# Evolution Evidence

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I'm not sure you know enough about evolution, what on earth is that;

Let's try to run thru a simple example. Say we have 3 mutations that are necessary to reach the current allele from a previous one. Again, for simplicity, let's say the probability of each mutation is 1/2.

As Skeptic said "Iin statistics, the probability of multiple unrelated events occurring is the product of their individual probabilities. "

So, for an individual in a single generation to have all 3 mutations is 1/2 x 1/2 x 1/2 = 1/8.

BUT, we are NOT dealing with "unrelated events". We are dealing with cumulative selection, which means related events. If the mutations come sequentially, then the probability of an individual getting the first mutation is 1/2. Now, that mutation is selected for (confers some advantage over current alleles) and becomes fixed. So now every individual has mutation A. The probability of an individual getting mutation B is now 1/2. The probability of an individual getting both B and C is 1/2 x 1/2 = 1/4.

Skeptic says "Whether a mutation gets fixed or not depends both on the extent of its effect, and the population size it occurs in."

This is untrue. As long as s (the selection coefficient) is at all positive, the equations are clear that the allele (mutation) will become fixed. The equation for change in frequency per generation is:

delta p = (1/2)spq/(1-q).

Notice that population size is not present. p and q are the frequency. I'm afraid Skeptic was referring to the probability of fixation by genetic drift. In the above equation, eventually p will equal 1. The lower the s, the longer this will take (because the larger s the larger delta p), but it will eventually happen.

But B is also selected for and becomes fixed (every individual now has the allele with mutation A and B). Now the odds of an individual getting mutation C (and thus having all 3 mutations A, B, and C) is 1/2.

This is how cumulative natural selection cuts down odds. The underlying premise is that all 3 mutations must appear in a single generation. Thus low probability. BUT, the data shows that this is not the case. Instead, natural selection is cumulative. This cuts down the probability. In our simplistic example the odds of getting all 3 mutations in a single individual went from 1/8 to basically 1/2.

Oh. How do you know which mutations are responsible for Lenski's strain's ability to use citrate when even he doesn't, though? If you don't, then how can you say whether Behe's guess is wrong or not?

Because we can treat Behe's guess as a hypothesis and test it against the data in Lenski's experiment. Behe says it's a "simple" overexpression of citT (the citrate transport protein). That basically means a change in either the transcription factor or repressor of citT. Either an enhancement of the transcription factor or inhibition of the repressor. Either would result in increased expression of citT. Which, according to Behe, would be enough to confer aerobic cit+.

Let's look at the expected consequence if that were true. The ability to utilize citrate occurred in only one strain and only after 30,000 generations. Such a simple single modification should have shown up in multiple strains since even a slight increase in citT would have conferred a survival advantage. Also, if Behe's hypothesis were correct, then at least one Lenski's multiple colonies from before the 25,000 generation stage should also have evolved cit+ as the simple mutation independently happened in those colonies. Yet they did not.

So, Behe's hypothesis must be wrong. Whatever happened, it was not due to a simple change in either the transcription factor or repressor of citT. Such a change would be very probable and would not depend on previous changes. What we might have is a change in both the repressor and transcription factor. Perhaps a first change decreasing the binding strength of the repressor and then a change enhancing the binding of the transcription factor. But that is no longer "simple".

For one thing, mutations don't necessarily appear sequentially. Various mutations can happen and develop in parallel. In species with sexual reproduction or other genetic transfer, the mutations can develop in parallel in multiple individuals.

But I am addressing the specific situation, not these other hypotheticals. Obviously, if the situation you describe happens, the probability drops considerably because you now have more opportunities to get multiple mutations in the same individual in the same generation.

Yup, that's what I said. How does that disprove me?

You use the probability "the probability of multiple unrelated events occurring is the product of their individual probabilities". If there is one mutation that does the job, then the individual probability is 1/n, right? But if there are 2 mutations that confer the same activity, that probability now becomes 2/n, right? And possibly 3 becomes 3/n. All of these are a decrease in probability.

