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Rationally Speaking is a blog maintained by Prof. Massimo Pigliucci, a philosopher at the City University of New York. The blog reflects the Enlightenment figure Marquis de Condorcet's idea of what a public intellectual (yes, we know, that's such a bad word) ought to be: someone who devotes himself to "the tracking down of prejudices in the hiding places where priests, the schools, the government, and all long-established institutions had gathered and protected them." You're welcome. Please notice that the contents of this blog can be reprinted under the standard Creative Commons license.

Saturday, December 29, 2012

The philosophy of genetic drift

by Massimo Pigliucci

This morning I am following a session on genetic drift at the American Philosophical Association meetings in Atlanta. It is chaired by Tyler Curtain (University of North Carolina-Chapel Hill), the speaker is Charles Pence (Notre Dame), and the commenters are Lindley Darden (Maryland-College Park) and Lindsay Craig (Idaho). [Note: I’ve written myself about this concept, for instance in chapter 1 of Making Sense of Evolution. Check also these papers in the journal Philosophy & Theory in Biology: Matthen and Millstein et al.]

The title of Charles' talk was "It's ok to call genetic drift a force," a position — I should state right at the beginning — with which I actually disagree. Let the fun begin! Drift has always been an interesting and conceptually confusing issue in evolutionary biology, and of course it plays a crucial role in mathematical population genetic theory. Drift has to do with stochastic events in generation-to-generation population sampling of gametes. The strength of drift is inversely proportional to population size, which also means it has an antagonistic effect to natural selection (whose strength is directly proportional to population size).

Charles pointed out that one popular interpretation of drift among philosophers is "whatever causes fail to differentiate based on fitness." The standard example is someone being struck by lightening, the resulting death clearly having nothing to do with that individual's fitness. I'm pretty sure this is not what population geneticists mean by drift. If that were the case, a mass extinction caused by an asteroid (that is, a cause that has nothing to do with individual fitness) would also count as drift. Indeed, discussions of drift — even among biologists — often seem to confuse a number of phenomena that have little to do with each other, other than the very generic property of being "random."

What about the force interpretation then? This is originally due to Elliott Sober (1984), who developed a conceptual model of the Hardy-Weinberg equilibrium in population genetics based on an analogy with Newtonian forces. H-W is a simple equation that describes the genotypic frequencies in a population where no evolutionary processes are at work: no selection, no mutation, no migration, no assortative (i.e., non random) mating, and infinite population size (which implies no drift).

The force interpretation is connected to the (also problematic, see Making Sense of Evolution, chapter 8) concept of adaptive landscape in evolutionary theory. This is a way to visualize the relationship between allelic frequencies and selection: the latter will move populations "upwards" (i.e., toward higher fitness) on any slope in the landscape, while drift will tend to shift populations randomly around the landscape.

The controversy about thinking of drift as a force began in 2002 with a paper by Matthen and Ariew, followed by another one by Brandon in 2006. The basic point was that drift inherently does not have a direction, and therefore cannot be analogized to a force in the physical (Newtonian) sense. As a result, the force metaphor fails.

Stephens (2004) claimed that drift does have direction, since it drives populations toward less and less heterozygosity (or more and more homozygosity). Charles didn't buy this, and he is right. Stephens is redefining "direction" for his own purposes, as heterozygosity does not appear on the adaptive landscape, making Stephens' response entirely artificial and not consonant with accepted population genetic theory.

Filler (2009) thinks that drift is a force because it has a mathematically specific magnitude and can unify a wide array of seemingly disparate phenomena. Another bad answer, I think (and, again, Charles also had problems with this). First off, forces don't just have magnitude, they also have direction, which, again, is not the case for drift. Sober was very clear on this, since he wanted to think of evolutionary "forces" as vectors that can be combined or subtracted. Second, it seems that if one follows Filler far too many things will begin to count as "forces" that neither physicists nor biologists would recognize as such.

Charles' idea is to turn to the physicists and see whether there are interesting analogs of drift in the physical world. His chosen example was Brownian motion, the random movement of small objects like dust particles. Brownian motion is well understood and mathematically rigorously described. Charles claimed that the equation for Brownian motion "looks" like the equation for a stochastic force, which makes it legitimate to translate the approach to drift.

