really consider selection in your model, the probability of a double mutant no longer is correctly described by the multiplication rule of probabilities. Before you cluck and tell me I need to take a basic probability course along with Harshman, just go ahead and show what you model predicts for the situation I described here. Don't just wag your head and say "the physics of rmns is governed by a nested series of binomial distributions"; go ahead and show how your model would describe the relatively commonplace scenario described here.

Bill, a population e5 replicating for e10 generations gives the exact same sample space as a population of e10 replicating for e5 generations. This is why with the huge populations' malaria can attain, it doesn't take very many generations for a double beneficial mutation to occur. And as long as mutations are random independent events, the multiplication rule will apply when computing the joint probability of two or more particular mutations occurring. Natural selection through absolute reproductive fitness can improve this probability by increasing the number of replications of the particular variants. That is the physics of rmns.

[Bill Rogers]

I'm happy with the arguments I've laid out. I've got nothing to add in rebuttal to you that I've not said already. So I think we're done. I am, anyway.

[Alan Kleinman MD PhD]

Just when the fun has started you want to leave? I was so much hoping for you to present some empirical examples of your claims. You know how much I enjoy your examples. Enjoy your pizza and beer up in the bleachers.

[Dennis Feenstra]

Alan, does your model
a) calculate the probability of a single organism gaining two beneficial mutations at the same time after an x amount of generations,
or does your model
b) calculate the probability of a single beneficial mutation to emerge in an individual within a population, as well as the time it takes for such a beneficial mutation to become fixed in that population,

after which it would take the same amount of generations for a new (second) beneficial mutation to emerge within an individual that already has the first beneficial mutation?

Reading Bill's criticism of your model, it seems it's a) instead of b).

[Alan Kleinman MD PhD]

On Monday, October 9, 2017 at 9:45:03 AM UTC-7, Dennis Feenstra wrote:
> Alan, does your model
> a) calculate the probability of a single organism gaining two beneficial mutations at the same time after an x amount of generations,

I've published two papers on rmns (random mutation and natural selection). The first paper gives the mathematics which governs rmns for a single selection pressure targeting a single genetic locus. It shows how a lineage accumulates the mutations which allow it to adapt to this single selection pressure. The second paper addresses how rmns operates when multiple simultaneous selection pressures targeting multiple genetic loci operates. The editor of the journal which published these papers asked me to write a layman's abstract to explain how this mathematics works for those not well versed in probability theory. This abstract is not behind a paywall and can be found at: http://www.statisticsviews.com/details/news/10604248/Laymans-abstract-Random-mutation-and-natural-selection-a-predictable-phenomenon.html

> or does your model
> b) calculate the probability of a single beneficial mutation to emerge in an individual within a population, as well as the time it takes for such a beneficial mutation to become fixed in that population,

Fixation of a beneficial mutation is neither necessary nor sufficient for rmns to operate.

>
> after which it would take the same amount of generations for a new (second) beneficial mutation to emerge within an individual that already has the first beneficial mutation?

The probability of a beneficial mutation occurring is dependent on the number of replications a particular variant can achieve. Those replications can occur in a single generation if the population is large enough or over a number of generations if the population is smaller, that is if the population has sufficient absolute reproductive fitness for the particular environment.

>
> Reading Bill's criticism of your model, it seems it's a) instead of b).

Bill is in a state of bliss over his criticisms of my model.

[Bob Casanova]

On Sun, 08 Oct 2017 18:48:40 -0400, the following appeared

You're welcome. I knew it was a joke, since you obviously
haven't committed suicide. ;-)

[Dennis Feenstra]

This is a rework of my post: noticed some errors and decided to streamline it. Apologies.

> I've published two papers on rmns (random mutation and natural selection). The first paper gives the mathematics which governs rmns for a single selection pressure targeting a single genetic locus. It shows how a lineage accumulates the mutations which allow it to adapt to this single selection pressure. The second paper addresses how rmns operates when multiple simultaneous selection pressures targeting multiple genetic loci operates.

I'll simply take your word for it (the two published papers), since I have no access to these papers themselves. Hopefully no hard feelings.

> Fixation of a beneficial mutation is neither necessary nor sufficient for rmns to operate.

That is true, but the point is the multiplication rule only counts for a single lineage, irregardless if others within a population has the same first beneficial mutation.

In your layman's abstract you state, quote:
"Since mutations are random events, the joint probability of multiple beneficial mutations occurring on a lineage in a population will be governed by the multiplication rule of probabilities."

Then what about a number of lineages in a single population which acquired the first mutation by means of fixation (high fitness increasing the probability of survival for any organism with the first mutation)?

Does your model account for a single beneficial mutation spreading through a population, where each independent lineage carrying the first mutation has an equal chance of gaining a secondary beneficial mutation?

[John Harshman]

On 10/9/17 11:36 AM, Dennis Feenstra wrote:
>> I've published two papers on rmns (random mutation and natural
>> selection). The first paper gives the mathematics which governs
>> rmns for a single selection pressure targeting a single genetic
>> locus. It shows how a lineage accumulates the mutations which allow
>> it to adapt to this single selection pressure. The second paper
>> addresses how rmns operates when multiple simultaneous selection
>> pressures targeting multiple genetic loci operates.

> I'll simply take your word for it, since I have no access to the papers themselves. Hopefully no hard feelings.

Don't take his word for it. He's wrong. He never deals with selection at
all, just mutation.

[Dennis Feenstra]

Op maandag 9 oktober 2017 21:05:02 UTC+2 schreef John Harshman:

> On 10/9/17 11:36 AM, Dennis Feenstra wrote:
> Don't take his word for it. He's wrong. He never deals with selection at
> all, just mutation.

I am not taking his word in a sense that I agree with him. It's more that his papers are something which I can't verify in any meaningful way. Hence I can and will only adress whatever he says outside his papers.

[Alan Kleinman MD PhD]

John, when are you going to learn what a sample space is and that there are more theorems in probability theory than just the addition rule which you regularly apply incorrectly.

[Alan Kleinman MD PhD]

Here is the fundamental governing equation for rmns:
.
P(X)=(1−(1-P(Beneficial)𝜇)^(n∗nG)) where;

X is the particular beneficial mutation,
P(beneficial) is the probability of all possible mutation that can occur at the particular site that it is the beneficial mutation,

𝜇 is the mutation rate

[Alan Kleinman MD PhD]

On Monday, October 9, 2017 at 12:00:02 PM UTC-7, Dennis Feenstra wrote:
> This is a rework of my post: noticed some errors and decided to streamline it. Apologies.
>
> > I've published two papers on rmns (random mutation and natural selection). The first paper gives the mathematics which governs rmns for a single selection pressure targeting a single genetic locus. It shows how a lineage accumulates the mutations which allow it to adapt to this single selection pressure. The second paper addresses how rmns operates when multiple simultaneous selection pressures targeting multiple genetic loci operates.
>
> I'll simply take your word for it (the two published papers), since I have no access to these papers themselves. Hopefully no hard feelings.

Not at all.

>
> > Fixation of a beneficial mutation is neither necessary nor sufficient for rmns to operate.
>
> That is true, but the point is the multiplication rule only counts for a single lineage, irregardless if others within a population has the same first beneficial mutation.

Every evolutionary step by rmns for any lineage on any evolutionary trajectory will be governed by the multiplication rule.

>
> In your layman's abstract you state, quote:
> "Since mutations are random events, the joint probability of multiple beneficial mutations occurring on a lineage in a population will be governed by the multiplication rule of probabilities."
>
> Then what about a number of lineages in a single population which acquired the first mutation by means of fixation (high fitness increasing the probability of survival for any organism with the first mutation)?

The progenitor of the lineage obtains the particular mutation as an error on replication. All the descendants from this original progenitor carry the mutation simply by replication without error. It is the next beneficial mutation which occurs on one of the descendants which is governed by the multiplication rule.

>
> Does your model account for a single beneficial mutation spreading through a population, where each independent lineage carrying the first mutation has an equal chance of gaining a secondary beneficial mutation?

The terminology "spreading through a population" is physically incorrect. If you want to understand rmns correctly, think of it as a clade working on a step by step genetic level. The ability to extend the clade is dependent on the absolute reproductive fitness of the terminal variant on the clade. If the variant does not have sufficient absolute reproductive fitness, the probability of another beneficial mutation occurring on one of its members remains low. A good demonstration of this can be seen at: https://www.youtube.com/watch?v=yybsSqcB7mE

[Sean Dillon]

On Monday, October 9, 2017 at 2:45:02 PM UTC-5, Alan Kleinman MD PhD wrote:
> On Monday, October 9, 2017 at 12:00:02 PM UTC-7, Dennis Feenstra wrote:
> > This is a rework of my post: noticed some errors and decided to streamline it. Apologies.
> >
> > > I've published two papers on rmns (random mutation and natural selection). The first paper gives the mathematics which governs rmns for a single selection pressure targeting a single genetic locus. It shows how a lineage accumulates the mutations which allow it to adapt to this single selection pressure. The second paper addresses how rmns operates when multiple simultaneous selection pressures targeting multiple genetic loci operates.
> >
> > I'll simply take your word for it (the two published papers), since I have no access to these papers themselves. Hopefully no hard feelings.
> Not at all.
> >
> > > Fixation of a beneficial mutation is neither necessary nor sufficient for rmns to operate.
> >
> > That is true, but the point is the multiplication rule only counts for a single lineage, irregardless if others within a population has the same first beneficial mutation.
> Every evolutionary step by rmns for any lineage on any evolutionary trajectory will be governed by the multiplication rule.

Except that evolution doesn't always happen along a single lineage. Multiple lineages within a population may all contribute toward the evolution of the entire population. The arising of a novel beneficial mutation within a lineage may contribute to a lineage's evolution, but so may the sharing of genetic material with other lineages.

> >
> > In your layman's abstract you state, quote:
> > "Since mutations are random events, the joint probability of multiple beneficial mutations occurring on a lineage in a population will be governed by the multiplication rule of probabilities."
> >
> > Then what about a number of lineages in a single population which acquired the first mutation by means of fixation (high fitness increasing the probability of survival for any organism with the first mutation)?
> The progenitor of the lineage obtains the particular mutation as an error on replication. All the descendants from this original progenitor carry the mutation simply by replication without error. It is the next beneficial mutation which occurs on one of the descendants which is governed by the multiplication rule.

Again: beneficial mutation #2 may not arise novelly within the same lineage, but may come from another lineage, in which it has already arisen. This is ESPECIALLY true in sexually reproducing species, in which every new generation is a mixing of previously divergent lineages.

So the question is NOT the odds of 2 beneficial mutations arising in the same lineage, but the odds of 2 beneficial mutations arising ANYwhere in the same population, and eventually being brought together.

> >
> > Does your model account for a single beneficial mutation spreading through a population, where each independent lineage carrying the first mutation has an equal chance of gaining a secondary beneficial mutation?
> The terminology "spreading through a population" is physically incorrect. If you want to understand rmns correctly, think of it as a clade working on a step by step genetic level. The ability to extend the clade is dependent on the absolute reproductive fitness of the terminal variant on the clade. If the variant does not have sufficient absolute reproductive fitness, the probability of another beneficial mutation occurring on one of its members remains low. A good demonstration of this can be seen at: https://www.youtube.com/watch?v=yybsSqcB7mE

In what way does this video demonstrate what you claim it demonstrates?

[John Harshman]

See, Dennis? Nothing whatsoever about selection, just mutation.

[Öö Tiib]

What rule? The school I was taught 2 addition rules of probability. For
mutually exclusive events A and B the probability is:
P(A or B) = P(A) + P(B)
For mutually nonexclusive events A and B it is:
P(A or B) = P(A) + P(B) - P(A and B)

Did you mean one of these or some third one? Where John "regularly"
applies either of those incorrectly? Can you cite?

[Dennis Feenstra]

Op maandag 9 oktober 2017 21:45:02 UTC+2 schreef Alan Kleinman MD PhD:

> > Does your model account for a single beneficial mutation spreading through a population, where each independent lineage carrying the first mutation has an equal chance of gaining a secondary beneficial mutation?
> The terminology "spreading through a population" is physically incorrect. If you want to understand rmns correctly, think of it as a clade working on a step by step genetic level. The ability to extend the clade is dependent on the absolute reproductive fitness of the terminal variant on the clade. If the variant does not have sufficient absolute reproductive fitness, the probability of another beneficial mutation occurring on one of its members remains low. A good demonstration of this can be seen at: https://www.youtube.com/watch?v=yybsSqcB7mE

I think this is the crucial point here:
["The ability to extend the clade is dependent on the absolute reproductive fitness of the terminal variant on the clade. If the variant does not have sufficient absolute reproductive fitness, the probability of another beneficial mutation occurring on one of its members remains low."]
That's the statement I was looking for.

So, correct me if I am wrong, but what you're ultimately saying is that when a population is exposed to 2 lethal selection pressures suddenly, the probability of a secondary beneficial mutation emerging remains low; because the first mutation has not reached absolute reproductive fitness.