But here you are assuming that the mutation will be one of the needed mutations. It could just be another completely unrelated mutation.

If unrelated, it's not included in the probability calculation. The probability equation is only based upon "required" mutations. You said "Just that more required mutations means more unlikely for all of them to happen."

So, we are only talking about the probability of a "required" mutation.

I never said anything about later mutations. Just that more required mutations means more unlikely for all of them to happen. If you like I can explain that further: in statistics, the probability of multiple unrelated events occurring is the product of their individual probabilities.

As I noted above, the claim is based on unrelated events. But cumulative evolution means that the events are no longer unrelated. Now, you go on to say "For multiple slightly related events, the probability of all of them happening is more complicated than just multiplying, but is still lower the more events there are." But the underlying premise here is that those multiple events have to happen at the same time. IOW, in the same individual. Again, not the situation we are facing in natural selection. Because previous mutations become fixed, we are only dealing with one event at a time. Not multiple events.

Since the previous mutations can have an effect on what the result of additional mutations would be, the later mutations can have a higher or lower chance of developing than before the previous mutations had happened.

Not "developing". The mutations still have the same chance of appearing. But because of what has gone before, the later mutations will have different selection coefficients. That is, different effects on survival and reproduction. And thus change whether the later mutation will be selected for or against, or how strongly each way. The previous mutations don't affect the chance of "appearing", but affect selection of the later mutations.

Hm, I had missed the part where the original was anaerobic before it was put into a plasmid. In any case, it still counters what you said:

These plasmids were made from E coli, rather than other species. So I still think that Behe taught you something

The key is that the plasmids were made. By humans. Not made by the E. coli. So 1) it doesn't counter what I said (since the plasmid did come from another species -- humans in this case) and 2) Behe didn't teach me anything, because Behe still witheld evidence. On their own, E. coli have never made plasmids with citT in them in order to boost production of citT.

I thought he made it appear that his guess was a guess?

But his guess doesn't match the data we already have. Behe made it appear that his guess was possible. It's not.

Edited by lucaspa
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Lucaspa,

This is untrue. As long as s (the selection coefficient) is at all positive' date=' the equations are clear that the allele (mutation) will become fixed. The equation for change in frequency per generation is: delta p = (1/2)spq/(1-q).

Notice that population size is not present. p and q are the frequency. I'm afraid Skeptic was referring to the probability of fixation by genetic drift. In the above equation, eventually p will equal 1. The lower the s, the longer this will take (because the larger s the larger delta p), but it will eventually happen.[/quote']

Drift is always present, it's just not relevant when the effective population size (N) is very high, but that's actually quite rare for large animals. Skeptic is 100% right to say that both 'N' and 's' (selection coefficient) matters. The equation for the probability of fixation is given by the diffusion approximation (which is based on the Wright-Fisher model, combining drift + selection);

$P(s,N) = \displaystyle\frac{1-\mbox{exp}(-s/2)}{1-\mbox{exp}(-2Ns)}$

(it's only one way to write the result, here, h (dominance) = 0.5 and the effective population size = 0.5 * actual population size).

This equation gives the probability of fixation, as you can see, the effective population size is in it.

This is all about probability. If a beneficial mutation appears, according to your deterministic equation, it will increase in frequency. But this is misleading, even highly beneficial mutations are lost; even if you're the fittest in the group (and having a single beneficial mutation is no guarantee for that), you can still be struck by lightning, be killing by a virus, et cetera... Beneficial mutations are lost all the time, they are just less likely to be lost.

The equation you used is a naive equation only used in basic textbooks (and perhaps in other circumstances, but it must be quite rare), it's certainly not used by any serious scientist to evaluate the probability of fixation, we rely on the diffusion approximation or we use exact models (Moran, Wright-Fisher, et cetera...).

The lower the s, the longer this will take (because the larger s the larger delta p), but it will eventually happen.

The lower the s, the longer it will take = intuitive, but wrong.

