Well, repeated mutations of the same gene rising to high frequency in different populations experiencing the same conditions is just one of those magic operations of chance.

And when mutations of the same genes rise to high frequencies in human populations with low UV exposure, that's even more magical chance.

maybe i didn't write that clearly. a priori, one might chalk depigmentation in cave fish up to drift (this was, i believe, darwin's hypothesis). the molecular evidence--multiple convergences, including independent mutations in the same gene--is powerful evidence that it is instead due to strong positive selection.

I have picked up somewhere that pigment cells use a lot of energy to make the pigment - so that loss of pigmentation has been explained as evolving as a metabolic economy measure in these cells.

I wasn't aiming at you - not on this, anyhow. Other people.

To me the unclear part was this:

[...] the presumably short time period that these fish populations have been isolated (I say presumably short because I can't find any numbers on this, but the different populations can interbreed freely) [...]

I wondered how the heck isolated populations could be interbreeding - it took me a while to realize you were talking about fertile hybrids produced in captivity, not in the wild. Granted, I'm a little slow sometimes.

As for selection vs drift, I agree more with p-ter's post than with his comment. I think both convergence and multiplicity of alleles underlying that convergence are actually consistent with drift. When purifying selection on a gene is removed, why can't several different loss-of-function alleles all drift upward (regardless of whether the scope is one population or several populations)? This could be called "convergent decay." To illustrate the same argument with a different interlocutor:

Well, repeated mutations of the same gene rising to high frequency in different populations experiencing the same conditions is [sarcastically] just one of those magic operations of chance.

...OK, granted, it's not "chance" - but it could just be parallel cases of loss of function, by drift, of a gene which no longer experiences purifying selection because of novel conditions. That doesn't mean that selection is operating. If neither positive nor negative selection operates, various loss-of-function alleles must drift upward.

But, a short timescale (evidenced by fertile hybrids) means a high selection coefficient, as implied in p-ter's post; it seems to me like those are the things which really make us reject drift here.

What the diversity of loss-of-function alleles demonstrates is that the phenotype is derived and convergent, rather than being present in a non-cave-dwelling ancestor. But that doesn't rule out "convergent decay", and so it's a further question whether the pallid eyeless guys are fitter (ie, whether it drift or was it positive selection that fixed that phenotype).

But - maybe I'm confused about some or all of this.

Hey GCochran ... great article in Edge ... about the best there.

I heard the story bgc is giving but for blindness among cavefish before. I hadn't thought of it applying to pigment.

When purifying selection on a gene is removed, why can't several different loss-of-function alleles all drift upward (regardless of whether the scope is one population or several populations)? This could be called "convergent decay."

I think that's a fair point--if, say, the common ancestor of a number of species had a gene for smelling compound X, then that gene became a pseudogene in all the species that adapted to environments without compound X, that wouldn't necessarily be evidence for positive selection. In the pigmentation case, it's plausible loss of function could be constrained to a couple loci due to pleiotropic effects.

I think having a number on the divergence times between the populations of cavefish here is pretty important--if, like i guess, it's pretty recent, that's stonger evidence for positive selection. One could also look at the sequence around these loci for other evidence of selection (in LD, diversity, etc.)

If providing the function cost anything at all, then it would be easy for the net fitness effect to turn negative when the purpose of of the function went away. In that case there would be positive selection for null variants, which acts far more rapidly than drift, at least for populations of any size. On the other hand, cave fish populations might be quite small. Some, like the desert pupfish, certainly are.

if, say, the common ancestor of a number of species had a gene for smelling compound X, then that gene became a pseudogene in all the species that adapted to environments without compound X, that wouldn't necessarily be evidence for positive selection.

This is why I never understand drift - how could that be - how could this pseudogene make it to fixation without there being some advantage to losing its function? I probably just can't grasp the math, but I find it hard to believe that a trait without any advantage whatsoever can manage to swamp an entire population.

ziel,
You can more clearly intuit how this can happen randomly if you contemplate the larger picture: particularly, the fact that the vast majority of new neutral alleles will go extinct rather than fixing. Almost all will go extinct almost immediately; a paltry few will reach a significant frequency, and most of those will also go extinct fairly soon.

What's on the other side of the balance, is the fact that the supply of new mutations is rather plentiful and totally indefatigable.

I probably just can't grasp the math, but I find it hard to believe that a trait without any advantage whatsoever can manage to swamp an entire population.

any new neutral mutation has a 1/N probability of reaching fixation in the population (where N is the effective population size). there are many mutations that could possibly knock out the function of a gene. over time, all of these mutations will occur in someone many, many times. so if there's no selection against those mutations, the probability that one of them will reach fixation in the population is 1.

