Random Genetic Drift: a controversy?

Over my time as a dilettante observer of the science blogging community, I have noticed a certain frisson of controversy over the idea of random genetic drift. Sewall Wright, who with Ronald Fisher and J. B. S. Haldane (Bill Bryson’s observations on Haldane’s research into diving and decompression are entertaining) established the science of population genetics, is credited with coining the phrase in 1929. Thanks to Professor Joe Felsenstein for pointing out his seminal paper.

Will Provine has written a much admired biography of Sewall Wright, Sewall Wright and Evolutionary Biology, and yet has expressed doubt about the significance of genetic drift, culminating in his recent work, The “Random Genetic Drift” Fallacy, available as an E book here. This has caused a storm of comment on the internet. At the ID-friendly blog currently run by lawyer Barry Arrington, there was a portentous post by “News” which generated immense interest and four comments that I failed to notice and it was only when Larry Moran criticized Provine’s book recently at The Sandwalk that I became aware of its existence.

In ignorance of Provine’s doubts, I’ve recently expressed my own inability to grasp the significance of the effect for evolution. Allan Miller has been very gentle and patient with me and OM’s computer simulation was most helpful. In the commments, Joe Felsenstein links to his 1971 paper which should give the mathematically inclined food for thought. It just made my head spin!

So I’m hoping that someone can gently take me by the hand and lead me to the promised land where the effects of random genetic drift are clear to all. I have purchased Provine’s book. At less than three dollars and only 180 pages, why would I not?

172 thoughts on “Random Genetic Drift: a controversy?

  1. Alan Fox,

    I believe Alan Miller is referring to drift’s role in enhancing exploration of the “adaptive landscape” (I put this in quotes because I prefer to think of it as more of a metaphor than an aspect of reality – though others might disagree). Say that you have two peaks in the landscape, representing two fitness optima. One of them is higher than the other, but if an organism is stuck on the lower (local) optima it may have a hard time evolving to the higher (global) optima because in order to do so it must descend into areas of the landscape that have lower fitness in order to move around, and selection will generally not favor this, especially if the fitness troughs are quite low.

    However, drift can facilitate movement around the landscape by randomly altering gene frequencies, thus making it easier to move away from one peak and potentially moving toward another.

    If that sounds horrifically vague – and it probably does! – check out this nice primer from the NCBI:

    http://www.ncbi.nlm.nih.gov/books/NBK21852/

  2. Alan Fox,

    Now, this is a bold claim! How does a process that in the absence of selection will, as Neil says, lead to loss of the alleles that don’t fix, increase the chances of new variation entering the gene pool? This might be the nub of my doubt over drift.

    Do you think drift eliminates variation more than selection does? It’s the other way round. Because of the directional component, selected alleles fix faster and are harder to topple than drift-fixed ones.

    Drift doesn’t increase the chances of new variation entering. That’s mutation, migration and recombination’s job. It does increase the chances of variation sticking around, because it eliminates it more slowly than ‘hard’ selection. So it allows (for example) one half of Behe’s CCC double mutations to reach a certain level in the population before disappearing, creating a substantial additional probability that the double will occur within it, or between two subpopulations with one component each, despite the fact that selection cannot assist the singletons. Same for a new mutation that was initially recessive (as most are). Were it not for drift, new mutations in diploids would rarely get anywhere.

    In such instances, and more generally too, drift allows the traversal of a path that mutation & selection alone could not access. I stand by my bold claim!

  3. Allan Miller,

    Were it not for drift, new mutations in diploids would rarely get anywhere.

    Although I guess in the absence of drift they would not be lost either! Hard to even imagine a scenario without drift.

  4. It may be of interest that, as a practical application, the addition of some simulated ‘thermal shaking’ to search algorithms does much the same thing as drift, in a manner anticipated by Wright long before computing became practical. eg simulated annealing.

  5. Allan Miller,

    Simulated annealing would be like having the population size gradually grow larger, and asking whether the global optimum was found.

    But yes, there is a distinct analogy of the movement among adaptive peaks and the Metropolis Algorithm, which is the basis of the simulated annealing strategy. Wright felt that the processes of genetic drift could play an important role here. Fisher and others have been more skeptical that such situations are common.