But I'm pretty sure that physicists themselves don't think of Brownian motion as a force. Having a mathematical description of stochastic effects (which we do have, both for Brownian motion and for drift — and by the way, the two look very different!) is not the same as having established that the thing one is modeling is a force. Indeed, Charles granted that one could push back on his suggestion, and reject that either drift or Brownian motion are forces. I'm inclined to take that route.

A second set of objections to the idea of drift as a force (other than it doesn't have direction) is concerned with the use of null models, or inertial states, in scientific theorizing. H-W is supposed to describe what happens when nothing happens, so to speak, in populations of organisms. According to Brandon, however, drift is inherent in biological populations, so that drift is the inertial state itself, not one of the "forces" that move populations away from such state.

Charles countered that for a Newtonian system gravity also could be considered "constitutive," the way Brandon thinks of drift, but that would be weird. Charles also object that it is no good to argue that one could consider Newtonian bodies in isolation from the rest of the universe, because similar idealizations can be invoked for drift, most famously the above mentioned assumption of infinite population size. This is an interesting point, but I think the broader issue here is the very usefulness of null models in science in general, and in biology in particular (I am skeptical of their use, at least as far as inherently statistical problems of the kind dealt with by organismal biology are concerned, see chapter 10 of Making Sense).

Broadly speaking, one of the commentators (Darden) questioned the very benefit of treating drift as a force, considering that obviously biologists have been able to model drift using rigorous mathematical models that simply do not require a force interpretation. Indeed, not even selection can always be modeled as a vector with intensity and direction: neither the case of stabilizing selection nor that of disruptive selection fit easily in that mold, because in both instances selection acts to (respectively) decrease or increase a trait's variance, not its mean. Moreover, as I pointed out in the discussion, assortative mating is also very difficult to conceptualize as a vector with directionality, which makes the whole attempt at thinking of evolutionary "forces" ever more muddled and not particularly useful. Darren's more specific point was that while it is easy to think of natural selection as a mechanism, it is hard to think of drift as a mechanism (indeed, she outright denied that it is one), which again casts doubt on what there is to gain from thinking of drift as a force. The second commentator (Craig) also questioned the usefulness of the force metaphor for drift, even if defensible along the lines outlined by Pence and others.

Even more broadly, haven't physicists themselves moved away from talk of forces? I mean, let's not forget that Newtonian mechanics is only an approximation of relativity theory, and that "forces" in physics are actually interpreted in terms of fields and associated particles (as in the recently much discussed Higgs field and particle). Are we going to reinterpret this whole debate in terms of biological fields of some sort? Isn't it time that biologists (and philosophers of biology) let go of their physics envy (or their envy of philosophy of physics)?


  1. Well the first problem is that selection isn't a force either. F=MA. What mass is being accelerated in natural selection?

    Calling it a force is just a metaphor. You are arguing over the use of a metaphor. A pretty useless endeavor at best. Find some specific prediction, effect or phenomena to argue over.

    And anyway physics does have entropic force. Elasticity for example is an entropic force. On the macro-scale we see a real force but on the micro-scale we see it is driven by a tendency toward randomness. That rubber band is useful exactly because of randomness.

  2. Minor point: "The strength of drift is inversely proportional to population size, which also means it has an antagonistic effect to natural selection (whose strength is directly proportional to population size)." -I'm not quite sure follow what this means. It makes it sound like there is a factor of N^2 between the rate of drift and selection. In what sense is the strength of selection proportional to population size? Are you are referring to the result that Ns is an important compound parameter in models with selection and drift? If so this might not be quite correct as worded. To obtain this result we have rescaled time to be in units of N generations so and selection changes the frequency at a rate proportional to Ns and N doesn't appear in the rate of drift (as it has been scaled out).

    Or perhaps you were referring to something else.

    Graham Coop

  3. ppnl,

    > Well the first problem is that selection isn't a force either. F=MA. What mass is being accelerated in natural selection? <

    As much as I’m not sympathetic to the idea of forces in biology, that’s a bizarre objection. Not all forces in physics are expressed in terms of mass!

    > Calling it a force is just a metaphor. <

    It is. But so is calling a force a force...

    > A pretty useless endeavor at best. <

    Not at all. The underlying point of the debate is a meta-theoretical one, which incidentally includes a number of philosophers who don’t think the concept of force is meaningful or sufficiently well define — even in physics!


