Richard Dawkins' views on non-random natural selection

[jimmypippa]

In answer to the questions about other books, I seem to recall that "The Theory of Evolution" by Maynard Smith (I have an old Pelican copy, the latest edition has a foreword by Richard Dawkins, IIRC) is reasonable at that.

[susu.exp]

A few questions/points.

1. Could someone point to similar alternative books (ie aimed at the general public)to those of Dawkins which more 'correctly' explain evolution by using the 'correct' definition of random etc?

I wish there was one... Two books come to mind, which do an OK job, despite not being about the topic:
David M. Raups "Extinction: bad genes or bad luck?", which introduces random walks with a lower absorbing boundary.
and
Steven J. Goulds "Full House: The spread of excellence from Plato to Darwin", which introduces random walks with a lower reflective boundary and an upper absorbing boundary.
What happens in populations can be modeled as a random walk with an upper and lower absorbing boundary (the so-called Moran Model, named after the biologist whose dispute with Dawkins came up earlier in the thread. The Wright-Fisher model discussed earlier models sucessive generations as steps and is a random process with two absorbing states - extinction and fixation of the allele - the Moran model models each birth and death as a step and fulfills the criteria of a random walk. To nitpick Goulds book: what he describes is better seen as a random process with two absorbing states than a random walk - a slight technical inaccuracy) and so you can get a good impression from the two books. Gould work has the downside of lots of baseball, illustrating that he´s talking about something "quite general about systems" - my personal preference would have been thermodynamics, which would nicely tie in with the good popular literature on that.
That being said, there are technical books that are pretty accessible - Martin A. Nowaks "Evolutionary dynamics" is nice. It does require some maths (differential equations, difference equations, some linear algebra, handling of indices), but it does pay off IMHO.

But a good popular book about stochasticity in evolution is still something we lack - and I´ve noted before I see an increasing tendency of creationists to use this gap in popular knowledge as one they can try and cram their deity in. A little while age, they were pushing a computer program called "Mendels accountant", which showed evolution didn´t work. Now, there was nothing obviously wrong with it (apart from the outcome), it faithfully modeled population genetics. It got mutation and selection absolutely correct and it even did model drift correctly. So what was the problem? The program artificially restricted maximum population sizes to 1000. Real population sizes of course aren´t thus restricted (there´s more than 6 billion of us and let´s not even look at how large the population of gut bacteria is in each of us). Because of the interplay of mutations, drift and selection every population will inevitably go extinct at some point. The smaller the population, the shorter the expected time to extinction gets. And that´s where the program gets it all wrong. But this difference is basically produced by the changes in drift (the mutation and selection terms are the same, no matter how large your population is). Hence the creationists could claim that the program was accurate, because it faithfully modeled selection and mutation. It did not accurately model drift as it happens in larger populations.

And that´s the crux of the matter. Evolution by natural selection and mutation alone does not work and can not work. Hence it´s easy for creationists to shoot down this strawman version of evolution. Evolution by natural selection, mutation and drift does work and is supported by all the evidence we have. Given that drift is the fundamental part of evolution that the lay audience is the least familiar with, the strategy of ignoring drift or misusing drift by creationists is obvious. Any woo is best off using the less understood bits of science to milead lay audiences. Which is why you´ll find significantly less Newtonian mechanics woo than general relativity woo. And fields of science using probability theory (evolution has creationism, thermodynamics has rather sadding numbers of patent applications for perpetuum mobiles and quantum mechanics gave rise to the infamous time cube) are the ones suffering from the worst woo - they are based on maths that don´t feature heavy in school and which is rather counterintuitive. Humans prefer non-probabilistic explanations (it´s easy to find the adaptive benefit in strict cause and effect thinking).
The best defense is education.

2. This argument has been reminding me of Dawkins' chapter in The Extended Phenotype - 'An Agony in Five Fits' where he discusses how he has not been using the term 'fitness' because of the confusion around the term and its many meanings.

Ironically he´s off on one of them: Fitness[3]. It´s not the reproductive success of an individual, but the expected reproductive success. The number of offspring an individual has is a random variable and its fitness is the expected value of that random variable. Imagine an individuals offspring number determined by the roll of a die. It´ll have 1,2,3,4,5 or 6 offspring, each with a probability of 1/6. The fitness will be 3.5 regardless of what is rolled. Note that the individual will never have the same number of offspring. Drift is the cumulative effect of the differences between fitness and actual offspring number.