This is why I never understand drift - how could that be - how could this pseudogene make it to fixation without there being some advantage to losing its function? I probably just can't grasp the math, but I find it hard to believe that a trait without any advantage whatsoever can manage to swamp an entire population.

no math needed though. isn't the current empirical finding still that most molecular polymorphism is neutral? IOW, no matter what a prior theory you might have problems grokking, you need to plug into your prior assumptions the reality that on the molecular level if you don't know anything about a polymorphism you should assume it's neutral.

also, see cites for the nearly neutral theory of the waters of the maths you do wish to surf....

If providing the function cost anything at all, then it would be easy for the net fitness effect to turn negative when the purpose of of the function went away. In that case there would be positive selection for null variants, which acts far more rapidly than drift, at least for populations of any size. On the other hand, cave fish populations might be quite small. Some, like the desert pupfish, certainly are.

Aside from the pop size asterisk, I think this point prevails over the point I was trying to make.

(Although if I were more relatively anti-adaptionist than I am, I might object that it's more deductive than empirical - to the extent that that matters).

There may be some ambiguity in this discussion between drift and mutation pressure. Drift, by definition, has no preferred direction, but mutation pressure tends in the direction of reducing the size or functionality of existing organs. E.g., mutations affecting the eyes are far more likely to reduce vision than to improve it. In the absence of selection to maintain vision (as in dark caves), the accumulation of mutations (not necessarily all of the same kind) will eventually result in blindness. Whether there is enough time for mutation pressure to explain the loss of vision, pigmentation, etc, in caves is a quantitative matter. With mutation rates of the order of 1 in 100,000 per generation per locus this may seem unlikely, but there may be many different mutations potentially affecting a trait, so the overall rate of deterioration for a trait may be much higher than 1 in 100,000.

Thanks - comments and links very helpful. At least, I think I'll be able to appreciate the selection/drift debates a little more.

One of the mutation involved here is a frameshift that totally changes the protein: another changes a significant amino acid.


Neither is the most neutral-looking mutation that ever came down the pike.

Neither is the most neutral-looking mutation that ever came down the pike.

well, both are certainly functional. but the type of mutation conatains no information about the selection coefficient on it, the devil's advocate would say. a mutation that changes a neutral phenotype is necessarily neutral.

pter -- *no* information? might be a little strong. regression analysis with results of expermental evolution studies ( like lenski) would prob show sig mutual information btwn variant functional category and value of s. likely also applicable to diploid though obviously empiricalvalues of s much more fraught.

a mutation that changes a neutral phenotype is necessarily neutral

Provided that is its only effect. Part of the problem is that mutations affecting a trait like pigmentation may have all sorts of other effects (e.g. on metabolism) that are not so obvious.

"a mutation that changes a neutral phenotype is necessarily neutral"

Er, what? Neutrality is something that always requires a sotto voce "ceteris paribus" because it can only be used to describe extant variation within a fixed environment. It's a comparison between two possible states of an organism and a judgment that they're interchangeable as far as inclusive fitness is concerned. A novel mutant that isn't freely interchangeable in this sense is necessarily non-neutral; likewise, a change in the environmental conditions can make a previously neutral variant become non-neutral. There's no such thing as a neutral phenotype in se.

So the question is about our ability to infer fitness consequences, and the Devil's Advocate is wrong: the type of mutation does too give us some information about the range of selection coefficients it might have. It's just probabilistic and needs to be interpreted in the light of a larger body of information. There are probably ways to quantify this with some empirical help, even using existing tools.

yes, ok, people make fair points--the distributions of selection coefficients on mutations of different types are certainly different.

but conditional on knowing the effect of a mutation (in this case, they have a massive impact on pigmentation, and potentially other things), the type of mutation (frameshift, etc) carries no additional information with regards to selection.

isn't the current empirical finding still that most molecular polymorphism is neutral?

The key word is polymorphism. Under neutral selection, you would expect to see polymorphism. If one variant becomes fixed, that probably means that it has some advantage.

In other words, Ziel's intuition is correct. A single mutation isn't likely to become fixed if it is neutral. Of course, in very small populations is becomes more likely.

A single mutation isn't likely to become fixed if it is neutral

a single mutation isn't likely to become fixed if it's beneficial either.

a single mutation isn't likely to become fixed if it's beneficial either

So if you see that a single mutation has become fixed, then it is very likely to be beneficial.

So if you see that a single mutation has become fixed, then it is very likely to be beneficial.


Not necessarily. In a population of N diploid individuals, in which all alleles at a locus are selectively neutral, and in the absence of further mutations, any single existing mutation has a probability 1/2N of ultimately becoming fixed by genetic drift, since one of the 2N genes in the population is bound to be fixed, and each of them has an equal chance. In a large population 1/2N is very small, but in a small population, such as the founders of a cave species, it may be substantial.

The classic '2s' formula for the probability of fixation of an advantageous mutation, where s is its selective advantage, is only valid for large populations. In small populations it must be greater than 1/2N, which itself may be greater than 2s. (At least, I think so.... I haven't checked the 'bibles'.)