    > It makes it sound like there is a factor of N^2 between the rate of drift and selection. <

    No, it just means that they are inversely proportional to each other, but one is also proportional to population size, the other inversely so. This is a good primer on the whole shebang: http://goo.gl/AnGUs

    > In what sense is the strength of selection proportional to population size? <

    In the sense that the more individuals there are in the population the less the population is subject to stochastic fluctuations (drift), which in turn means that natural selection is more effective because of decreased noise.

    > selection changes the frequency at a rate proportional to Ns and N doesn't appear in the rate of drift <

    Not sure what you mean by Ns, the correct parameter is actually often referred to Ne, the effective population size (i.e., the number of individuals actually reproducing, which is usually lower than N, the total number of individual in the population).

  4. Massimo. Sorry I should have been clearer in my notation N is the [effective] population size, s is the selection coefficient [difference in relative fitness between the two homozygotes, in a simple diploid model] in my previous comment. Thanks for pointing me to Hartl and Clark, however, I am familiar with population genetics so do not need an introduction. My point was this:
    If we measure time in our model in generations, the rate at which frequency changes due to selection is not a function of the population size [just the selection coefficient s]. The rate of genetic drift [i.e. the variance in allele frequencies] is an inversely proportional to the effective population size. There is, to my knowledge, no simple model of selection and drift where "one is also proportional to population size, the other inversely so." if they are measured on the same time-scale, as they should be.

    The result you refer to where the strength of selection depends on the population size [e.g. N s in the above notation], can be found by taking the diffusion limit e.g. of the Wright-Fisher model. To take this limit our time-scale is rescaled in units of the population size. On this new time-scale, the rate of change in frequency due to selection is then proportional to the population size and the selection coefficient [Ns]. The rate of drift is, on this new time-scale, independent of the population size.

    There’s obviously a variety of models other than this simple diploid model and a variety of ways to take this time-scale limit. However, for most practical purposes in popgen models either the rate of drift or the rate of allele frequency change due to selection are proportional to selection but not both [when they are measured on the same time-scale].

    Anyway this was just a minor quibble, but I just wanted to clarify that point.


  5. Yes you can talk about forces without mass. But it anything moves at all then you will have to talk about mass. And if nothing moves then any force is canceled by an equal and opposite force leaving no resultant force at all.

    And no, physical force is not a metaphor. Or if it is then so is mass, energy, charge, spin, momentum...

    If everything is a metaphor then we don't even need the word metaphor.

    Force is used as a metaphor in many domains. For example force of personality, political force, intellectual force...

    These things can't even be quantified or even a direction of the force agreed on. For example was Robert Bork a force for good or evil in constitutional law? I think he was a nut but people differ.

    Some metaphorical uses of force can be quantified. But unless you can use it to do work and extract energy it isn't really a force.

    Gould had the idea of the left wall of complexity in which he argued that evolution did not have a direction except for that caused by its initial condition. This is analogous to the physical fact that time appears to not have a direction except for that caused by the universes initial condition. This creates real forces in nature. For example dense collections of particles can disperse and do work on their surroundings. A stretched rubber band will exert a force and can do work because its molecules are trying to increase their entropy.

    So metaphorically there can be said to be a force toward greater complexity (Somewhat contra Gould's point...) but it really is just a metaphor. We can easily see that the force toward complexity and entropic force are kindred concepts using similar logic. But they are also very different things. One can do actual work while the other can't.

    So I have no problem with the force metaphor in evolution but it should be remembered that it is just a metaphor. You usually can't do calculations with it.

    1. ppnl,

      I don't disagree with your general claims, but I actually do think there is a problem in using the force metaphor in biology, because of large disanalogies with the case of physics.

      As for force in physics not being a metaphor, you are correct within Newtonian mechanics, because force is formally defined mathematically. But my understanding is that in more modern, post-Newtonian, physics talk of force has been largely replaced, especially in quantum mechanics. Either way, I don't really have a bone to pick as far as physics is concerned.


  6. I agree that there are large dis-analogies (But Gould's left wall of complexity really is a very close analog of entropy and the direction of time from physics.) but that is why I insist on calling it a metaphor. Metaphors will always have dis-analogies. A lawyer is really not much like a snake.