That being said, I disagree with Dawkins there. "Mass" in physics meant something different to Newton, then it does to Einstein. Should physicists scrag the term? Not to speak of things like "time". Technical terms do change their meaning as new theories are accepted and fitness generally refers to the expected number of offspring an organism has. You go inclusive and you use the mean fitness of carriers of an allele.

3.One specific question and my main one:

In various models there is often the assumption of 'random mating'. What is then usually pointed out is that in real populations this is an assumption that often does not in fact exist - ie mating is not random.

The 'random' here in 'random mating' means what?

That the probability of two organisms mating is independent from any genes. This can be violated if there is sexual selection, or there is a spatial structure to the population. In fact it´s even violated if there is sexual dimorphism (the probability of some new mutant alleles in two males or two females being recombined in the next generation is generally close to 0). In other words: It´s simplifying things a lot. According to the unified neutral theory of biodiversity and biogeography, random mating doesn´t happen in real populations, because organisms the spatial distribution of organisms is a random variable (first irony arising from using random as statistically independent)... And usually this assumtion is used in deterministic approximations with infinite populations (where in fact all randomness vanishes and the error you make by assuming random mating gets lost as well - irony number 2).

From my interpretation of this thread it does not mean equiprobable. Or does it? I'm sure sometimes I've seen it expressed as the possibility that any egg fuses with any sperm?

Well, even that wouldn´t be random mating... Make that "any two gametes".

So when it is stated for the study of a real population that the mating is likely to be 'non-random', non-random means what?
Predetermined?
Adaptive? Is all this really an argument about what is 'adaptive' and what is 'nonadaptive'?

Well, it basically means that real populations:
- are finite.
- are distributed in space.
- often contain different sexes.
- often have sexual selection going on

[sprite]

3.One specific question and my main one:

In various models there is often the assumption of 'random mating'. What is then usually pointed out is that in real populations this is an assumption that often does not in fact exist - ie mating is not random.

The 'random' here in 'random mating' means what?

That the probability of two organisms mating is independent from any genes.

From my interpretation of this thread it does not mean equiprobable. Or does it? I'm sure sometimes I've seen it expressed as the possibility that any egg fuses with any sperm?

Well, even that wouldn´t be random mating... Make that "any two gametes".

So in this instance the 'random' as used by mathematicians does in fact mean equiprobable and this use of 'random' is accepted as being one of more than one use of 'random' by mathematicians - 'random' being used for other meanings as well as 'equiprobable'?

In fact, haven't there been strong arguments before about random not meaning 'equiprobable' in maths circles?

What I'm asking is - does this not show that 'random' has more than one meaning even when used by the mathematical modellers as in 'random mating' where random does in fact mean equiprobable?

[mizvekov]

What I'm asking is - does this not show that 'random' has more than one meaning even when used by the mathematical modellers as in 'random mating' where random does in fact mean equiprobable?

At this point it would be useful if you pointed out exactly where you have read this.

[sprite]

What I'm asking is - does this not show that 'random' has more than one meaning even when used by the mathematical modellers as in 'random mating' where random does in fact mean equiprobable?

At this point it would be useful if you pointed out exactly where you have read this.

What, that random mating means equiprobable mating?

From my interpretation of this thread it does not mean equiprobable. Or does it? I'm sure sometimes I've seen it expressed as the possibility that any egg fuses with any sperm?

Well, even that wouldn´t be random mating... Make that "any two gametes".

Which I interpreted as meaning - yes, random is meaning that the model is one where any two gametes might fuse.

[mizvekov]

What, that random mating means equiprobable mating?

Yes, exactly.

[sprite]

What, that random mating means equiprobable mating?

Yes, exactly.

So you are saying that though the model is one where any two gametes are potentially likely to fuse this does not in fact mean that their fusing is equiprobable?
What would make it equiprobable?

ETA I'm speaking strictly in terms of the use of 'random' in the model - of course it is not random/equiprobable in the real world.

[mizvekov]

What, that random mating means equiprobable mating?

Yes, exactly.

So you are saying that though the model is one where any two gametes are potentially likely to fuse this does not in fact mean that their fusing is equiprobable?
What would make it equiprobable?

ETA I'm speaking strictly in terms of the use of 'random' in the model - of course it is not random/equiprobable in the real world.