However, the criticism on this board is that your example (paper) demonstrates a scenario which is
a) not the standard scenario which organisms are exposed to.
b) those populations are exposed suddenly to 2 selection pressures. That sounds to me like extraordinary conditions usually found during extinction events. Otherwise all species alive today would be long dead.

_______________________________________________________

Op woensdag 6 september 2017 23:00:05 UTC+2 schreef Alan Kleinman MD PhD:
> John, do you think that microevolutionary changes can add up to a macroevolutionary change?

And this is really the crux isn't it? You don't believe in macroevolutionary change because your paper demonstrates that it takes too long to accumilate beneficial mutations.

But does it really? To me it demonstrates extraordinary circumstances which does not reflect the numerous variables in nature. Your model doesn't seperate microorganisms from large multicellular organisms either.

What about areas of many square kilometers where organisms are subjected to everyday selection pressures? What about major extinction events leaving a low percentage of survivors to exploit all the new niches and resources available?

[Alan Kleinman MD PhD]

John, n*nG is the measure of absolute reproductive fitness. You might have a chance to understand this if you knew what a sample space is.

[Alan Kleinman MD PhD]

On Monday, October 9, 2017 at 1:10:02 PM UTC-7, Sean Dillon wrote:
> On Monday, October 9, 2017 at 2:45:02 PM UTC-5, Alan Kleinman MD PhD wrote:
> > On Monday, October 9, 2017 at 12:00:02 PM UTC-7, Dennis Feenstra wrote:
> > > This is a rework of my post: noticed some errors and decided to streamline it. Apologies.
> > >
> > > > I've published two papers on rmns (random mutation and natural selection). The first paper gives the mathematics which governs rmns for a single selection pressure targeting a single genetic locus. It shows how a lineage accumulates the mutations which allow it to adapt to this single selection pressure. The second paper addresses how rmns operates when multiple simultaneous selection pressures targeting multiple genetic loci operates.
> > >
> > > I'll simply take your word for it (the two published papers), since I have no access to these papers themselves. Hopefully no hard feelings.
> > Not at all.
> > >
> > > > Fixation of a beneficial mutation is neither necessary nor sufficient for rmns to operate.
> > >
> > > That is true, but the point is the multiplication rule only counts for a single lineage, irregardless if others within a population has the same first beneficial mutation.
> > Every evolutionary step by rmns for any lineage on any evolutionary trajectory will be governed by the multiplication rule.
>
> Except that evolution doesn't always happen along a single lineage. Multiple lineages within a population may all contribute toward the evolution of the entire population. The arising of a novel beneficial mutation within a lineage may contribute to a lineage's evolution, but so may the sharing of genetic material with other lineages.

Sure multiple lineages can take different evolutionary trajectories to adaptation to a given selection pressure by rmns. But how does sharing genetic material change this process? HIV does recombination (shares genetic material) but three drug therapy still works. Do you understand why the sharing of genetic material does not make a difference? If you don't understand why, read this paper: https://www.ncbi.nlm.nih.gov/pubmed/25645658

>
> > >
> > > In your layman's abstract you state, quote:
> > > "Since mutations are random events, the joint probability of multiple beneficial mutations occurring on a lineage in a population will be governed by the multiplication rule of probabilities."
> > >
> > > Then what about a number of lineages in a single population which acquired the first mutation by means of fixation (high fitness increasing the probability of survival for any organism with the first mutation)?
> > The progenitor of the lineage obtains the particular mutation as an error on replication. All the descendants from this original progenitor carry the mutation simply by replication without error. It is the next beneficial mutation which occurs on one of the descendants which is governed by the multiplication rule.
>
> Again: beneficial mutation #2 may not arise novelly within the same lineage, but may come from another lineage, in which it has already arisen. This is ESPECIALLY true in sexually reproducing species, in which every new generation is a mixing of previously divergent lineages.

What makes you think beneficial mutation #2 will be transferred laterally to a variant with beneficial mutation #1, why not detrimental mutation X or neutral mutation Y.

>
> So the question is NOT the odds of 2 beneficial mutations arising in the same lineage, but the odds of 2 beneficial mutations arising ANYwhere in the same population, and eventually being brought together.

So compute the probability of 2 beneficial mutations arising ANYwhere in the population and recombining in one descendant. If you have trouble doing that calculation, I can show you how to do it. You can read about it at https://www.ncbi.nlm.nih.gov/pubmed/25645658

> > >
> > > Does your model account for a single beneficial mutation spreading through a population, where each independent lineage carrying the first mutation has an equal chance of gaining a secondary beneficial mutation?
> > The terminology "spreading through a population" is physically incorrect. If you want to understand rmns correctly, think of it as a clade working on a step by step genetic level. The ability to extend the clade is dependent on the absolute reproductive fitness of the terminal variant on the clade. If the variant does not have sufficient absolute reproductive fitness, the probability of another beneficial mutation occurring on one of its members remains low. A good demonstration of this can be seen at: https://www.youtube.com/watch?v=yybsSqcB7mE
>
> In what way does this video demonstrate what you claim it demonstrates?

The video demonstrates the beneficial mutation followed by amplification of the beneficial mutation cycle of rmns.

[Alan Kleinman MD PhD]

John has made two mathematical blunders trying to apply the addition rule to circumstances which are not governed by either form of the addition rule. The first instance was when he thought that doubling population size doubles the probability of a beneficial mutation occurring. He is trying to apply the addition rule to complimentary events. The second instance occurred when he thought that a series of microevolutionary changes add up to a macroevolutionary change. Microevolutionary changes are linked by the multiplication rule for joint independent events, not the addition rule for mutually exclusive events or arbitrary events.

[John Harshman]

See, Dennis? He has absolutely no clue about this, and no amount of
explanation will budge him as much as a millimeter.

[Sean Dillon]

On Monday, October 9, 2017 at 3:55:02 PM UTC-5, Alan Kleinman MD PhD wrote:
> On Monday, October 9, 2017 at 1:10:02 PM UTC-7, Sean Dillon wrote:
> > On Monday, October 9, 2017 at 2:45:02 PM UTC-5, Alan Kleinman MD PhD wrote:
> > > On Monday, October 9, 2017 at 12:00:02 PM UTC-7, Dennis Feenstra wrote:
> > > > This is a rework of my post: noticed some errors and decided to streamline it. Apologies.
> > > >
> > > > > I've published two papers on rmns (random mutation and natural selection). The first paper gives the mathematics which governs rmns for a single selection pressure targeting a single genetic locus. It shows how a lineage accumulates the mutations which allow it to adapt to this single selection pressure. The second paper addresses how rmns operates when multiple simultaneous selection pressures targeting multiple genetic loci operates.
> > > >
> > > > I'll simply take your word for it (the two published papers), since I have no access to these papers themselves. Hopefully no hard feelings.
> > > Not at all.
> > > >
> > > > > Fixation of a beneficial mutation is neither necessary nor sufficient for rmns to operate.
> > > >
> > > > That is true, but the point is the multiplication rule only counts for a single lineage, irregardless if others within a population has the same first beneficial mutation.
> > > Every evolutionary step by rmns for any lineage on any evolutionary trajectory will be governed by the multiplication rule.
> >
> > Except that evolution doesn't always happen along a single lineage. Multiple lineages within a population may all contribute toward the evolution of the entire population. The arising of a novel beneficial mutation within a lineage may contribute to a lineage's evolution, but so may the sharing of genetic material with other lineages.
> Sure multiple lineages can take different evolutionary trajectories to adaptation to a given selection pressure by rmns. But how does sharing genetic material change this process? HIV does recombination (shares genetic material) but three drug therapy still works. Do you understand why the sharing of genetic material does not make a difference? If you don't understand why, read this paper: https://www.ncbi.nlm.nih.gov/pubmed/25645658

Maybe I've been unclear, Alan, but I'm not paying to read your paper. So if you want to make a claim, support it here, not there.

The sharing of genetic material means that a second beneficial mutation does not have to occur in the same lineage as a first beneficial mutation, in order for both mutations to benefit the population as a whole over time. Intra-population genetics isn't a cladistic tree, it is an intermingling... web? Not the perfect visual, but the point is, lineages cross and connect and share all the time.

> >
> > > >
> > > > In your layman's abstract you state, quote:
> > > > "Since mutations are random events, the joint probability of multiple beneficial mutations occurring on a lineage in a population will be governed by the multiplication rule of probabilities."
> > > >
> > > > Then what about a number of lineages in a single population which acquired the first mutation by means of fixation (high fitness increasing the probability of survival for any organism with the first mutation)?
> > > The progenitor of the lineage obtains the particular mutation as an error on replication. All the descendants from this original progenitor carry the mutation simply by replication without error. It is the next beneficial mutation which occurs on one of the descendants which is governed by the multiplication rule.
> >
> > Again: beneficial mutation #2 may not arise novelly within the same lineage, but may come from another lineage, in which it has already arisen. This is ESPECIALLY true in sexually reproducing species, in which every new generation is a mixing of previously divergent lineages.
> What makes you think beneficial mutation #2 will be transferred laterally to a variant with beneficial mutation #1, why not detrimental mutation X or neutral mutation Y.

Mutations #1 and #2, each being beneficial in their own right, will both trend toward comprising an every larger portion of the population. So pretty soon, there will be LOTS of carriers of each mutation. Detrimental mutations, by contrast, get selected out. Not instantly, but they trend in that direction. So each of the mutant strains will have a lot of "traders" sharing genes with other lineages. And many (probably most) of those exchanges WILL be for the "wrong" genetic material. But because it happens a lot, SOME of those shares will be the right ones.

It is easy to win the lottery if you buy enough tickets.

> > So the question is NOT the odds of 2 beneficial mutations arising in the same lineage, but the odds of 2 beneficial mutations arising ANYwhere in the same population, and eventually being brought together.
> So compute the probability of 2 beneficial mutations arising ANYwhere in the population and recombining in one descendant. If you have trouble doing that calculation, I can show you how to do it. You can read about it at https://www.ncbi.nlm.nih.gov/pubmed/25645658

How about you post that here?

I actually posted about this elsewhere on the board:

IOW... using very low numbers for ease of math:

Let's say we have a dynamically stable population of 10 asexually reproducing individuals. There exist potential beneficial mutations A and B, each of which has an independent 1/10 chance of occurring novelly in any given individual.

The odds of A and B arising in a single individual is 1% (.1^2), as we all understand... simple multiplicative probability.

What are the odds of A arising in some individual in a generation? By my calculations about 65% = (1-(1-.1)^10). B has the same odds. So - if I'm calculating correctly, the odds of A and/or B occurring in a given generation is about 87.75% = (1-(1-.65)^2).

So the odds of A or B occurring in a given generation, then the other mutation happening in a descendent of that mutant comes to 87.75% * (1-(1-.1)^X), where X is the total number of descendents of the original mutant. Of course, then we need to unpack X. Because how large X will be is a factor of the number of generations, and the relative selective advantage mutation A (or B) conveys to carriers, in light all selective pressures in the population's environment . We cannot calculate how many generations it will take to get an AB mutant by this method, without determining those variables. (Variables that, to the best of what you've shared with us, your model doesn't seem to include.) That said, we can safely say that the odds of AB through A-then-B are higher than the odds of a spontaneous AB mutant in virtually all cases, and that these aggregate odds go up with the number of generations.

However, neither of the above scenarios reflect the reality in a population with the ability to share mutations among lineages (which is most populations). In those cases, we are not looking at AB-spontaneously, or A-then-B, but rather A,B-then-AB. In other words, the two mutations just have to both arise independently SOMEWHERE in the population. And the odds of that are calcultated by (1-(1-.1)^Y), where Y is the total number of individuals that have been born in the population since the introduction of the selection pressure(s). Not in a particular lineage, but in ANYWHERE IN THE POPULATION. If the population is in dynamic equilibrium vis-a-vis size (which is typical of scenarios in which evolution can occur), this is essentially a question of the number of generations.

Once we HAVE at least one A and one B mutant, it is a matter of figuring how long it is likely to take for those mutations to be brought together by lateral sharing. Assuming that both A and B are in fact net-beneficial, in light of existing pressures in aggregate (and if they aren't, they aren't beneficial mutations), both mutant strains will trend toward an ever larger share of the overall population. The greater the share of the population that is constituted by either kind of mutant, the greater the odds that an A and a B mutant will exchange the genetic material necessary to bring about an AB hybrid.

What are the variables would have to be taken into account to determine the likely speed of this event? Well, you'd have to know the selective advantage of each mutation, in light of all selective pressure. You would have to know the rate of lateral transfer between individuals. You'd have to know the overall size of the genome. (For a more general, holistic model, you'd also have to include population size, mutation rate, generation time, etc... which we are taking as givens or ignoring for the purposes of example).