So if you see that a single mutation has become fixed, then it is very likely to be beneficial.

Not quite. Let's pretend an allele can only change frequency due to either drift or positive selection, but not both.

P(fix | change due to drift) = 1/2N

P(fix | change not due to drift) = 2s

P(change not due to drift | fix) = [P(change not due to drift) * 2s] / P(fix)

P(change due to drift | fix) = [P(change due to drift) * 1/2N] / P(fix)

Comparing these last two -- if we observe a new mutant fixing, what's the probability that it was due to drift or selection -- breaks down to comparing:

(1 - P(change due to drift)) * 2s

vs.

P(change due to drift) * 1/2N

N and s we could figure out in principle, but the rub is the quantity P(change due to drift) -- the probability that a new mutant is neutral rather than favored.

In this toy example, what matters is how P(drift) compares to 4Ns / (4Ns + 1). If P(drift) is less than it, selection was more likely the cause of change; if greater than it, drift was more likely; if equal, we can't tell.

Although we have a quantitative criterion, we can't figure out where P(drift) belongs in any given case -- and so we have to go by qualitative things like "it changes a protein," "the population was pretty large," "the selective advantage in experiments is huge," etc.

(writing this at 7am, so feel free to fix typos)

The classic '2s' formula for the probability of fixation of an advantageous mutation, where s is its selective advantage, is only valid for large populations.

The key assumption regarding N is that 2Ns is large enough for e^(-2Ns) to be ~ 0. How "approximately," I don't know.

Even if we don't use approximations, the fixation probability is still a function of N and s only, which are already in the expressions to be compared. It'll just look a lot uglier!

The important part is that we can't know the prior probability of a new mutant being neutral.

Even if we don't use approximations, the fixation probability is still a function of N and s only, which are already in the expressions to be compared. It'll just look a lot uglier!

No, it also depends on the mutation rate. The reason I wouldn't expect neutral mutations to fix, ever, is that new ones keep coming along.

Of course, if the population is small enough, the chance of fixation becomes significant - both because 1/2N is larger, and because the mutation rate of the population is lower.

The likelihood of a given mutation having an advantage s, s > 0, depends upon the degree to which the population in question is well-adapted to the environment it's currently in. If the population is poorly adapted to that environment - which would likely be the case in a recently established population of cave fish - there would be a lot of room for improvement, and the probability of a mutation with s well above zero would be drastically increased. Of course selection would also operate strongly on standing variation, to the degree that existing variants happened to solve the new problems of cave life. You would expect rapid adaptive genetic change in such a population, far more rapid than in ancestral stocks that stayed in rivers or lakes.

No, it also depends on the mutation rate. The reason I wouldn't expect neutral mutations to fix, ever, is that new ones keep coming along.

If you want to introduce mutation, that's also true for selected alleles -- they mutate also, and so technically will rarely be at 100% in the population. Even when a new neutral mutant shows up, it exists in a single copy, and so could be easily lost in a couple generations by drift. And unlike a favored allele, it doesn't have anything to give it an extra boost once its frequency is high enough to avoid being lost soon.

So, nearly fixed neutral alleles face little competition from new neutral mutants, unlike a favored allele -- where a new mutant may do the job better.

At equilibrium, the homozygosity in a drift-mutation model is 1 / (4Nu + 1), where u is the mutation rate. Plug in values of 2N and u, and you'll see that unless u is really high compared to population size, drift will essentially "fix" one version of the neutral allele, i.e. it will be within some small error of 100%.

For humans, typical mutation rate is 2.5 x 10^(-8), and 4N ancestrally was about 10,000. So at equilibrium, homozygosity will be 99.975%. It may take a very long time, and it may jump around a lot in the meantime, but unless you're looking at a site with an unusually high mutation rate, drift removes essentially all variation.

The likelihood of a given mutation having an advantage s, s > 0, depends upon the degree to which the population in question is well-adapted to the environment it's currently in.

Right. The big problem is how to quantify "degree of adaptedness" -- revolution by better ways of measuring things.

For humans, typical mutation rate is 2.5 x 10^(-8), and 4N ancestrally was about 10,000. So at equilibrium, homozygosity will be 99.975%. It may take a very long time, and it may jump around a lot in the meantime, but unless you're looking at a site with an unusually high mutation rate, drift removes essentially all variation.

If the question is whether cave fish are blind because of drift or selection, the above points to selection. It is exceedingly unlikely that a neutral mutant would fix, given that is starts out as a single copy. In any reasonable time scale, you would expect, at most, polymorphism at the relevant locus.

If the question is whether cave fish are blind because of drift or selection, the above points to selection. It is exceedingly unlikely that a neutral mutant would fix, given that is starts out as a single copy.

Surely this depends partly on the size of the founding population. I guess that in most cave systems it is very small - certainly much smaller than 10,000. It might be smaller than 10. Not that I am advocating drift (or mutation pressure) against selection, just trying to keep an open mind.