It would mean that every member of the population is equally likely to mate with each other (recombine) which does not happen in the real world.
Susu pointed this out above, but there is
1) Different sexes, which for example means two males are never going to have offspring together.
2) Populations are distributed in a geometric space, which means that members which are far apart are less likely to mate than members which are nearby.
3) Sexual selection occurs, which means some members might have genes which make them more likely to mate with partners which have certain phenotypes than others.

[susu.exp]

So in this instance the 'random' as used by mathematicians does in fact mean equiprobable and this use of 'random' is accepted as being one of more than one use of 'random' by mathematicians - 'random' being used for other meanings as well as 'equiprobable'?

As noted above, it means "statistically independent" in this case and that´s not a mathematically adequate use. Note that equiprobability is not a decisive factor. Take a population. Divide it into two groups, depending on whether the digit sum of an organisms birth date is odd or even. Now assume that organisms are twice as likely to mate within any particular member of their own group than with the other one. You´d still have random mating as defined above.

In fact, haven't there been strong arguments before about random not meaning 'equiprobable' in maths circles?

Yes. As noted there, this particular notion stems from misreading an old fashioned definition of random variables as functions of a continuous uniformly distributed random variable on [0,1]. A definition that is equivalent to the modern one, but for didactic reasons isn´t used today.

What I'm asking is - does this not show that 'random' has more than one meaning even when used by the mathematical modellers as in 'random mating' where random does in fact mean equiprobable?

Well, apart from not meaning equiprobable, one should note that "random mating" was a term introduced before random variables had a mathematical definition (it appears first in a 1899 article by Pearson, random variables got their first definition in the 1910s).

That it´s not employing a standard definition should be obvious considering articles like:
BODMER and FELSENSTEIN (1967) "LINKAGE AND SELECTION: THEORETICAL ANALYSIS OF THE DETERMINISTIC TWO LOCUS RANDOM MATING MODEL", Genetics 57: 237-255

[sprite]

What, that random mating means equiprobable mating?

Yes, exactly.

So you are saying that though the model is one where any two gametes are potentially likely to fuse this does not in fact mean that their fusing is equiprobable?
What would make it equiprobable?

ETA I'm speaking strictly in terms of the use of 'random' in the model - of course it is not random/equiprobable in the real world.

It would mean that every member of the population is equally likely to mate with each other (recombine) which does not happen in the real world.
Susu pointed this out above, but there is
1) Different sexes, which for example means two males are never going to have offspring together.
2) Populations are distributed in a geometric space, which means that members which are far apart are less likely to mate than members which are nearby.
3) Sexual selection occurs, which means some members might have genes which make them more likely to mate with partners which have certain phenotypes than others.

You are not reading what I'm writing.
As I've said twice before, I'm talking about the use of the words 'random' and 'non-random' by mathematical modellers when they model populations.

Why is it ok to use the terms random and non-random to mean equiprobable (in the model) and biased (in reality) respectively when, according to mjpam, for mathematicians even the biased is 'random' ie both are random?

[mizvekov]

You are not reading what I'm writing.
As I've said twice before, I'm talking about the use of the words 'random' and 'non-random' by mathematical modellers when they model populations.

Why is it ok to use the terms random and non-random to mean equiprobable (in the model) and biased (in reality) respectively when, according to mjpam, for mathematicians even the biased is 'random' ie both are random?

I'm asking where you have read random used like this exactly because I want to to give you a concise answer.
It could be obsolete literature, it could be an article meant to lay people, etc.

[sprite]

So in this instance the 'random' as used by mathematicians does in fact mean equiprobable and this use of 'random' is accepted as being one of more than one use of 'random' by mathematicians - 'random' being used for other meanings as well as 'equiprobable'?

As noted above, it means "statistically independent" in this case and that´s not a mathematically adequate use. Note that equiprobability is not a decisive factor. Take a population. Divide it into two groups, depending on whether the digit sum of an organisms birth date is odd or even. Now assume that organisms are twice as likely to mate within any particular member of their own group than with the other one. You´d still have random mating as defined above.

So it does boil down to 'adaptive' and 'non-adaptive'.

In fact, haven't there been strong arguments before about random not meaning 'equiprobable' in maths circles?

Yes. As noted there, this particular notion stems from misreading an old fashioned definition of random variables as functions of a continuous uniformly distributed random variable on [0,1]. A definition that is equivalent to the modern one, but for didactic reasons isn´t used today.

What I'm asking is - does this not show that 'random' has more than one meaning even when used by the mathematical modellers as in 'random mating' where random does in fact mean equiprobable?