Of course, this is still a drastically simplified model. In reality, there are innumerable minor and major selection pressures on any given population at any given time, which is why most populations are not constantly growing. And there may be any number of mutations that are beneficial against any number of different pressures, all working toward fixation all the time, in a great and potentially constant cascade, while in constant dynamic interaction with the rest of the local and global ecosphere.

You'll notice how I stopped running the numbers in the last half of this post. Why? Because we don't HAVE a way (at this point) to mathematically ascertain the appropriate numbers to plug into those variables. And neither do you. But it can be empirically observed that lateral transfer HAS played a massive, ongoing role in the development of life (it is the entire reason sexual reproduction is a thing), so a model that excludes it does not represent a factually accurate general-case model of evolution. I don't have to point you to examples of quantitative studies to demonstrate that.

[Alan Kleinman MD PhD]

On Monday, October 9, 2017 at 1:35:02 PM UTC-7, Dennis Feenstra wrote:
> Op maandag 9 oktober 2017 21:45:02 UTC+2 schreef Alan Kleinman MD PhD:
> > > Does your model account for a single beneficial mutation spreading through a population, where each independent lineage carrying the first mutation has an equal chance of gaining a secondary beneficial mutation?
> > The terminology "spreading through a population" is physically incorrect. If you want to understand rmns correctly, think of it as a clade working on a step by step genetic level. The ability to extend the clade is dependent on the absolute reproductive fitness of the terminal variant on the clade. If the variant does not have sufficient absolute reproductive fitness, the probability of another beneficial mutation occurring on one of its members remains low. A good demonstration of this can be seen at: https://www.youtube.com/watch?v=yybsSqcB7mE
>
> I think this is the crucial point here:
> ["The ability to extend the clade is dependent on the absolute reproductive fitness of the terminal variant on the clade. If the variant does not have sufficient absolute reproductive fitness, the probability of another beneficial mutation occurring on one of its members remains low."]
> That's the statement I was looking for.
>
> So, correct me if I am wrong, but what you're ultimately saying is that when a population is exposed to 2 lethal selection pressures suddenly, the probability of a secondary beneficial mutation emerging remains low; because the first mutation has not reached absolute reproductive fitness.

When a population has to evolve to two selection pressures simultaneously, the two pressures interfere with the ability to amplify any beneficial mutation for one or the other selection pressure. In order to improve absolute reproductive fitness, a member of the population must get a double beneficial mutation. This can happen if you have extremely large populations.

>
> However, the criticism on this board is that your example (paper) demonstrates a scenario which is
> a) not the standard scenario which organisms are exposed to.

The mathematical model I had published is applicable to all example of rmns. Feel free to post a real, measurable and repeatable example that contradicts this mathematics.

> b) those populations are exposed suddenly to 2 selection pressures. That sounds to me like extraordinary conditions usually found during extinction events. Otherwise all species alive today would be long dead.

This mathematical model applies to the Lenski experiment as well as all other real, measurable and repeatable examples of rmns. rmns is the exceptional response to selection pressures, extinction is the usual response to selection pressures. Google this term; "how many species have gone extinct"

>
> _______________________________________________________
>
> Op woensdag 6 september 2017 23:00:05 UTC+2 schreef Alan Kleinman MD PhD:
> > John, do you think that microevolutionary changes can add up to a macroevolutionary change?
>
> And this is really the crux isn't it? You don't believe in macroevolutionary change because your paper demonstrates that it takes too long to accumilate beneficial mutations.

The complexity of the selection conditions determines the probability of the evolutionary process by rmns of occurring. rmns only works efficiently with a single selection pressure targeting a single gene.

>
> But does it really? To me it demonstrates extraordinary circumstances which does not reflect the numerous variables in nature. Your model doesn't seperate microorganisms from large multicellular organisms either.

rmns only works well in a low selection pressure environment with only a single directional selection pressure. Additional directional selection pressures confound the rmns process. This model applies to the evolution by rmns of weeds to herbicides, insects to herbicides, rodents to rodenticides. It works the same way in all replicators.

>
> What about areas of many square kilometers where organisms are subjected to everyday selection pressures? What about major extinction events leaving a low percentage of survivors to exploit all the new niches and resources available?

Populations survive and have the best absolute reproductive fitness in the lowest selection pressure environments. Populations can be subject to multiple simultaneous selection pressures and still survive and reproduce but their ability to evolve by rmns will be very limited, these populations drift. A good example of this is hiv subject to three selection pressures targeting just two genes. These pressures don't drive the population to extinction but they interfere with the amplification of any beneficial mutation for one drug or another thus giving effective treatment for the disease.

[Alan Kleinman MD PhD]

Why would I abandon the correct explanation for how rmns works?

[Dennis Feenstra]

Op maandag 9 oktober 2017 22:55:02 UTC+2 schreef Alan Kleinman MD PhD:

> What makes you think beneficial mutation #2 will be transferred laterally to a variant with beneficial mutation #1, why not detrimental mutation X or neutral mutation Y.

The point is, as I understand it Alan, that the appearance of beneficial mutation #2 will always be in an organism with beneficial mutation #1. Why?

Because after a member of this population gains beneficial mutation #1, this mutation has an advantage on becoming more common in a population. Reproductive success for any organism with this mutation increases.

What happens when beneficial mutation #1 has successfully fixated itself in the vast majority of the population?
We get to a similar point where the population had not yet acquired beneficial mutation #1.

Many members with beneficial mutation #1 will not be the first to acquire beneficial mutation #2. They will get detrimental mutation X or neutral mutation Y. However, within the same 'x' amount of generations one member of the population will get beneficial mutation #2.

Most members that didn't have beneficial mutation #1 will resemble the minority within a population after an x amount of generations. If they carry detrimental mutations, this will be even worse.

Sure, beneficial mutation #2 may appear in a member solely with neutral mutation Z. However, this member may reproduce with another that has beneficial mutation #1. Some of their offspring will have both beneficial mutations.

[Alan Kleinman MD PhD]

On Monday, October 9, 2017 at 2:25:02 PM UTC-7, Sean Dillon wrote:
> On Monday, October 9, 2017 at 3:55:02 PM UTC-5, Alan Kleinman MD PhD wrote:
> > On Monday, October 9, 2017 at 1:10:02 PM UTC-7, Sean Dillon wrote:
> > > On Monday, October 9, 2017 at 2:45:02 PM UTC-5, Alan Kleinman MD PhD wrote:
> > > > On Monday, October 9, 2017 at 12:00:02 PM UTC-7, Dennis Feenstra wrote:
> > > > > This is a rework of my post: noticed some errors and decided to streamline it. Apologies.
> > > > >
> > > > > > I've published two papers on rmns (random mutation and natural selection). The first paper gives the mathematics which governs rmns for a single selection pressure targeting a single genetic locus. It shows how a lineage accumulates the mutations which allow it to adapt to this single selection pressure. The second paper addresses how rmns operates when multiple simultaneous selection pressures targeting multiple genetic loci operates.
> > > > >
> > > > > I'll simply take your word for it (the two published papers), since I have no access to these papers themselves. Hopefully no hard feelings.
> > > > Not at all.
> > > > >
> > > > > > Fixation of a beneficial mutation is neither necessary nor sufficient for rmns to operate.
> > > > >
> > > > > That is true, but the point is the multiplication rule only counts for a single lineage, irregardless if others within a population has the same first beneficial mutation.
> > > > Every evolutionary step by rmns for any lineage on any evolutionary trajectory will be governed by the multiplication rule.
> > >
> > > Except that evolution doesn't always happen along a single lineage. Multiple lineages within a population may all contribute toward the evolution of the entire population. The arising of a novel beneficial mutation within a lineage may contribute to a lineage's evolution, but so may the sharing of genetic material with other lineages.
> > Sure multiple lineages can take different evolutionary trajectories to adaptation to a given selection pressure by rmns. But how does sharing genetic material change this process? HIV does recombination (shares genetic material) but three drug therapy still works. Do you understand why the sharing of genetic material does not make a difference? If you don't understand why, read this paper: https://www.ncbi.nlm.nih.gov/pubmed/25645658
>
> Maybe I've been unclear, Alan, but I'm not paying to read your paper. So if you want to make a claim, support it here, not there.
>
> The sharing of genetic material means that a second beneficial mutation does not have to occur in the same lineage as a first beneficial mutation, in order for both mutations to benefit the population as a whole over time. Intra-population genetics isn't a cladistic tree, it is an intermingling... web? Not the perfect visual, but the point is, lineages cross and connect and share all the time.

Here's the distribution function which governs random recombination for example with HIV:
f (x, y) = 2!/(x!y!(2 − x − y)!)*(nA/n)^x *(nB/n)^y *(nC/n)^(2−x−y)
where (x + y ⩽ 2) and
n – is the total population size.
nA – is the number of members in the population with beneficial allele A.
nB – is the number of members in the population with beneficial allele B.
nC – is the number of members in the population that have neither beneficial allele A nor beneficial allele B.
To get the probability of an nA member recombining with an nB member, set x=y=1. You had better have lots of A's and B's in the population to have a reasonable probability for this to occur and very few C's. The problem for HIV is that it has lots of C's and few A's and B's.
<snip>

[Sean Dillon]

On Monday, October 9, 2017 at 4:30:02 PM UTC-5, Alan Kleinman MD PhD wrote:
> On Monday, October 9, 2017 at 1:35:02 PM UTC-7, Dennis Feenstra wrote:
> > Op maandag 9 oktober 2017 21:45:02 UTC+2 schreef Alan Kleinman MD PhD:
> > > > Does your model account for a single beneficial mutation spreading through a population, where each independent lineage carrying the first mutation has an equal chance of gaining a secondary beneficial mutation?
> > > The terminology "spreading through a population" is physically incorrect. If you want to understand rmns correctly, think of it as a clade working on a step by step genetic level. The ability to extend the clade is dependent on the absolute reproductive fitness of the terminal variant on the clade. If the variant does not have sufficient absolute reproductive fitness, the probability of another beneficial mutation occurring on one of its members remains low. A good demonstration of this can be seen at: https://www.youtube.com/watch?v=yybsSqcB7mE
> >
> > I think this is the crucial point here:
> > ["The ability to extend the clade is dependent on the absolute reproductive fitness of the terminal variant on the clade. If the variant does not have sufficient absolute reproductive fitness, the probability of another beneficial mutation occurring on one of its members remains low."]
> > That's the statement I was looking for.
> >
> > So, correct me if I am wrong, but what you're ultimately saying is that when a population is exposed to 2 lethal selection pressures suddenly, the probability of a secondary beneficial mutation emerging remains low; because the first mutation has not reached absolute reproductive fitness.
> When a population has to evolve to two selection pressures simultaneously, the two pressures interfere with the ability to amplify any beneficial mutation for one or the other selection pressure. In order to improve absolute reproductive fitness, a member of the population must get a double beneficial mutation. This can happen if you have extremely large populations.

Your statement above is only meaningfully true if either of those pressures is the primary delimiter of the population. Otherwise, higher fitness relative to the rest of the population will allow a beneficially mutant population to increase both in relative frequency and absolute number.

For example, let us imagine a species of deer, for which the primary population delimiter is the amount of available food. There are other selection pressures, but that's the one that is actually holding the population back from getting larger.

Now let's say we introduce a couple of new selection pressures to the mix... say, a new, moderately effective predator, and an unusual heat wave. BOTH of those things will kill off some of the deer... those that are least well-suited to the new environmental conditions. However, because the amount of available food has not changed, the remaining deer will simply get more food and be able to have more babies. In this way, despite the new pressures, the population remains in dynamic equilibrium.

Now say a mutant arises that is faster, and thus better able to escape the predators. Despite the fact that this mutation does nothing to counteract the heat, this mutation will allow that individual and its descendents to outsurvive non-mutants. As such, the mutants will become a larger portion of the population with each passing generation. And given that the population is in dynamic equilibrium, that also means that the mutants will be increasing in absolute number.

Now, within a few generations, in a different lineage altogether, there is born a foal with a mutation for better heat regulation. The descendents of this deer will ALSO have a selective advantage, relative to deer without. And as such, with each passing generation, this mutant population will ALSO tend to comprise an ever larger share of the population. There will come a time when both the fast-mutants and the cool-mutants are of sufficient number that they cannot HELP but interbreed. And when that happens, at least some of the offspring will be fast-cool-mutants, who will tend to outcompete either ancestor population, and will trend toward fixation in the population.

THAT is how evolution happens in nature.

Because neither of the selection pressures are the big thing that is putting an absolute cap on the population, it is the RELATIVE rather than ABSOLUTE advantage of beneficial mutations that allows them to thrive within the population.

Your model doesn't model that. It doesn't HAVE to, because the scenarios you are holding your model up against do not resemble the above.

