The Argument Clinic

[Roy (34-year veteran)]

@Giltil

I think it is you who should take the time to review the passage I am referring to entitled « prescribing fitness effects of mutations », with a particular focus on the two quantities that define gamma, ie., theta and q.

I think it is you who should review the passage you are referring to, since you clearly haven’t read it properly.

Here’s the passage about θ and q. I’ve highlighted the relevant text:

The second parameter γ can be viewed as controlling the fraction of mutations that have a large absolute fitness effect. Instead of specifying γ directly, we select two quantities that are more intuitive and together define γ. The first is θ, a threshold value that defines a “high-impact mutation.” The second is q, the fraction of mutations that exceed this threshold in their effect. For example, a user can first define a high-impact mutation as one that results in 10% or more change in fitness (θ = 0.1) relative to the scale factor and then specify that 0.001 of all mutations (q = 0.001) be in this category.

So q defines the fraction of “high-impact” mutations, and θ defines how high that impact is. But θ isn’t an absolute change in fitness, it’s a change “relative to the scale factor”.

What’s the scale factor?

It’s defined on the previous page:

Our function, expressed by Equation (1), maps a random number x, drawn from a set of uniformly distributed random numbers, to a fitness effect d(x) for a given random mutation as follows:

d(x) = d_sf exp(-ax^γ), 0 ≤ x ≤ 1 (1)

Here d_sf is the scale factor which is equal to the extreme value which d(x) assumes when x = 0. We allow this scale factor to have two separate values, one for deleterious mutations and the other for favorable ones. These scale factors are defined relative to the initial fitness value assumed for the population before we introduce new mutations. In Mendel, we assume this initial fitness value to be 1.0. For deleterious mutations, since lethal mutations exist, we choose d_{sf_del} = −1. For favorable mutations, we allow the user to specify the (positive) scale factor d_{sf_fav}. Normally, this would be a small value (for example, 0.001 to 0.1), since it is only in very special situations that a single beneficial mutation would have a very large effect.

So even though you can set a minimum threshold θ for some fraction of beneficial mutations, that threshold value is then scaled down by at least an order of magnitude. And although it’s called a threshold value, the maths given suggests that the fitness change is at the threshold, rather than above it.^[1] This threshold value, which apparently can be between 0.001 and 0.1, is applied to a scale factor which is also between 0.001 and 0.1, leading to a beneficial mutation fitness effect range of 0.001×0.001 = 0.000001 to 0.1×0.1 = 0.01 - the range shown in the screenshot above.

Mendel’s accountant uses different fitness effect ranges for deleterious vs beneficial mutations. It does not allow beneficial mutations to have a fitness effect greater than 0.01.

Perhaps next time you want to condescendingly tell some-one to “take the time to review the passage I am referring to”, you should review it yourself first to ensure you aren’t hoist by your own petard.

Meanwhile, you owe @CrisprCAS9 (and anyone else who has wasted time on your patronizing garbage) an apology.

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1. I may be wrong about this, but even if I am the existence of the scaling factor refutes Giltil’s claims. ↩︎

[Roy (34-year veteran)]

P.S. I read your first two sources, and neither of them supported your claims. I see no reason to read a third one you might cite.

[Giltil (Gilbert Thill)]

@Roy

This threshold value, which apparently can be between 0.001 and 0.1, is applied to a scale factor which is also between 0.001 and 0.1, leading to a beneficial mutation fitness effect range of 0.001×0.001 = 0.000001 to 0.1×0.1 = 0.01 - the range shown in the screenshot above

My understanding is as follow:
The scale factor for favorable mutations doesn’t necessarily belong to the 0,001 to 0,1 interval. The text says the following: *normally, it would be a small value (for example, 0,001 to 0,*1).
But that doesn’t necessarily mean that the user cannot specify intervals with higher values.
Regarding theta, the threshold value, I don’t know why you say that it has to be between 0,001 and 0,1. The text says the following : for example, a user can first define a high-impact mutation as one that results in 10% or more change in fitness (theta=0,1) relative to the scale factor. So I don’t see why the user could not choose for theta values above 0,1, for example 0,5.

@Roy

Mendel’s accountant uses different fitness effect ranges for deleterious vs beneficial mutations. It does not allow beneficial mutations to have a fitness effect greater than 0.01

What if the user sets the scale factor for beneficial mutations at 0,1, theta at 0,2 and q at 0,01 ? In that case, wouldn’t be the case that Mendel would allow room for a quite substantial number of beneficial mutations having a fitness effect greater than 0,1?