Well, apart from not meaning equiprobable, one should note that "random mating" was a term introduced before random variables had a mathematical definition (it appears first in a 1899 article by Pearson, random variables got their first definition in the 1910s).

That it´s not employing a standard definition should be obvious considering articles like:
BODMER and FELSENSTEIN (1967) "LINKAGE AND SELECTION: THEORETICAL ANALYSIS OF THE DETERMINISTIC TWO LOCUS RANDOM MATING MODEL", Genetics 57: 237-255

Thanks susu.
So 'random' as in when a model 'assumes random mating' means in fact an assumption of no adaptive bias and not that there is equal probability that any two gametes might fuse.

[sprite]

You are not reading what I'm writing.
As I've said twice before, I'm talking about the use of the words 'random' and 'non-random' by mathematical modellers when they model populations.

Why is it ok to use the terms random and non-random to mean equiprobable (in the model) and biased (in reality) respectively when, according to mjpam, for mathematicians even the biased is 'random' ie both are random?

I'm asking where you have read random used like this exactly because I want to to give you a concise answer.
It could be obsolete literature, it could be an article meant to lay people, etc.

Hanna kokko's 'Mathematical Modelling for Field Biologists'

And at least one paper IIRC, Kondrashov's 'Classification of hypotheses on the advantage of amphimixis'.
(Have to rush off for now but will check later).

In both cases they are making points about possible consequences of 'the assumption of random mating' in models.
I'm just curious about what 'random' (and non-random') means in these contexts as it is not defined and would not even be distinguishing between two different things according to how 'random' is being defined by especially mjpam.

[mizvekov]

In both cases they are making points about possible consequences of 'the assumption of random mating' in models.
I'm just curious about what 'random' (and non-random') means in these contexts as it is not defined and would not even be distinguishing between two different things according to how 'random' is being defined by especially mjpam.

I don't know why you are still asking this after susu above made it quite clear that 'random mating' is a term that was introduced into biology before random was defined in mathematics, almost a century ago.
You should just not read here into the words separately and try to make sense of it, and instead look at exactly what biologists mean with 'random mating'.

[susu.exp]

So it does boil down to 'adaptive' and 'non-adaptive'.

Not really. It does boils down to: If our population was infinite and there was no selection, would we see the Hardy-Weinberg equilibrium. I.e. "random mating" removes all effects that disturb HW apart from selection and drift.
The "adaptive" vs. "non-adaptive" distinction would matter to a disturbance of HW through selection, not through non-random mating.

So 'random' as in when a model 'assumes random mating' means in fact an assumption of no adaptive bias and not that there is equal probability that any two gametes might fuse.

No. It´s just no genetic bias apart from adaptive biases. Assume youve got an allele A with a frequency of f_A and an allele A' with a frequency of f_A'. Now, adaptive bias would lead to changes in the frequency. These don´t matter we get new frequencies for both. Under random mating, we expect AA to have a frequency of f_A², A'A' of f_A'² and AA' of 2f_Af_A'. Anything that disturbs this expected value further - a preference of A to mate with A (assortative mating) or with A' (dissortative mating) would remove random mating.

[sprite]

So it does boil down to 'adaptive' and 'non-adaptive'.

Not really. It does boils down to: If our population was infinite and there was no selection, would we see the Hardy-Weinberg equilibrium. I.e. "random mating" removes all effects that disturb HW apart from selection and drift.
The "adaptive" vs. "non-adaptive" distinction would matter to a disturbance of HW through selection, not through non-random mating.

So 'random' as in when a model 'assumes random mating' means in fact an assumption of no adaptive bias and not that there is equal probability that any two gametes might fuse.

No. It´s just no genetic bias apart from adaptive biases. Assume youve got an allele A with a frequency of f_A and an allele A' with a frequency of f_A'. Now, adaptive bias would lead to changes in the frequency. These don´t matter we get new frequencies for both. Under random mating, we expect AA to have a frequency of f_A², A'A' of f_A'² and AA' of 2f_Af_A'. Anything that disturbs this expected value further - a preference of A to mate with A (assortative mating) or with A' (dissortative mating) would remove random mating.

susu - that has clarified those particular points well.

[mjpam]

the so-called Moran Model, named after the biologist whose dispute with Dawkins came up earlier in the thread.

Actually, the Moran model is named after P. A. P. Moran, not Larry Moran (see: e.g., Blythe and McKane (2007)).