The lower the |s|, the longer it will take = Counter intuitive, but true. Yep, the average time to fixation is the same for s = 0.1 and s = -0.1, even if the latter is deleterious (but, of course, the probability of fixation is higher for s = 0.1).

...and that's why evolution cannot be correctly understood without a healthy dose of mathematics.

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Thanks to God that Made All the Laws,When he made the Earth,You can say Controlled Evolution: Working on his time table :

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Thanks to God that Made All the Laws,When he made the Earth,You can say Controlled Evolution: Working on his time table :

I sure hope you posted that as comic relief, and not a serious reprsentation of your views on the subject.

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Aside from that this is a very good thread, though. Nice post, PhDP.

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Lucaspa,

Drift is always present, it's just not relevant when the effective population size (N) is very high, but that's actually quite rare for large animals. Skeptic is 100% right to say that both 'N' and 's' (selection coefficient) matters. The equation for the probability of fixation is given by the diffusion approximation (which is based on the Wright-Fisher model, combining drift + selection);

$P(s,N) = \displaystyle\frac{1-\mbox{exp}(-s/2)}{1-\mbox{exp}(-2Ns)}$

(it's only one way to write the result, here, h (dominance) = 0.5 and the effective population size = 0.5 * actual population size).

This equation gives the probability of fixation, as you can see, the effective population size is in it.

This is all about probability. If a beneficial mutation appears, according to your deterministic equation, it will increase in frequency. But this is misleading, even highly beneficial mutations are lost; even if you're the fittest in the group (and having a single beneficial mutation is no guarantee for that), you can still be struck by lightning, be killing by a virus, et cetera... Beneficial mutations are lost all the time, they are just less likely to be lost.

The equation you used is a naive equation only used in basic textbooks (and perhaps in other circumstances, but it must be quite rare), it's certainly not used by any serious scientist to evaluate the probability of fixation, we rely on the diffusion approximation or we use exact models (Moran, Wright-Fisher, et cetera...).

The lower the s, the longer it will take = intuitive, but wrong.

The lower the |s|, the longer it will take = Counter intuitive, but true. Yep, the average time to fixation is the same for s = 0.1 and s = -0.1, even if the latter is deleterious (but, of course, the probability of fixation is higher for s = 0.1).

...and that's why evolution cannot be correctly understood without a healthy dose of mathematics.

Yes, but why do we still have reptiles, or crocodiles, or any form of life really. if an organisms resides in a population with a certain genome and phenome and all the other -omes it should change on a gradient really quite smoothly in relation to the probability distribution or diffusion right? Such as in X time regardless a crocodile will have X genetic difference or phenotypes or what not right? It would seem as if the eyeball itself should eventually be changed by such. I would think the only thing that fixes a giving trait in some population reproducing with variance would be natural selection, such as if you happen to live in the ocean.

so if the environment ultimately interacts with any system coupled to it, in this case a organism, how would you quantify that which would predict say why any particular species stays a species so long while others go extinct and or change?

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Can we forget the science for a minute we can go on forever and a day . In the begining there was creation wether you hold true to the single atom containing the building blocks of life or purely evolutionist theory. Our we missing the point evolution yes darwin yes how did it all get going. Can we think beyond creationism and what before that before the universes creation?

Are we subscribing to pure evolution and not conforming to deliberate creation and everything going according to it . Come on you can play with as many chemicals for as long as you like but what about religion is it a creation

of some fundamentalist viewpoint what about christianity . My thoughts on the matter are subscribing purely to intelligence , natural selection crossing the species barriers and evolving reactions yes life moves on but does it do it by accident or is it deliberate. Why then do we have a whole range of accounts that stem to religion we are dismissing thousands of people that have stood testiment to a higher being and supernatural forces, without wanting to go into ghostbusting territory , are we only beginning to learn more through intelligence . If we discover something new we dont say it didnt exist before we learn and then we move on . Science and time alike stop for no man or women as the case maybe , but do we miss so much in that race for higher intelligence . Backtrack for a minute . lets Say the universe was created according to genesis and im no expert on this by the way , lets suppose god wanted a bit of fun being the creator of so much everything according to plan im having some time out and im going to have a bit of fun . Thats what baffles us god has a sense of humour and he has kept us tied up in knots over it for an age . God the creator has set us up for his own amusement its like reading the funnys in the daily newspaper listening in to some of the purely evolutionist theorists and that is not a put down.