  6. Dave Carlson,

    That’s right, although the 2-dimensionality of the landscape is unsatisfactory for conveying the idea that dimensionality itself is increased by drift. Every time an evolutionary step is taken, more genetic space is revealed beyond it. Drift (like recombination) increases the number of directions in which paths can open up.

  7. Allan Miller: […]the Metropolis Algorithm[…]

    Conjures up the analysis of power balance in a dystopian future!

    Worse yet. Named after Nicholas Metropolis, a mathematician at Los Alamos National Laboratory, who was involved in inventing it while developing the hydrogen bomb. (One of his co-authors on the paper was Edward Teller). Hard to get much more dystopian than that.

  8. For those who were trying to figure out how strong was the effect of genetic drift when selection is also present, let me provide a formula for the probability of fixation of a gene. If allele A is initially present in a standard Wright-Fisher model of genetic drift, with an initial gene frequency of p in a diploid population of constant size N, and if the fitnesses of the three genotypes aa, Aa, and AA are in the geometric series 1 : 1+s :  (1+s)^2, then the fixation probability of allele A is

        \[U(p)  =  \frac{1\: -\: e^{-4Nsp}}{1\: -\: e^{-4Ns}}\]

    This is Motoo Kimura’s result of 1958 and 1962. P.A.P. Moran showed some bounds on the true fixation probability for this simple pattern of selection in the Wright-Fisher model that show how extraordinarily accurate Kimura’s formula is in this case.

    Compare the value for s with the value for s = 0, which is simply U(p) = p, and you’ll see how strong natural selection will be in the face of genetic drift: how much genetic drift lowers the fixation probability below 1, and how much bigger the fixation probability is than the expectation under neutrality.

    This does not deal with all the cases discussed in this thread but it should give people a good feel for the interaction of genetic drift and natural selection in a simple case.

  9. Joe Felsenstein,

    A few illustrative examples using the formula:

    (s=selection coefficient, p=initial frequency=neutral expectation, N=allele population size):

    s=0.001 (just 1 extra birth per 1000), p=1/N (single copy):

    Fixation probability U(p) approaches a constant 0.4% at about N=1100 and beyond. p diminishes with increasing N (1 copy is an increasingly smaller proportion of the total, so is less and less likely to be the winner of a neutral contest), but a single-copy advantageous allele has the same probability of fixing regardless of population size, provided N>1100 for this s.

    But U(p)/p – the multiple of the selected probability over the neutral expectation – changes as follows

    N=500 2.31
    N=1000 4.07
    N=10000 39.92
    N=100000 399.2

    ie, as the neutral expectation for a given allele goes down with increasing N, this diminution is balanced by proportionate increase in the selected expectation.

    If we hold p constant with increasing N (ie comparing a single-copy in a population of 500 with an allele at 1/500th frequency in various other populations):

    N=500 U(p) = 0.46%
    N=10000 U(p) = 7.69%

    The increase in U(p) is approximately linear with increase in N up to N=90,000, where U(p) is about 50%. But then things start to climb more rapidly. At N= a million and more, such an allele with current proportion of 1/500 (just 2000 copies in a million) is almost certain to fix.

    Of course, drift is not all about fixation, and s is unlikely to be constant temporally and laterally. But it does illustrate the underpinnings of an adaptationist leaning.

  10. Allan Miller,

    Just two comments on what you said:

    p = 1/N is two copies per population, because these are diploids. (For haploids just replace 4N in the formulas by 2N). For one copy per population use p = 1/(2N).

    The increase of U(p)/p as N passes about 1100 is well-known. The more general rule is that natural selection really begins to have a noticeable effect somewhere above 4Ns = 1.

    A useful approximation to the probability of fixation of one copy in a large population is U(\frac{1}{2N}) \approx 2s. This was discovered by J.B.S. Haldane in 1927 by branching process methods.

  11. Joe Felsenstein,

    p=1/N is two copies per population, because these are diploids.

    Yes, but I defined N as ‘allele population size’ (should perhaps have been locus population size). But I may indeed have misled myself by doing that but not changing the formula accordingly.

  12. Joe Felsenstein,

    The increase of U(p)/p as N passes about 1100 is well-known.

    It was actually the fact that U(p) itself approaches a constant that I was noting. The rate of change of U(p)/p becomes visually linear at pretty small N.