[Roy (34-year veteran)]

@Giltil

@Roy

This threshold value, which apparently can be between 0.001 and 0.1, is applied to a scale factor which is also between 0.001 and 0.1, leading to a beneficial mutation fitness effect range of 0.001×0.001 = 0.000001 to 0.1×0.1 = 0.01 - the range shown in the screenshot above

My understanding is as follow:
The scale factor for favorable mutations doesn’t necessarily belong to the 0,001 to 0,1 interval. The text says the following: *normally, it would be a small value (for example, 0,001 to 0,*1).
But that doesn’t necessarily mean that the user cannot specify intervals with higher values.

It doesn’t necessarily mean that they can, either.

Do you have any evidence that they can?

@Giltil

Regarding theta, the threshold value, I don’t know why you say that it has to be between 0,001 and 0,1.

I told you. It’s because that’s what would produce the maximum fitness range shown in the screenshot above.

@Giltil

The text says the following : for example, a user can first define a high-impact mutation as one that results in 10% or more change in fitness (theta=0,1) relative to the scale factor. So I don’t see why the user could not choose for theta values above 0,1, for example 0,5.

The text doesn’t say they can. Do you have any evidence that they can?

@Giltil

@Roy

Mendel’s accountant uses different fitness effect ranges for deleterious vs beneficial mutations. It does not allow beneficial mutations to have a fitness effect greater than 0.01

What if the user sets the scale factor for beneficial mutations at 0,1, theta at 0,2 and q at 0,01 ? In that case, wouldn’t be the case that Mendel would allow room for a quite substantial number of beneficial mutations having a fitness effect greater than 0,1?

No.

Even if Mendel’s accountant allowed that, and you haven’t show that it could, that would just allow for a small number of beneficial mutations^[1], with a fitness effect greater than (theta × scaling factor) = 0.02.

Where’s that apology to @CrisprCAS9 ? Why haven’t you responded to his post?

You said it was possible to “run [Mendel’s accountant] with settings where fitness increases”. Either demonstrate that, or admit you can’t.

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1. Using the default fraction for beneficial mutations and the maximum number of mutations the program can handle gives just 0.01×0.0001×40m = 400 such beneficial mutations in the entire simulation run, which works out at 0.04 per ‘organism’. ↩︎

[John_Harshman]

@RonSewell

I think it has more to do with his fallacious genetics.

One might add his inability to understand coalescence in the absence of a bottleneck and his inability to read a phylogenetic tree.

[CrisprCAS9]

One thing to consider:

We reiterate that Mendel uses the same value for γ, and thus the same values for θ and q, for both favorable and deleterious mutations.

If the shape parameters of the distributions of beneficial and deleterious mutations are the same, then with the ratio set to 0.5 and in the absence of selection the two must cancel out. Actually, not even, since equal shape parameters would produce some number of beneficials greater than 1, but no ->1 deleterious (since >=1 would just be lethal).

So we know that with selection and with the ratio at 0.5, fitness must increase. If they’re telling the truth about the shape parameters being equal for both beneficial and deleterious.

But…

Huh. Would you look at that, they’re lying. Shocking.

[Roy (34-year veteran)]

@CrisprCAS9

One thing to consider:

We reiterate that Mendel uses the same value for γ, and thus the same values for θ and q, for both favorable and deleterious mutations.
…

Huh. Would you look at that, they’re lying. Shocking.

Technically they do use the same values for γ, θ and q for beneficial and deleterious mutations. They just apply a scaling factor of between 0.1 and 0.001 to the beneficial mutations afterwards.

[CrisprCAS9]

@Roy

They just apply a scaling factor of between 0.1 and 0.001 to the beneficial mutations afterwards.

Well excellent then. That means it should be no trouble at all for @Giltil to download the program, set the scale factor to 1, and show the results.

In fact, I’d suggest that any further comments from him relying on MA without such a demonstration should be met with derisive laughter and immediate dismissal.

Of course, he should feel free to try and support GE without reference to MA. You know, by providing the class of mutations that could cause GE in the first place.

[Faizal_Ali]

@CrisprCAS9

Well excellent then. That means it should be no trouble at all for @Giltil to download the program, set the scale factor to 1, and show the results.

In fact, I’d suggest that any further comments from him relying on MA without such a demonstration should be met with derisive laughter and immediate dismissal.

I agree. It should be no problem if @Giltil was correct in what he is claiming.

[Rumraket (Mikkel R.)]

@Roy

They just apply a scaling factor of between 0.1 and 0.001 to the beneficial mutations afterwards.

Now this might seem like they’re trying to stack the deck in some way, but I actually think that isn’t particularly unrealistic.

The effect of the scaling factor is that it makes beneficial mutations of the same magnitude of fitness effect as deleterious mutations (say +2% vs -2%), comparatively more rare.