Lets suppose having taken some time out from creation lets call it a tea break and a bit of fun. Introduce a species were from a higher intelligence

lets crash land a mating pair of aliens from another part of the universe so pro creation. Things went a little bit wrong with the evolutionary process so iyll introduce adam and eve and iyll leave the best of the primitive race in also . Higher intelligence and evolution . So if we believe that the is other forms of intelligence in the universe , read the bible it tells us that the is so religion recognizes this . Have we moved to fast having read much of the bible and learnt much from science we have to introduce higher intelligence into the equation of evolution . Atheists have there place aswell .

Lets suppose something else time , In what time man has existed in our planet how long have we been here 11 secs in that 500 billion years or whatever time we consider . Whos to say time is linear lets say time is circular if we subscribe to this we hav a real job finding the join dont we .

The way we all seem to be going on this planet is we will be lucky to reach twelve seconds alters your perception of time really doesnt it . Lets introduce somethink else who controls time if we look at a stopwatch and click the little button it stops the clock then click again and restart .

Our we doomed to failure well lets look at that satanists might say lets raise hell and bring about the end lets not worry about the environment who cares the may not say that also , but then again dont many people in christianity

think along the same lines in the end game we have the mercifull bountys

bestowed upon us , thats not to say were in a egg and spoon race and there will be a prize ceremony at the end. Time its an important function evolution its an important function intelligence masterplans important function .

Freewill participate as you will . Kind regards pantheon.

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Drift is always present, it's just not relevant when the effective population size (N) is very high, but that's actually quite rare for large animals.

Yes, drift is always present. But the probability for fixation and the time it takes for fixation dramatically change with population size. When s = 0 (genetic drift), the probability for fixation is P = 1/2N. Where N = the effective population size. So, if you have a population with N = 10, the probability is 1/20 or 0.05. Take the population to 100 and the probability of fixation drops to 1/200 or 0.005. If the population is 5000, the probability for fixation is 1/10,000. A population size of 5,000 is not that rare for large animals.

There is also the time it takes for fixation. The time to fixation by genetic drift is 2N generations. Again, you can see the effect of increasing population size. If N = 10, the time to fixation is 20 generations. But if N = 1,000,000, the time to fixation = 2,000,000 generations. For bacteria this isn't going to take long since a generation is 20 minutes. But for large with a generation time of as little as 2 years, this woulod be 4 million years, which is just about the average lifespan of a species.

So, as N increases, the probability that a mutation will be fixed by drift decreases dramatically while the time to fixation increases dramatically. This means that, in what we consider "small" populations (1,000 individuals), the importance of drift is negligible.

The equation you gave was about the ultimate probability of a particular mutation being fixed when selection and drift interact. The one I get from Futuyma's evolutionary biology pg 93 (derived by Kimura) is:

P = (1 - e^2Nsq)/(1 - e^-4Nq) where e = the base of natural logarithms = 2.718, N = effective population size, s = selection coefficient, and q = the initial frequency of the allele in the population. For a mutation, q = 1/2N

This equation gives the probability of fixation, as you can see, the effective population size is in it.

However, when s>0 and the population is "large", then the equation reduces to P = 2s and N disappears.

If a beneficial mutation appears, according to your deterministic equation, it will increase in frequency. But this is misleading, even highly beneficial mutations are lost; even if you're the fittest in the group (and having a single beneficial mutation is no guarantee for that), you can still be struck by lightning, be killing by a virus, et cetera... Beneficial mutations are lost all the time, they are just less likely to be lost.