    It’s counter-intuitive that the number of competitors should have no effect on a selected allele’s chances, above a threshold. The relationship p~2s always had me scratching my head. It can beat ’em all with the same likelihood, however many it has to deal with – I suppose because when an allele has an advantage, all competitors are automatically placed at a disadvantage.

  13. Allan Miller:
    It’s counter-intuitive that the number of competitors should have no effect on a selected allele’s chances, above a threshold. The relationship p~2s always had me scratching my head. It can beat ’em all with the same likelihood, however many it has to deal with – I suppose because when an allele has an advantage, all competitors are automatically placed at a disadvantage.

    When an allele is rare almost all of its competitors have the common allele. It’s reproduction is then essentially independent of the reproduction of the other copies of the rare allele. We can consider the probability of loss of each copy’s descendants. The probability that they will all get lost is the probability that the rare allele will get lost.

    The result is that, to this approximation, the probability that the allele will be lost is then a function of the number of copies of it in the population, and the probability of loss will then basically be (approximately) independent of the number of copies of the common allele.

    Another way of putting this is that once there are more than about 1/s copies of the favorable allele in the population, it has a high probability of fixing, as the probability that they all get lost is then small. For your example of s = 0.001 that would mean once there are 1000 copies, the allele will be quite likely to increase to fixation, no matter how many copies of the other allele there are.

  14. Dave Carlson,

    Thanks for trying to help, Dave, though I’m probably incorrigible.. And welcome to to TSZ. Did you look at the simulation by OM I linked to in the OP? It makes sense to me.

    Thanks for the link. I see:

    Random and selective forces should not be thought of as simple antagonists. Random drift may counteract the force of selection, but it can enhance it as well. The outcome of the evolutionary process is a result of the simultaneous operation of these two forces. Figure 26-8 illustrates these possibilities. Note that there are multiple adaptive peaks in this landscape. Because of random drift, a population under selection does not ascend an adaptive peak smoothly

    I’m still having the problem that drift, in my understanding, being completely random in its effect, will on average have no impact on the overall outcome of adaptation. I do see that drift can be very important in speciation, accelerating the process of breeding populations becoming reproductively isolated.

  15. Oh and…

    Of course there is no question of the significance of drift in sections of DNA that are not subject to selection i. e. non-functional.

  16. Alan Fox,

    I’m still having the problem that drift, in my understanding, being completely random in its effect, will on average have no impact on the overall outcome of adaptation. I do see that drift can be very important in speciation, accelerating the process of breeding populations becoming reproductively isolated.

    It opens up additional pathways towards adaptation. If a species cannot change unless that change is beneficial, then once it has soaked all the beneficial change out of a current genome, it’s pretty much stuck where it is. New mutations are all relatively ‘downhill’, and so are selected against. Variation is squeezed out of the population, and it is likely headed for extinction, as diseases and predators get a ‘fix’ on its static genome.

  17. Allan Miller:
    Alan Fox,

    Do you think drift eliminates variation more than selection does? It’s the other way round. Because of the directional component, selected alleles fix faster and are harder to topple than drift-fixed ones.

    I haven’t got to the point of being able to say anything about drift other than I think I now see what it is! I have no reason not to think that selection drives fixation. It’s the non-directional random nature of drift that makes it difficult for me to see what part it plays in outcomes. If it makes fixation faster or slower, that is fine. But surely I can’t be mistaken in wondering how a random effect could influence which allele fixes.

    Drift doesn’t increase the chances of new variation entering. That’s mutation, migration and recombination’s job.

    I do realise that. I’m not confused over how genomic variation is initially generated.

    It does increase the chances of variation sticking around, because it eliminates it more slowly than ‘hard’ selection.

    I’m not trying to be obtuse (maybe I don’t need to try) but you have lost me here.

    So it allows (for example) one half of Behe’s CCC double mutations to reach a certain level in the population before disappearing, creating a substantial additional probability that the double will occur within it, or between two subpopulations with one component each, despite the fact that selection cannot assist the singletons. Same for a new mutation that was initially recessive (as most are).

    Now I’m confused again. I see the advantage of neutral alleles sticking around so that when niches open, close or change, selection has ready-present variation to select from. I must have it backwards as I thought, in the absence of selection, the tendency is for one allel to fix at the expense of all others for any given locus.

    Were it not for drift, new mutations in diploids would rarely get anywhere.

    What I am not grasping is why that is precisely so.