I don’t think that’s an unrealistic assumption. Speaking of their frequency of occurrence, extremely deleterious mutations (that reduce fitness by 50% or more, or whatever, and lethal mutations do of course exist) are not all that incredibly rare, whereas extremely beneficial mutations of a similarly large positive effect, if they aren’t straight up reversions of the deleterious mutations, are extremely rare in comparison.

The worst problems with MA I see are that

1. It can’t simulate evolution at the population sizes that conventional population genetics says shouldn’t lead to fitness decline (in which case it’s literally completely and utterly worthless as supposed evidential support for the concept of GE),
2. Perhaps even worse when it comes to realism, the program doesn’t and can’t simulate diminishing returns epistasis. In the program the DFE is fixed over time and doesn’t change with changes in absolute fitness as it does in the real world. In reality, at very high fitness, the pool of beneficial mutations shrinks because many basic cellular functions have already climbed either to local or global peaks, in which case there isn’t any more gains to be had there. Conversely as you move further down from the peaks in the fitness landscape, many more paths for regaining fitness open up.

These two problems means MA absolutely cannot in any way substantiate the central claim of GE. As a piece of evidence, it isn’t any. It demonstrates nothing. Any appeal to results obtained in MA invoked as support of GE can be dismissed for those reasons.

[Roy (34-year veteran)]

@Rumraket

@Roy

They just apply a scaling factor of between 0.1 and 0.001 to the beneficial mutations afterwards.

Now this might seem like they’re trying to stack the deck in some way, but I actually think that isn’t particularly unrealistic.

The effect of the scaling factor is that it makes beneficial mutations of the same magnitude of fitness effect as deleterious mutations (say +2% vs -2%), comparatively more rare.

I don’t think that’s an unrealistic assumption.

But they’re already making beneficial mutations much rarer than deleterious ones, by defaulting to having only 1/1000 mutations be beneficial. There’s no need to apply that rareness twice.

[Rumraket (Mikkel R.)]

@Roy

But they’re already making beneficial mutations much rarer than deleterious ones, by defaulting to having only 1/1000 mutations be beneficial. There’s no need to apply that rareness twice.

That raises another question about the “true” shape of the distribution for both beneficial and deleterious mutations, and whether the same shape of the curve can actually be assumed for both beneficial and deleterious mutations (with the beneficial one just being more… suppressed?). Another problem with MA, and simulations in general of this sort that simulate at an abstract level, is that very abstraction is not really a correct representation of reality. It is a work of convenience, and Sanford has basically taken Kimura’s curve and assumed it’s some sort of work handed down on stone tablets (he always babbles about the naturalness of the Weibull distribution etc.). The 11th commandment given to Moses. It’s absurd.

I don’t think there really IS a one “true” shape of the DFE. It’s always context dependent, both environment and genetic background affects it. The fact that the fitness effect of a mutation in reality depends both on environment and genetic background isn’t captured in this simulation either. It doesn’t simulate all the different types of epistatic interactions.

Some times this idea that there’s a single neat equation that fully captures some complex phenomenon, like the magnitude of fitness effects of mutations under all conditions, is just a pipedream. The best approximation probably has 10 terms at least, and barely any of them are constant.

Edit: I should add that, I don’t think your statement is true. I think large-effect beneficial mutations are much, much, much more rare than large effect deleterious mutations. Not just by a factor of 1000.

Suppose 1 out of 1000 deleterious mutations reduce fitness by 90%, a huge drop. Such a mutation would be basically immediately outcompeted. That would imply, if the ratio of beneficials to deleterious is 1:1000, that 1 in 1 million of all mutations have a beneficial effect of 90%. But it’s NOWHERE near that. So there must be SOME sort of scale factor at work in addition to the ratio alone. While a 90% gain in fitness should be possible, and possible not just from reversion (after all novel adaptations are possible that don’t just revert a previous change), it can’t be merely a case of 1 in 1 million, because then we’d see such massively beneficial mutations often in experiments with viruses and bacteria. And we basically never do.

[Giltil (Gilbert Thill)]

@Roy

Even if Mendel’s accountant allowed that, and you haven’t show that it could, that would just allow for a small number of beneficial mutations[1], with a fitness effect greater than (theta × scaling factor) = 0.02.

My understanding is different from yours here. In order to compute the fitness above which a beneficial mutation would be defined as a high-impact mutation (let’s called this value Fhib), rather than multiplying theta with the scaling factor, I would use the following formula: Fhib=scale factor + scale factor x theta.
So if:
scale factor = 0,1
Theta=0,2
We have Fhib= 0,12

[Roy (34-year veteran)]

@Rumraket

@Roy

But they’re already making beneficial mutations much rarer than deleterious ones, by defaulting to having only 1/1000 mutations be beneficial. There’s no need to apply that rareness twice.