[susu.exp]

Actually, the Moran model is named after P. A. P. Moran, not Larry Moran (see: e.g., Blythe and McKane (2007)).

I hang my head in shame. Yes, that´s absolutely correct and I got them confused.

[mjpam]

I think that and my previous post in this thread is about all I can do for now; there IS a new paper on constructive neutral evolution being written right now, and they should have it out within the coming year sometime. I'll let you know when that happens.

Could this be it:

Stoltzfus, A. (2009) Climbing Mount Probable: Mutation as a Cause of Nonrandomness in Evolution. Journal of Heredity, 100(5): 637-647.

[Psi Wavefunction]

I think that and my previous post in this thread is about all I can do for now; there IS a new paper on constructive neutral evolution being written right now, and they should have it out within the coming year sometime. I'll let you know when that happens.

Could this be it:

Stoltzfus, A. (2009) Climbing Mount Probable: Mutation as a Cause of Nonrandomness in Evolution. Journal of Heredity, 100(5): 637-647.

Not it but I just saw that one on a recent Googling spree. A lot of math, IIRC (cell biologist here: me like pictures, me no like equations; equations complicated, pictures easy. Yeah. Statistics can turn pictures into math. That's all the math me needs. No moar. )

The new paper involves several authors, and would be a little less dry; Stoltzfus tends to write a little dense. His coauthors should hopefully fix that a little

Actually, a much less dense (and quite interesting) application of neutral theory can be found in Lukes et al. 2009 PNAS, especially towards the end. (free access hereor here; both sites are down at the moment; possibly because of a current power outage in one of the biol buildings (why the fuck would the servers be kept there anyway!?))

[allanm]

My Two Cents by Kent Brockman

Drift.

If alleles do not affect their own survival by virtue of their consequences, then they are subject to drift alone. True neutrality at a locus demands that every sequence possess equal fitness. Otherwise, sequence would matter - if a beneficial allele X arises, then all sequences not-X are instantly rendered relatively detrimental. But from any starting population of neutral alleles, numbered 1 to N, we can be sure that one of those alleles will come to be the ancestor at its locus in every single member of a future population.

In respect of the starting population, then, drift is not biased. The favoured allele is as ‘random’ as one throw of an N-sided dice. Of course, during the evolution of the allele’s progress, we would note that, as some of the original N numbered alleles are lost, their places are taken by varying numbers of survivors. The more one particular survivor comes to dominate, the more we would be inclined to bet on its ultimate success – this is what is presumably meant by the suggestion made elsewhere that “Drift is biased in favour of the most numerous allele”. But … that doesn’t stop drift being a random, unbiased process with respect to any starting population. When we come back at an intermediate point and note that allele X is now in 50% of the population, that doesn’t mean that drift has become biased. Essentially, we can completely ignore the actual character of the alleles involved – they are meaningless sequences. If 50% of them are the same, so what? That simply means that drift from a previous starting population has proceeded part-way to fixation. But this population too contains a single future “ancestor of everyone” – it may be a descendant of the original allele X, or it may be some other – which is how new mutations can become fixed.

So, with respect to a starting population, drift will fix a random one of their number by the non-random (but unbiased) process of sampling.

Selection

If an allele can influence its own survival, then it can be subject to selection … and drift. Until it helps its first bearer to survive, then it is in exactly the same boat as its neutral cousin. As far as recessive alleles are concerned, that is their fate for some time to come, until either copies are met, or there is a mutation to dominance. And genes are not selected in every life … though it is nigh impossible to tell in any given case. In those lives that they do not influence, frequencies must change by drift, even for non-neutral alleles.

So … a part of Natural Selection is governed by …uh … ‘chance’ – opportunities for an allele to influence its own survival are dictated by circumstances. On those occasions, the allele is still, unavoidably, subject to drift.

I guess this is why NS is not quite “the exact opposite of random”, if by NS we mean the way in which a non-neutral allele progresses through a population (there are plenty who insist that NS is the cause of any allele’s frequency change in a population, but I reserve it for fitness differentials). The “exact opposite of random” would depend on your definition of random in the first place, of course, but we might suggest “entirely predictable”, or “fixed” – selection isn’t quite that, but it certainly ain’t bleedin’ random!

As a practical matter, drift and selection may be impossibly tangled. The desire to tease out adaptive evolution from non-adaptive requires statistical analysis of the numbers, and the reality of any apparent departure from the ‘null hypothesis’ of drift depends on the confidence level chosen.