    In such instances, and more generally too, drift allows the traversal of a path that mutation & selection alone could not access. I stand by my bold claim!

    Well, all organisms currently alive managed that unimaginably detailed and unbroken chain of being from the first life on Earth. But there is the important point that fitness landscapes are dynamic rather than static.

  18. Allan Miller: Allan Miller on August 24, 2015 at 12:03 pm said:

    AF;

    I’m still having the problem that drift, in my understanding, being completely random in its effect, will on average have no impact on the overall outcome of adaptation. I do see that drift can be very important in speciation, accelerating the process of breeding populations becoming reproductively isolated.

    It opens up additional pathways towards adaptation. If a species cannot change unless that change is beneficial, then once it has soaked all the beneficial change out of a current genome, it’s pretty much stuck where it is. New mutations are all relatively ‘downhill’, and so are selected against. Variation is squeezed out of the population, and it is likely headed for extinction, as diseases and predators get a ‘fix’ on its static genome.

    I see we cross-posted.

    OK, you’ve convinced me of the need for drift. You’ve convinced me there is drift. All that remains is for me to see how drift achieves what is attributed to it.

  19. Allan Miller: It opens up additional pathways towards adaptation. If a species cannot change unless that change is beneficial, then once it has soaked all the beneficial change out of a current genome, it’s pretty much stuck where it is. New mutations are all relatively ‘downhill’, and so are selected against.

    I don’t see that as an argument for drift. I see it as an argument for maintaining a degree of variation within the population. My understanding is that “drift” is typically used to refer to fixation of alleles, which reduces variation.

  20. Alan Fox,

    Now I’m confused again. I see the advantage of neutral alleles sticking around so that when niches open, close or change, selection has ready-present variation to select from. I must have it backwards as I thought, in the absence of selection, the tendency is for one allel to fix at the expense of all others for any given locus.

    That’s true in the presence of selection too (and even more so), apart from frequency-dependent effects. Selection fixes alleles much more surely and quickly than drift. But regardless, although the processes of selection and drift are eliminating variation, mutation is adding it. Because drift eliminates variation more slowly, a population can support a greater number of alleles.

    Me: Were it not for drift, new mutations in diploids would rarely get anywhere.

    Alan: What I am not grasping is why that is precisely so.

    Most new mutations are recessive. This means that, even if advantageous, this advantage is not displayed in heterozygotes (where the novel allele is masked by the wild type). Only when it becomes common enough to form homozygotes does selection become significant. Until that point, the main motor is drift.

  21. Neil Rickert,

    I don’t see that as an argument for drift. I see it as an argument for maintaining a degree of variation within the population. My understanding is that “drift” is typically used to refer to fixation of alleles, which reduces variation.

    I think that would be an incorrect assessment of the role of drift. Although drift is engaged in eliminating variation, it is also (perhaps paradoxically) engaged in promoting it, in tandem with new mutation. You can only increase a novel allele to significant frequency by ‘eliminating’ some of its rivals. The processes of increase and decrease are simultaneous. It’s all frequency change, and frequencies add up to 1.

  22. Allan Miller: Most new mutations are recessive. This means that, even if advantageous, this advantage is not displayed in heterozygotes (where the novel allele is masked by the wild type). Only when it becomes common enough to form homozygotes does selection become significant. Until that point, the main motor is drift.

    Is there light dawning? OK so, in a population of sexually reproducing diploid organisms, rare (having recently appeared by some mutational event, recombination etc) recessive alleles (no phenotypic effect in homozygous heterozygous form) that are neutral in the particular niche would be more likely to be lost from the gene pool if drift were absent? What process will result in the loss of some alleles if they are all neutral in the current niche if not drift? I. e. where selection is not operating and we have been able to design an experiment that eliminates or counteracts drift.

    ETA correction: heterozygous HT Allan Miller

  23. It might be best illustrated with a tweak to OM’s model. There is no mutation or selection as it stands. If mutation were added, we would see a dynamic pattern where a number of alleles were constantly drifting towards fixation/elimination, but with a constant shift away from any current state. Fixation of one colour would be prevented by novel alleles drifting upwards. The number of alleles sustained at equilibrium would be a function of population size and mutation rate.

    If selection were added, more fixations would occur, more rapidly, and novel alleles would be less likely to be able to gain frequency, because more would be at a disadvantage. The number of colours at equilibrium would be fewer.