We are talking apples and oranges. I am talking about the inevitability of fixation under selection and you are talking about the effect of genetic drift upon probability of fixation. Yes, when s > 0 the equation says that the frequency will increase. However, yes, you can lose the single individual initially possesing the mutation to accident. Thus, because of genetic drift, an advantageous mutation does not always become fixed in a population. But that doesn't change the deterministic equation; it adds another process.

The equations are clear that, looking at selection, the inevitable effect of positive selection (s > 0) is to fix an allele (mutation) in the population. When s < 0, the inevitable effect of selection is to eliminate that allele from the population. When s = 0, the effect of genetic drift is to either fix or eliminate the new mutation.

However, once the mutation is in several individuals, losing ALL the individuals becomes -- in your terms -- so improbable as to not happen. In that case, the equations are clear that fixation is inevitable. And we end up with the situation I outlined.

The equation you used is a naive equation only used in basic textbooks (and perhaps in other circumstances, but it must be quite rare), it's certainly not used by any serious scientist to evaluate the probability of fixation, we rely on the diffusion approximation or we use exact models (Moran, Wright-Fisher, et cetera...).

The equation I gave is the standard equation to determine the change in frequency from generation to generation under selection. What you have done is changed the terms from a selective advantageous allele will deterministically be fixed to the probability of a particular advantageous mutation being fixed. Yes, you can lose a mutation thru genetic drift but, barring that, the equations are clear that, if s > 0, then the mutation will be fixed. And this ruins the "unrelated probability" that Skeptic is using.

The lower the s, the longer it will take = intuitive, but wrong.

The lower the |s|, the longer it will take = Counter intuitive, but true.

Yep, the average time to fixation is the same for s = 0.1 and s = -0.1, even if the latter is deleterious (but, of course, the probability of fixation is higher for s = 0.1).

Remember, we were talking about selection, not drift. If s = -0.1, what you have is not going to be fixation, but elimination. If s < 0, then delta p will be negative and eventually p will = 0 and that allele will be eliminated from the population, not fixed. What you are trying to say is not that the time to fixation will be the same, but rather the time to either fixation or complete elimination (p = 0) depends on the absolute value of s.

You can get fixation of slightly deleterious alleles with genetic drift. However, at your example of s = -0.1, then plug that into the equation above and see what the probabilities are.

In the begining there was creation wether you hold true to the single atom containing the building blocks of life or purely evolutionist theory.

Define "purely evolutionist theory".

To say it again: EVOLUTION IS NOT ATHEISM. Nor does evolution deal with "the universes [sic] creation". That is cosmology which is part of physics, not biology.

Are we subscribing to pure evolution and not conforming to deliberate creation and everything going according to it .

No. We are talking science, and science is agnostic when it comes to "creation". The most science can say for a theist is this:

"IF you believe in deity and creation for reasons outside of science, then science will tell you the material causes deity used to create. IOW, science will tell you how deity created."Come on you can play with as many chemicals for as long as you like but what about religion is it a creation

of some fundamentalist viewpoint what about christianity .

My thoughts on the matter are subscribing purely to intelligence , natural selection crossing the species barriers and evolving reactions yes life moves on but does it do it by accident or is it deliberate.

Natural selection is "deliberate". As we noted above, the selection part of natural selection is deterministic. What we are saying is that deity does not directly manufacture new species. IF there is a deity, then evolution by natural selection is the secondary cause by which deity creates species. You need to look up "secondary cause". It's a theological term, not a scientific one.

Why then do we have a whole range of accounts that stem to religion we are dismissing thousands of people that have stood testiment to a higher being and supernatural forces,

That's the evidence of the existence of deity: the personal experiences of people. However, because those experiences are not "intersubjective" -- not everyone has them -- they are not part of science.

Science is a limited form of knowing. Science can only deal with material causes. Science cannot say whether there is also a supernatural component to causes. Evolution by natural selection is sufficient as a material cause for the origin of species and the designs in plants and animals. The additional material cause of manufacture by an intelligent entity is not needed. Is deity needed for evolution to function? Science can't answer.