I think the mathematicians might have to take a chill-pill on this one. Yes, there is a technical definition, and maybe it’s this and maybe it’s that. But English-speaking people (including non-mathematical biologists) will always mean something by “random” that will forever get the mathematicians’ goat. The mathematicians know EXACTLY what we mean, and will spend the rest of their lives trying to get us numpties to understand.

OK, I blether - you want a crystalline discussion of the issues, try here:

http://en.wikipedia.org/wiki/Talk:Randomness#Disputed

[mizvekov]

My Two Cents by Kent Brockman

Drift.

If alleles do not affect their own survival by virtue of their consequences, then they are subject to drift alone. True neutrality at a locus demands that every sequence possess equal fitness. Otherwise, sequence would matter - if a beneficial allele X arises, then all sequences not-X are instantly rendered relatively detrimental. But from any starting population of neutral alleles, numbered 1 to N, we can be sure that one of those alleles will come to be the ancestor at its locus in every single member of a future population.

Be careful with "we can be sure". Even if the allele is truly neutral, we can't predict when exactly it will be fixated, only mean time to fixation, hence why it's stochastic.

In respect of the starting population, then, drift is not biased. The favoured allele is as ‘random’ as one throw of an N-sided dice.

Only because this unlikely population has no variety of neutral alleles, but otherwise, the favored allele is the most frequent one. If all alleles have an equal frequency, then yes ofcourse it would be 'unbiased' as far die.

Of course, during the evolution of the allele’s progress, we would note that, as some of the original N numbered alleles are lost, their places are taken by varying numbers of survivors. The more one particular survivor comes to dominate, the more we would be inclined to bet on its ultimate success – this is what is presumably meant by the suggestion made elsewhere that “Drift is biased in favour of the most numerous allele”. But … that doesn’t stop drift being a random, unbiased process with respect to any starting population.

Nobody disagrees that drift is random, afterall it's a result of the random sampling of a population. But the bias seen here clearly results from looking identical alleles as the same thing. Your position would make sense if you took alleles to be 'different alleles' even if they are identical to others. The yes, looking at it this way, drift does not favor particularly any one of them.

When we come back at an intermediate point and note that allele X is now in 50% of the population, that doesn’t mean that drift has become biased. Essentially, we can completely ignore the actual character of the alleles involved – they are meaningless sequences. If 50% of them are the same, so what? That simply means that drift from a previous starting population has proceeded part-way to fixation. But this population too contains a single future “ancestor of everyone” – it may be a descendant of the original allele X, or it may be some other – which is how new mutations can become fixed.

Answered above, I think.

So, with respect to a starting population, drift will fix a random one of their number by the non-random (but unbiased) process of sampling.

Whaat? This makes no sense. Besides contradicting yourself, drift is random, afterall it's the result of the random sampling of the population. Also, why would you even qualify a non-random process as unbiased? This does not compute my friend.

Selection

If an allele can influence its own survival, then it can be subject to selection … and drift. Until it helps its first bearer to survive, then it is in exactly the same boat as its neutral cousin. As far as recessive alleles are concerned, that is their fate for some time to come, until either copies are met, or there is a mutation to dominance.

You make here the unfounded assumption that recessive alleles cannot offer fitness advantage. They can even if they are accompanied of a dominant one in diploids. See heterozygous advantage to malaria in Sickle Cell Anemia alleles.

And genes are not selected in every life … though it is nigh impossible to tell in any given case. In those lives that they do not influence, frequencies must change by drift, even for non-neutral alleles.

So … a part of Natural Selection is governed by …uh … ‘chance’ – opportunities for an allele to influence its own survival are dictated by circumstances. On those occasions, the allele is still, unavoidably, subject to drift.

I guess this is why NS is not quite “the exact opposite of random”, if by NS we mean the way in which a non-neutral allele progresses through a population (there are plenty who insist that NS is the cause of any allele’s frequency change in a population, but I reserve it for fitness differentials). The “exact opposite of random” would depend on your definition of random in the first place, of course, but we might suggest “entirely predictable”, or “fixed” – selection isn’t quite that, but it certainly ain’t bleedin’ random!

As a practical matter, drift and selection may be impossibly tangled. The desire to tease out adaptive evolution from non-adaptive requires statistical analysis of the numbers, and the reality of any apparent departure from the ‘null hypothesis’ of drift depends on the confidence level chosen.