> >
> > However, the criticism on this board is that your example (paper) demonstrates a scenario which is
> > a) not the standard scenario which organisms are exposed to.
> The mathematical model I had published is applicable to all example of rmns. Feel free to post a real, measurable and repeatable example that contradicts this mathematics.
> > b) those populations are exposed suddenly to 2 selection pressures. That sounds to me like extraordinary conditions usually found during extinction events. Otherwise all species alive today would be long dead.
> This mathematical model applies to the Lenski experiment as well as all other real, measurable and repeatable examples of rmns. rmns is the exceptional response to selection pressures, extinction is the usual response to selection pressures. Google this term; "how many species have gone extinct"
> >
> > _______________________________________________________
> >
> > Op woensdag 6 september 2017 23:00:05 UTC+2 schreef Alan Kleinman MD PhD:
> > > John, do you think that microevolutionary changes can add up to a macroevolutionary change?
> >
> > And this is really the crux isn't it? You don't believe in macroevolutionary change because your paper demonstrates that it takes too long to accumilate beneficial mutations.
> The complexity of the selection conditions determines the probability of the evolutionary process by rmns of occurring. rmns only works efficiently with a single selection pressure targeting a single gene.
> >
> > But does it really? To me it demonstrates extraordinary circumstances which does not reflect the numerous variables in nature. Your model doesn't seperate microorganisms from large multicellular organisms either.
> rmns only works well in a low selection pressure environment with only a single directional selection pressure. Additional directional selection pressures confound the rmns process. This model applies to the evolution by rmns of weeds to herbicides, insects to herbicides, rodents to rodenticides. It works the same way in all replicators.

CIDE CIDE CIDE CIDE. I'm sensing a pattern: artificially deadly selection pressures with very limited possible responses, applied multiply and simultaneously with the express intent of wiping out a population. Those are not the sorts of circumstances in which evolution can occur, you're right about that much. But the "confounding" effect of the multiple selection pressures has everything to do with the other factors involved... that the pressures are highly deadly, simultaneously applied, and extremely targeted.

> >
> > What about areas of many square kilometers where organisms are subjected to everyday selection pressures? What about major extinction events leaving a low percentage of survivors to exploit all the new niches and resources available?
> Populations survive and have the best absolute reproductive fitness in the lowest selection pressure environments. Populations can be subject to multiple simultaneous selection pressures and still survive and reproduce but their ability to evolve by rmns will be very limited, these populations drift.

That depends entirely on the intensity of the pressures, and whether any of them in fact represent an absolute delimiting factor for the population as a whole.

> A good example of this is hiv subject to three selection pressures targeting just two genes. These pressures don't drive the population to extinction but they interfere with the amplification of any beneficial mutation for one drug or another thus giving effective treatment for the disease.

What makes the cocktail so effective is that it first kills off a majority of the population, then interferes with the virus's very ability to reproduce, deeply slowing down (but not entirely stopping) the virus' ability to adapt evolutionarily. Given long enough, the virus can still outfox the treatment (and has done in some cases).

[Dennis Feenstra]

I'll use a different format for responding. The basic one is a bit annoying.

Alan states: "When a population has to evolve to two selection pressures simultaneously, the two pressures interfere with the ability to amplify any beneficial mutation for one or the other selection pressure. In order to improve absolute reproductive fitness, a member of the population must get a double beneficial mutation. This can happen if you have extremely large populations."

I'll sort of agree with this statement. However,
a) many species have many populations over multiple continents.
b) Two lethal selection pressures acting upon an entire population isn't really common.
c) Selection pressures force populations of organisms to move across vast distances.
d) As long as the first beneficial mutation can become fixed in the population, and the population size either remains the same or grows, the second beneficial mutation will appear in the population with roughly the same probability as the first beneficial mutation did.



Alan states: "The mathematical model I had published is applicable to all example of rmns. Feel free to post a real, measurable and repeatable example that contradicts this mathematics."

Your model seems to apply to a single lineage only, rather than all the lineages within a population, after the first beneficial mutation became fixed.



Alan states: "This mathematical model applies to the Lenski experiment as well as all other real, measurable and repeatable examples of rmns. rmns is the exceptional response to selection pressures, extinction is the usual response to selection pressures. Google this term; "how many species have gone extinct"

Oh I know. The vast, vast, vast majority of organisms have gone extinct. Of course it has also been calculated that around 8.7 million species are alive today. On top of that the fossil record shows significant diversification after an extinction event; invading the empty niches left behind by those extinct.



Alan states: "The complexity of the selection conditions determines the probability of the evolutionary process by rmns of occurring. rmns only works efficiently with a single selection pressure targeting a single gene."

That depends entirely on how lethal those selection pressures are and how it affects the overall fitness of a population. Yes, the second selection pressure may simply be too much and drive the population to extinction.

Or it may not be much of an issue after a certain point, or simply forces a population to migrate.

[Alan Kleinman MD PhD]

On Monday, October 9, 2017 at 2:45:02 PM UTC-7, Dennis Feenstra wrote:
> Op maandag 9 oktober 2017 22:55:02 UTC+2 schreef Alan Kleinman MD PhD:
> > What makes you think beneficial mutation #2 will be transferred laterally to a variant with beneficial mutation #1, why not detrimental mutation X or neutral mutation Y.
>
> The point is, as I understand it Alan, that the appearance of beneficial mutation #2 will always be in an organism with beneficial mutation #1. Why?

The evolutionary trajectory for rmns must take a path of ever-increasing fitness in order for it to work (ever improving absolute reproductive fitness). A good empirical example of this can be found at: https://classes.soe.ucsc.edu/bme207/Fall09/Lecture%2013/Science%202006%20Weinreich.pdf "Darwinian Evolution Can Follow Only Very Few Mutational Paths
to Fitter Proteins"

>
> Because after a member of this population gains beneficial mutation #1, this mutation has an advantage on becoming more common in a population. Reproductive success for any organism with this mutation increases.

Certainly, as long as no other selection pressures interfere with this amplification.

>
> What happens when beneficial mutation #1 has successfully fixated itself in the vast majority of the population?

If the variant with beneficial mutation #1 has amplified sufficiently, you have a reasonable probability of beneficial mutation #2 occurring on some member with beneficial mutation #1 improving the fitness of this new variant compared to the variant with mutation #1 alone.

> We get to a similar point where the population had not yet acquired beneficial mutation #1.
>
> Many members with beneficial mutation #1 will not be the first to acquire beneficial mutation #2. They will get detrimental mutation X or neutral mutation Y. However, within the same 'x' amount of generations one member of the population will get beneficial mutation #2.

Detrimental mutations to variants with mutation #1 simply reduces the population size for the next beneficial mutation.

>
> Most members that didn't have beneficial mutation #1 will resemble the minority within a population after an x amount of generations. If they carry detrimental mutations, this will be even worse.

My computations bracket the upper limits of the probabilities which govern this process. Detrimental mutations only lower the probabilities.

>
> Sure, beneficial mutation #2 may appear in a member solely with neutral mutation Z. However, this member may reproduce with another that has beneficial mutation #1. Some of their offspring will have both beneficial mutations.

See the post I made to Sean to see how to do this computation.

[John Harshman]

And, as you can see, that's all he has.

[Dennis Feenstra]

Alan states: "Detrimental mutations to variants with mutation #1 simply reduces the population size for the next beneficial mutation."

Yes, except that those individuals with detrimental mutations do not contribute significantly to the gene pool, hence the size of a population doesn't really have to change all that much. Which means that the same probability for beneficial mutation #2 (mutation occurs after the same x amount of generations).

John states: "And, as you can see, that's all he has. "
While I am inclined to agree that his arguments remain the same despite the criticism, I am willing to see where this discussion goes.

[jillery]

On Mon, 9 Oct 2017 12:06:31 -0700 (PDT), Dennis Feenstra
<dennisf...@gmail.com> wrote:

>Sigh, I have to get used to this system of discussion. This is a rework of my post: noticed some errors and decided to streamline it. Apologies.


It takes time to get used to any new system.

What might help is to separate in your mind necessary parts of Usenet
from contingent parts of the specific application you use, ie Google
Groups.

For instance, I found GG's text editing causes more problems than it
solves. Other GG users have said they use a separate text editor, and
use GG only to cut-and-paste, and send and receive posts.


>Op maandag 9 oktober 2017 19:30:02 UTC+2 schreef Alan Kleinman MD PhD:
>> I've published two papers on rmns (random mutation and natural selection). The first paper gives the mathematics which governs rmns for a single selection pressure targeting a single genetic locus. It shows how a lineage accumulates the mutations which allow it to adapt to this single selection pressure. The second paper addresses how rmns operates when multiple simultaneous selection pressures targeting multiple genetic loci operates. The editor of the journal which published these papers asked me to write a layman's abstract to explain how this mathematics works for those not well versed in probability theory. This abstract is not behind a paywall and can be found at: http://www.statisticsviews.com/details/news/10604248/Laymans-abstract-Random-mutation-and-natural-selection-a-predictable-phenomenon.html

>
>I'll simply take your word for it (the two published papers), since I have no access to these papers themselves. Hopefully no hard feelings.
>

>> Fixation of a beneficial mutation is neither necessary nor sufficient for rmns to operate.
>
>That is true, but the point is the multiplication rule only counts for a single lineage, irregardless if others within a population has the same first beneficial mutation.
>

>In your layman's abstract you state, quote:
>"Since mutations are random events, the joint probability of multiple beneficial mutations occurring on a lineage in a population will be governed by the multiplication rule of probabilities."
>
>Then what about a number of lineages in a single population which acquired the first mutation by means of fixation (high fitness increasing the probability of survival for any organism with the first mutation)?
>

>Does your model account for a single beneficial mutation spreading through a population, where each independent lineage carrying the first mutation has an equal chance of gaining a secondary beneficial mutation?

Good luck getting a coherent answer.

--
I disapprove of what you say, but I will defend to the death your right to say it.

Evelyn Beatrice Hall
Attributed to Voltaire

[Dennis Feenstra]

Op dinsdag 10 oktober 2017 00:40:02 UTC+2 schreef Dennis Feenstra:

> Alan states: "Detrimental mutations to variants with mutation #1 simply reduces the population size for the next beneficial mutation."
>
> Yes, except that those individuals with detrimental mutations do not contribute significantly to the gene pool, hence the size of a population doesn't really have to change all that much. Which means that the same probability for beneficial mutation #2 (mutation occurs after the same x amount of generations).

Let me add an example for this comment of mine:

Suppose we have a population of X, with a mutation rate of Y.
Beneficial mutations are rare and will occur at rate Z^-#.

The population is exposed to an external selection pressure.
Whatever the numbers are, we can establish that within 100-200 generations one individual has a beneficial mutation [1].

The population becomes smaller of course due to the selection pressure, making it easier for our beneficial mutation [1] to become fixed in our population. The selection pressure dissapears and our population grows again, possibly even exceeding their initial population size.

Climate change happens. A new selection pressure occurs. Population size slowly diminishes. After roughly the same amount of generations, a new beneficial mutation [2] emerges in one individual. And the cycle repeats.

As long as we know the population size and use the same mutation rate, and we can be assured beneficial mutation #1 is fixed, beneficial mutation #2 will occur within 100 generations. If the population is smaller, it'll occur within a larger amount of generations.

Sounds like Bill's argument, doesn't it? For a good reason.

[Alan Kleinman MD PhD]

On Monday, October 9, 2017 at 3:10:02 PM UTC-7, Dennis Feenstra wrote:
> I'll use a different format for responding. The basic one is a bit annoying.
>
> Alan states: "When a population has to evolve to two selection pressures simultaneously, the two pressures interfere with the ability to amplify any beneficial mutation for one or the other selection pressure. In order to improve absolute reproductive fitness, a member of the population must get a double beneficial mutation. This can happen if you have extremely large populations."
>
> I'll sort of agree with this statement. However,
> a) many species have many populations over multiple continents.

Each on their own particular evolutionary trajectories

> b) Two lethal selection pressures acting upon an entire population isn't really common.

Are you saying that drought, floods, disease, starvation, thermal stress, disease, predation, toxins, accidents, ... can't and don't occur simultaneously? What do you think happens to herd animals during the winter when they lack food? Or when a population is subject to both drought and predation? Multiple simultaneous selection pressures are the rule, not the exception in the real world.

> c) Selection pressures force populations of organisms to move across vast distances.

Of course, that's the common way populations adapt to selection pressures. Adapting by rmns is far too slow a process to adapt to most selection pressures.

> d) As long as the first beneficial mutation can become fixed in the population, and the population size either remains the same or grows, the second beneficial mutation will appear in the population with roughly the same probability as the first beneficial mutation did.

As long as no other selection pressures interfere with the amplification process.

>
>
>
> Alan states: "The mathematical model I had published is applicable to all example of rmns. Feel free to post a real, measurable and repeatable example that contradicts this mathematics."
>
> Your model seems to apply to a single lineage only, rather than all the lineages within a population, after the first beneficial mutation became fixed.

Not so. I based the derivation on an example of rmns where there were multiple different variants evolving to a single targeted selection pressure.
https://classes.soe.ucsc.edu/bme207/Fall09/Lecture%2013/Science%202006%20Weinreich.pdf
Each evolutionary trajectory has its own particular set of nested binomial probability equations.