  24. Allan Miller: You can only increase a novel allele to significant frequency by ‘eliminating’ some of its rivals.

    This has to be what I am missing. How does drift know which one to pick?

  25. I missed this comment and I’d like belatedly to pick up on it.

    petrushka:
    Unless I’ve totally misunderstood what has been said, I’d say that drift has the following attributes or characteristics:

    1. Drift will be most pronounced in non-functional DNA, (Maybe this is a big DUH, but Moran also argues that 90 percent of DNA in humans is non-functional, so most evolutionary change will be drift in non-functional code.)
    2. Drift doesn’t necessarily do anything, but it is useful as a molecular clock and in tracing lineages. This should be of great interest for evolutionary biologists, because it might provide a more fine-grained picture of lineages.
    3. Drift in non-functional code may occasionally result in a new function.

    Absolutely no problem with any of that. All makes sense.

    4. Drift may also occur in functional code when alleles are equivalent or nearly equivalent.

    Or this.

    5. The net result of all this is that mutations resulting in positive selection will be a minority of the total molecular change.

    Well, OK, taking Homo sapiens as an example, if 90+% of the human genome is non-functional, then fair enough. How much variation that accumulates in non-functional DNA ends up contributing to adaptation? Has it been established or could it, in theory, be established by experiment or otherwise?

  26. Alan Fox,

    Is there light dawning? OK so, in a population of sexually reproducing diploid organisms, rare (having recently appeared by some mutational event, recombination etc) recessive alleles (no phenotypic effect in homozygous heterozygous [AM] form) that are neutral in the particular niche would be more likely to be lost from the gene pool if drift were absent? What process will result in the loss of some alleles if they are all neutral in the current niche if not drift?

    No, it’s drift that eliminates them as well, as I noted earlier in the thread. But drift can promote an allele to significant frequency, as well of getting rid of it. You and Neil seem to have a one-sided view of the process. Increase in frequency of one allele is decrease for the other, and vice versa. Fixation of one is extinction of the other. They are simultaneous.

  27. Alan Fox,

    This has to be what I am missing. How does drift know which one to pick?

    It doesn’t. How does a roulette ball know which cell to end up in? All one can say in the simple neutral case is that one allele will drift towards fixation and all others towards extinction. They all have the same 1/2N probability of being the survivor, but there will, with certainty, be such a survivor, and a bunch of losers.

  28. Allan Miller: You and Neil seem to have a one-sided view of the process. Increase in frequency of one allele is decrease for the other, and vice versa. Fixation of one is extinction of the other. They are simultaneous.

    I really think I understand that alleles compete for fixation at one locus and it is a game that only one can win and the others die. Maybe my problem is not seeing the need for more randomness. How does the random process of drift contribute to the statistically non-random process of selection? Is it just a matter of altering the rate at which alleles fix or disappear?

  29. Allan Miller: How does a roulette ball know which cell to end up in?

    In my experience, it’s done with magnets! But there is a serious point in that the roulette ball has no memory. Each spin is an independent event unaffected by the previous history (assuming the equipment is utterly fair). Selection is non-random but drift events are random, they will have no cumulative or directional effect.

    I’m still not getting it, am I? Feel under no obligation to continue to indulge me.

  30. Alan Fox,

    In my experience, it’s done with magnets! But there is a serious point in that the roulette ball has no memory. Each spin is an independent event unaffected by the previous history (assuming the equipment is utterly fair). Selection is non-random but drift events are random, they will have no cumulative or directional effect.

    I’m still not getting it, am I? Feel under no obligation to continue to indulge me.

    Heh! I see in you an earlier incarnation of myself. 😉

    I think the fundamental thing to grasp is that drift and selection are both random. This is a point I resisted for a while, but it does make sense. The meaning of random here is simply ‘subject to a probability distribution’. The basic process is generational sampling, which includes both sample error and bias. For effective neutrality, there is no bias, but at all other selective differentials there is an element of both bias and sample error. When you turn the selective ‘knob’ from the neutral position a tiny increment, you don’t turn drift off, and you’ve barely turned selection on at all. Each further tiny increment introduces a little more bias which damps drift slightly.

    Perhaps what confuses is that one thinks of neutrality as ‘wandering’, and selection as ‘directional’, whereas in fact there is a strong directional component to drift too; it’s just that you can’t tell which way it’s likely to go. The directional component is, at all s values, towards fixation for something.