Evolution is a non-linear, very chaotic process. You can't really 'untangle' drift from selection and not lose a lot of important emergent effects.

I think the mathematicians might have to take a chill-pill on this one. Yes, there is a technical definition, and maybe it’s this and maybe it’s that. But English-speaking people (including non-mathematical biologists) will always mean something by “random” that will forever get the mathematicians’ goat. The mathematicians know EXACTLY what we mean, and will spend the rest of their lives trying to get us numpties to understand.

I agree, but Richard never get's on this side of evolution, and he makes these statements that highly contradict it. So maybe while he might be doing good teaching all kinds of people by keeping it simple, someone who wants to get into ie population genetics will have to 'unlearn' many things he says.

[allanm]

My Two Cents by Kent Brockman

Drift.

If alleles do not affect their own survival by virtue of their consequences, then they are subject to drift alone. True neutrality at a locus demands that every sequence possess equal fitness. Otherwise, sequence would matter - if a beneficial allele X arises, then all sequences not-X are instantly rendered relatively detrimental. But from any starting population of neutral alleles, numbered 1 to N, we can be sure that one of those alleles will come to be the ancestor at its locus in every single member of a future population.

Be careful with "we can be sure". Even if the allele is truly neutral, we can't predict when exactly it will be fixated, only mean time to fixation, hence why it's stochastic.

We can be sure that it will – we cannot be sure when.

In respect of the starting population, then, drift is not biased. The favoured allele is as ‘random’ as one throw of an N-sided dice.

Only because this unlikely population has no variety of neutral alleles, but otherwise, the favored allele is the most frequent one. If all alleles have an equal frequency, then yes ofcourse it would be 'unbiased' as far die.

No, my point was that, under drift, the detailed classification of the alleles does not matter. Take any group of N undefined instances of a locus, and one will (at some probabilistically-influenced point in the future) become the LCA at this locus. If half this N are actually of type A, and 25% each of type B and C respectively, then that says something about the probability that this winner will be drawn from the classes A, B or C. Such a population will most likely get to all-A, and a damn sight quicker than a single A in a sea of not-A’s. But (ignoring mutation) that A+B+C population is but a stage on the evolutionary path from a single A to a population consisting entirely of descendants of that single A - the path from inception to fixation (or extinction, agreed). As an aside, I think more could be made of the 50% 'tipping point' in an allele's progress - we always talk of time to fixation. If more than half the population have it, then it is both established as a 'typical' character, and the favourite to win if fitnesses remain unchanged.

Of course, during the evolution of the allele’s progress, we would note that, as some of the original N numbered alleles are lost, their places are taken by varying numbers of survivors. The more one particular survivor comes to dominate, the more we would be inclined to bet on its ultimate success – this is what is presumably meant by the suggestion made elsewhere that “Drift is biased in favour of the most numerous allele”. But … that doesn’t stop drift being a random, unbiased process with respect to any starting population.

Nobody disagrees that drift is random, afterall it's a result of the random sampling of a population. But the bias seen here clearly results from looking identical alleles as the same thing. Your position would make sense if you took alleles to be 'different alleles' even if they are identical to others. The yes, looking at it this way, drift does not favor particularly any one of them.

Which I was. Perverse, perhaps, but that’s how I look at it. I think I am guilty of frequent misuse of “allele”, when I simply mean a single instance of a sequence, not a class of like sequences …

So, with respect to a starting population, drift will fix a random one of their number by the non-random (but unbiased) process of sampling.

Whaat? This makes no sense. Besides contradicting yourself, drift is random, afterall it's the result of the random sampling of the population. Also, why would you even qualify a non-random process as unbiased? This does not compute my friend.

I agree. Perhaps I could insert my thought processes: “So, with respect to a starting population [each distinguished only by the fact that it is a distinct unit], drift will fix a random [equiprobable] one of their number by the non-random [er … wrong!] (but unbiased [each generation’s sampling process is the same as the last]) process of sampling.

No clearer, but that’s what I was driving at.

[mizvekov]

Be careful with "we can be sure". Even if the allele is truly neutral, we can't predict when exactly it will be fixated, only mean time to fixation, hence why it's stochastic.

We can be sure that it will – we cannot be sure when.

If you discount things like the population becoming extinct before, and other such inconveniences, then yes
Otherwise, I think we are on the same page there

[kiki5711]

“allele”

sounds like a pretty name