>
>
>
> Alan states: "This mathematical model applies to the Lenski experiment as well as all other real, measurable and repeatable examples of rmns. rmns is the exceptional response to selection pressures, extinction is the usual response to selection pressures. Google this term; "how many species have gone extinct"
>
> Oh I know. The vast, vast, vast majority of organisms have gone extinct. Of course it has also been calculated that around 8.7 million species are alive today. On top of that the fossil record shows significant diversification after an extinction event; invading the empty niches left behind by those extinct.

The point is that selection pressures are much more likely to cause extinction, not to lead to successful adaptation by rmns. rmns only works efficiently under very specific circumstances.
Selection reduces the diversity of populations, mutations increase the diversity of populations.

>
>
>
> Alan states: "The complexity of the selection conditions determines the probability of the evolutionary process by rmns of occurring. rmns only works efficiently with a single selection pressure targeting a single gene."
>
> That depends entirely on how lethal those selection pressures are and how it affects the overall fitness of a population. Yes, the second selection pressure may simply be too much and drive the population to extinction.

Each additional selection pressure introduces its own set of binomial probability equations into the evolutionary trajectory where each of these binomial probability equations is linked to the others by the multiplication rule. This is why a population adapting to multiple simultaneous selection pressures has a very low probability of accomplishing this evolutionary process.

>
> Or it may not be much of an issue after a certain point, or simply forces a population to migrate.

This is a much more rational explanation of how a population would respond to cold stress.

[Sean Dillon]

Here is the problem with what you're expressing here:

If alleles A and B are in fact individually beneficial, the balance of the population WILL change over time in favor of As and Bs over Cs, even if Cs start dominant. In the competition for resources, A and B may not have advantage over each other, they BOTH have advantage over C. Even if allele-A suffers in the face of pressure-B, and vice versa, C suffers in the face of both pressures. So the dominance of C itself does not provide a compelling explanation for why the HIV population struggles to evolve.

So if that alone isn't the reason the virus is evolving so slowly, what IS? Well...

1. The population has been drastically reduced, to below a threshold where evolution can be expected to happen.
2. The anti-virals in use are highly genetically targetted, admitting very few possible mutational solutions.
3. The supply of a delimiting resource (in this case, cells) has been drastically reduced by drugs that interfere with viral cell receptors. This limits reproduction and therefore population growth.

Honestly, it is an ingeneous piece of medicine. And that's actually why it (and other human-invented combination "cides") make such a poor example for studying how evolution happens. Because -- while nature has killed off many, many species -- it has never come up with such intelligently deadly combinations of selection pressures.

[Alan Kleinman MD PhD]

It's more than enough.

[Alan Kleinman MD PhD]

On Monday, October 9, 2017 at 3:40:02 PM UTC-7, Dennis Feenstra wrote:
> Alan states: "Detrimental mutations to variants with mutation #1 simply reduces the population size for the next beneficial mutation."
>
> Yes, except that those individuals with detrimental mutations do not contribute significantly to the gene pool, hence the size of a population doesn't really have to change all that much. Which means that the same probability for beneficial mutation #2 (mutation occurs after the same x amount of generations).

The probability of a beneficial mutation occurring is dependent on the number of replications, not the number of generations.

>
> John states: "And, as you can see, that's all he has. "
> While I am inclined to agree that his arguments remain the same despite the criticism, I am willing to see where this discussion goes.

I think all the empirical evidence which substantiates the mathematical model is more than enough to justify the model. And I do mean "all", there are no real, measurable and repeatable examples of rmns that don't obey the mathematics of this model.

[Alan Kleinman MD PhD]

On Monday, October 9, 2017 at 4:10:02 PM UTC-7, Dennis Feenstra wrote:
> Op dinsdag 10 oktober 2017 00:40:02 UTC+2 schreef Dennis Feenstra:
> > Alan states: "Detrimental mutations to variants with mutation #1 simply reduces the population size for the next beneficial mutation."
> >
> > Yes, except that those individuals with detrimental mutations do not contribute significantly to the gene pool, hence the size of a population doesn't really have to change all that much. Which means that the same probability for beneficial mutation #2 (mutation occurs after the same x amount of generations).
>
> Let me add an example for this comment of mine:
>
> Suppose we have a population of X, with a mutation rate of Y.
> Beneficial mutations are rare and will occur at rate Z^-#.
>
> The population is exposed to an external selection pressure.
> Whatever the numbers are, we can establish that within 100-200 generations one individual has a beneficial mutation [1].

The principle random trial for rmns is the replication. If X is large enough, it may take far fewer generations than 100-200. In fact, for a bacteria doubling every generation, it only takes 30 generations to get e9 members under ideal circumstances.

>
> The population becomes smaller of course due to the selection pressure, making it easier for our beneficial mutation [1] to become fixed in our population. The selection pressure dissapears and our population grows again, possibly even exceeding their initial population size.
>
> Climate change happens. A new selection pressure occurs. Population size slowly diminishes. After roughly the same amount of generations, a new beneficial mutation [2] emerges in one individual. And the cycle repeats.
>
> As long as we know the population size and use the same mutation rate, and we can be assured beneficial mutation #1 is fixed, beneficial mutation #2 will occur within 100 generations. If the population is smaller, it'll occur within a larger amount of generations.
>
> Sounds like Bill's argument, doesn't it? For a good reason.

It's kinda a rough approximation of a single selection pressure targeting a single gene but what makes you think a climate change only targets a single gene. How many biological enzymes have functional behavior dependent on temperature?

[Dennis Feenstra]

Alan states: "Are you saying that drought, floods, disease, starvation, thermal stress, disease, predation, toxins, accidents, ... can't and don't occur simultaneously? What do you think happens to herd animals during the winter when they lack food? Or when a population is subject to both drought and predation? Multiple simultaneous selection pressures are the rule, not the exception in the real world."

Except that predation is not a constant lethal pressure forced upon a population. In fact, animals reduce their casualities to predation in a variety of ways: they act like herds or hide underground.

When there's a drought animals move to find new sources of water or are already adapted to low levels of water. Populations don't always instantly die or become instantly very small.

The bottom line is, I simply do not agree with your model nor with your use of those selection pressures. Populations gain beneficial mutations, which will become fixed in populations, after which the population can recover from the dentrimental effects of a selection pressure and grow in size again.

Famines, floods, earthquakes; they might all occur at the same time. Or they might not. Plenty of time to amplify a beneficial mutation, plenty of time to grow a population and plenty of time to accumilate a new beneficial mutation.

[Dennis Feenstra]

Op dinsdag 10 oktober 2017 01:25:02 UTC+2 schreef Alan Kleinman MD PhD:

> The probability of a beneficial mutation occurring is dependent on the number of replications, not the number of generations.

Is there an avarage of replications for an individual organism's lifetime? Yes? Then it can be calculated per generation. No? Then your model is just as useless.

[Alan Kleinman MD PhD]

The empirical evidence shows that recombination has no significant effect on the evolution of drug resistance with HIV (the fastest evolving replicator known). Lateral transfer of genetic material has no significant impact on the rmns phenomenon. Of course if you have any empirical evidence which shows otherwise, post it.

[Dennis Feenstra]

Op dinsdag 10 oktober 2017 01:35:03 UTC+2 schreef Alan Kleinman MD PhD:

> It's kinda a rough approximation of a single selection pressure targeting a single gene but what makes you think a climate change only targets a single gene. How many biological enzymes have functional behavior dependent on temperature?

And what do we and other animals do as a reaction to extreme temperature differences? Again, you're asserting a very lethal scenario.

[Alan Kleinman MD PhD]

On Monday, October 9, 2017 at 4:35:03 PM UTC-7, Dennis Feenstra wrote:
> Alan states: "Are you saying that drought, floods, disease, starvation, thermal stress, disease, predation, toxins, accidents, ... can't and don't occur simultaneously? What do you think happens to herd animals during the winter when they lack food? Or when a population is subject to both drought and predation? Multiple simultaneous selection pressures are the rule, not the exception in the real world."
>
> Except that predation is not a constant lethal pressure forced upon a population. In fact, animals reduce their casualities to predation in a variety of ways: they act like herds or hide underground.

So predators don't select out the weaker and slower variants?

>
> When there's a drought animals move to find new sources of water or are already adapted to low levels of water. Populations don't always instantly die or become instantly very small.

That's right, they don't evolve by rmns.

>
> The bottom line is, I simply do not agree with your model nor with your use of those selection pressures. Populations gain beneficial mutations, which will become fixed in populations, after which the population can recover from the dentrimental effects of a selection pressure and grow in size again.

So post your empirical evidence which contradicts my model. Do you think the Lenski experiment would work better if he not only used starvation but also used thermal stress on his bacteria? Or are you going to claim that starvation and thermal stress are lethal?

>
> Famines, floods, earthquakes; they might all occur at the same time. Or they might not. Plenty of time to amplify a beneficial mutation, plenty of time to grow a population and plenty of time to accumilate a new beneficial mutation.

Sure that can happen but it is a slow arduous process for a population to evolve by rmns made worse when multiple selection pressures are acting simultaneously. Migration is a much more sensible form of adaptation.

[Alan Kleinman MD PhD]

It is only useless for those who don't understand how rmns works.

[Alan Kleinman MD PhD]

You don't get it. Even if the temperature change is small, it will still select out the weaker variants. Consider the Lenski experiment where instead of starvation alone, he runs the experiment at a non-optimal temperature. Do you think that rmns will work more quickly under this circumstance with two weak selection pressures than with a single weak selection pressure? It will not because the amplification of a beneficial mutation for the starvation pressure will be impaired by the thermal stress and the amplification of a beneficial mutation for thermal stress will be impaired by the starvation pressure. What you don't seem to understand is that selection pressures are stressors that kill or impair the replication of some or all members of a population.

[Dennis Feenstra]

"So predators don't select out the weaker and slower variants?"

The weakest and slowest, sure. That doesn't mean that a weaker and slower individual will always fall prey. They might be saved because of the herd behavior, and become just as good at defending the herd.

"That's right, they don't evolve by rmns."

I never said they did. You brought up droughts as a selection pressure. And I gave examples as to how many populations reduce the effect of such a pressure.

"Do you think the Lenski experiment would work better if he not only used starvation but also used thermal stress on his bacteria?"

If thermal stress doesn't vaporize an entire population within a few generations and if there is room within the container where the thermal stress is reduced, sure.

[Alan Kleinman MD PhD]

On Monday, October 9, 2017 at 5:25:02 PM UTC-7, Dennis Feenstra wrote:
> "So predators don't select out the weaker and slower variants?"
>
> The weakest and slowest, sure. That doesn't mean that a weaker and slower individual will always fall prey. They might be saved because of the herd behavior, and become just as good at defending the herd.
>
> "That's right, they don't evolve by rmns."
>
> I never said they did. You brought up droughts as a selection pressure. And I gave examples as to how many populations reduce the effect of such a pressure.

The point you are missing is that rmns is a very slow and arduous process when more than a single targeted selection pressure is acting on the population at a time. It takes huge numbers of replications for each beneficial mutation and that's when only one selection pressure is acting at a time.

>
>
> "Do you think the Lenski experiment would work better if he not only used starvation but also used thermal stress on his bacteria?"
>
> If thermal stress doesn't vaporize an entire population within a few generations and if there is room within the container where the thermal stress is reduced, sure.

But the adaptation process will be slower than the thousand generations per beneficial mutation that the experiment takes with only the starvation selection pressure acting alone if the experiment works at all with the two selection pressures. And that's with a population size of e8. Additional selection pressures do not speed up rmns, it slows the process.

[jillery]

You have used the above example several times before. As a refresher
of Lenski's LTEE:

<https://en.wikipedia.org/wiki/E._coli_long-term_evolution_experiment>

Part of the methodology of LTEE is that once a day, every day, 1% of
the population in 12 flasks is transferred to 12 new flasks. All
populations are equally nutrient limited, meaning the amount is
specifically designed so that every population uses up all the
nutrients before the next day's transfer. So there's lots of natural
selection going on to both duplicate and survive.

IIUC your prediction is, given a case where one of Lenski's E.coli
populations faces both starvation stress and thermal stress, two
things will happen:

1) the total number of random mutations (RM) in that population will
*decrease* (how to measure?).

2) the fitness (NS) of that population will *decrease*, as measured by
a reduced number of individuals at the end of the day.

My challenge to you, Alan Kleinman MD PhD, is to model the above
scenario with your mathematical formula for multiplication rule of
probability, and show how it calculates those results. If you are
successful, that should give pause to those who claim your formula
doesn't model natural selection; a significant victory, yes?

[Sean Dillon]

Listen, Alan: let's set aside recombination for a second. According to you, your model doesn't event account for relative selection. You seem to think that beneficial mutants A and B will remain low in quantity relative to base genome C over time. That's nonsensical.

But now let's pick recombination back up. In every sexually reproducing species in the world, recombination happens in literally EVERY generation. And you think that isn't a factor in evolution? If so, WHY isn't that a factor? The burden here is on you.