Say the universe was created according to genesis and im no expert on this by the way ,

"according to genesis" is a material cause. And no, it is not possible that the universe was created that way.

Introduce a species were from a higher intelligence

lets crash land a mating pair of aliens from another part of the universe so pro creation.

This is manufacture by the "higher intelligence". You have the entity making the species elsewhere and placing it on the planet. This has been refuted by the scientific data. We can, thru genetics, detect if this happened. It did not.

Have we moved to fast having read much of the bible and learnt much from science we have to introduce higher intelligence into the equation of evolution.

No. There is no need to introduce direct manufacture by a "higher intelligence". We don't need that material cause.

Pantheon, it is POSSIBLE that a "higher intelligence" created the universe by the Big Bang, galaxies, stars, and planets by gravity, life by chemistry, and the diversity of life by evolution. Science can't tell you "yes" or "no" to this. What science can tell you is that the method of creation in the Bible is wrong.

Yes, but why do we still have reptiles, or crocodiles, or any form of life really. if an organisms resides in a population with a certain genome and phenome and all the other -omes it should change on a gradient really quite smoothly in relation to the probability distribution or diffusion right?

No. What you are forgetting is natural selection. This time in the form of purifying selection. Because crocodiles are very good at earning their living by being crocodiles and because they are well-adapted to that niche, as long as the niche remains the same, selection will keep the crocodiles the same. Almost ANY mutation is going to be deleterious to a population that is well-adapted to their environment. Therefore s < 0 and selection will eliminate that mutation and act to keep the population the same.

The species can still change thru genetic drift. However, a population that is well-adapted to its environment/niche is probably going to be large in terms of genetic drift. So change by genetic drift is going to be very slow.

As it happens, the species of crocodile living now are NOT the same species that lived 50 or 100 million years ago. But they are still very similar because of purifying selection: their niche has not changed much in that time. How you "predict" is look at the niche. If the environment and the niche are pretty much the same, then there will be little evolutionary change. Major evolutionary change comes when a population is able to exploit new niches or the environment changes to radically alter the niche. For instance, look at the radiation of the finches on the Galapagos or mammals after the dinos went extinct. Lots of new, unfilled niches for the species to exploit.

It would seem as if the eyeball itself should eventually be changed by such. I would think the only thing that fixes a giving trait in some population reproducing with variance would be natural selection, such as if you happen to live in the ocean.

There are studies showing that if a trait is under two or more positive selections, then that trait cannot be changed. That's how you get "bauplan".

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Lucaspa,

I'll answer your post, but first I want to write a little note about the history of my field. I always find these discussions about drift quite funny. The fact is; nobody believe in drift. Except a small group of people; those who actually study it, that is; theoretical population geneticists and molecular evolutionary biologists, those concerned with how the different mechanisms of evolution shape life. The most funny thing is that drift, and the neutral theory, has achieved such a dominance over population genetics in a short period of time, yet nobody knows about this. Why ? Because it's actually quite complicated, the maths are not always easy to follow for those with no training in math. and it's counter intuitive (probably the key issue, deterministic selection is much easier to understand). In the last couple of years (actually, about 15 years) the neutral theory has been challenged, and I think it will fall, if it's not already done, but there is no way, simply no way we will get back to this naive view that evolution can be explained by the simple pseudo-equation "evolution = variation (mutation) + selection".

If we want evolution to be taken seriously, we'll have to stop whining about creationists and try to teach our theory correctly, and it implies, in my opinion, a bigger emphasis on the foundation of evolution; population genetics, and a more realistic description of the natural selection.

About "selection" vs "selection + drift". If you talk about the probability of fixation, you have to discuss drift (and draft, but that's another issue). Evolution is a stochastic process, not a deterministic one. When you use a deterministic equation with only selection to make a point that any mutation with s>0 will reach fixation, you are making a huge mistake. First of all, it is NOT an equation used to discuss probability of fixation, and as I previously explained, s>0 is no guarantee that the mutation isn't neutral (just look at the definition of "neutral").