That raises another question about the “true” shape of the distribution for both beneficial and deleterious mutations, and whether the same shape of the curve can actually be assumed for both beneficial and deleterious mutations (with the beneficial one just being more… suppressed?).

I can think of several reasons why it wouldn’t be, including

• there’s a hard limit on the deleteriousness of mutations, but not on the beneficence;
• beneficial mutations can increase fitness by more than deleterious ones can reduce it;
• badly deleterious mutations will be far more common than greatly beneficial ones, but that isn’t true of slightly deleterious and slightly beneficial ones.

But these sorts of flaws are present in all simulations. They’re just approximations.

Edit: I should add that, I don’t think your statement is true. I think large-effect beneficial mutations are much, much, much more rare than large effect deleterious mutations. Not just by a factor of 1000.

Suppose 1 out of 1000 deleterious mutations reduce fitness by 90%, a huge drop. Such a mutation would be basically immediately outcompeted. That would imply, if the ratio of beneficials to deleterious is 1:1000, that 1 in 1 million of all mutations have a beneficial effect of 90%. But it’s NOWHERE near that. So there must be SOME sort of scale factor at work in addition to the ratio alone. While a 90% gain in fitness should be possible, and possible not just from reversion (after all novel adaptations are possible that don’t just revert a previous change), it can’t be merely a case of 1 in 1 million, because then we’d see such massively beneficial mutations often in experiments with viruses and bacteria. And we basically never do.

I don’t think a 90% gain of fitness is as massively beneficial as you seem to imply. It just means producing on average 2 offspring rather than 1. In a population of millions it’d take about ten generations to even be noticeable.

[Rumraket (Mikkel R.)]

@Roy

I don’t think a 90% gain of fitness is as massively beneficial as you seem to imply.

I’m not implying anything about this magnitude of effect other than the actual percentage gain. The more important point is that they aren’t just as rare as the ratio between beneficial to deleterious would seem to imply because then we’d see them all the time. While examples do exist, they’re extremely rare, or a “just” reversions of strongly deleterious mutations.

[Roy (34-year veteran)]

@Giltil

@Roy

Even if Mendel’s accountant allowed that, and you haven’t show that it could, that would just allow for a small number of beneficial mutations[1], with a fitness effect greater than (theta × scaling factor) = 0.02.

My understanding is different from yours here. In order to compute the fitness above which a beneficial mutation would be defined as a high-impact mutation (let’s called this value Fhib), rather than multiplying theta with the scaling factor, I would use the following formula: Fhib=scale factor + scale factor x theta.
So if:
scale factor = 0,1
Theta=0,2
We have Fhib= 0,12

Why should anyone care what you would do? According to that paper, Mendel’s accountant multiplies the fitness by the scaling factor.

I’m taking this as an admission that you cannot actually demonstrate that Mendel’s accountant can be run with settings where fitness increases, but don’t have the integrity to say that.

Added: Giltil’s ‘understanding’ would lead to the threshold for high-impact deleterious mutations in MA being so extreme that lethal mutations wouldn’t qualify as being high-impact.

[Roy (34-year veteran)]

@Rumraket

@Roy

I don’t think a 90% gain of fitness is as massively beneficial as you seem to imply.

I’m not implying anything about this magnitude of effect other than the actual percentage gain. The more important point is that they aren’t just as rare as the ratio between beneficial to deleterious would seem to imply because then we’d see them all the time. While examples do exist, they’re extremely rare, or a “just” reversions of strongly deleterious mutations.

I’m thinking of the Kishony lab bacterial plate experiment, where any mutation that allows a bacteria to survive in the next section is a gain of >90% fitness.

[Rumraket (Mikkel R.)]

@Roy

I’m thinking of the Kishony lab bacterial plate experiment, where any mutation that allows a bacteria to survive in the next section is a gain of >90% fitness.

Yes, same here. It would have to be under conditions where an organism faces some novel challenge that has a strong negative influence, or alternatively there is some very large possible gain to be had from (say) an enzyme suddenly being able to access a new highly abundant carbon source. Such situations do occur in nature, certainly many times on ecological scales and over geological time, but once this gain has occurred, it’s back to much longer periods of tiny fluctuations.

[CrisprCAS9]

@Giltil

My understanding

I don’t care what your ‘understanding’ is. Show it in the program or go away.

[Rumraket (Mikkel R.)]

Btw in case anyone is interested, here’s a recent article on diminishing returns espistasis which, at least to me, is a really interesting subject in it’s own right:

Patterns and Mechanisms of Diminishing Returns from Beneficial Mutations