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)?