You were trying to make a point about the probability of fixation when you said any mutation with s>0 will reach fixation, yet you used an equation which has nothing to do with this. When you say "The equations are clear that, looking at selection, the inevitable effect of positive selection (s > 0) is to fix an allele (mutation) in the population." It's completely off the mark. If you're talking about the near-inevitability of fixation for a mutation with a large effect (s>>1/2N), and if the mutation is already established in the population, then yes, you can ignore drift. But this is not frequent, s = 0.1 might seem small, but it's actually much larger than most beneficial mutations (just take a look at Lynch's new book on the evolution of the genome, 2007).

In short, your equation is completely irrelevant to this question, and yes, population size matters. I completely agree that it doesn't always matter, it's actually a quite complicated debate, but you can't completely ignore it as you do.

Yes, you can lose a mutation thru genetic drift but, barring that, the equations are clear that, if s > 0, then the mutation will be fixed.

It's only clear because you don't use the right equation.

Remember, we were talking about selection, not drift. If s = -0.1, what you have is not going to be fixation, but elimination. If s < 0, then delta p will be negative and eventually p will = 0 and that allele will be eliminated from the population, not fixed. What you are trying to say is not that the time to fixation will be the same, but rather the time to either fixation or complete elimination (p = 0) depends on the absolute value of s.

Remember, we're talking about evolution, we're talking about fixation, we're not talking about an idealized world with only selection.

About the average time to fixation;

You can have fixation with s<0.

You can have extinction with s>0.

The higher the 's', the more likely you are to witness fixation.

But this has nothing to do with the average time to fixation. Your claim that the time to fixation (if fixation there is, as I said) depends on 's' = it's wrong, the time to fixation depends on '|s|', and I pointed this out because it's an interesting result of theoretical population genetics. Most people assume, as you did, that the average time to fixation must always be longer when 's' is least beneficial.

So, as N increases, the probability that a mutation will be fixed by drift decreases dramatically while the time to fixation increases dramatically. This means that, in what we consider "small" populations (1,000 individuals), the importance of drift is negligible.

As always; it depends on the value of 's'. If s is close to 0, then drift will matters, even if the size of the population is very high, and the substitution rate will be constant, so the time to fixation won't really matter.

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this naive view that evolution can be explained by the simple pseudo-equation "evolution = variation (mutation) + selection".

Evolution, no. But adaptation does = variation + selection. Genetic drift can change populations, but it won't give adaptations.

Evolution is a stochastic process, not a deterministic one. When you use a deterministic equation with only selection to make a point that any mutation with s>0 will reach fixation, you are making a huge mistake. First of all, it is NOT an equation used to discuss probability of fixation, and as I previously explained, s>0 is no guarantee that the mutation isn't neutral (just look at the definition of "neutral").

You were trying to make a point about the probability of fixation when you said any mutation with s>0 will reach fixation, yet you used an equation which has nothing to do with this. When you say "The equations are clear that, looking at selection, the inevitable effect of positive selection (s > 0) is to fix an allele (mutation) in the population." It's completely off the mark. If you're talking about the near-inevitability of fixation for a mutation with a large effect (s>>1/2N), and if the mutation is already established in the population, then yes, you can ignore drift. But this is not frequent, s = 0.1 might seem small, but it's actually much larger than most beneficial mutations (just take a look at Lynch's new book on the evolution of the genome, 2007).

Actually, if you look at natural populations, s is often > 0.1. And s = 0.1 is already a "large" s. For a long time evolutionary biologists thought that most s were 0.01 or less. So, I don't know where Lynch got his data. We should compare sources (the original peer-reviewed papers) from Futuyma and Lynch.

If s > 1/4N, then selection is more important than drift. At that point you can ignore drift. So, for s = 0.01 (much smaller than your s = 0.1), then drift is unimportant at a population of 250 or more. Both of these statements come from Futuyma's Evolutionary Biology, Chapter 22.