    We could adapt a roulette wheel to evolve. Spin the wheel once and peel off the number the ball lands on. Spin it again and duplicate that number, pasting it in the space just vacated. Keep doing this and you will get the same number in every pocket, sure as eggs.

    Now add a magnet. This increases the likelihood for some numbers, and decreases it for others – it introduces a bias. But it does not introduce certainty. When the ball settles in a particular pocket, is that drift or bias at work? When fixation has occurred, was it drift or bias that achieved it?

  31. Allan,

    Keep doing this and you will get the same number in every pocket, sure as eggs.

    What if Alan is skeptical of eggs? How sure are eggs, anyway?

    I think the fundamental thing to grasp is that drift and selection are both random. The meaning of random here is simply ‘subject to a probability distribution’. For effective neutrality, there is no bias, but at all other selective differentials there is an element of both bias and sample error.

    Right. Fit individuals can die without reproducing, and fitter alleles can even disappear from the population this way. Less fit individuals can get lucky, and their alleles may even fix. But the bias is in favor of fitness.

  32. Am I the only one who thinks — with regard to Larry Moran and the strong claim that drift is the dominant mode of change — that most drift and most change happens in non-functional code?

  33. petrushka,

    If most code is non-functional, then naturally most change takes place in it, and most of that change is drift alone. But Moran’s case is that substantial change in functional code is also down to drift. It is a viewpoint popularised by Stephen Jay Gould, and I think has its roots in a reaction against ‘adaptationism’ – the idea that just about everything about an organism has an explanation in selective advantage. This mainly gets sticky when applied to humans.

    I would describe myself as adaptationist, in that I think most phenotypic characteristics are the largely advantageous remainder of filtered alleles with variable differentials, though I would hesitate to concoct a particular causal explanation of how that advantage is implemented in many cases. But as one can see from working with the formulae, the power of exponentiation provided by compounding offspring provides a surprisingly strong arrow for quite small advantages. Still, drift has an important role, and the remarkable result that drift moves towards fixation, not wandering, deserves to be better known. It’s the baseline process, and makes evolution inevitable. Adaptive alleles with the same advantage will drift against each other.

  34. As the subject of genetic drift and my doubts about its rôle in adaptive evolution has come up in another thread, rather than derail, I thought we could continue here.

  35. Copying from the other thread:

    [Alan Fox,]

    I see all that and agree OM’s visualization of the “balls from a bag” was instructive. I’m sure this is a reasonable model. My question remains as how this links in to adaptation.

    That’s a slightly different question – to some extent, drift opposes adaptation. But the point was about variation. In increasing the variation available, drift provides the raw material for adaptation should the environment change, or a recombinational event generates a beneficial chimera that might not arise without it.

    What I’m hoping for is clarification on ” drift provides the raw material for adaptation should the environment change,” as I don’t see drift as providing raw material, rather causing alleles to fix and losing others from the gene pool. But I’m also not quite following this either “or a recombinational event generates a beneficial chimera that might not arise without it”. Could Allan or anyone help me out here?

  36. Alan:

    What I’m hoping for is clarification on ” drift provides the raw material for adaptation should the environment change,” as I don’t see drift as providing raw material, rather causing alleles to fix and losing others from the gene pool.

    I addressed that in the other thread:

    Alan:

    The phrase “in increasing the variation available” sounds like assuming that is what is happening. How this happens is what I am hoping to grasp.

    keiths:

    That’s what Allan is getting at here:

    Different local fixations are in train in different parts of the population and at different loci. It creates a patchwork effect, because gene flow is somewhat ‘viscous’ – a fact obscured or ignored by many population genetic models.

  37. keiths: Different local fixations are in train in different parts of the population and at different loci. It creates a patchwork effect, because gene flow is somewhat ‘viscous’ – a fact obscured or ignored by many population genetic models.

    Rather than quote Allan Miller, try explaining what you think he means in your own words. If you want to help me understand, that is.

  38. And in the meantime, my understanding of Allan’s point is that large populations can be considered aggregates of small populations so that assuming gene flow is homogeneous across a large population is not necessarily justified.

  39. Alan,

    And in the meantime, my understanding of Allan’s point is that large populations can be considered aggregates of small populations so that assuming gene flow is homogeneous across a large population is not necessarily justified.