Then let me step back and ask this... at what level of detail do your conclusions match the evidence? Are you actually matching numbers to numbers? Or is it just "my model says evolution won't happen, and evolution hasn't happened in this scenario"?

If the prior, I'd like to see the actual data for all your examples please. Here. Not through a link I'd have to pay for. HIV drugs, herbicide, rodenticide, etc. Show me the actual numerical expectations of your model, and show me the actual numerical empirical results. I'll believe them when I can see them and evaluate them. And I'm not saying I'll accept your model of evolution if you can supply this... that's just the precondition for even considering it.

If the latter, then your model isn't worth the electronic paper it is printed on, because there are plenty of other explanations that account for that result, that don't require rewriting all of modern biology.

[Peter Nyikos]

On Monday, October 9, 2017 at 5:05:02 PM UTC-4, Alan Kleinman MD PhD wrote:
> On Monday, October 9, 2017 at 1:30:02 PM UTC-7, Öö Tiib wrote:
> > On Monday, 9 October 2017 22:45:02 UTC+3, Alan Kleinman MD PhD wrote:

> > > On Monday, October 9, 2017 at 12:05:02 PM UTC-7, John Harshman wrote:
> > > > On 10/9/17 11:36 AM, Dennis Feenstra wrote:

> > > > >> I've published two papers on rmns (random mutation and natural
> > > > >> selection). The first paper gives the mathematics which governs
> > > > >> rmns for a single selection pressure targeting a single genetic
> > > > >> locus. It shows how a lineage accumulates the mutations which allow
> > > > >> it to adapt to this single selection pressure. The second paper
> > > > >> addresses how rmns operates when multiple simultaneous selection
> > > > >> pressures targeting multiple genetic loci operates.

> > > > > I'll simply take your word for it, since I have no access to the papers themselves. Hopefully no hard feelings.

> > > >
> > > > Don't take his word for it. He's wrong. He never deals with selection at
> > > > all, just mutation.

> > > John, when are you going to learn what a sample space is and that there are more theorems in probability theory than just the addition rule which you regularly apply incorrectly.
> >
> > What rule? The school I was taught 2 addition rules of probability. For
> > mutually exclusive events A and B the probability is:
> > P(A or B) = P(A) + P(B)
> > For mutually nonexclusive events A and B it is:
> > P(A or B) = P(A) + P(B) - P(A and B)
> >
> > Did you mean one of these or some third one? Where John "regularly"
> > applies either of those incorrectly? Can you cite?
> John has made two mathematical blunders trying to apply the addition rule to circumstances which are not governed by either form of the addition rule. The first instance was when he thought that doubling population size doubles the probability of a beneficial mutation occurring.

Please explain why this is a mistake. It sure doesn't look like one to me.


> He is trying to apply the addition rule to complimentary events.

That's because the probability of a mutation occurring to one
individual is disjoint from the probability of it occurring to
any other individual in the same population.

> The second instance occurred when he thought that a series of microevolutionary changes add up to a macroevolutionary change.

"add up to" is not a mathematical statement in this context.
It is simply a statement of belief that an unspecified number
of successive microevolutionary changes result in a
macroevolutionary change from the first in the series to
the last in the series.

I submit the horse family as being an example. I told John that
you never said anything one way or the other about whether
the change from Hyracotherium to Equus was microevolutionary
or macroevolutionary. He found that hard to believe, and he
believes you are a YEC who cannot stomach evolutionary change
of that magnitude.

What do you have to say to all this?

> Microevolutionary changes are linked by the multiplication rule for joint independent events,

...applied to populations of drastically variable size. Given enough
Hyracotheriums, the minor mutation that gave the world Orohippus
may have had a high probability. And so on down the long sequence

Hyracotherium/Eohippus - Orohippus - Epihippus - Mesohippus -
Miohippus - Parahippus - Merychippus - Dinohippus - Plesippus - Equus.
http://www.talkorigins.org/faqs/horses/horse_evol.html

> not the addition rule for mutually exclusive events or arbitrary events.

So what?


Peter Nyikos
Professor, Dept. of Mathematics -- standard disclaimer--
University of South Carolina

[Bob Casanova]

On Mon, 9 Oct 2017 12:44:35 -0700 (PDT), the following
appeared in talk.origins, posted by Alan Kleinman MD PhD
<klei...@sti.net>:

>On Monday, October 9, 2017 at 12:10:02 PM UTC-7, Dennis Feenstra wrote:
>> Op maandag 9 oktober 2017 21:05:02 UTC+2 schreef John Harshman:

>> > On 10/9/17 11:36 AM, Dennis Feenstra wrote:
>> > Don't take his word for it. He's wrong. He never deals with selection at
>> > all, just mutation.
>>

>> I am not taking his word in a sense that I agree with him. It's more that his papers are something which I can't verify in any meaningful way. Hence I can and will only adress whatever he says outside his papers.
>Here is the fundamental governing equation for rmns:
>.

>P(X)=(1?(1-P(Beneficial)?)^(n?nG)) where;

>X is the particular beneficial mutation,
>P(beneficial) is the probability of all possible mutation that can occur at the particular site that it is the beneficial mutation,

>? is the mutation rate

>n is the population size
>nG is the number of generations that n replicates.
>n*nG can be written in more general terms for a population which varies every generation as a double summation of n for each generation over the total number of generations.

OK. Please point to exactly which part models selection.

>Every evolutionary step by rmns on an evolutionary trajectory is of the form above where the joint probability of the evolutionary trajectory occurring is computed using the multiplication rule of each individual probability equation.

Where's the "ns" in your "fundamental governing equation"?
All I see is the "rm" part. Be specific.
--

Bob C.

"The most exciting phrase to hear in science,
the one that heralds new discoveries, is not
'Eureka!' but 'That's funny...'"

- Isaac Asimov

[Sean Dillon]

I disagree with your prediction. I think what you would find is that, at the end of the day, there would be roughly as many e. Coli in the double-stressed samples as the single stressed samples. All that would be different is the NATURE of the e. Coli in the respective samples. In the double-stressed samples, the population would be made up on individuals that are more heat resistant.

The starvation stressor is the population delimiter here. It creates a bright-line maximum for the number of individuals that can be supported. The heat stressor would kill off some of the population (or hinder their reproduction). But that just means that the individuals who were not hindered (or even who were LESS hindered) by the heat would have more food available, and thus would reproduce more, making up the difference.

Thus, there would be just as many instances of reproduction as in any other sample, and just as many opportunities for a mutation beneficial toward EITHER stressor to occur. And IF such a mutation occurs, it will give the mutant a relative advantage over the rest of the population that will lead its descendants to comprise an ever greater share of the population. They don't have to have mutations that are beneficial against BOTH stressors for this to occur. It is enough to be better than the rest of the population against EITHER stressor.

It is like that old joke: Two guys are out camping, and suddenly they hear a bear bellowing, heading their direction. One of the guys pulls out running shoes and starts lacing up. The other guy says "What are you doing?! You can't outrun a bear!!" The first guy says "I don't have to outrun the bear... I just have to outrun you."

Relative fitness matters.

The only exceptions to this would be situations in which ALL individuals are hindered in their reproduction. This would slow the entire population's ability to fully take advantage of the available resources. And if it slows the populational rate of reproduction to the point where it approaches the death rate, it may even hold a population at a new, lower population equilibrium. And that WILL impact the populations ability to evolve.

[John Harshman]

It's a mistake because it's an approximation that only works if the
probability is small. Then again, the expected number of mutations does
double if the population size doubles. The actual mistake was saying one
when I meant the other.

>> He is trying to apply the addition rule to complimentary events.
>
> That's because the probability of a mutation occurring to one
> individual is disjoint from the probability of it occurring to
> any other individual in the same population.

But what Alan is talking about isn't that but the probability of two
particular mutations occurring in a single individual.

>> The second instance occurred when he thought that a series of microevolutionary changes add up to a macroevolutionary change.
>
> "add up to" is not a mathematical statement in this context.
> It is simply a statement of belief that an unspecified number
> of successive microevolutionary changes result in a
> macroevolutionary change from the first in the series to
> the last in the series.
>
> I submit the horse family as being an example. I told John that
> you never said anything one way or the other about whether
> the change from Hyracotherium to Equus was microevolutionary
> or macroevolutionary. He found that hard to believe, and he
> believes you are a YEC who cannot stomach evolutionary change
> of that magnitude.
>
> What do you have to say to all this?
>
>> Microevolutionary changes are linked by the multiplication rule for joint independent events,
>
> ...applied to populations of drastically variable size. Given enough
> Hyracotheriums, the minor mutation that gave the world Orohippus
> may have had a high probability. And so on down the long sequence
>
> Hyracotherium/Eohippus - Orohippus - Epihippus - Mesohippus -
> Miohippus - Parahippus - Merychippus - Dinohippus - Plesippus - Equus.
> http://www.talkorigins.org/faqs/horses/horse_evol.html
>
>> not the addition rule for mutually exclusive events or arbitrary events.
>
> So what?

Note that so far Alan has said nothing at all about selection. He
doesn't model selection. He calls selection "amplification" and he
doesn't deal with "amplification" in his math.

[Dennis Feenstra]

_______________________________
Alan states: "The probability of a beneficial mutation occurring is dependent on the number of replications, not the number of generations. "
_______________________________

As mutation rates are based on the rate of replication of cells (ie, per cell division), you can infer the mutation rate which would occur during the lifetime of an organism. You can then also infer the rate of the occurence of mutations within a number of generations of the population given that the rate of replication of the cells remains the same. That's kinda what I meant.


_______________________________
Alan states: "The point you are missing is that rmns is a very slow and arduous process when more than a single targeted selection pressure is acting on the population at a time."
_______________________________

It depends entirely on those selection pressures and how they independently influence population size. Does the selection pressure outright kill individuals? Or does it slow down the reproduction process? Does it only target the weakest, which is always the case in stable and growing populations? Does the selection pressure occur consistently and often? How big and how stable is a population with multiple selection pressures in nature to begin with? Are those populations often at a size not optimal for evolution? These are important questions.

Say we have selection pressure: predation (sp:p) and selection pressure temperature change (sp:tc).
sp:p outright kills individuals.
sp:tc may lower the number of reproduction events.
Both sp:p and sp:tc lower the population size to a new equilibrium.

If an individual gains a beneficial mutation in regards to sp:p, it will have the same chance to reproduce in regards to the other individuals. However, because it is outrunning predators easily, it has a greater chance to contribute to the gene pool than those indidivuals that got caught.


Now I don't have enough knowledge on probability theory to see if your model actually includes selection and competition, so I'll leave that to others. However, combined with all the criticism so far, there are other facts I take into account to know that you're probably wrong.

Be it the arising nested hierarchies when comparing genomes, observations made in evolutionary developmentary biology (evo devo), the geologic column and the necessity for deep time and many different local environmental conditions, as well as the fossil record being consistent and concordant with evolutionary theory:

http://freethoughtblogs.com/pharyngula/files/2013/03/trilobiterichness.png

https://sites.google.com/site/evolutionoftheelephant/_/rsrc/1432345810024/ances/ebolusyon_ng_elepante_evolution_of_elephants.jpg

https://i.pinimg.com/originals/1f/bb/20/1fbb2013fa69d034e23c38261eaa271e.jpg

http://www.nhm.ac.uk/content/dam/nhmwww/discover/human-evolution/human-evolution-family-tree-with-skulls-graphic-hero.jpg

[Peter Nyikos]

My bad. I was absent-mindedly assuming what you also carelessly
assumed.

> It's a mistake because it's an approximation that only works if the
> probability is small. Then again, the expected number of mutations does
> double if the population size doubles. The actual mistake was saying one
> when I meant the other.

Yes, thanks for bailing us both out. :-) :-(

> >> He is trying to apply the addition rule to complimentary events.
> >
> > That's because the probability of a mutation occurring to one
> > individual is disjoint from the probability of it occurring to
> > any other individual in the same population.
>
> But what Alan is talking about isn't that but the probability of two
> particular mutations occurring in a single individual.

If so, he is very bad at expressing himself.

Has anyone actually seen those two papers, as opposed to just the abstract?