It seems that you are making drift much more important than it is.

In short, your equation is completely irrelevant to this question, and yes, population size matters. I completely agree that it doesn't always matter, it's actually a quite complicated debate, but you can't completely ignore it as you do.

I didn't ignore it. I simply pointed out, by the math, where N drops out. And again, we are talking about differnt things. You are talking about the probability of any given mutation being fixed.

1. Yes, that will depend on an interaction between drift and selection. When the number of individuals with the variation is small, chance can eliminate the individuals -- thus lowering the overall probability of fixation.

2. What's more, as p approaches 1, the delta p per generation is going to get less and less. And many times there will be an equilibrium between the 2 alleles. This did happen in Lenski's experiment. This also lowers the probability of fixation.

However, in addressing the problem Skeptic brought up, we are still facing the fact that we are not dealing with independent events. Not all 3 mutations for a trait have to appear within a single generation. If they appear sequentially, then selection is going to increase the frequency of that mutation in the population. Do you deny this? Even if we argue about probability of fixation, do you argue that the effect of selection is going to be to increase (rather rapidly) the frequency of the mutation in the population? This is going to mean that it is much more likely that the second mutation will happen in an individual that already has the first mutation. Thus the probability calculations are not going to be what Skeptic thinks they are.

Do you disagree? If so, why?

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Thus the probability calculations are not going to be what Skeptic thinks they are.

Unless you argue that the probability of the mutation is 1, or that the correlation between the mutations is 1, then you have not countered my point. Seriously, what I said was almost tautological.

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• 2 weeks later...

That is definatly an intresting article, but creationists could still put forward an argument

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That is definatly an intresting article, but creationists could still put forward an argument

Who are you talking to, arnoldschwartz? Which article? Is it possible you mean the one in the OP? You should use the quote function of the site to avoid miscommunications and unecessary confusion.

Also, just what arguments do you think creationists could put forward? 'God did it' is not an argument, it's an unsupportable personal belief with no basis in reality and zero evidence in its favor.

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Lucasca,

Actually, if you look at natural populations, s is often > 0.1. And s = 0.1 is already a "large" s. For a long time evolutionary biologists thought that most s were 0.01 or less. So, I don't know where Lynch got his data. We should compare sources (the original peer-reviewed papers) from Futuyma and Lynch.

Futuyma actually says that, on average, beneficial mutation have a coefficient of 's' around 0.1 ? I would be surprised by this. Can you give me the exact reference ? It's an elementary textbook I doubt he covers the complex question of the distribution of fitness effects.

And BTW, it doesn't really mean anything is 's' is around 0.1 unless it remains positive for a long time, this is why molecular evolutionary biology is so useful to answer these kind of questions, it allows us to study long-term patterns.

If s > 1/4N, then selection is more important than drift. I didn't ignore it. I simply pointed out, by the math, where N drops out. And again, we are talking about differnt things. You are talking about the probability of any given mutation being fixed.

[it's s>1/(2N) BTW, and it's a little too optimistic]

Actually, you said;

As long as s (the selection coefficient) is at all positive, the equations are clear that the allele (mutation) will become fixed.

It's a question of probability of fixation, you say it will become fixed (probability approx. 1). And then for some reason you used an equation which has nothing to do with this, it's just an equation to calculate the expected change in frequency with selection, you'll never find this kind of use in a serious paper.

I never said drift was more important, I said it was more important when the product 'Ns' was small. You said pop size didn't matter, and you even said that, as long as s>0, the "equations" (i.e.: the inappropriate equations) showed that fixation would occur. The math, and the science, says otherwise, it's basic population genetics.

Do you disagree? If so, why?

I disagree with the incorrect use of mathematics and the thing you said about the time of fixation, I also think you tend to simplify evolution too much. For your argument against Behe; I couldn't care less. I'm not interested in creationists, unless they publish in serious journal (hint: they won't). I'm much more concerned about the bad use of evolutionary theory by evolutionists.

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