    We should just recognize that it is a metaphor and move on. Language needs metaphor and can't do without them.

    Relativity does replace gravitational force with curved space but that is just a metaphor for the underlying math. You can still do force calculations and do work with falling bodies. Its just that relativity gives slightly different results from classical physics. The best way to start to get a grasp on the difference is with a visual metaphor. That metaphor is substantially wrong but conceptually points in the correct direction. All concepts have a domain of applicability. The domain of applicability for force is much larger than most. The fact that at some point we can see what force is "made of" and so deconstruct it changes nothing.

  7. So would philosophers of biology giving up the force concept altogether constitute progress in your opinion?

    1. Mark,

      yes, since one of the goals of philosophy of biology is to make meta-theoretical sense of how biology works. And don't tell me that's of no use to biologists, since that's not the point. What biologists do is in turn of little use to philosophers...


  8. It would be progress in the same sense as it would be progress if biologists stopped using the intent metaphor. For example "birds evolved flight in order to avoid predators". If you are overly literal this seems to imply birds had forethought. This seems bad but there are no simple clear alternatives.

    The problem is when you use language you are literally swimming in metaphor. Is that literal or is that a metaphor?

    1. > It would be progress in the same sense as it would be progress if biologists stopped using the intent metaphor. <

      No, the difference is that biologists are concerned with the actual deployment of the theory, while philosophers are concerned with the meta-theoretical statements made or implied by biologists' usage.


  9. Well yes but that is what I thought I was saying. The intent metaphor and the force metaphor are similar in that if we misread how the metaphor was intended we generate confusion. Worse yet if we are unclear in our own head how we are using them.

    And this is where the utility of philosophy is at. It helps to nail down intended meaning rather than a different implied meaning from a different take on the inevitable metaphorical content of language.

    We swim in metaphor the way a fish swims in water. For that reason it is often invisible to us. One of the main uses of philosophy is to study the water.

  10. "I'm pretty sure this is not what population geneticists mean by drift. If that were the case, a mass extinction caused by an asteroid (that is, a cause that has nothing to do with individual fitness) would also count as drift."

    That's a population bottleneck, a classic example of genetic drift.

    1. That *causes* a bottleneck, and therefore drift, but the mass extinction was not caused by drift. Careful not to confuse cause and effect...

  11. In preparation for writing this article http://onlinelibrary.wiley.com/doi/10.1002/bies.201100178/abstract, I spent some time doing an unscientific survey of evolutionary biologists, oversampling theoretical population geneticists, and asking each of them to define genetic drift. The diversity of answers I got back was staggering. I very rarely got the same thing twice (although admittedly, they were sometimes variations on a theme, but not always).

    In the Wright paper I quote, the very founder of the concept goes on a rant about how everybody else is misusing it. In Wright's view, "genetic drift" means change in allele frequency, "steady genetic drift" including directional terms such as directional selection and recurrent mutation, with "random genetic drift" meaning any variance-increasing term, including fluctuating selection as well as accidents of sampling.

    Then I started listening to every time I heard someone use the term "drift" at one conference. The use of the term in a question was a pretty reliable predictor of the speaker having no idea exactly what they were being asked.

    It seems rather premature to ask about the deeper philosophical meaning of genetic drift is, when the relevant scientific community can't even devise a halfway consistent meaning. I think some descriptive work would be a better starting point. Actually, I think the terms should be outright abolished. Everybody thinks it means something different, so the term impedes rather than improves communication.

    1. Joanna,

      interesting, but what's wrong with a simple "drift is the sampling error of gametes due to small population size"?

    2. That is close to the definition I used to use. But this category of definitions turned out to be much less common than I had thought. For example, this definition isn't the one used by prominent drift advocates, from Sewall Wright to Mike Lynch. I think this is a potentially coherent and useful concept, but to avoid confusion with other people's very different definitions I now call it "sampling drift".

      But your version of it needs a tweak. Sampling drift is important even in extremely large populations, eg with respect to the fixation or extinction of a new advantageous mutation. So the definition should refer not to a small total population size, but to a small number of copies of the allele in question. The former obviously implies the latter, but the converse is not true. Note that the definition basically loses its clarity once you introduce an "effective" population size.


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