Peter Nyikos
Professor, Dept. of Mathematics -- standard disclaimer--
University of South Carolina

http://people.math.sc.edu/nyikos/

[Alan Kleinman MD PhD]

On Monday, October 9, 2017 at 6:50:02 PM UTC-7, jillery wrote:
> On Mon, 9 Oct 2017 16:57:15 -0700 (PDT), Alan Kleinman MD PhD

> wrote:
>
> >On Monday, October 9, 2017 at 4:45:02 PM UTC-7, Dennis Feenstra wrote:
> >> Op dinsdag 10 oktober 2017 01:35:03 UTC+2 schreef Alan Kleinman MD PhD:
> >> > It's kinda a rough approximation of a single selection pressure targeting a single gene but what makes you think a climate change only targets a single gene. How many biological enzymes have functional behavior dependent on temperature?
> >>
> >> And what do we and other animals do as a reaction to extreme temperature differences? Again, you're asserting a very lethal scenario.
> >You don't get it. Even if the temperature change is small, it will still select out the weaker variants. Consider the Lenski experiment where instead of starvation alone, he runs the experiment at a non-optimal temperature. Do you think that rmns will work more quickly under this circumstance with two weak selection pressures than with a single weak selection pressure? It will not because the amplification of a beneficial mutation for the starvation pressure will be impaired by the thermal stress and the amplification of a beneficial mutation for thermal stress will be impaired by the starvation pressure. What you don't seem to understand is that selection pressures are stressors that kill or impair the replication of some or all members of a population.
>
>
> You have used the above example several times before. As a refresher
> of Lenski's LTEE:
>
> <https://en.wikipedia.org/wiki/E._coli_long-term_evolution_experiment>
>
> Part of the methodology of LTEE is that once a day, every day, 1% of
> the population in 12 flasks is transferred to 12 new flasks. All
> populations are equally nutrient limited, meaning the amount is
> specifically designed so that every population uses up all the
> nutrients before the next day's transfer. So there's lots of natural
> selection going on to both duplicate and survive.
>
> IIUC your prediction is, given a case where one of Lenski's E.coli
> populations faces both starvation stress and thermal stress, two
> things will happen:
>
> 1) the total number of random mutations (RM) in that population will
> *decrease* (how to measure?).

I never said anything like this. In fact, the mutation rate may increase when a population is stressed, especially starvation and thermal stress.

>
> 2) the fitness (NS) of that population will *decrease*, as measured by
> a reduced number of individuals at the end of the day.

That I believe may very well happen. Clearly, that has happened under starvation stress, only between 3 and 4 generations per day when under ideal circumstances bacteria will reproduce every 20 minutes or so.

>
> My challenge to you, Alan Kleinman MD PhD, is to model the above
> scenario with your mathematical formula for multiplication rule of
> probability, and show how it calculates those results. If you are
> successful, that should give pause to those who claim your formula
> doesn't model natural selection; a significant victory, yes?

No problem, every example of rmns works in the same way. First, the way you would model rmns for the starvation selection pressure alone is to recognize that a specific sequence of mutations can give improve improved fitness (both absolute and relative) to the starvation selection pressure. Lenski has already demonstrated this. Call the first mutation in the sequence giving improved fitness for starvation S1, the second S2, the third S3 and so on. Then the governing probability equation for this evolutionary trajectory is:
P(S1)P(S2)P(S3)...=(1−(1-P(BeneficialS1)𝜇)^(n))*(1−(1-P(BeneficialS2)𝜇)^(nS1))*(1−(1-P(BeneficialS3)𝜇)^(nS1S2))...
Where n is the initial total population size, nS1 in the number of replications of the members with mutation S1, nS1S2 is the number of replications of members with both the S1 and S2 mutations and so on.
.
The way you would model rmns for the thermal stress selection pressure alone is to recognize that a specific sequence of mutations can give improve improved fitness (both absolute and relative) to the thermal stress selection pressure. Call the first mutation in this sequence giving improved fitness for thermal stress T1, the second T2, the third T3 and so on. Then the governing probability equation for this evolutionary trajectory is:
P(T1)P(T2)P(T3)...=(1−(1-P(BeneficialT1)𝜇)^(n))*(1−(1-P(BeneficialT2)𝜇)^(nT1))*(1−(1-P(BeneficialT3)𝜇)^(nT1T2))...
Where n is the initial total population size, nT1 in the number of replications of the members with mutation T1, nT1T2 is the number of replications of members with both the T1 and T2 mutations and so on.
.
For the combined selection pressures of both starvation and thermal stress, the corresponding probability equation is:
P(S1)P(T1)P(S2)P(T2)P(S3)P(T3)...=(1−(1-P(BeneficialS1)𝜇)^(n))*(1−(1-P(BeneficialT1)𝜇)^(nS1))(1−(1-P(BeneficialS2)𝜇)^(nS1T1))*(1−(1-P(BeneficialT2)𝜇)^(nS1T1S2))*(1−(1-P(BeneficialS3)𝜇)^(nS1T1S2T2))*(1−(1-P(BeneficialT3)𝜇)^(nS1T1S2T2S3))...
where n is the total population size, nS1 is the number of replications of members with the S1 mutation, nS1T1 is the number of replications of members with the S1 and T1 mutations, nS1T1S2 is the number of replications of members with the S1, T1 and S2 mutations, nS1T1S2T2 is the number of replications of members with the S1, T1, S2 and T2 mutations and so on.
.
Unless natural selection can amplify each of these subpopulations at every step of the evolutionary trajectory, the probability of a lineage taking this evolutionary trajectory will be low. With population sizes attainable by HIV and malaria, a two selection pressure evolutionary trajectory is feasible. I suspect that if Lenski were to do this experiment without driving his populations to extinction, he would see drift, not directional selection due to the broad spectrum of genetic loci targeted by starvation and thermal stress as compared to antimicrobial selection pressures which generally target only a single genetic locus.

[John Harshman]

He is indeed.

No. They're paywalled in a low-impact journal that I imagine few
libraries get. But he's been kind enough to post the math he thinks
deals with natural selection. It doesn't. You will also note that
whenever he says anything it isn't either natural selection or random
mutation; it's "rmns" as if there were just one thing to be discussed.

[Alan Kleinman MD PhD]

A simple way to know this is a blunder is to consider this circumstance. Let the population size be n and the probability of a beneficial mutation is 0.6, then if you double the population size to 2n is the probability 1.2? The replication is the random trial. No matter how many replications occur, there will always be at least a small probability that the beneficial mutation will not occur. A portion of the probability curve is approximately linear but the interesting stuff occurs in the non-linear portion of the probability curve.

>
>
> > He is trying to apply the addition rule to complimentary events.
>
> That's because the probability of a mutation occurring to one
> individual is disjoint from the probability of it occurring to
> any other individual in the same population.
>
> > The second instance occurred when he thought that a series of microevolutionary changes add up to a macroevolutionary change.
>
> "add up to" is not a mathematical statement in this context.
> It is simply a statement of belief that an unspecified number
> of successive microevolutionary changes result in a
> macroevolutionary change from the first in the series to
> the last in the series.

The reality is that microevolutionary changes are mathematically linked by the multiplication rule for random independent events. rmns will not be correctly understood until this mathematical fact becomes part of the biologists' lexicon.

>
> I submit the horse family as being an example. I told John that
> you never said anything one way or the other about whether
> the change from Hyracotherium to Equus was microevolutionary
> or macroevolutionary. He found that hard to believe, and he
> believes you are a YEC who cannot stomach evolutionary change
> of that magnitude.
>
> What do you have to say to all this?

What I can't stomach is the udder failure of biologists to correctly describe rmns. This failure has led to multidrug-resistant microbes, multi-herbicide resistant weeds, multi-pesticide resistant insects and less than durable cancer treatments.
.
I have never studied the age of the earth and I have never looked at the change from Hyracotherium to Equus.

>
> > Microevolutionary changes are linked by the multiplication rule for joint independent events,
>
> ...applied to populations of drastically variable size. Given enough
> Hyracotheriums, the minor mutation that gave the world Orohippus
> may have had a high probability. And so on down the long sequence
>
> Hyracotherium/Eohippus - Orohippus - Epihippus - Mesohippus -
> Miohippus - Parahippus - Merychippus - Dinohippus - Plesippus - Equus.
> http://www.talkorigins.org/faqs/horses/horse_evol.html

Recombination can give striking phenotypic differences as seen with canines. But the alleles have to exist in the gene pool. If a gene pool does not have the correct alleles, no amount of breeding can bring about these alleles. But you can get Great Danes and Chihuahuas out of the same gene pool but they are both still canines.

>
> > not the addition rule for mutually exclusive events or arbitrary events.
>
> So what?

If you want to correctly understand the mathematics of rmns, that's what!

[Alan Kleinman MD PhD]

On Tuesday, October 10, 2017 at 8:40:04 AM UTC-7, Bob Casanova wrote:
> On Mon, 9 Oct 2017 12:44:35 -0700 (PDT), the following
> appeared in talk.origins, posted by Alan Kleinman MD PhD

> <kle:

>
> >On Monday, October 9, 2017 at 12:10:02 PM UTC-7, Dennis Feenstra wrote:
> >> Op maandag 9 oktober 2017 21:05:02 UTC+2 schreef John Harshman:
> >> > On 10/9/17 11:36 AM, Dennis Feenstra wrote:
> >> > Don't take his word for it. He's wrong. He never deals with selection at
> >> > all, just mutation.
> >>
> >> I am not taking his word in a sense that I agree with him. It's more that his papers are something which I can't verify in any meaningful way. Hence I can and will only adress whatever he says outside his papers.
> >Here is the fundamental governing equation for rmns:
> >.
> >P(X)=(1?(1-P(Beneficial)?)^(n?nG)) where;
> >X is the particular beneficial mutation,
> >P(beneficial) is the probability of all possible mutation that can occur at the particular site that it is the beneficial mutation,
> >? is the mutation rate
> >n is the population size
> >nG is the number of generations that n replicates.
> >n*nG can be written in more general terms for a population which varies every generation as a double summation of n for each generation over the total number of generations.
>
> OK. Please point to exactly which part models selection.
>
> >Every evolutionary step by rmns on an evolutionary trajectory is of the form above where the joint probability of the evolutionary trajectory occurring is computed using the multiplication rule of each individual probability equation.
>
> Where's the "ns" in your "fundamental governing equation"?
> All I see is the "rm" part. Be specific.

n*nG is simply the total number of replications which is the measure of absolute fitness to reproduce. That is how you measure natural selection.

[Alan Kleinman MD PhD]

John, you really should put some effort into this and plot out the probability curve. It is easy to do. You can use a program like Excel, put the equation in, plot some points and draw the curve. Until you get to the non-linear portion of the curve, the expected number of mutations is <<1.

[John Harshman]

Whatever are you talking about? The expected number of mutations equals
mutation rate per replication times number of replications. Period.
Whether it's less than 1 depends on those two parameters, and it
increases linearly with each.

[Alan Kleinman MD PhD]

Don't expect any beneficial mutations until lot and lots of replications have occurred. How many replications? You won't know using a linearized probability curve.

[John Harshman]

I see that you don't know the difference between the expected number of
events and the probability of at least one event. Odd.

[Dennis Feenstra]

Apologies, but I found this rather asinine.

Alan states "If a gene pool does not have the correct alleles, no amount of breeding can bring about these alleles."

Then what about the genome duplications found in a genus or on a family level? Surely they must come from somewhere and have to contribute to the diversity on that clade-level.

And what about polyploidy in a lot of fish and amphibian genomes? How does your initial common ancestor without those duplications account for this? Remember, if it's not in the original genome, it can't happen!

"But you can get Great Danes and Chihuahuas out of the same gene pool but they are both still canines. "

Really now? And canines are still canids! Which includes foxes, raccoon dogs, wolves and domestic dogs. So somehow canines share a common ancestral population, but canids do not?

And if you accept it for canids, you have to accept it for ursidae (bears and dog-bears, the latter being extinct). But if you accept this, then all canids and all ursidae must share a common ancestral population. Confirmed by means of the fossil record and the genetic relationship between canids and ursidae.

You can keep doing this for every species and you'll inevitably end up with nested hierarchies only.

[jillery]

I could be wrong. You did say above that RMNS would work less
quickly. You weren't clear whether your predicted slowdown was from a
reduction in RM or NS or both.

>> 2) the fitness (NS) of that population will *decrease*, as measured by
>> a reduced number of individuals at the end of the day.
>That I believe may very well happen.

That's not what you said. You said RMNS would not work as well,
without qualification. Why are you backpedaling here?

>Clearly, that has happened under starvation stress, only between 3 and 4 generations per day when under ideal circumstances bacteria will reproduce every 20 minutes or so.

You act as if you don't understand my challenge. You need to show
that your mathematical model actually predicts the slowdown you claim
it does. You would do that showing a calculated result using:

1) no restrictions,
2) starvation stress only,
3) thermal stress only, and
4) both starvation and thermal stress.

>> My challenge to you, Alan Kleinman MD PhD, is to model the above
>> scenario with your mathematical formula for multiplication rule of
>> probability, and show how it calculates those results. If you are
>> successful, that should give pause to those who claim your formula
>> doesn't model natural selection; a significant victory, yes?

>No problem, every example of rmns works in the same way. First, the way you would model rmns for the starvation selection pressure alone is to recognize that a specific sequence of mutations can give improve improved fitness (both absolute and relative) to the starvation selection pressure. Lenski has already demonstrated this. Call the first mutation in the sequence giving improved fitness for starvation S1, the second S2, the third S3 and so on. Then the governing probability equation for this evolutionary trajectory is:

>P(S1)P(S2)P(S3)...=(1?(1-P(BeneficialS1)?)^(n))*(1?(1-P(BeneficialS2)?)^(nS1))*(1?(1-P(BeneficialS3)?)^(nS1S2))...