    And the implication of that is that you get more variation than you would with thorough mixing, since there is local “quasi-fixation” in the subpopulations. The allele that fixes at a given locus in one subpopulation will differ from the allele that fixes at the same locus in another subpopulation.

  40. keiths:
    Alan,

    And the implication of that is that you get more variation than you would with thorough mixing, since there is local “quasi-fixation” in the subpopulations.The allele that fixes at a given locus in one subpopulation will differ from the allele that fixes at the same locus in another subpopulation.

    Yet the sub-population gets less diverse, unless sufficient new variation replaces the losses. What rôle is drift playing here?

  41. Alan Fox: Yet the sub-population gets less diverse, unless sufficient new variation replaces the losses. What rôle is drift playing here?

    To continue, genetic drift is an effect that is utterly random, leading, especially in small populations, to the fixation of any one neutral allele at the expense of others. Mutations (in the broadest sense) supply new alleles, if those new alleles are immediately lethal or deleterious, they will be weeded out by selection, otherwise they will proliferate.

    How does genetic drift contribute to adaptive change?

  42. Alan,

    Yet the sub-population gets less diverse, unless sufficient new variation replaces the losses. What rôle is drift playing here?

    Fixation, whether due to selection or to drift, decreases variation within the subpopulation. The difference is that with selection, it’s the advantageous alleles that fix. With drift, you get a random sampling of different alleles. Hence more variation.

  43. Alan Fox,

    But I’m also not quite following this either “or a recombinational event generates a beneficial chimera that might not arise without it”. Could Allan or anyone help me out here?

    Given drift, alleles with selection coefficient below the beneficial threshold (effectively neutral or worse) can increase in the population for a period before disappearing. I’m sure Joe could provide the equations – though they would probably be of the ‘efficient mixing’ kind, but the idea would be the same. While such alleles are around, they may recombine, and hit upon a beneficial variant. This is an important factor missed in Behe’s Plasmodium argument. If the double mutant ‘needs to’ occur, his calculations had the two mutations A and B only occurring in the same lineage. But in fact A and B subpopulations can arise through drift, even if A and B are detrimental, and AB arise by recombination. So you need to add the probability that AB will occur in that way, and because each added member of A has a chance with each member of B (and vice versa) these probabilities escalate significantly as the subpopulations grow.

    Alan Fox,

    Yet the sub-population gets less diverse, unless sufficient new variation replaces the losses. What rôle is drift playing here?

    Because it causes allele progress to be more leisurely than selection, it allows alleles to stick around longer than selection would. Fancifiully, it’s chucking novel variants up before the court of selection, and saying “how about this one? No? OK, what about …”.

    Or trying a visualisation of a mental map, if all was selection, this would colour the entire population red. But drift plus mutation adds pockets of varying shades of pink, constantly shifting in and out unless one of them gets grabbed by selection and promoted to fixation by that.

    Subpopulations get less diverse, but the overall population is more varied, with drift. I wish I had the time (and the skillz!) to code a visualisation.

  44. keiths: Fixation, whether due to selection or to drift, decreases variation within the subpopulation.

    I’ve already said this. It’s mutation, in the broadest sense (including meiosis, recombination, crossing over), that provide variation

    The difference is that with selection, it’s the advantageous alleles that fix.

    Again, I’ve already said that. The niche drives adaptive change.

    With drift, you get a random sampling of different alleles.

    I’ve already said that. The fixation of any allele, which must be neutral or near-enough neutral to be invisible to selection, is random.

    Hence more variation.

    That is where I’m unable to follow. Expand on “hence”!

  45. Allan,

    Subpopulations get less diverse, but the overall population is more varied, with drift. I wish I had the time (and the skillz!) to code a visualisation.

    Did OMagain publish his M&M code? Perhaps we could modify it instead of reinventing the wheel.

  46. Alan Fox,

    I’ve already said this. It’s mutation, in the broadest sense (including meiosis, recombination, crossing over), that provide variation

    Sort of. If there are 2 alleles in a population, it’s more varied than if there is only 1. However, mutation only generates a single copy. I would say that a population which is 50/50 A and B is ‘more varied’ than one which is 1 A vs 9999 B. It’s population processes (inc. drift) that make the difference once we have the variant.

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