>Where n is the initial total population size, nS1 in the number of replications of the members with mutation S1, nS1S2 is the number of replications of members with both the S1 and S2 mutations and so on.

So plug in some sample numbers and calculate the result.

>The way you would model rmns for the thermal stress selection pressure alone is to recognize that a specific sequence of mutations can give improve improved fitness (both absolute and relative) to the thermal stress selection pressure. Call the first mutation in this sequence giving improved fitness for thermal stress T1, the second T2, the third T3 and so on. Then the governing probability equation for this evolutionary trajectory is:

>P(T1)P(T2)P(T3)...=(1?(1-P(BeneficialT1)?)^(n))*(1?(1-P(BeneficialT2)?)^(nT1))*(1?(1-P(BeneficialT3)?)^(nT1T2))...

>Where n is the initial total population size, nT1 in the number of replications of the members with mutation T1, nT1T2 is the number of replications of members with both the T1 and T2 mutations and so on.

So plug in some sample numbers and calculate the result.

>For the combined selection pressures of both starvation and thermal stress, the corresponding probability equation is:

>P(S1)P(T1)P(S2)P(T2)P(S3)P(T3)...=(1?(1-P(BeneficialS1)?)^(n))*(1?(1-P(BeneficialT1)?)^(nS1))(1?(1-P(BeneficialS2)?)^(nS1T1))*(1?(1-P(BeneficialT2)?)^(nS1T1S2))*(1?(1-P(BeneficialS3)?)^(nS1T1S2T2))*(1?(1-P(BeneficialT3)?)^(nS1T1S2T2S3))...

>where n is the total population size, nS1 is the number of replications of members with the S1 mutation, nS1T1 is the number of replications of members with the S1 and T1 mutations, nS1T1S2 is the number of replications of members with the S1, T1 and S2 mutations, nS1T1S2T2 is the number of replications of members with the S1, T1, S2 and T2 mutations and so on.

So plug in some sample numbers and calculate the result.

>Unless natural selection can amplify each of these subpopulations at every step of the evolutionary trajectory, the probability of a lineage taking this evolutionary trajectory will be low. With population sizes attainable by HIV and malaria, a two selection pressure evolutionary trajectory is feasible. I suspect that if Lenski were to do this experiment without driving his populations to extinction, he would see drift, not directional selection due to the broad spectrum of genetic loci targeted by starvation and thermal stress as compared to antimicrobial selection pressures which generally target only a single genetic locus.

Thank you for saying again your prediction. So now plug in some
sample numbers and calculate the results of the 4 cases I specified
above, and see if your mathematical model makes the predictions you
say it does.

If what you claim is true, this would show that your mathematical
model does account for selection.

[Alan Kleinman MD PhD]

On Tuesday, October 10, 2017 at 4:20:04 PM UTC-7, jillery wrote:
> On Tue, 10 Oct 2017 14:17:32 -0700 (PDT), Alan Kleinman MD PhD

The slowdown is due to disruption of the NS portion of rmns. The rmns process works is a cycle of beneficial mutation (the rm part) followed by amplification of the beneficial mutation (the ns part). Simultaneous selection pressures disrupt the amplification of any mutation which might be beneficial for one or another of the selection pressures.

>
>
> >> 2) the fitness (NS) of that population will *decrease*, as measured by
> >> a reduced number of individuals at the end of the day.
> >That I believe may very well happen.
>
>
> That's not what you said. You said RMNS would not work as well,
> without qualification. Why are you backpedaling here?

I'm not sure what you mean by "the fitness (NS) of that population". Fitness is a property of individuals in a population. It could happen that a population can still increase subject to selection pressures but still not evolve by rmns. The population size of a particular variant must increase for rmns to have a chance to work on that lineage.

>
>
> >Clearly, that has happened under starvation stress, only between 3 and 4 generations per day when under ideal circumstances bacteria will reproduce every 20 minutes or so.
>
>
> You act as if you don't understand my challenge. You need to show
> that your mathematical model actually predicts the slowdown you claim
> it does. You would do that showing a calculated result using:
>
> 1) no restrictions,
> 2) starvation stress only,
> 3) thermal stress only, and
> 4) both starvation and thermal stress.

See below

>
>
> >> My challenge to you, Alan Kleinman MD PhD, is to model the above
> >> scenario with your mathematical formula for multiplication rule of
> >> probability, and show how it calculates those results. If you are
> >> successful, that should give pause to those who claim your formula
> >> doesn't model natural selection; a significant victory, yes?
>
> >No problem, every example of rmns works in the same way. First, the way you would model rmns for the starvation selection pressure alone is to recognize that a specific sequence of mutations can give improve improved fitness (both absolute and relative) to the starvation selection pressure. Lenski has already demonstrated this. Call the first mutation in the sequence giving improved fitness for starvation S1, the second S2, the third S3 and so on. Then the governing probability equation for this evolutionary trajectory is:
> >P(S1)P(S2)P(S3)...=(1?(1-P(BeneficialS1)?)^(n))*(1?(1-P(BeneficialS2)?)^(nS1))*(1?(1-P(BeneficialS3)?)^(nS1S2))...
> >Where n is the initial total population size, nS1 in the number of replications of the members with mutation S1, nS1S2 is the number of replications of members with both the S1 and S2 mutations and so on.
>
>
> So plug in some sample numbers and calculate the result.

I have in my publications. It's easy to do, I used a spreadsheet that has graphics capabilities. If you don't have spreadsheet software, you can get a copy of OpenOffice. Plug in some numbers for different population sizes and see what happens. And remember, population size is a consequence of replications, the measure of absolute reproductive fitness.

>
>
> >The way you would model rmns for the thermal stress selection pressure alone is to recognize that a specific sequence of mutations can give improve improved fitness (both absolute and relative) to the thermal stress selection pressure. Call the first mutation in this sequence giving improved fitness for thermal stress T1, the second T2, the third T3 and so on. Then the governing probability equation for this evolutionary trajectory is:
> >P(T1)P(T2)P(T3)...=(1?(1-P(BeneficialT1)?)^(n))*(1?(1-P(BeneficialT2)?)^(nT1))*(1?(1-P(BeneficialT3)?)^(nT1T2))...
> >Where n is the initial total population size, nT1 in the number of replications of the members with mutation T1, nT1T2 is the number of replications of members with both the T1 and T2 mutations and so on.
>
>
> So plug in some sample numbers and calculate the result.

Been there, done that.

>
>
> >For the combined selection pressures of both starvation and thermal stress, the corresponding probability equation is:
> >P(S1)P(T1)P(S2)P(T2)P(S3)P(T3)...=(1?(1-P(BeneficialS1)?)^(n))*(1?(1-P(BeneficialT1)?)^(nS1))(1?(1-P(BeneficialS2)?)^(nS1T1))*(1?(1-P(BeneficialT2)?)^(nS1T1S2))*(1?(1-P(BeneficialS3)?)^(nS1T1S2T2))*(1?(1-P(BeneficialT3)?)^(nS1T1S2T2S3))...
> >where n is the total population size, nS1 is the number of replications of members with the S1 mutation, nS1T1 is the number of replications of members with the S1 and T1 mutations, nS1T1S2 is the number of replications of members with the S1, T1 and S2 mutations, nS1T1S2T2 is the number of replications of members with the S1, T1, S2 and T2 mutations and so on.
>
>
> So plug in some sample numbers and calculate the result.

All done.

>
>
> >Unless natural selection can amplify each of these subpopulations at every step of the evolutionary trajectory, the probability of a lineage taking this evolutionary trajectory will be low. With population sizes attainable by HIV and malaria, a two selection pressure evolutionary trajectory is feasible. I suspect that if Lenski were to do this experiment without driving his populations to extinction, he would see drift, not directional selection due to the broad spectrum of genetic loci targeted by starvation and thermal stress as compared to antimicrobial selection pressures which generally target only a single genetic locus.
>
>
> Thank you for saying again your prediction. So now plug in some
> sample numbers and calculate the results of the 4 cases I specified
> above, and see if your mathematical model makes the predictions you
> say it does.

3 cases and I have already run the numbers and have the results peer-reviewed and published by experts in the field.

>
> If what you claim is true, this would show that your mathematical
> model does account for selection.

The number of replications for each variant at each evolutionary step is the measure of absolute fitness to reproduce for each variant. It is easy to evaluate these equations, even I could do it and did do it.

[Tim Norfolk]

On Monday, October 9, 2017 at 5:05:02 PM UTC-4, Alan Kleinman MD PhD wrote:
<snip>

> John has made two mathematical blunders trying to apply the addition rule to circumstances which are not governed by either form of the addition rule. The first instance was when he thought that doubling population size doubles the probability of a beneficial mutation occurring.

<snip>
It does, as a very good approximation, if the mutation rate is low.

[Tim Norfolk]

I have not. My reading is that the DrDr has learnt a little bit, and now thinks that he knows it all.

[jillery]

Got it, thank you.

>> >> 2) the fitness (NS) of that population will *decrease*, as measured by
>> >> a reduced number of individuals at the end of the day.
>> >That I believe may very well happen.
>>
>>
>> That's not what you said. You said RMNS would not work as well,
>> without qualification. Why are you backpedaling here?
>I'm not sure what you mean by "the fitness (NS) of that population".

I refer to what you also call "amplification". I have already
stipulated it can be measured from changes in population each day. Do
you agree?

>Fitness is a property of individuals in a population. It could happen that a population can still increase subject to selection pressures but still not evolve by rmns. The population size of a particular variant must increase for rmns to have a chance to work on that lineage.

Fitness is also a property of populations, but there's no need to
quibble about that. Just how your mathematical formula predicts
whatever version of natural selection (NS) you think it predicts.

Then you should have no problem evaluating your equations here and
now. ISTM to be in your self-interest to do so. Why wouldn't you
want to show that your mathematical formula models selection, and poke
your thumbs in Harshman's rhetorical eyes?

[Dennis Feenstra]

Op woensdag 11 oktober 2017 02:10:04 UTC+2 schreef Alan Kleinman MD PhD:

> Simultaneous selection pressures disrupt the amplification of any mutation which might be beneficial for one or another of the selection pressures.

That depends entirely on what kind of selection pressures you're using, the potential effect of phenotypical plasticity (specifically behavioral), and whether you give your population all the opportunities they would otherwise have in nature.

Starvation and thermal stressors? Seriously? Why not a lighter form of malnutrition and smaller temperature differences? I still can't wrap my head around the idea of using these two selection pressures as some sort of normal for what we ought to expect.

It also depends on whether you apply them to micro organisms and what kind of micro organisms (some might already have a dominant beneficial mutation for one selection pressure).

It then also depends on whether you apply them to micro organisms or their complex multi cellular counter parts. While micro organisms reply solely on replication, with whatever HGT takes place, higher organisms always recombine their DNA during reproduction, between any two variant lineages.


While your objections *may* be valid for unicellular and simple multicellular populations, which may explain why it took some of them 3 billion years to become sufficiently complex to begin with, I can't imagine your overly simplistic use of probability theory working on higher organisms, which is what your stance on evolution seems to imply.

If both simultaneous selection pressures (climate change and predation) only shrink the population up to a certain point and still slightly increase mutation rates, while the selection pressures continue to kill the weaker variants, you're going to get to a point where a beneficial mutation is going to get fixed. Why? Because any organism with beneficial mutation #1 has a better chance of survival and reproduction against selection pressure #1. That same organism has the same chance to survive and reproduce against selection pressure #2 as everyone else.

[Dennis Feenstra]

correction to: "which may explain why it took some of them 3 billion years to become sufficiently complex to begin with,"

should be: Which may explain why it took life some 3 billion years to become sufficiently complex multicellular organisms.

[Dennis Feenstra]

Another bloody correction. Good job me.

"While micro organisms reply solely on replication"

should be While certain micro organisms rely only on replication.

[jillery]

Good job. Better you should catch your own nits than some other nit
picker.... although nit picking is a way many social primates increase
bonding *-)

[Bob Casanova]

On Tue, 10 Oct 2017 16:00:34 -0700 (PDT), the following
appeared in talk.origins, posted by Dennis Feenstra
<dennisf...@gmail.com>:

Or he could read "The Ancestor's Tale", which shows the same
thing.

[Bob Casanova]

On Tue, 10 Oct 2017 14:48:04 -0700 (PDT), the following

appeared in talk.origins, posted by Alan Kleinman MD PhD

<klei...@sti.net>:

No, you measure selection by *relative* reproductive success
between genotypes. Where in your "fundamental governing
equation" is the comparison? AFAICT it isn't there, so
please enlighten me.

[Sean Dillon]

An excellent read.

[Alan Kleinman MD PhD]

Am I the only one on this forum who has actually plotted the probability of a beneficial mutation occurring as a function of the number of replications? I hope you and John had fun playing hooky from your probability theory class.